<article>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#article09_06_19_1520218</id>
	<title>A Mathematician's Lament &mdash; an Indictment of US Math Education</title>
	<author>ScuttleMonkey</author>
	<datestamp>1245434700000</datestamp>
	<htmltext>Scott Aaronson recently had "<a href="http://www.maa.org/devlin/LockhartsLament.pdf">A Mathematician's Lament</a>" [PDF], Paul Lockhardt's indictment of K-12 math education in the US, pointed out to him and takes some time to <a href="http://scottaaronson.com/blog/?p=410">examine the finer points</a>.  <i>"Lockhardt says pretty much everything I've wanted to say about this subject since the age of twelve, and does so with the thunderous rage of an Old Testament prophet.  If you like math, and more so if you think you don't like math, I implore you to read his essay with every atom of my being. Which is not to say I don't have a few quibbles  [...] In the end, Lockhardt's lament is subversive, angry, and radical ... but if you know anything about math and anything about K-12 'education' (at least in the United States), I defy you to read and find a single sentence that isn't permeated, suffused, soaked, and encrusted with truth."</i></htmltext>
<tokenext>Scott Aaronson recently had " A Mathematician 's Lament " [ PDF ] , Paul Lockhardt 's indictment of K-12 math education in the US , pointed out to him and takes some time to examine the finer points .
" Lockhardt says pretty much everything I 've wanted to say about this subject since the age of twelve , and does so with the thunderous rage of an Old Testament prophet .
If you like math , and more so if you think you do n't like math , I implore you to read his essay with every atom of my being .
Which is not to say I do n't have a few quibbles [ ... ] In the end , Lockhardt 's lament is subversive , angry , and radical ... but if you know anything about math and anything about K-12 'education ' ( at least in the United States ) , I defy you to read and find a single sentence that is n't permeated , suffused , soaked , and encrusted with truth .
"</tokentext>
<sentencetext>Scott Aaronson recently had "A Mathematician's Lament" [PDF], Paul Lockhardt's indictment of K-12 math education in the US, pointed out to him and takes some time to examine the finer points.
"Lockhardt says pretty much everything I've wanted to say about this subject since the age of twelve, and does so with the thunderous rage of an Old Testament prophet.
If you like math, and more so if you think you don't like math, I implore you to read his essay with every atom of my being.
Which is not to say I don't have a few quibbles  [...] In the end, Lockhardt's lament is subversive, angry, and radical ... but if you know anything about math and anything about K-12 'education' (at least in the United States), I defy you to read and find a single sentence that isn't permeated, suffused, soaked, and encrusted with truth.
"</sentencetext>
</article>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28396003</id>
	<title>Anecdotal at the very best</title>
	<author>Anonymous</author>
	<datestamp>1245406980000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>Perhaps you went to a crappy public school with no advanced or "gifted" track, or you weren't slotted for it.  (This is not to say that all public school in the US are crappy, but you can certainly find them.)  I attended public school and went to college with a better education than a lot of students who went to the best private academies.</p></htmltext>
<tokenext>Perhaps you went to a crappy public school with no advanced or " gifted " track , or you were n't slotted for it .
( This is not to say that all public school in the US are crappy , but you can certainly find them .
) I attended public school and went to college with a better education than a lot of students who went to the best private academies .</tokentext>
<sentencetext>Perhaps you went to a crappy public school with no advanced or "gifted" track, or you weren't slotted for it.
(This is not to say that all public school in the US are crappy, but you can certainly find them.
)  I attended public school and went to college with a better education than a lot of students who went to the best private academies.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393035</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28414983</id>
	<title>This crap is why we have "Math Explorations."</title>
	<author>tillerman35</author>
	<datestamp>1245591000000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>I'm all for "math is cool," and "let's explore," but this guy seriously torques me off.  My kids are currently suffering from the influence of people like him.  They have taken the basics out of math and substituted this useless "math explorations" curriculum.  Other folks have written better criticisms, but suffice it to say that the vast majority of kids don't benefit from all this "exploration" and "visualization" and the ones who do would have had those epiphanies anyway without any help whatsoever.</p><p>The BETTER way is to stick to the basics and train teachers to recognize kids who have a mathematically artistic talent and then remove them to an environment where it can flourish.  That's tough for a couple of reasons.  First, those kids might not actually get good grades.  The author of TFA is entirely correct that the basics bore them which results in inattention and lack of motivation.  Second, when they ARE good, removing them will lower the overall test scores of the class.  Since teachers' pay and bonus structures are based on their students' test scores, there would be a strong monetary motivation to intentionally fail to recognize them.</p><p>Assuming that those two problems can be overcome (big assumption there), you continue to train the "artistic" kids in the basics, but only just enough to get by.  The rest of the time, you motivate them in a way that would make the author of TFA happy.</p><p>The problem is, people have this wonderful but sadly mistaken belief that ALL kids can benefit from artistic mathematics when in fact most can't.  Compounding the problem is the bizarre theory that teaching the artistic mathematics will somehow magically result in the basics becoming trivially easy.  It doesn't.  And unfortunately, our kids have to fail spectacularly in order to teach the education system this simple fact.  "Luckily," that's what they're doing in droves.</p></htmltext>
<tokenext>I 'm all for " math is cool , " and " let 's explore , " but this guy seriously torques me off .
My kids are currently suffering from the influence of people like him .
They have taken the basics out of math and substituted this useless " math explorations " curriculum .
Other folks have written better criticisms , but suffice it to say that the vast majority of kids do n't benefit from all this " exploration " and " visualization " and the ones who do would have had those epiphanies anyway without any help whatsoever.The BETTER way is to stick to the basics and train teachers to recognize kids who have a mathematically artistic talent and then remove them to an environment where it can flourish .
That 's tough for a couple of reasons .
First , those kids might not actually get good grades .
The author of TFA is entirely correct that the basics bore them which results in inattention and lack of motivation .
Second , when they ARE good , removing them will lower the overall test scores of the class .
Since teachers ' pay and bonus structures are based on their students ' test scores , there would be a strong monetary motivation to intentionally fail to recognize them.Assuming that those two problems can be overcome ( big assumption there ) , you continue to train the " artistic " kids in the basics , but only just enough to get by .
The rest of the time , you motivate them in a way that would make the author of TFA happy.The problem is , people have this wonderful but sadly mistaken belief that ALL kids can benefit from artistic mathematics when in fact most ca n't .
Compounding the problem is the bizarre theory that teaching the artistic mathematics will somehow magically result in the basics becoming trivially easy .
It does n't .
And unfortunately , our kids have to fail spectacularly in order to teach the education system this simple fact .
" Luckily , " that 's what they 're doing in droves .</tokentext>
<sentencetext>I'm all for "math is cool," and "let's explore," but this guy seriously torques me off.
My kids are currently suffering from the influence of people like him.
They have taken the basics out of math and substituted this useless "math explorations" curriculum.
Other folks have written better criticisms, but suffice it to say that the vast majority of kids don't benefit from all this "exploration" and "visualization" and the ones who do would have had those epiphanies anyway without any help whatsoever.The BETTER way is to stick to the basics and train teachers to recognize kids who have a mathematically artistic talent and then remove them to an environment where it can flourish.
That's tough for a couple of reasons.
First, those kids might not actually get good grades.
The author of TFA is entirely correct that the basics bore them which results in inattention and lack of motivation.
Second, when they ARE good, removing them will lower the overall test scores of the class.
Since teachers' pay and bonus structures are based on their students' test scores, there would be a strong monetary motivation to intentionally fail to recognize them.Assuming that those two problems can be overcome (big assumption there), you continue to train the "artistic" kids in the basics, but only just enough to get by.
The rest of the time, you motivate them in a way that would make the author of TFA happy.The problem is, people have this wonderful but sadly mistaken belief that ALL kids can benefit from artistic mathematics when in fact most can't.
Compounding the problem is the bizarre theory that teaching the artistic mathematics will somehow magically result in the basics becoming trivially easy.
It doesn't.
And unfortunately, our kids have to fail spectacularly in order to teach the education system this simple fact.
"Luckily," that's what they're doing in droves.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394833</id>
	<title>Re:You can convince me</title>
	<author>ObsessiveMathsFreak</author>
	<datestamp>1245402540000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><blockquote><div><p>Lockhart's essay is an interesting read, really, but on some level it boils down to "Those unworthy schlubs treating Mathematics as a tool don't deserve it. It belongs to the artists, the dreamers, the purists!"</p></div></blockquote><p>Basically. While mathematics can indeed be an art form, a certain amount of slogging through the basics is required of anyone who wishes to learn it. Euclid reputedly said that there was no Royal Road to geometry(mathematics), and that is as true today as it was in Euclid's time. Mathematics requires effort.</p><p>I remember the algebra problems of secondary school.</p><blockquote><div><p>Simplify: (x+2x^2+3)(x^3+2(x+1)^2+2)+3x^2 +2x+1</p></div></blockquote><p>I did sums like this and dozens like it. Hundreds, and that's just in algebra. Doing those sums over and over, making mistakes, finding patterns all added to my knowledge and abilities in manipulating symbols which I use to this day. Yes it was slog work. Yes it was boring. Yes it was "pointless". But I did it and I'm better at algebra for it. The same is true for most things in mathematics, right down all the way to basic arithmetic(times tables anyone?) and all the way up to graduate school(Prove any distribution is the limit of a sequence of functions!).</p><p>It's true, mathematics can be made easier to learn though more engaging, and more systematic presentations. But you cannot completely exorcise exercises from the curriculum, no mater how pointless students think they are. Learning anything is not something that can be done easily, for anyone. It takes effort. I am reminded of Mr. Miagi's "Wax on, wax off", itself a variation of the thousands of repetitive and "pointless" motions that young martial arts students must perform over and over before they can proceed to "real" training.</p><p>You really do have to get the basics right before you move on to the advanced techniques. This doesn't mean that learning the basics can't be interesting, but it does mean that you will have to learn them!</p></div>
	</htmltext>
<tokenext>Lockhart 's essay is an interesting read , really , but on some level it boils down to " Those unworthy schlubs treating Mathematics as a tool do n't deserve it .
It belongs to the artists , the dreamers , the purists ! " Basically .
While mathematics can indeed be an art form , a certain amount of slogging through the basics is required of anyone who wishes to learn it .
Euclid reputedly said that there was no Royal Road to geometry ( mathematics ) , and that is as true today as it was in Euclid 's time .
Mathematics requires effort.I remember the algebra problems of secondary school.Simplify : ( x + 2x ^ 2 + 3 ) ( x ^ 3 + 2 ( x + 1 ) ^ 2 + 2 ) + 3x ^ 2 + 2x + 1I did sums like this and dozens like it .
Hundreds , and that 's just in algebra .
Doing those sums over and over , making mistakes , finding patterns all added to my knowledge and abilities in manipulating symbols which I use to this day .
Yes it was slog work .
Yes it was boring .
Yes it was " pointless " .
But I did it and I 'm better at algebra for it .
The same is true for most things in mathematics , right down all the way to basic arithmetic ( times tables anyone ?
) and all the way up to graduate school ( Prove any distribution is the limit of a sequence of functions !
) .It 's true , mathematics can be made easier to learn though more engaging , and more systematic presentations .
But you can not completely exorcise exercises from the curriculum , no mater how pointless students think they are .
Learning anything is not something that can be done easily , for anyone .
It takes effort .
I am reminded of Mr. Miagi 's " Wax on , wax off " , itself a variation of the thousands of repetitive and " pointless " motions that young martial arts students must perform over and over before they can proceed to " real " training.You really do have to get the basics right before you move on to the advanced techniques .
This does n't mean that learning the basics ca n't be interesting , but it does mean that you will have to learn them !</tokentext>
<sentencetext>Lockhart's essay is an interesting read, really, but on some level it boils down to "Those unworthy schlubs treating Mathematics as a tool don't deserve it.
It belongs to the artists, the dreamers, the purists!"Basically.
While mathematics can indeed be an art form, a certain amount of slogging through the basics is required of anyone who wishes to learn it.
Euclid reputedly said that there was no Royal Road to geometry(mathematics), and that is as true today as it was in Euclid's time.
Mathematics requires effort.I remember the algebra problems of secondary school.Simplify: (x+2x^2+3)(x^3+2(x+1)^2+2)+3x^2 +2x+1I did sums like this and dozens like it.
Hundreds, and that's just in algebra.
Doing those sums over and over, making mistakes, finding patterns all added to my knowledge and abilities in manipulating symbols which I use to this day.
Yes it was slog work.
Yes it was boring.
Yes it was "pointless".
But I did it and I'm better at algebra for it.
The same is true for most things in mathematics, right down all the way to basic arithmetic(times tables anyone?
) and all the way up to graduate school(Prove any distribution is the limit of a sequence of functions!
).It's true, mathematics can be made easier to learn though more engaging, and more systematic presentations.
But you cannot completely exorcise exercises from the curriculum, no mater how pointless students think they are.
Learning anything is not something that can be done easily, for anyone.
It takes effort.
I am reminded of Mr. Miagi's "Wax on, wax off", itself a variation of the thousands of repetitive and "pointless" motions that young martial arts students must perform over and over before they can proceed to "real" training.You really do have to get the basics right before you move on to the advanced techniques.
This doesn't mean that learning the basics can't be interesting, but it does mean that you will have to learn them!
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393159</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393335</id>
	<title>Re:US K-12 MATH = Real world fail.</title>
	<author>Kratisto</author>
	<datestamp>1245440520000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>I'm not sure which is more concerning: That anyone still watches "Who Wants To Be A Millionaire," or that anyone is still surprised by the abject stupidity therein.</p></htmltext>
<tokenext>I 'm not sure which is more concerning : That anyone still watches " Who Wants To Be A Millionaire , " or that anyone is still surprised by the abject stupidity therein .</tokentext>
<sentencetext>I'm not sure which is more concerning: That anyone still watches "Who Wants To Be A Millionaire," or that anyone is still surprised by the abject stupidity therein.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392991</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28395827</id>
	<title>Re:Several Proxies</title>
	<author>elmodog</author>
	<datestamp>1245406200000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>Thanks for the links. They were helpful.</htmltext>
<tokenext>Thanks for the links .
They were helpful .</tokentext>
<sentencetext>Thanks for the links.
They were helpful.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392769</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28397289</id>
	<title>Some great teachers are alive and well</title>
	<author>Anonymous</author>
	<datestamp>1245413820000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>Mr. Tiber, St. Joseph's High School, Kenosha WI &#226;"&#194;I'm sure he's retired by now.</p><p>I'm an artist and very visual so math really wasn't my bag. In most of my math-related classes all through high school I would usually average a "C." I was taught, reluctantly but it was required, Advanced Geometry by this man and received an "A" for the entire semester. This man taught math the way my better art teachers taught painting and drawing. He was very passionate about mathematics, I think the true problem is that most teachers have no passion for whatever subject it is they teach. They're substitute teachers that happen to teach a specific subject all the time.</p><p>I don't think I ever thanked him for teaching me so well. I don't even think I was smart enough back then to even realize what he had done.</p></htmltext>
<tokenext>Mr. Tiber , St. Joseph 's High School , Kenosha WI   "   I 'm sure he 's retired by now.I 'm an artist and very visual so math really was n't my bag .
In most of my math-related classes all through high school I would usually average a " C. " I was taught , reluctantly but it was required , Advanced Geometry by this man and received an " A " for the entire semester .
This man taught math the way my better art teachers taught painting and drawing .
He was very passionate about mathematics , I think the true problem is that most teachers have no passion for whatever subject it is they teach .
They 're substitute teachers that happen to teach a specific subject all the time.I do n't think I ever thanked him for teaching me so well .
I do n't even think I was smart enough back then to even realize what he had done .</tokentext>
<sentencetext>Mr. Tiber, St. Joseph's High School, Kenosha WI â"ÂI'm sure he's retired by now.I'm an artist and very visual so math really wasn't my bag.
In most of my math-related classes all through high school I would usually average a "C." I was taught, reluctantly but it was required, Advanced Geometry by this man and received an "A" for the entire semester.
This man taught math the way my better art teachers taught painting and drawing.
He was very passionate about mathematics, I think the true problem is that most teachers have no passion for whatever subject it is they teach.
They're substitute teachers that happen to teach a specific subject all the time.I don't think I ever thanked him for teaching me so well.
I don't even think I was smart enough back then to even realize what he had done.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28399127</id>
	<title>Re:I Sympathize With Him But Too Idyllic</title>
	<author>Anonymous</author>
	<datestamp>1245431520000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>Those who can, do; those who can't, teach.  -George Bernard Shaw.</p></htmltext>
<tokenext>Those who can , do ; those who ca n't , teach .
-George Bernard Shaw .</tokentext>
<sentencetext>Those who can, do; those who can't, teach.
-George Bernard Shaw.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392903</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28396299</id>
	<title>Another thought in this space</title>
	<author>davidjohnburrowes</author>
	<datestamp>1245408480000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>For folks interested, another interesting view on mathematics teaching is in the book "Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States" by Liping Ma.  It's very thought provoking.  It doesn't persuade me to any particular solution, but definitely gives me more data to think about how we teach people things like mathematics.</htmltext>
<tokenext>For folks interested , another interesting view on mathematics teaching is in the book " Knowing and Teaching Elementary Mathematics : Teachers ' Understanding of Fundamental Mathematics in China and the United States " by Liping Ma .
It 's very thought provoking .
It does n't persuade me to any particular solution , but definitely gives me more data to think about how we teach people things like mathematics .</tokentext>
<sentencetext>For folks interested, another interesting view on mathematics teaching is in the book "Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States" by Liping Ma.
It's very thought provoking.
It doesn't persuade me to any particular solution, but definitely gives me more data to think about how we teach people things like mathematics.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28399635</id>
	<title>Re:A teachers take</title>
	<author>Borg Bucolic</author>
	<datestamp>1245438840000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p><div class="quote"><p>I am a teacher, albeit not a a math teacher but teaching in general has a lot of problems in the U.S.</p>  </div><p>I am a teacher of mathematics (high school), all the problems I see come from outside the classroom, not in it.</p></div>
	</htmltext>
<tokenext>I am a teacher , albeit not a a math teacher but teaching in general has a lot of problems in the U.S. I am a teacher of mathematics ( high school ) , all the problems I see come from outside the classroom , not in it .</tokentext>
<sentencetext>I am a teacher, albeit not a a math teacher but teaching in general has a lot of problems in the U.S.  I am a teacher of mathematics (high school), all the problems I see come from outside the classroom, not in it.
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394271</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28413507</id>
	<title>What to do with math?</title>
	<author>Anonymous</author>
	<datestamp>1245578280000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>I have a M. Sc. in math from a highly respected university.  Unfortunately, it is damn hard getting a job which really uses my knowledge.  Sometimes, it has been a determent.  I have been disqualified from jobs because I would be bored after a while.  Granted, this is true, but after you have been out of work for a while, you will take a job doing most things.  </p><p>So, what do you do with a degree in math, especially in a down economy.  Maybe go back and get some training as a auto mechanic?  Yes, there will be times when you are not very busy, but on the other hand, you will never be completely unemployed.  </p><p>The other problem is that there is no real place for someone without a Ph. D.  There probably are lots of Ph. D. out there looking for work tutoring, or doing things using considerably less than all that they know.  </p><p>So, what's the sense of really getting people all inspired and fired up with real math, if all you are doing is setting them up for a lifetime of disappointments?  Tell them up front that most mathematicians aren't going to amount to a hill of beans, and that is is time to rethink their career choices.  I am convinced that mathematicians talk young bright people into studying math so that they will have classrooms full of people in order to justify their career choices, without which them might be in a position to look for alternative choices like a short order chef or rest room attendant.  </p><p>Now, I wish that life were different.  I wish that every educated mathematician would have plenty of career choices in front of him.  Actually, I wish that on all students, but the obvious truth of the matter is that society would rather spend money on rescuing failed banks and auto manufactures developing obsoleted products than using the same money to stimulate the "arts and sciences".  I have read that the Soviet Union would do that, but I guess they have failed.  Too bad that we haven't realized a capitalistic society when in comes to rescuing billionaires who have made bad bets.</p></htmltext>
<tokenext>I have a M. Sc. in math from a highly respected university .
Unfortunately , it is damn hard getting a job which really uses my knowledge .
Sometimes , it has been a determent .
I have been disqualified from jobs because I would be bored after a while .
Granted , this is true , but after you have been out of work for a while , you will take a job doing most things .
So , what do you do with a degree in math , especially in a down economy .
Maybe go back and get some training as a auto mechanic ?
Yes , there will be times when you are not very busy , but on the other hand , you will never be completely unemployed .
The other problem is that there is no real place for someone without a Ph .
D. There probably are lots of Ph .
D. out there looking for work tutoring , or doing things using considerably less than all that they know .
So , what 's the sense of really getting people all inspired and fired up with real math , if all you are doing is setting them up for a lifetime of disappointments ?
Tell them up front that most mathematicians are n't going to amount to a hill of beans , and that is is time to rethink their career choices .
I am convinced that mathematicians talk young bright people into studying math so that they will have classrooms full of people in order to justify their career choices , without which them might be in a position to look for alternative choices like a short order chef or rest room attendant .
Now , I wish that life were different .
I wish that every educated mathematician would have plenty of career choices in front of him .
Actually , I wish that on all students , but the obvious truth of the matter is that society would rather spend money on rescuing failed banks and auto manufactures developing obsoleted products than using the same money to stimulate the " arts and sciences " .
I have read that the Soviet Union would do that , but I guess they have failed .
Too bad that we have n't realized a capitalistic society when in comes to rescuing billionaires who have made bad bets .</tokentext>
<sentencetext>I have a M. Sc. in math from a highly respected university.
Unfortunately, it is damn hard getting a job which really uses my knowledge.
Sometimes, it has been a determent.
I have been disqualified from jobs because I would be bored after a while.
Granted, this is true, but after you have been out of work for a while, you will take a job doing most things.
So, what do you do with a degree in math, especially in a down economy.
Maybe go back and get some training as a auto mechanic?
Yes, there will be times when you are not very busy, but on the other hand, you will never be completely unemployed.
The other problem is that there is no real place for someone without a Ph.
D.  There probably are lots of Ph.
D. out there looking for work tutoring, or doing things using considerably less than all that they know.
So, what's the sense of really getting people all inspired and fired up with real math, if all you are doing is setting them up for a lifetime of disappointments?
Tell them up front that most mathematicians aren't going to amount to a hill of beans, and that is is time to rethink their career choices.
I am convinced that mathematicians talk young bright people into studying math so that they will have classrooms full of people in order to justify their career choices, without which them might be in a position to look for alternative choices like a short order chef or rest room attendant.
Now, I wish that life were different.
I wish that every educated mathematician would have plenty of career choices in front of him.
Actually, I wish that on all students, but the obvious truth of the matter is that society would rather spend money on rescuing failed banks and auto manufactures developing obsoleted products than using the same money to stimulate the "arts and sciences".
I have read that the Soviet Union would do that, but I guess they have failed.
Too bad that we haven't realized a capitalistic society when in comes to rescuing billionaires who have made bad bets.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394205</id>
	<title>Re:it's really bad</title>
	<author>nine-times</author>
	<datestamp>1245443640000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p><div class="quote"><p>That is just one example of how horribly, horribly stupid the HS math curriculum is in the US.</p></div><p>I don't know, but to me that sounds more like evidence that the classes in elementary school and middle school are stupid.  You should understand basic logic and even basic geometry before you get to high school.  If a high school student isn't able to comprehend the idea of a geometry proof, then the education system has already failed him (or her).</p></div>
	</htmltext>
<tokenext>That is just one example of how horribly , horribly stupid the HS math curriculum is in the US.I do n't know , but to me that sounds more like evidence that the classes in elementary school and middle school are stupid .
You should understand basic logic and even basic geometry before you get to high school .
If a high school student is n't able to comprehend the idea of a geometry proof , then the education system has already failed him ( or her ) .</tokentext>
<sentencetext>That is just one example of how horribly, horribly stupid the HS math curriculum is in the US.I don't know, but to me that sounds more like evidence that the classes in elementary school and middle school are stupid.
You should understand basic logic and even basic geometry before you get to high school.
If a high school student isn't able to comprehend the idea of a geometry proof, then the education system has already failed him (or her).
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392911</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28443995</id>
	<title>About the actual man</title>
	<author>Anonymous</author>
	<datestamp>1245790260000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>http://www.maa.org/devlin/devlin\_03\_08.html</p><p>"Paul is a mathematics teacher at Saint Ann's School in Brooklyn, New York... "</p><p>and</p><p>'After several years teaching university mathematics, Paul eventually tired of it and decided he wanted to get back to teaching children. He secured a position at Saint Ann's School, where he says "I have happily been subversively teaching mathematics (the real thing) since 2000."</p><p>'He teaches all grade levels at Saint Ann's (K-12), and says he is especially interested in bringing a mathematician's point of view to very young children. "I want them to understand that there is a playground in their minds and that that is where mathematics happens. So far I have met with tremendous enthusiasm among the parents and kids, less so among the mid-level administrators," he wrote in an email to me.'</p></htmltext>
<tokenext>http : //www.maa.org/devlin/devlin \ _03 \ _08.html " Paul is a mathematics teacher at Saint Ann 's School in Brooklyn , New York... " and'After several years teaching university mathematics , Paul eventually tired of it and decided he wanted to get back to teaching children .
He secured a position at Saint Ann 's School , where he says " I have happily been subversively teaching mathematics ( the real thing ) since 2000 .
" 'He teaches all grade levels at Saint Ann 's ( K-12 ) , and says he is especially interested in bringing a mathematician 's point of view to very young children .
" I want them to understand that there is a playground in their minds and that that is where mathematics happens .
So far I have met with tremendous enthusiasm among the parents and kids , less so among the mid-level administrators , " he wrote in an email to me .
'</tokentext>
<sentencetext>http://www.maa.org/devlin/devlin\_03\_08.html"Paul is a mathematics teacher at Saint Ann's School in Brooklyn, New York... "and'After several years teaching university mathematics, Paul eventually tired of it and decided he wanted to get back to teaching children.
He secured a position at Saint Ann's School, where he says "I have happily been subversively teaching mathematics (the real thing) since 2000.
"'He teaches all grade levels at Saint Ann's (K-12), and says he is especially interested in bringing a mathematician's point of view to very young children.
"I want them to understand that there is a playground in their minds and that that is where mathematics happens.
So far I have met with tremendous enthusiasm among the parents and kids, less so among the mid-level administrators," he wrote in an email to me.
'</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393305</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393891</id>
	<title>Re:US K-12 MATH = Real world fail.</title>
	<author>Ogive17</author>
	<datestamp>1245442560000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>Simple questions get much harder when you're on national tv, sitting across a desk from a celebrity, with bright lights and cameras in your face.  I know because my gf was on the Japanese version about a decade ago. The question she ended up missing was something she knew, but for some reason she just couldn't come up with the answer will sitting in the chair.<br>
<br>
Maybe he knew it, maybe he didn't...   but I wouldn't use 'Who Wants to be a Millionaire' as an indicator.  When I first read your post, I wasn't sure what you were talking about either and it even took about 5 seconds after seeing the symbols to register what the answer was.</htmltext>
<tokenext>Simple questions get much harder when you 're on national tv , sitting across a desk from a celebrity , with bright lights and cameras in your face .
I know because my gf was on the Japanese version about a decade ago .
The question she ended up missing was something she knew , but for some reason she just could n't come up with the answer will sitting in the chair .
Maybe he knew it , maybe he did n't... but I would n't use 'Who Wants to be a Millionaire ' as an indicator .
When I first read your post , I was n't sure what you were talking about either and it even took about 5 seconds after seeing the symbols to register what the answer was .</tokentext>
<sentencetext>Simple questions get much harder when you're on national tv, sitting across a desk from a celebrity, with bright lights and cameras in your face.
I know because my gf was on the Japanese version about a decade ago.
The question she ended up missing was something she knew, but for some reason she just couldn't come up with the answer will sitting in the chair.
Maybe he knew it, maybe he didn't...   but I wouldn't use 'Who Wants to be a Millionaire' as an indicator.
When I first read your post, I wasn't sure what you were talking about either and it even took about 5 seconds after seeing the symbols to register what the answer was.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392991</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394097</id>
	<title>Re:I Sympathize With Him But Too Idyllic</title>
	<author>serutan</author>
	<datestamp>1245443280000</datestamp>
	<modclass>Insightful</modclass>
	<modscore>2</modscore>
	<htmltext><p>It's not necessary to put a perfect math teacher in every classroom. Elementary school teachers are perfectly capable of teaching a math curriculum that presents kids with mathematical concepts in game form as Lockhart mentions. Later in their school careers the kids who show interest and aptitude for math could be taught algebra etc, and the rest could stick with the mechanics of arithmetic that will enable them to deal with checkbooks and mortgages. I think our problem today is that we use a one-size-fits-all approach that evolved from the "new math" of the 1960s, which was aimed at teaching kids mathematical concepts instead of practical arithmetic. It was based on the theory that students would see the beauty and wonder of math, and as a result the mechanics would come naturally. That didn't happen, but rather than scrap the whole idea the education system kept the subject matter and devolved the teaching approach. There's a lot of window dressing but basically it's the same kind of rote instruction as before. I think the author's lament is that the system has been trying to teach the beauty of mathematics like a metal shop class.</p></htmltext>
<tokenext>It 's not necessary to put a perfect math teacher in every classroom .
Elementary school teachers are perfectly capable of teaching a math curriculum that presents kids with mathematical concepts in game form as Lockhart mentions .
Later in their school careers the kids who show interest and aptitude for math could be taught algebra etc , and the rest could stick with the mechanics of arithmetic that will enable them to deal with checkbooks and mortgages .
I think our problem today is that we use a one-size-fits-all approach that evolved from the " new math " of the 1960s , which was aimed at teaching kids mathematical concepts instead of practical arithmetic .
It was based on the theory that students would see the beauty and wonder of math , and as a result the mechanics would come naturally .
That did n't happen , but rather than scrap the whole idea the education system kept the subject matter and devolved the teaching approach .
There 's a lot of window dressing but basically it 's the same kind of rote instruction as before .
I think the author 's lament is that the system has been trying to teach the beauty of mathematics like a metal shop class .</tokentext>
<sentencetext>It's not necessary to put a perfect math teacher in every classroom.
Elementary school teachers are perfectly capable of teaching a math curriculum that presents kids with mathematical concepts in game form as Lockhart mentions.
Later in their school careers the kids who show interest and aptitude for math could be taught algebra etc, and the rest could stick with the mechanics of arithmetic that will enable them to deal with checkbooks and mortgages.
I think our problem today is that we use a one-size-fits-all approach that evolved from the "new math" of the 1960s, which was aimed at teaching kids mathematical concepts instead of practical arithmetic.
It was based on the theory that students would see the beauty and wonder of math, and as a result the mechanics would come naturally.
That didn't happen, but rather than scrap the whole idea the education system kept the subject matter and devolved the teaching approach.
There's a lot of window dressing but basically it's the same kind of rote instruction as before.
I think the author's lament is that the system has been trying to teach the beauty of mathematics like a metal shop class.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392903</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392921</id>
	<title>The way math is structured is disconnected from...</title>
	<author>blahplusplus</author>
	<datestamp>1245439020000</datestamp>
	<modclass>Interestin</modclass>
	<modscore>4</modscore>
	<htmltext><p>... interesting things kids want to do.</p><p>Lets face it a minority of people will like math, but matehmaticians have done a lot to make mathematics overly complicated.</p><p>I struggled with the symbolic format math was presented in highschool because it was so disconnected from the world, only as I got older did I realize how arbitrary and how that was only one way to present mathematics.  To really teach math one must learn how to observe first before one even gets into symbolic computation, math at it's most basic is about observing relationships, patterns of : Size, ratio, proportion, etc.   It's really a language invented to systematize structure and relationships of the real world, therefore how math is represented and structured and is taught matters a hell of a lot.</p><p>I've learned over the years that many mathematical systems are totally arbitrary are are more obtuse then they need to be, math comes from the simplest observations.  Math has built up a lot of cruft and wasteful jargon disconnecting math from the world.</p><p>For instance I had no idea for a long time that the way math is structured could be restructured when I was young and it was one group of peoples perspective on mathematical principles, I came across debates and alernative systems like:</p><p><a href="http://www.symmetryperfect.com/" title="symmetryperfect.com" rel="nofollow">http://www.symmetryperfect.com/</a> [symmetryperfect.com]</p><p>And it showed me how arbitrary mathematical systems and their structures really are and they are built to suit particular kinds of minds or cultures.</p><p>For instance the ancient mayans used shapes for numbers, instead of 1, 2, 3</p><p>See here:<br><a href="http://en.wikipedia.org/wiki/Maya\_numerals" title="wikipedia.org" rel="nofollow">http://en.wikipedia.org/wiki/Maya\_numerals</a> [wikipedia.org]</p><p>Math is a very rich subject which unfortunately has a lot of cultish like people who think themselves the gatekeepers of mathematics.</p><p>I've thought about writing a book in my spare time about how badly mathematicians and the academia has blinded themselves to simplifying mathematics by focusing too much on symbolic jargon and not teaching children how 'mathematical' relationships are related to our simplest observations of the world: Size, shape, form, color, motion, etc.</p></htmltext>
<tokenext>... interesting things kids want to do.Lets face it a minority of people will like math , but matehmaticians have done a lot to make mathematics overly complicated.I struggled with the symbolic format math was presented in highschool because it was so disconnected from the world , only as I got older did I realize how arbitrary and how that was only one way to present mathematics .
To really teach math one must learn how to observe first before one even gets into symbolic computation , math at it 's most basic is about observing relationships , patterns of : Size , ratio , proportion , etc .
It 's really a language invented to systematize structure and relationships of the real world , therefore how math is represented and structured and is taught matters a hell of a lot.I 've learned over the years that many mathematical systems are totally arbitrary are are more obtuse then they need to be , math comes from the simplest observations .
Math has built up a lot of cruft and wasteful jargon disconnecting math from the world.For instance I had no idea for a long time that the way math is structured could be restructured when I was young and it was one group of peoples perspective on mathematical principles , I came across debates and alernative systems like : http : //www.symmetryperfect.com/ [ symmetryperfect.com ] And it showed me how arbitrary mathematical systems and their structures really are and they are built to suit particular kinds of minds or cultures.For instance the ancient mayans used shapes for numbers , instead of 1 , 2 , 3See here : http : //en.wikipedia.org/wiki/Maya \ _numerals [ wikipedia.org ] Math is a very rich subject which unfortunately has a lot of cultish like people who think themselves the gatekeepers of mathematics.I 've thought about writing a book in my spare time about how badly mathematicians and the academia has blinded themselves to simplifying mathematics by focusing too much on symbolic jargon and not teaching children how 'mathematical ' relationships are related to our simplest observations of the world : Size , shape , form , color , motion , etc .</tokentext>
<sentencetext>... interesting things kids want to do.Lets face it a minority of people will like math, but matehmaticians have done a lot to make mathematics overly complicated.I struggled with the symbolic format math was presented in highschool because it was so disconnected from the world, only as I got older did I realize how arbitrary and how that was only one way to present mathematics.
To really teach math one must learn how to observe first before one even gets into symbolic computation, math at it's most basic is about observing relationships, patterns of : Size, ratio, proportion, etc.
It's really a language invented to systematize structure and relationships of the real world, therefore how math is represented and structured and is taught matters a hell of a lot.I've learned over the years that many mathematical systems are totally arbitrary are are more obtuse then they need to be, math comes from the simplest observations.
Math has built up a lot of cruft and wasteful jargon disconnecting math from the world.For instance I had no idea for a long time that the way math is structured could be restructured when I was young and it was one group of peoples perspective on mathematical principles, I came across debates and alernative systems like:http://www.symmetryperfect.com/ [symmetryperfect.com]And it showed me how arbitrary mathematical systems and their structures really are and they are built to suit particular kinds of minds or cultures.For instance the ancient mayans used shapes for numbers, instead of 1, 2, 3See here:http://en.wikipedia.org/wiki/Maya\_numerals [wikipedia.org]Math is a very rich subject which unfortunately has a lot of cultish like people who think themselves the gatekeepers of mathematics.I've thought about writing a book in my spare time about how badly mathematicians and the academia has blinded themselves to simplifying mathematics by focusing too much on symbolic jargon and not teaching children how 'mathematical' relationships are related to our simplest observations of the world: Size, shape, form, color, motion, etc.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393289</id>
	<title>Re:it's really bad</title>
	<author>Anonymous</author>
	<datestamp>1245440400000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>What are you talking about? Middle school geometry (that's what it is whether it's taught in high school or not) has really simply proofs where each line is the result of the application of a single proof rule. You don't need axiomatic or natural logic or type theory or any of that stuff. Even Euclid got by with a few axioms and a few (unnecessary) definitions.</p></htmltext>
<tokenext>What are you talking about ?
Middle school geometry ( that 's what it is whether it 's taught in high school or not ) has really simply proofs where each line is the result of the application of a single proof rule .
You do n't need axiomatic or natural logic or type theory or any of that stuff .
Even Euclid got by with a few axioms and a few ( unnecessary ) definitions .</tokentext>
<sentencetext>What are you talking about?
Middle school geometry (that's what it is whether it's taught in high school or not) has really simply proofs where each line is the result of the application of a single proof rule.
You don't need axiomatic or natural logic or type theory or any of that stuff.
Even Euclid got by with a few axioms and a few (unnecessary) definitions.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392911</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28396217</id>
	<title>Re:US School System compared to Europes School Sys</title>
	<author>0x000000</author>
	<datestamp>1245408000000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>I actually went to two different high schools. I switched the summer before my Junior year in school. This was because the high school I had been attending was having major issues with minorities fighting (the african americans and hispanics were bringing weapons to school), we had several knife stabbings at the school, and it caused many issues in general because of the way the school was run and where it was going. My dad figured it was easier to move, both closer to work, and into a new town than to have to worry about his kids going to a high school where fights were the daily norm and where no attention was being given to the rampant issues with drug use, alcohol abuse and fighting.</p><p>The second high school I went to was a higher class, more expensive town, and while the education there was generally better in terms of people wanting to be there it was not that much better. There were different levels of classes offered, but in those classes they were still catered to the lowest common denominator. This was a mostly chinese and white school compared to my previous school. The issue at hand was that the school and the school board were more willing to put money into sports and the sports programs and buying new football fields and tracks rather than improving the class rooms, providing new books, new computers and new equipment.</p><p>The first school was 1500 students in size, the second one was 1200 students in size, small? Not really. Not as large as some of the bigger US public high schools.</p></htmltext>
<tokenext>I actually went to two different high schools .
I switched the summer before my Junior year in school .
This was because the high school I had been attending was having major issues with minorities fighting ( the african americans and hispanics were bringing weapons to school ) , we had several knife stabbings at the school , and it caused many issues in general because of the way the school was run and where it was going .
My dad figured it was easier to move , both closer to work , and into a new town than to have to worry about his kids going to a high school where fights were the daily norm and where no attention was being given to the rampant issues with drug use , alcohol abuse and fighting.The second high school I went to was a higher class , more expensive town , and while the education there was generally better in terms of people wanting to be there it was not that much better .
There were different levels of classes offered , but in those classes they were still catered to the lowest common denominator .
This was a mostly chinese and white school compared to my previous school .
The issue at hand was that the school and the school board were more willing to put money into sports and the sports programs and buying new football fields and tracks rather than improving the class rooms , providing new books , new computers and new equipment.The first school was 1500 students in size , the second one was 1200 students in size , small ?
Not really .
Not as large as some of the bigger US public high schools .</tokentext>
<sentencetext>I actually went to two different high schools.
I switched the summer before my Junior year in school.
This was because the high school I had been attending was having major issues with minorities fighting (the african americans and hispanics were bringing weapons to school), we had several knife stabbings at the school, and it caused many issues in general because of the way the school was run and where it was going.
My dad figured it was easier to move, both closer to work, and into a new town than to have to worry about his kids going to a high school where fights were the daily norm and where no attention was being given to the rampant issues with drug use, alcohol abuse and fighting.The second high school I went to was a higher class, more expensive town, and while the education there was generally better in terms of people wanting to be there it was not that much better.
There were different levels of classes offered, but in those classes they were still catered to the lowest common denominator.
This was a mostly chinese and white school compared to my previous school.
The issue at hand was that the school and the school board were more willing to put money into sports and the sports programs and buying new football fields and tracks rather than improving the class rooms, providing new books, new computers and new equipment.The first school was 1500 students in size, the second one was 1200 students in size, small?
Not really.
Not as large as some of the bigger US public high schools.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393241</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393159</id>
	<title>You can convince me</title>
	<author>Anonymous</author>
	<datestamp>1245439920000</datestamp>
	<modclass>Insightful</modclass>
	<modscore>4</modscore>
	<htmltext><p>that math is better taught as an art than as a pragmatic problem-solving toolset when you can convince me that Pablo Picasso should have been forced to paint the Golden Gate bridge.</p><p>Society needs math as a tool in far greater quantity than math as an art. Socially-funded education serves the greater need of society. QED.</p><p>I survived public school mathematics. I still appreciate the beauty of patterns, especially the relatedness of art, music, and math. (<i>Godel, Escher, and Bach</i> really resonated for me. But that didn't make me a mathematical artist, any more than a musical composer or a woodblock printer.)</p><p>Lockhart's essay is an interesting read, really, but on some level it boils down to "Those unworthy schlubs treating Mathematics as a tool don't deserve it. It belongs to the artists, the dreamers, the purists!"</p><p>It's a pretty common arrogation in the math culture, it seems. I dont' recall sculptors ever being pissed at concrete workers or ironworkers. And I've never heard of any artist painter getting mad at the other kind of painter for not employing good artistic composition principle while painting the side of the barn.</p><p>Seriously. Math is both an art and a tool. The best artists find their art by themselves; they're not turned out by artist factories. School mathematics is to turn out the mathematical equivalent of bridge painters and ironworkers, because society needs those more (in greater quantity).</p></htmltext>
<tokenext>that math is better taught as an art than as a pragmatic problem-solving toolset when you can convince me that Pablo Picasso should have been forced to paint the Golden Gate bridge.Society needs math as a tool in far greater quantity than math as an art .
Socially-funded education serves the greater need of society .
QED.I survived public school mathematics .
I still appreciate the beauty of patterns , especially the relatedness of art , music , and math .
( Godel , Escher , and Bach really resonated for me .
But that did n't make me a mathematical artist , any more than a musical composer or a woodblock printer .
) Lockhart 's essay is an interesting read , really , but on some level it boils down to " Those unworthy schlubs treating Mathematics as a tool do n't deserve it .
It belongs to the artists , the dreamers , the purists !
" It 's a pretty common arrogation in the math culture , it seems .
I dont ' recall sculptors ever being pissed at concrete workers or ironworkers .
And I 've never heard of any artist painter getting mad at the other kind of painter for not employing good artistic composition principle while painting the side of the barn.Seriously .
Math is both an art and a tool .
The best artists find their art by themselves ; they 're not turned out by artist factories .
School mathematics is to turn out the mathematical equivalent of bridge painters and ironworkers , because society needs those more ( in greater quantity ) .</tokentext>
<sentencetext>that math is better taught as an art than as a pragmatic problem-solving toolset when you can convince me that Pablo Picasso should have been forced to paint the Golden Gate bridge.Society needs math as a tool in far greater quantity than math as an art.
Socially-funded education serves the greater need of society.
QED.I survived public school mathematics.
I still appreciate the beauty of patterns, especially the relatedness of art, music, and math.
(Godel, Escher, and Bach really resonated for me.
But that didn't make me a mathematical artist, any more than a musical composer or a woodblock printer.
)Lockhart's essay is an interesting read, really, but on some level it boils down to "Those unworthy schlubs treating Mathematics as a tool don't deserve it.
It belongs to the artists, the dreamers, the purists!
"It's a pretty common arrogation in the math culture, it seems.
I dont' recall sculptors ever being pissed at concrete workers or ironworkers.
And I've never heard of any artist painter getting mad at the other kind of painter for not employing good artistic composition principle while painting the side of the barn.Seriously.
Math is both an art and a tool.
The best artists find their art by themselves; they're not turned out by artist factories.
School mathematics is to turn out the mathematical equivalent of bridge painters and ironworkers, because society needs those more (in greater quantity).</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28401929</id>
	<title>Re:Cue the other subjects</title>
	<author>Lost Engineer</author>
	<datestamp>1245513720000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p><div class="quote"><p>and most of them can be traced to certain groups (*cough*<b>teacher's unions</b>*cough*) waging a 30 year war on public education</p></div><p>The fundies are all home schooled now.</p></div>
	</htmltext>
<tokenext>and most of them can be traced to certain groups ( * cough * teacher 's unions * cough * ) waging a 30 year war on public educationThe fundies are all home schooled now .</tokentext>
<sentencetext>and most of them can be traced to certain groups (*cough*teacher's unions*cough*) waging a 30 year war on public educationThe fundies are all home schooled now.
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393083</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28395279</id>
	<title>Re:Can't count</title>
	<author>mcgrew</author>
	<datestamp>1245403980000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>I hope you're not the one with the Holy Hand Grenade!</p></htmltext>
<tokenext>I hope you 're not the one with the Holy Hand Grenade !</tokentext>
<sentencetext>I hope you're not the one with the Holy Hand Grenade!</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392757</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28395665</id>
	<title>Re:Two mathematicians</title>
	<author>Bootsy Collins</author>
	<datestamp>1245405540000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>I love this.</htmltext>
<tokenext>I love this .</tokentext>
<sentencetext>I love this.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393275</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394295</id>
	<title>Re:The way math is structured is disconnected from</title>
	<author>jandrese</author>
	<datestamp>1245443940000</datestamp>
	<modclass>Insightful</modclass>
	<modscore>2</modscore>
	<htmltext>As a CS student I had to take a lot of math.  One thing that always struck me is that a lot of math is a lot like programming (this is not a coincidence) except that you're only allowed to use single letter (greek!) variable and function names. <br>
<br>
A lot of math reads like extremely bad Perl programs too, with tons of functionality on every line and no documentation except for a giant paragraph at the top written by someone who is apparently from Mars.<br>
<br>
On the other hand, a lot of math is just pattern recognition.  Realizing when you need to use one transform over another is a fundamental part of mathematics.  Maybe the language simplifies this task somehow?  I'm not sure.  It always seemed to obscure it more than anything else to me.</htmltext>
<tokenext>As a CS student I had to take a lot of math .
One thing that always struck me is that a lot of math is a lot like programming ( this is not a coincidence ) except that you 're only allowed to use single letter ( greek !
) variable and function names .
A lot of math reads like extremely bad Perl programs too , with tons of functionality on every line and no documentation except for a giant paragraph at the top written by someone who is apparently from Mars .
On the other hand , a lot of math is just pattern recognition .
Realizing when you need to use one transform over another is a fundamental part of mathematics .
Maybe the language simplifies this task somehow ?
I 'm not sure .
It always seemed to obscure it more than anything else to me .</tokentext>
<sentencetext>As a CS student I had to take a lot of math.
One thing that always struck me is that a lot of math is a lot like programming (this is not a coincidence) except that you're only allowed to use single letter (greek!
) variable and function names.
A lot of math reads like extremely bad Perl programs too, with tons of functionality on every line and no documentation except for a giant paragraph at the top written by someone who is apparently from Mars.
On the other hand, a lot of math is just pattern recognition.
Realizing when you need to use one transform over another is a fundamental part of mathematics.
Maybe the language simplifies this task somehow?
I'm not sure.
It always seemed to obscure it more than anything else to me.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392921</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28399463</id>
	<title>"Coach What's-His-Name"</title>
	<author>EEBaum</author>
	<datestamp>1245436080000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>On the first day of class, my college history teacher asked for a show of hands on how many had been in a high school history class taught by "Coach What's-His-Name".  Almost all the hands went up.  The situation is quite similar for high school math.  I had one HS math teacher who <i>wasn't</i> a coach, and she was even worse than the ones that were.</htmltext>
<tokenext>On the first day of class , my college history teacher asked for a show of hands on how many had been in a high school history class taught by " Coach What 's-His-Name " .
Almost all the hands went up .
The situation is quite similar for high school math .
I had one HS math teacher who was n't a coach , and she was even worse than the ones that were .</tokentext>
<sentencetext>On the first day of class, my college history teacher asked for a show of hands on how many had been in a high school history class taught by "Coach What's-His-Name".
Almost all the hands went up.
The situation is quite similar for high school math.
I had one HS math teacher who wasn't a coach, and she was even worse than the ones that were.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28397249</id>
	<title>Creative vs. Pedantic</title>
	<author>samwhite\_y</author>
	<datestamp>1245413580000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>I didn't see anybody give their experience with the "new math" experiment that was done a while back. If you think about this from a little distance you can see that there are two camps in mathematics education, the "Creatives" and the "Pedantics", the "new math" was an attempt by the "Creatives" (who Lockhart is clearly a member of) to inject "thinking" and "creative thought" into the mathematics curriculum. It was a total bust, primarily because the teachers teaching it really didn't understand the intentions behind this new curriculum and they reduced it to rote. Those in favor of "back to basics" would be in the "Pedantics" camp and have been making a comeback recently.</p><p>So here in a nutshell is the two opposing camps arguments.</p><p>Creatives argument against the Pedantics -- The Pedantic curriculum is a soul destroying exercise in rote and memorization leaving no room for a child to feel any inspiration or creativity.</p><p>Pedantics argument against the Creatives -- The Creatives assume the world to be filled with inspired teachers that won't reduce any curriculum to a pedantic exercise. If the quality of teachers is such that they can only teach pedantic material, you might as well have the children learn something useful and constructive even if it is boring and soul destroying.</p><p>I am an ex-mathematician and I am firmly in the "Pedantics" camp. I hate to see children that cannot add two digit number to two digit numbers without a calculator. That is the world that well meaning "Creatives" create.</p><p>Also, is there really that strong a correlation between the percentage of students that pass standardized tests on calculus and the overall success of the community? Russia has a very strong educational system, see what that got them. The general population of the U.S. would be considered be woefully uneducated by the standards of many other countries. But if you were to take any country with as large an immigrant population, I suspect you would see similar numbers. Over time the immigrants are absorbed into the main stream and their children do better. But could it be possible that these immigrants are also the source of the vitality of the U.S. economy and their education (or lack of it) is not the primary reason for why they make this nation so successful?</p></htmltext>
<tokenext>I did n't see anybody give their experience with the " new math " experiment that was done a while back .
If you think about this from a little distance you can see that there are two camps in mathematics education , the " Creatives " and the " Pedantics " , the " new math " was an attempt by the " Creatives " ( who Lockhart is clearly a member of ) to inject " thinking " and " creative thought " into the mathematics curriculum .
It was a total bust , primarily because the teachers teaching it really did n't understand the intentions behind this new curriculum and they reduced it to rote .
Those in favor of " back to basics " would be in the " Pedantics " camp and have been making a comeback recently.So here in a nutshell is the two opposing camps arguments.Creatives argument against the Pedantics -- The Pedantic curriculum is a soul destroying exercise in rote and memorization leaving no room for a child to feel any inspiration or creativity.Pedantics argument against the Creatives -- The Creatives assume the world to be filled with inspired teachers that wo n't reduce any curriculum to a pedantic exercise .
If the quality of teachers is such that they can only teach pedantic material , you might as well have the children learn something useful and constructive even if it is boring and soul destroying.I am an ex-mathematician and I am firmly in the " Pedantics " camp .
I hate to see children that can not add two digit number to two digit numbers without a calculator .
That is the world that well meaning " Creatives " create.Also , is there really that strong a correlation between the percentage of students that pass standardized tests on calculus and the overall success of the community ?
Russia has a very strong educational system , see what that got them .
The general population of the U.S. would be considered be woefully uneducated by the standards of many other countries .
But if you were to take any country with as large an immigrant population , I suspect you would see similar numbers .
Over time the immigrants are absorbed into the main stream and their children do better .
But could it be possible that these immigrants are also the source of the vitality of the U.S. economy and their education ( or lack of it ) is not the primary reason for why they make this nation so successful ?</tokentext>
<sentencetext>I didn't see anybody give their experience with the "new math" experiment that was done a while back.
If you think about this from a little distance you can see that there are two camps in mathematics education, the "Creatives" and the "Pedantics", the "new math" was an attempt by the "Creatives" (who Lockhart is clearly a member of) to inject "thinking" and "creative thought" into the mathematics curriculum.
It was a total bust, primarily because the teachers teaching it really didn't understand the intentions behind this new curriculum and they reduced it to rote.
Those in favor of "back to basics" would be in the "Pedantics" camp and have been making a comeback recently.So here in a nutshell is the two opposing camps arguments.Creatives argument against the Pedantics -- The Pedantic curriculum is a soul destroying exercise in rote and memorization leaving no room for a child to feel any inspiration or creativity.Pedantics argument against the Creatives -- The Creatives assume the world to be filled with inspired teachers that won't reduce any curriculum to a pedantic exercise.
If the quality of teachers is such that they can only teach pedantic material, you might as well have the children learn something useful and constructive even if it is boring and soul destroying.I am an ex-mathematician and I am firmly in the "Pedantics" camp.
I hate to see children that cannot add two digit number to two digit numbers without a calculator.
That is the world that well meaning "Creatives" create.Also, is there really that strong a correlation between the percentage of students that pass standardized tests on calculus and the overall success of the community?
Russia has a very strong educational system, see what that got them.
The general population of the U.S. would be considered be woefully uneducated by the standards of many other countries.
But if you were to take any country with as large an immigrant population, I suspect you would see similar numbers.
Over time the immigrants are absorbed into the main stream and their children do better.
But could it be possible that these immigrants are also the source of the vitality of the U.S. economy and their education (or lack of it) is not the primary reason for why they make this nation so successful?</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28399413</id>
	<title>Re:The way math is structured is disconnected from</title>
	<author>Anonymous</author>
	<datestamp>1245435360000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>Several posters touched on other good points, but I'd like to point out that those "better performing" countries, especially in Asia, do not share our "total graduation" philosophy. If a kid doesn't do well in school, he is encouraged to leave. This significantly bumps up their test scores, making comparison between those countries and the US a false one. It's why their scores are always better than us -- but that makes those scores useful to the academic sector, since they can always try to argue for more money. (Which can then be sucked into school administration's pockets. If they do it fast enough, teachers and students will never see a dime's worth of improvement!)</p></htmltext>
<tokenext>Several posters touched on other good points , but I 'd like to point out that those " better performing " countries , especially in Asia , do not share our " total graduation " philosophy .
If a kid does n't do well in school , he is encouraged to leave .
This significantly bumps up their test scores , making comparison between those countries and the US a false one .
It 's why their scores are always better than us -- but that makes those scores useful to the academic sector , since they can always try to argue for more money .
( Which can then be sucked into school administration 's pockets .
If they do it fast enough , teachers and students will never see a dime 's worth of improvement !
)</tokentext>
<sentencetext>Several posters touched on other good points, but I'd like to point out that those "better performing" countries, especially in Asia, do not share our "total graduation" philosophy.
If a kid doesn't do well in school, he is encouraged to leave.
This significantly bumps up their test scores, making comparison between those countries and the US a false one.
It's why their scores are always better than us -- but that makes those scores useful to the academic sector, since they can always try to argue for more money.
(Which can then be sucked into school administration's pockets.
If they do it fast enough, teachers and students will never see a dime's worth of improvement!
)</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393115</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393883</id>
	<title>Re:Cue the other subjects</title>
	<author>david\_thornley</author>
	<datestamp>1245442500000</datestamp>
	<modclass>Insightful</modclass>
	<modscore>3</modscore>
	<htmltext><p>
What studies I've seen show approximately no difference between children who have been in day care and children with a stay-at-home parent.  (Okay, there's some detail differences early on, but they fade).
</p><p>
The important thing is the parents' attitude.  Young children will emulate their parents, and will try to please them.  If the parents make it clear that education will please them, and put enough time and effort into monitoring it to make that perfectly clear, and to be able to tell the difference between learning things and getting good grades, the children will respond appropriately.
</p><p>
A parent who wants to encourage education, and isn't totally swamped with other things that he or she is basically incapable of parenting, can find a way to do so.</p></htmltext>
<tokenext>What studies I 've seen show approximately no difference between children who have been in day care and children with a stay-at-home parent .
( Okay , there 's some detail differences early on , but they fade ) .
The important thing is the parents ' attitude .
Young children will emulate their parents , and will try to please them .
If the parents make it clear that education will please them , and put enough time and effort into monitoring it to make that perfectly clear , and to be able to tell the difference between learning things and getting good grades , the children will respond appropriately .
A parent who wants to encourage education , and is n't totally swamped with other things that he or she is basically incapable of parenting , can find a way to do so .</tokentext>
<sentencetext>
What studies I've seen show approximately no difference between children who have been in day care and children with a stay-at-home parent.
(Okay, there's some detail differences early on, but they fade).
The important thing is the parents' attitude.
Young children will emulate their parents, and will try to please them.
If the parents make it clear that education will please them, and put enough time and effort into monitoring it to make that perfectly clear, and to be able to tell the difference between learning things and getting good grades, the children will respond appropriately.
A parent who wants to encourage education, and isn't totally swamped with other things that he or she is basically incapable of parenting, can find a way to do so.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393137</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28404195</id>
	<title>Another teacher's take</title>
	<author>trveler</author>
	<datestamp>1245491220000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>Read "The Seven Lesson Schoolteacher" by John Taylor Gatto.

Gatto is an award-winning schoolteacher in New York State, and he takes much the same anaylsis as Lockhart does for math to the entire industry of education. Only Gatto wrote his piece in 1992.

<a href="http://www.newciv.org/whole/schoolteacher.txt" title="newciv.org" rel="nofollow">http://www.newciv.org/whole/schoolteacher.txt</a> [newciv.org]</htmltext>
<tokenext>Read " The Seven Lesson Schoolteacher " by John Taylor Gatto .
Gatto is an award-winning schoolteacher in New York State , and he takes much the same anaylsis as Lockhart does for math to the entire industry of education .
Only Gatto wrote his piece in 1992 . http : //www.newciv.org/whole/schoolteacher.txt [ newciv.org ]</tokentext>
<sentencetext>Read "The Seven Lesson Schoolteacher" by John Taylor Gatto.
Gatto is an award-winning schoolteacher in New York State, and he takes much the same anaylsis as Lockhart does for math to the entire industry of education.
Only Gatto wrote his piece in 1992.

http://www.newciv.org/whole/schoolteacher.txt [newciv.org]</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394271</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394339</id>
	<title>Assuming you could "fix the teachers"...</title>
	<author>Anonymous</author>
	<datestamp>1245444120000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>Assuming you could fix the teachers, you could always combine math and science more closely. After all, mathematics started as an attempt to quantify and understand the world through a more precise language and physics, chemistry, biology, economics etc. all make more sense when explained mathematically.</p><p>Since we're dreaming here, math at home could also help the process too. After all, no one needs to learn to speak by the time they hit kindergarten. Parents can really help there kids by explaining how they use math in their jobs.</p><p>On a side note, I took my Ph.D. in Ops. Research (which lived in Engineering at my university) and my masters in math, so my opinion is colored by too much university training. Also, I hated math until I started to teach myself out of old text books around 6th grade. Then it got much better. It didn't hurt that my dad was an engineer; hence the "math at home" comment.</p></htmltext>
<tokenext>Assuming you could fix the teachers , you could always combine math and science more closely .
After all , mathematics started as an attempt to quantify and understand the world through a more precise language and physics , chemistry , biology , economics etc .
all make more sense when explained mathematically.Since we 're dreaming here , math at home could also help the process too .
After all , no one needs to learn to speak by the time they hit kindergarten .
Parents can really help there kids by explaining how they use math in their jobs.On a side note , I took my Ph.D. in Ops .
Research ( which lived in Engineering at my university ) and my masters in math , so my opinion is colored by too much university training .
Also , I hated math until I started to teach myself out of old text books around 6th grade .
Then it got much better .
It did n't hurt that my dad was an engineer ; hence the " math at home " comment .</tokentext>
<sentencetext>Assuming you could fix the teachers, you could always combine math and science more closely.
After all, mathematics started as an attempt to quantify and understand the world through a more precise language and physics, chemistry, biology, economics etc.
all make more sense when explained mathematically.Since we're dreaming here, math at home could also help the process too.
After all, no one needs to learn to speak by the time they hit kindergarten.
Parents can really help there kids by explaining how they use math in their jobs.On a side note, I took my Ph.D. in Ops.
Research (which lived in Engineering at my university) and my masters in math, so my opinion is colored by too much university training.
Also, I hated math until I started to teach myself out of old text books around 6th grade.
Then it got much better.
It didn't hurt that my dad was an engineer; hence the "math at home" comment.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28395907</id>
	<title>Re:You can convince me</title>
	<author>nine-times</author>
	<datestamp>1245406620000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p><div class="quote"><p>I dont' recall sculptors ever being pissed at concrete workers or ironworkers.</p></div><p>Yeah, but it's also worth recognizing that your average concrete worker might not be the best person to teach a sculpture class.</p></div>
	</htmltext>
<tokenext>I dont ' recall sculptors ever being pissed at concrete workers or ironworkers.Yeah , but it 's also worth recognizing that your average concrete worker might not be the best person to teach a sculpture class .</tokentext>
<sentencetext>I dont' recall sculptors ever being pissed at concrete workers or ironworkers.Yeah, but it's also worth recognizing that your average concrete worker might not be the best person to teach a sculpture class.
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393159</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28408995</id>
	<title>Re:US School System compared to Europes School Sys</title>
	<author>Anonymous</author>
	<datestamp>1245578040000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>I am unsure about the size of my school (freshman class of 500, senior class of 300, 1800 students total) compared to others, but even though we had three different levels of math at my school, some students still did not do well (there own failings) but others couldn't do well enough (there was nothing offered after AP Calc AB - which I finished junior year technically two years ahead of people I was told were "just as smart as I was", and AP Calc BC was not available at my school).</p><p>I tend to think that the problem is above individual schools - at the school boards, NEA, and state and federal testing requirements.  The school administrators are being told to run them as cheap diploma mills (meaning no classes less than a specific size no matter what - say goodbye to advanced classes) where no students fail a grade, good teachers aren't rewarded any more or any better than bad teachers (meaning not even the good teachers will bother to help or challenge advanced students that are obviously interested), and yet every student that graduates has to just barely pass a standardized test developed by people who are completely divorced from the concept of teaching or learning (meaning that the focus of the school isn't on promoting the best students to see as far as they can go, the focus is on babying the lazy students - they were very smart about things they were interested in, so they weren't dumb by any stretch of the imagination - so they simply don't fail the test outright).</p><p>But above all, I think the blame lies squarely on the shoulders of the parents of students.  They were not interested enough in the future of their kids to care about their kids' intellect or education.  The saddest part is that their grandkids will turn out the exact same way, and the cycle continues.</p><p>And there isn't anything you, nor I, nor teachers, nor the government can do to stop the endless cycle.  Another brick in the wall, indeed.</p></htmltext>
<tokenext>I am unsure about the size of my school ( freshman class of 500 , senior class of 300 , 1800 students total ) compared to others , but even though we had three different levels of math at my school , some students still did not do well ( there own failings ) but others could n't do well enough ( there was nothing offered after AP Calc AB - which I finished junior year technically two years ahead of people I was told were " just as smart as I was " , and AP Calc BC was not available at my school ) .I tend to think that the problem is above individual schools - at the school boards , NEA , and state and federal testing requirements .
The school administrators are being told to run them as cheap diploma mills ( meaning no classes less than a specific size no matter what - say goodbye to advanced classes ) where no students fail a grade , good teachers are n't rewarded any more or any better than bad teachers ( meaning not even the good teachers will bother to help or challenge advanced students that are obviously interested ) , and yet every student that graduates has to just barely pass a standardized test developed by people who are completely divorced from the concept of teaching or learning ( meaning that the focus of the school is n't on promoting the best students to see as far as they can go , the focus is on babying the lazy students - they were very smart about things they were interested in , so they were n't dumb by any stretch of the imagination - so they simply do n't fail the test outright ) .But above all , I think the blame lies squarely on the shoulders of the parents of students .
They were not interested enough in the future of their kids to care about their kids ' intellect or education .
The saddest part is that their grandkids will turn out the exact same way , and the cycle continues.And there is n't anything you , nor I , nor teachers , nor the government can do to stop the endless cycle .
Another brick in the wall , indeed .</tokentext>
<sentencetext>I am unsure about the size of my school (freshman class of 500, senior class of 300, 1800 students total) compared to others, but even though we had three different levels of math at my school, some students still did not do well (there own failings) but others couldn't do well enough (there was nothing offered after AP Calc AB - which I finished junior year technically two years ahead of people I was told were "just as smart as I was", and AP Calc BC was not available at my school).I tend to think that the problem is above individual schools - at the school boards, NEA, and state and federal testing requirements.
The school administrators are being told to run them as cheap diploma mills (meaning no classes less than a specific size no matter what - say goodbye to advanced classes) where no students fail a grade, good teachers aren't rewarded any more or any better than bad teachers (meaning not even the good teachers will bother to help or challenge advanced students that are obviously interested), and yet every student that graduates has to just barely pass a standardized test developed by people who are completely divorced from the concept of teaching or learning (meaning that the focus of the school isn't on promoting the best students to see as far as they can go, the focus is on babying the lazy students - they were very smart about things they were interested in, so they weren't dumb by any stretch of the imagination - so they simply don't fail the test outright).But above all, I think the blame lies squarely on the shoulders of the parents of students.
They were not interested enough in the future of their kids to care about their kids' intellect or education.
The saddest part is that their grandkids will turn out the exact same way, and the cycle continues.And there isn't anything you, nor I, nor teachers, nor the government can do to stop the endless cycle.
Another brick in the wall, indeed.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393241</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28395577</id>
	<title>Re:The way math is structured is disconnected from</title>
	<author>Anonymous</author>
	<datestamp>1245405180000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>You should probably think that through a little bit more.</p><p>The performance levels you're talking about are measured by standardized tests, so increasingly intensive standard teaching methods will exhibit symptoms of increased performance.</p><p>Should probably read the article.</p></htmltext>
<tokenext>You should probably think that through a little bit more.The performance levels you 're talking about are measured by standardized tests , so increasingly intensive standard teaching methods will exhibit symptoms of increased performance.Should probably read the article .</tokentext>
<sentencetext>You should probably think that through a little bit more.The performance levels you're talking about are measured by standardized tests, so increasingly intensive standard teaching methods will exhibit symptoms of increased performance.Should probably read the article.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393115</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28396045</id>
	<title>Re:Single Best Fix: Introducing Discrete Mathemati</title>
	<author>shemyazaz</author>
	<datestamp>1245407220000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>I am in agreement with the above. However, I think the use of discrete mathematics needs to be spread throughout the entire curriculum. Expecting kids to progress intellectually just because you force feed them formulas is a bit on the ridiculous side.I was one of those who never managed to "get" mathematics in school. Mostly because of the teaching methods utilizing rote memorization. My conceptual learning style just didn't allow me to absorb the information without proper applications. It took a very dedicated college professor to show me how easy mathematics can actually be when you know exactly what you are trying to do, and why.

I think that the proper implimentation of conceptual teaching methods would solve at least some if not most of  our math problems in primary and secondary education.

The author's idea that math be treated as an optional subject kinda bothers me. Yes you can treat it as a form of art, and it helps if you don't stifle the creative tendencies of those few who are already interested in math, but a general understanding of math is a necessary component for understanding many other things in this world.</htmltext>
<tokenext>I am in agreement with the above .
However , I think the use of discrete mathematics needs to be spread throughout the entire curriculum .
Expecting kids to progress intellectually just because you force feed them formulas is a bit on the ridiculous side.I was one of those who never managed to " get " mathematics in school .
Mostly because of the teaching methods utilizing rote memorization .
My conceptual learning style just did n't allow me to absorb the information without proper applications .
It took a very dedicated college professor to show me how easy mathematics can actually be when you know exactly what you are trying to do , and why .
I think that the proper implimentation of conceptual teaching methods would solve at least some if not most of our math problems in primary and secondary education .
The author 's idea that math be treated as an optional subject kinda bothers me .
Yes you can treat it as a form of art , and it helps if you do n't stifle the creative tendencies of those few who are already interested in math , but a general understanding of math is a necessary component for understanding many other things in this world .</tokentext>
<sentencetext>I am in agreement with the above.
However, I think the use of discrete mathematics needs to be spread throughout the entire curriculum.
Expecting kids to progress intellectually just because you force feed them formulas is a bit on the ridiculous side.I was one of those who never managed to "get" mathematics in school.
Mostly because of the teaching methods utilizing rote memorization.
My conceptual learning style just didn't allow me to absorb the information without proper applications.
It took a very dedicated college professor to show me how easy mathematics can actually be when you know exactly what you are trying to do, and why.
I think that the proper implimentation of conceptual teaching methods would solve at least some if not most of  our math problems in primary and secondary education.
The author's idea that math be treated as an optional subject kinda bothers me.
Yes you can treat it as a form of art, and it helps if you don't stifle the creative tendencies of those few who are already interested in math, but a general understanding of math is a necessary component for understanding many other things in this world.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394873</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28398733</id>
	<title>Re:A teachers take</title>
	<author>Anonymous</author>
	<datestamp>1245426780000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>"and care for it like a price flower."</p><p>A for effort then.</p><p>Yes, I do believe you're a teacher in the US.  I also think you need to brush up on your vocabulary.  I don't think "talent" means what you think it means, because as far as I've been able to determine most US schools very much do not base anything on talent.  Except the football team.</p></htmltext>
<tokenext>" and care for it like a price flower .
" A for effort then.Yes , I do believe you 're a teacher in the US .
I also think you need to brush up on your vocabulary .
I do n't think " talent " means what you think it means , because as far as I 've been able to determine most US schools very much do not base anything on talent .
Except the football team .</tokentext>
<sentencetext>"and care for it like a price flower.
"A for effort then.Yes, I do believe you're a teacher in the US.
I also think you need to brush up on your vocabulary.
I don't think "talent" means what you think it means, because as far as I've been able to determine most US schools very much do not base anything on talent.
Except the football team.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394271</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28395895</id>
	<title>Re:The way math is structured is disconnected from</title>
	<author>Anonymous</author>
	<datestamp>1245406560000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p><div class="quote"><p>but rather because they don't feel the pressure to excel like students in other cultures.</p></div><p>And why do you suppose that they don't feel that pressure? American pupils may not excel at math, but even among the math underachievers there are smart ones who see the low pay and level of respect that engineering and science receive in our culture. In the United States we glorify and shower wealth upon the athletes, lawyers, businessmen, and politicians who are often willfully ignorant of math and science. These smart students see these wealthy and powerful individuals who couldn't write a proof to save their lives and yet they somehow end up with the best houses, the nicest cars, the most money and generally look down upon scientists and engineers while gleefully outsourcing their jobs to those low-wage Asian countries where rote-memorization scientists and engineers become the next wage slaves of American international corporations. If we want good students to become scientists, engineers, or yes even mathematicians then we have to start rewarding those positions in our society instead of outsourcing their jobs and treating them like dirt.</p></div>
	</htmltext>
<tokenext>but rather because they do n't feel the pressure to excel like students in other cultures.And why do you suppose that they do n't feel that pressure ?
American pupils may not excel at math , but even among the math underachievers there are smart ones who see the low pay and level of respect that engineering and science receive in our culture .
In the United States we glorify and shower wealth upon the athletes , lawyers , businessmen , and politicians who are often willfully ignorant of math and science .
These smart students see these wealthy and powerful individuals who could n't write a proof to save their lives and yet they somehow end up with the best houses , the nicest cars , the most money and generally look down upon scientists and engineers while gleefully outsourcing their jobs to those low-wage Asian countries where rote-memorization scientists and engineers become the next wage slaves of American international corporations .
If we want good students to become scientists , engineers , or yes even mathematicians then we have to start rewarding those positions in our society instead of outsourcing their jobs and treating them like dirt .</tokentext>
<sentencetext>but rather because they don't feel the pressure to excel like students in other cultures.And why do you suppose that they don't feel that pressure?
American pupils may not excel at math, but even among the math underachievers there are smart ones who see the low pay and level of respect that engineering and science receive in our culture.
In the United States we glorify and shower wealth upon the athletes, lawyers, businessmen, and politicians who are often willfully ignorant of math and science.
These smart students see these wealthy and powerful individuals who couldn't write a proof to save their lives and yet they somehow end up with the best houses, the nicest cars, the most money and generally look down upon scientists and engineers while gleefully outsourcing their jobs to those low-wage Asian countries where rote-memorization scientists and engineers become the next wage slaves of American international corporations.
If we want good students to become scientists, engineers, or yes even mathematicians then we have to start rewarding those positions in our society instead of outsourcing their jobs and treating them like dirt.
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393115</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28395005</id>
	<title>Re:it's really bad</title>
	<author>the phantom</author>
	<datestamp>1245403080000</datestamp>
	<modclass>Informativ</modclass>
	<modscore>2</modscore>
	<htmltext>You are confusing mathematics with arithmetic.  Arithmetic is the manipulation of digits that are used to represent numbers in order to get a result.  That is, addition, subtraction, multiplication, etc.  In arithmetic, it is important to "show your work" in that it helps an instructor to understand what you have done, and where you might have made mistakes.  Arithmetic is a subfield of mathematics, but does not comprise the whole.  Mathematics, on the other hand, is the search for a certain kind of "truth."  In mathematics, we start with a set of assumptions about how the universe works (we call these axioms), then use logic to work out what those axioms imply.  A proof consists of the details of the logical process used to work out new truths.<br> <br>

You might want to have a look through the articles on Wikipedia about <a href="http://en.wikipedia.org/wiki/Logic" title="wikipedia.org">logic</a> [wikipedia.org], <a href="http://en.wikipedia.org/wiki/First-order\_logic" title="wikipedia.org">predicate-logic</a> [wikipedia.org], and <a href="http://en.wikipedia.org/wiki/Mathematical\_proof" title="wikipedia.org">mathematical proofs</a> [wikipedia.org].</htmltext>
<tokenext>You are confusing mathematics with arithmetic .
Arithmetic is the manipulation of digits that are used to represent numbers in order to get a result .
That is , addition , subtraction , multiplication , etc .
In arithmetic , it is important to " show your work " in that it helps an instructor to understand what you have done , and where you might have made mistakes .
Arithmetic is a subfield of mathematics , but does not comprise the whole .
Mathematics , on the other hand , is the search for a certain kind of " truth .
" In mathematics , we start with a set of assumptions about how the universe works ( we call these axioms ) , then use logic to work out what those axioms imply .
A proof consists of the details of the logical process used to work out new truths .
You might want to have a look through the articles on Wikipedia about logic [ wikipedia.org ] , predicate-logic [ wikipedia.org ] , and mathematical proofs [ wikipedia.org ] .</tokentext>
<sentencetext>You are confusing mathematics with arithmetic.
Arithmetic is the manipulation of digits that are used to represent numbers in order to get a result.
That is, addition, subtraction, multiplication, etc.
In arithmetic, it is important to "show your work" in that it helps an instructor to understand what you have done, and where you might have made mistakes.
Arithmetic is a subfield of mathematics, but does not comprise the whole.
Mathematics, on the other hand, is the search for a certain kind of "truth.
"  In mathematics, we start with a set of assumptions about how the universe works (we call these axioms), then use logic to work out what those axioms imply.
A proof consists of the details of the logical process used to work out new truths.
You might want to have a look through the articles on Wikipedia about logic [wikipedia.org], predicate-logic [wikipedia.org], and mathematical proofs [wikipedia.org].</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393543</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28399785</id>
	<title>Re:Oh give it a rest</title>
	<author>Anonymous</author>
	<datestamp>1245441180000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>I agree completely.  Public elementary school is meant to teach competency and basic familiarity with a broad range of topics.  People who have a natural affinity toward a particular discipline will hopefully not be bored by the stuff that is meant to make literate citizens.  For instance, in history class do we spend a lot of time learning how to be a historian, research, uncover primary sources, cross-reference, etc.?  No, because we know most kids won't be historians and that that's what college is for anyways.  We need to teach who assassinated President Garfield.  Because reasonable, educated adults should simply know some things.</p></htmltext>
<tokenext>I agree completely .
Public elementary school is meant to teach competency and basic familiarity with a broad range of topics .
People who have a natural affinity toward a particular discipline will hopefully not be bored by the stuff that is meant to make literate citizens .
For instance , in history class do we spend a lot of time learning how to be a historian , research , uncover primary sources , cross-reference , etc. ?
No , because we know most kids wo n't be historians and that that 's what college is for anyways .
We need to teach who assassinated President Garfield .
Because reasonable , educated adults should simply know some things .</tokentext>
<sentencetext>I agree completely.
Public elementary school is meant to teach competency and basic familiarity with a broad range of topics.
People who have a natural affinity toward a particular discipline will hopefully not be bored by the stuff that is meant to make literate citizens.
For instance, in history class do we spend a lot of time learning how to be a historian, research, uncover primary sources, cross-reference, etc.?
No, because we know most kids won't be historians and that that's what college is for anyways.
We need to teach who assassinated President Garfield.
Because reasonable, educated adults should simply know some things.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392993</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393859</id>
	<title>Math as art</title>
	<author>sweetser</author>
	<datestamp>1245442440000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>Just turn all your math into movie, and the crowds will follow (someday).

<p>Doug
<br> <a href="http://visualphysics.org/" title="visualphysics.org" rel="nofollow">VisualPhysics.org</a> [visualphysics.org]</p></htmltext>
<tokenext>Just turn all your math into movie , and the crowds will follow ( someday ) .
Doug VisualPhysics.org [ visualphysics.org ]</tokentext>
<sentencetext>Just turn all your math into movie, and the crowds will follow (someday).
Doug
 VisualPhysics.org [visualphysics.org]</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392895</id>
	<title>tl;dr</title>
	<author>Anonymous</author>
	<datestamp>1245438960000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>Having not read the actual PDF, I wonder if having a bunch of mathematically disinclined women teaching math to young students would have something to do with it?

Note: I'm not trying to be misogynistic, just my anecdotal observations.

If the shit really hit the fan, I think I'd rather enjoy being a high school advanced math/computer science teacher.  Aren't school districts hurting for qualified people in those positions?</htmltext>
<tokenext>Having not read the actual PDF , I wonder if having a bunch of mathematically disinclined women teaching math to young students would have something to do with it ?
Note : I 'm not trying to be misogynistic , just my anecdotal observations .
If the shit really hit the fan , I think I 'd rather enjoy being a high school advanced math/computer science teacher .
Are n't school districts hurting for qualified people in those positions ?</tokentext>
<sentencetext>Having not read the actual PDF, I wonder if having a bunch of mathematically disinclined women teaching math to young students would have something to do with it?
Note: I'm not trying to be misogynistic, just my anecdotal observations.
If the shit really hit the fan, I think I'd rather enjoy being a high school advanced math/computer science teacher.
Aren't school districts hurting for qualified people in those positions?</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393947</id>
	<title>Dummy's books</title>
	<author>zymano</author>
	<datestamp>1245442800000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>Are excellent for newbies.  Well written with good examples and graphics.</p></htmltext>
<tokenext>Are excellent for newbies .
Well written with good examples and graphics .</tokentext>
<sentencetext>Are excellent for newbies.
Well written with good examples and graphics.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393475</id>
	<title>Re:US School System compared to Europes School Sys</title>
	<author>Quiet\_Desperation</author>
	<datestamp>1245441060000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>Not sure where you went to school, but in my high school, you took the class most appropriate to your abilities at the time. Some were taking basic math and algebra in 10th grade while I was in a precalculus class. In 12th grade I was in an early morning advanced calculus class taught by a professor from the local university.</p><p>There is no "math class" at that level anymore, at least in my experience. Even middle school was like that because I got my advanced algebra there.</p><p>As for the essay linked by the original article. it smacks of the "whole language" approach that swept through schools here in California in the 1980s and 1990s, much to its detriment. I actually went into the article expecting to agree with Mr. Mathematician, but wound up thinking the guy is a loon (after slogging through *TWO* overwrought analogies). I get what he wants, but you don't toss out the basic foundations of functional mathematics to accomplish it.</p></htmltext>
<tokenext>Not sure where you went to school , but in my high school , you took the class most appropriate to your abilities at the time .
Some were taking basic math and algebra in 10th grade while I was in a precalculus class .
In 12th grade I was in an early morning advanced calculus class taught by a professor from the local university.There is no " math class " at that level anymore , at least in my experience .
Even middle school was like that because I got my advanced algebra there.As for the essay linked by the original article .
it smacks of the " whole language " approach that swept through schools here in California in the 1980s and 1990s , much to its detriment .
I actually went into the article expecting to agree with Mr. Mathematician , but wound up thinking the guy is a loon ( after slogging through * TWO * overwrought analogies ) .
I get what he wants , but you do n't toss out the basic foundations of functional mathematics to accomplish it .</tokentext>
<sentencetext>Not sure where you went to school, but in my high school, you took the class most appropriate to your abilities at the time.
Some were taking basic math and algebra in 10th grade while I was in a precalculus class.
In 12th grade I was in an early morning advanced calculus class taught by a professor from the local university.There is no "math class" at that level anymore, at least in my experience.
Even middle school was like that because I got my advanced algebra there.As for the essay linked by the original article.
it smacks of the "whole language" approach that swept through schools here in California in the 1980s and 1990s, much to its detriment.
I actually went into the article expecting to agree with Mr. Mathematician, but wound up thinking the guy is a loon (after slogging through *TWO* overwrought analogies).
I get what he wants, but you don't toss out the basic foundations of functional mathematics to accomplish it.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393035</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394313</id>
	<title>Re:Eh.</title>
	<author>chris\_eineke</author>
	<datestamp>1245444000000</datestamp>
	<modclass>Insightful</modclass>
	<modscore>2</modscore>
	<htmltext><p>90\% of the student population isn't interested in math because it's taught in the way and by the people he talks about in his text.</p><p><em>*insert snide comment about reading comprehension here*</em></p></htmltext>
<tokenext>90 \ % of the student population is n't interested in math because it 's taught in the way and by the people he talks about in his text .
* insert snide comment about reading comprehension here *</tokentext>
<sentencetext>90\% of the student population isn't interested in math because it's taught in the way and by the people he talks about in his text.
*insert snide comment about reading comprehension here*</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392961</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28395681</id>
	<title>Re:Half Steps</title>
	<author>itsdapead</author>
	<datestamp>1245405600000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p><div class="quote"><p>This man is a beautiful dreamer.  I don't think his rather Platonic vision of the perfect math class will ever be acheivable.</p> </div><p>Haven't read the whole TFA yet, but  he's nailed the <i>problem</i> nicely on the first page: typical school math is too often presented as a laundry list of silly things to remember how to do. When you've done that, instead of going on to do some interesting stuff with the tricks you've learned, your reward is to learn a whole set of new, slightly more complicated, silly things to do.
</p><p>His solution seems a bit too predicated on the idea that Pure Math floats everybody's boat: Sure pure maths is important*, School Math needs to make an impression on future engineers, accountants, architects, chefs, etc. - plus the world would be a much better shape if Joe Sixpack had been encouraged to make the link between that thing about the rice and the chessboard and a credit card bill. Professional mathematicians (and many<nobr> <wbr></nobr>/.ers) seem to have a hard time thinking down to anything below undergraduate level<nobr> <wbr></nobr>:-)</p><p><div class="quote"><p>and does nothing for the vast majority of us who don't use calculus or even algebra in our day-to-day lives</p></div><p>Well, if you use a spreadsheet for planning you're using algebra concepts (except I've seen a depressing number of people who use pocket calculator or windows calc to work out what numbers to fill into Excel because, of course, in class, spreadsheets are only for the annual cat &amp; dog survey). Part of the reason people don't use math in everyday life is that it doesn't occur to them that they <i>could</i>.</p><p><div class="quote"><p>First, *use* math to solve real problems and explain real scientific principles</p></div><p>...and the important word there is "real" as in "something someone might actually want to do in the <i>real world</i> - not the bizarro parallel mathworld in which Grandma decides to divide her $3600 windfall between Alice, Bob and Sufia in the ratio 2:3:4. That's what you get when someone adds some "real world" problems to their curriculum buy taking the old math practice exercises and making up stories around them.
</p><p>Of course, you could ask the kids to help Grandma come up with a fair way to divide her winnings amongst her grandchildren - but then the danger is that they might come up with a workable solution that doesn't use a ratio and we're "doing" ratio in this lesson.

</p><p>The worst cases of this include things like standard probability questions with grafted-on contexts where the events are clearly not independent.

</p><p>Trouble is, although it is possible to identify a real problem, find some math in it that kids can identify and tackle, present it with just the Goldilocks optimum amount of clues and structure then work out how to fit that into a curriculum... it is much, much quicker and cheaper to find someone to take textbook math exercises, wrap stories around them and call them "real world mathematical problems". Ker-ching!

</p><p>The other problem is that you find that kids that do well on a page of exercises crash and burn when they are asked to walk and chew gum at the same time by applying the same math to a real problem (especially if they have to <i>spot</i> the math to use) - and this looks bad on the report card and takes up valuable "learning to do some harder exercises" time.</p><p><div class="quote"><p>Second, incorporate the history of math into math class.</p></div><p>Not just history: a bit more "learn about what real math can do" and a bit less "learn to do very simple math". Bring in topical issue ("can you spot the problem with these figures from the newspaper" is an inexhaustible source!) There's a tendency in math education to never talk about something if kids wouldn't be able to complete a page of exercises on it or memorize the proof.



</p><p>* Pure math is, of course, vital: if physicists didn't have a supply of abstract math to find practical applications for, how would they annoy mathematicians?<nobr> <wbr></nobr>:-)</p></div>
	</htmltext>
<tokenext>This man is a beautiful dreamer .
I do n't think his rather Platonic vision of the perfect math class will ever be acheivable .
Have n't read the whole TFA yet , but he 's nailed the problem nicely on the first page : typical school math is too often presented as a laundry list of silly things to remember how to do .
When you 've done that , instead of going on to do some interesting stuff with the tricks you 've learned , your reward is to learn a whole set of new , slightly more complicated , silly things to do .
His solution seems a bit too predicated on the idea that Pure Math floats everybody 's boat : Sure pure maths is important * , School Math needs to make an impression on future engineers , accountants , architects , chefs , etc .
- plus the world would be a much better shape if Joe Sixpack had been encouraged to make the link between that thing about the rice and the chessboard and a credit card bill .
Professional mathematicians ( and many /.ers ) seem to have a hard time thinking down to anything below undergraduate level : - ) and does nothing for the vast majority of us who do n't use calculus or even algebra in our day-to-day livesWell , if you use a spreadsheet for planning you 're using algebra concepts ( except I 've seen a depressing number of people who use pocket calculator or windows calc to work out what numbers to fill into Excel because , of course , in class , spreadsheets are only for the annual cat &amp; dog survey ) .
Part of the reason people do n't use math in everyday life is that it does n't occur to them that they could.First , * use * math to solve real problems and explain real scientific principles...and the important word there is " real " as in " something someone might actually want to do in the real world - not the bizarro parallel mathworld in which Grandma decides to divide her $ 3600 windfall between Alice , Bob and Sufia in the ratio 2 : 3 : 4 .
That 's what you get when someone adds some " real world " problems to their curriculum buy taking the old math practice exercises and making up stories around them .
Of course , you could ask the kids to help Grandma come up with a fair way to divide her winnings amongst her grandchildren - but then the danger is that they might come up with a workable solution that does n't use a ratio and we 're " doing " ratio in this lesson .
The worst cases of this include things like standard probability questions with grafted-on contexts where the events are clearly not independent .
Trouble is , although it is possible to identify a real problem , find some math in it that kids can identify and tackle , present it with just the Goldilocks optimum amount of clues and structure then work out how to fit that into a curriculum... it is much , much quicker and cheaper to find someone to take textbook math exercises , wrap stories around them and call them " real world mathematical problems " .
Ker-ching ! The other problem is that you find that kids that do well on a page of exercises crash and burn when they are asked to walk and chew gum at the same time by applying the same math to a real problem ( especially if they have to spot the math to use ) - and this looks bad on the report card and takes up valuable " learning to do some harder exercises " time.Second , incorporate the history of math into math class.Not just history : a bit more " learn about what real math can do " and a bit less " learn to do very simple math " .
Bring in topical issue ( " can you spot the problem with these figures from the newspaper " is an inexhaustible source !
) There 's a tendency in math education to never talk about something if kids would n't be able to complete a page of exercises on it or memorize the proof .
* Pure math is , of course , vital : if physicists did n't have a supply of abstract math to find practical applications for , how would they annoy mathematicians ?
: - )</tokentext>
<sentencetext>This man is a beautiful dreamer.
I don't think his rather Platonic vision of the perfect math class will ever be acheivable.
Haven't read the whole TFA yet, but  he's nailed the problem nicely on the first page: typical school math is too often presented as a laundry list of silly things to remember how to do.
When you've done that, instead of going on to do some interesting stuff with the tricks you've learned, your reward is to learn a whole set of new, slightly more complicated, silly things to do.
His solution seems a bit too predicated on the idea that Pure Math floats everybody's boat: Sure pure maths is important*, School Math needs to make an impression on future engineers, accountants, architects, chefs, etc.
- plus the world would be a much better shape if Joe Sixpack had been encouraged to make the link between that thing about the rice and the chessboard and a credit card bill.
Professional mathematicians (and many /.ers) seem to have a hard time thinking down to anything below undergraduate level :-)and does nothing for the vast majority of us who don't use calculus or even algebra in our day-to-day livesWell, if you use a spreadsheet for planning you're using algebra concepts (except I've seen a depressing number of people who use pocket calculator or windows calc to work out what numbers to fill into Excel because, of course, in class, spreadsheets are only for the annual cat &amp; dog survey).
Part of the reason people don't use math in everyday life is that it doesn't occur to them that they could.First, *use* math to solve real problems and explain real scientific principles...and the important word there is "real" as in "something someone might actually want to do in the real world - not the bizarro parallel mathworld in which Grandma decides to divide her $3600 windfall between Alice, Bob and Sufia in the ratio 2:3:4.
That's what you get when someone adds some "real world" problems to their curriculum buy taking the old math practice exercises and making up stories around them.
Of course, you could ask the kids to help Grandma come up with a fair way to divide her winnings amongst her grandchildren - but then the danger is that they might come up with a workable solution that doesn't use a ratio and we're "doing" ratio in this lesson.
The worst cases of this include things like standard probability questions with grafted-on contexts where the events are clearly not independent.
Trouble is, although it is possible to identify a real problem, find some math in it that kids can identify and tackle, present it with just the Goldilocks optimum amount of clues and structure then work out how to fit that into a curriculum... it is much, much quicker and cheaper to find someone to take textbook math exercises, wrap stories around them and call them "real world mathematical problems".
Ker-ching!

The other problem is that you find that kids that do well on a page of exercises crash and burn when they are asked to walk and chew gum at the same time by applying the same math to a real problem (especially if they have to spot the math to use) - and this looks bad on the report card and takes up valuable "learning to do some harder exercises" time.Second, incorporate the history of math into math class.Not just history: a bit more "learn about what real math can do" and a bit less "learn to do very simple math".
Bring in topical issue ("can you spot the problem with these figures from the newspaper" is an inexhaustible source!
) There's a tendency in math education to never talk about something if kids wouldn't be able to complete a page of exercises on it or memorize the proof.
* Pure math is, of course, vital: if physicists didn't have a supply of abstract math to find practical applications for, how would they annoy mathematicians?
:-)
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393305</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28397641</id>
	<title>thoughts from a math teacher</title>
	<author>entropiccanuck</author>
	<datestamp>1245416940000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>IAAMT, last year 8th grade at a high minority pop, low income school.  This next year I'll be teaching Algebra 1 at a high school.  I agree with many of the points in Lockhart's article, with the primary exception being that this problem isn't already being addressed by some in education.
<p>
Math has been gutted of meaning, but this is changing.  There are solid curricula out there that are being used, such as <a href="http://www.mathimp.org/index.html" title="mathimp.org" rel="nofollow">IMP</a> [mathimp.org] ( the Interactive Math Program) or PBL (Project/Problem Based Learning) style lessons.  An example of PBL that I used last year with my 8th graders was in modeling a bride.  They were given a plausible scenario (school buildings are getting a 2nd story added on to reduce the number of portable classrooms, they had to design and model a bridge between these 2nd stories.)  So, we went out and measured distances, built newpaper bridges and tested how much weight they could hold to find relationships for thickness v. load and length v. load, calculated needed load support based on population, class flow, 8th grader mass, etc., graphed some data in Excel, and used their formula and data to built a cost-optimized bridge.  They had fun exploring some rich problems (and some frustration, as it did require some thought) and gained a better grasp of linear relationships, a key concept in 8th grade. </p><p>
This type of teaching isn't widespread, but it was being advocated by my college advisers.
One of the problems with doing this kind of math  is the lack of public support.  In the school district I'm in, about half the high schools were giving an option to use IMP to students, but parents complained and such, and now only a few charter schools use it.  Still, support is starting to spread some, so the more interesting approaches are being slowly revived.</p><p>

For those interested in this topic, check out <a href="http://www.amazon.com/Whats-Math-Got-Subject-Important/dp/0670019526/ref=cm\_cr\_pr\_product\_top" title="amazon.com" rel="nofollow">What's math got to do with it?</a> [amazon.com]" by Jo Boaler (new edition out later this month.)</p></htmltext>
<tokenext>IAAMT , last year 8th grade at a high minority pop , low income school .
This next year I 'll be teaching Algebra 1 at a high school .
I agree with many of the points in Lockhart 's article , with the primary exception being that this problem is n't already being addressed by some in education .
Math has been gutted of meaning , but this is changing .
There are solid curricula out there that are being used , such as IMP [ mathimp.org ] ( the Interactive Math Program ) or PBL ( Project/Problem Based Learning ) style lessons .
An example of PBL that I used last year with my 8th graders was in modeling a bride .
They were given a plausible scenario ( school buildings are getting a 2nd story added on to reduce the number of portable classrooms , they had to design and model a bridge between these 2nd stories .
) So , we went out and measured distances , built newpaper bridges and tested how much weight they could hold to find relationships for thickness v. load and length v. load , calculated needed load support based on population , class flow , 8th grader mass , etc. , graphed some data in Excel , and used their formula and data to built a cost-optimized bridge .
They had fun exploring some rich problems ( and some frustration , as it did require some thought ) and gained a better grasp of linear relationships , a key concept in 8th grade .
This type of teaching is n't widespread , but it was being advocated by my college advisers .
One of the problems with doing this kind of math is the lack of public support .
In the school district I 'm in , about half the high schools were giving an option to use IMP to students , but parents complained and such , and now only a few charter schools use it .
Still , support is starting to spread some , so the more interesting approaches are being slowly revived .
For those interested in this topic , check out What 's math got to do with it ?
[ amazon.com ] " by Jo Boaler ( new edition out later this month .
)</tokentext>
<sentencetext>IAAMT, last year 8th grade at a high minority pop, low income school.
This next year I'll be teaching Algebra 1 at a high school.
I agree with many of the points in Lockhart's article, with the primary exception being that this problem isn't already being addressed by some in education.
Math has been gutted of meaning, but this is changing.
There are solid curricula out there that are being used, such as IMP [mathimp.org] ( the Interactive Math Program) or PBL (Project/Problem Based Learning) style lessons.
An example of PBL that I used last year with my 8th graders was in modeling a bride.
They were given a plausible scenario (school buildings are getting a 2nd story added on to reduce the number of portable classrooms, they had to design and model a bridge between these 2nd stories.
)  So, we went out and measured distances, built newpaper bridges and tested how much weight they could hold to find relationships for thickness v. load and length v. load, calculated needed load support based on population, class flow, 8th grader mass, etc., graphed some data in Excel, and used their formula and data to built a cost-optimized bridge.
They had fun exploring some rich problems (and some frustration, as it did require some thought) and gained a better grasp of linear relationships, a key concept in 8th grade.
This type of teaching isn't widespread, but it was being advocated by my college advisers.
One of the problems with doing this kind of math  is the lack of public support.
In the school district I'm in, about half the high schools were giving an option to use IMP to students, but parents complained and such, and now only a few charter schools use it.
Still, support is starting to spread some, so the more interesting approaches are being slowly revived.
For those interested in this topic, check out What's math got to do with it?
[amazon.com]" by Jo Boaler (new edition out later this month.
)</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28397563</id>
	<title>Re:tl;dr</title>
	<author>bezking</author>
	<datestamp>1245416340000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>Yup. Mod parent up, please.</htmltext>
<tokenext>Yup .
Mod parent up , please .</tokentext>
<sentencetext>Yup.
Mod parent up, please.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392895</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28399975</id>
	<title>Re:I Sympathize With Him But Too Idyllic</title>
	<author>oh2</author>
	<datestamp>1245530580000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>In education research the kind of students hes dreaming of are often referred to as "Rockwellian learners"...</htmltext>
<tokenext>In education research the kind of students hes dreaming of are often referred to as " Rockwellian learners " .. .</tokentext>
<sentencetext>In education research the kind of students hes dreaming of are often referred to as "Rockwellian learners"...</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392903</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394943</id>
	<title>Re:US School System compared to Europes School Sys</title>
	<author>hxftw</author>
	<datestamp>1245402840000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>So you've attended most US schools then?</htmltext>
<tokenext>So you 've attended most US schools then ?</tokentext>
<sentencetext>So you've attended most US schools then?</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393241</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393127</id>
	<title>Re:it's really bad</title>
	<author>Anonymous</author>
	<datestamp>1245439800000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>I was taught the logic part of the deal and I still hated proofs. You decide.</htmltext>
<tokenext>I was taught the logic part of the deal and I still hated proofs .
You decide .</tokentext>
<sentencetext>I was taught the logic part of the deal and I still hated proofs.
You decide.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392911</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393329</id>
	<title>Re:it's really bad</title>
	<author>Gat0r30y</author>
	<datestamp>1245440460000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>This is "teaching to the test" at its worst.  Proofs are on the exams to get money.  Improved curriculum doesn't do anything if the standardized exams don't change too.  I had plenty of good teachers, who wanted to teach - and ended up basically prepping students to perform well on standardized exams just so funding wouldn't get slashed. <br> While we are on the subject - the whole public school system is no longer really teaching kids anything of value.  Its basically an expensive babysitting service.  What exactly is a high school graduate qualified for anymore?</htmltext>
<tokenext>This is " teaching to the test " at its worst .
Proofs are on the exams to get money .
Improved curriculum does n't do anything if the standardized exams do n't change too .
I had plenty of good teachers , who wanted to teach - and ended up basically prepping students to perform well on standardized exams just so funding would n't get slashed .
While we are on the subject - the whole public school system is no longer really teaching kids anything of value .
Its basically an expensive babysitting service .
What exactly is a high school graduate qualified for anymore ?</tokentext>
<sentencetext>This is "teaching to the test" at its worst.
Proofs are on the exams to get money.
Improved curriculum doesn't do anything if the standardized exams don't change too.
I had plenty of good teachers, who wanted to teach - and ended up basically prepping students to perform well on standardized exams just so funding wouldn't get slashed.
While we are on the subject - the whole public school system is no longer really teaching kids anything of value.
Its basically an expensive babysitting service.
What exactly is a high school graduate qualified for anymore?</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392911</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394347</id>
	<title>Re:True story ....</title>
	<author>nine-times</author>
	<datestamp>1245444120000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p><div class="quote"><p>If that's indicative of how math is taught nowadays, we're all hosed.</p></div><p>Meh, I would sooner guess that it's indicative of how retarded philosophy is in modern academia.  It's just not taken seriously, and in the cases that it is, it's an exercise in being an obtuse pompous ass.  From some of the philosophy professors I've met and listened to, I would guess that you may as well have been talking to a high school art teacher.
</p><p>(no offense to any philosophy professors out there, but if you're a good one, then I hope you know what I'm referring to)</p></div>
	</htmltext>
<tokenext>If that 's indicative of how math is taught nowadays , we 're all hosed.Meh , I would sooner guess that it 's indicative of how retarded philosophy is in modern academia .
It 's just not taken seriously , and in the cases that it is , it 's an exercise in being an obtuse pompous ass .
From some of the philosophy professors I 've met and listened to , I would guess that you may as well have been talking to a high school art teacher .
( no offense to any philosophy professors out there , but if you 're a good one , then I hope you know what I 'm referring to )</tokentext>
<sentencetext>If that's indicative of how math is taught nowadays, we're all hosed.Meh, I would sooner guess that it's indicative of how retarded philosophy is in modern academia.
It's just not taken seriously, and in the cases that it is, it's an exercise in being an obtuse pompous ass.
From some of the philosophy professors I've met and listened to, I would guess that you may as well have been talking to a high school art teacher.
(no offense to any philosophy professors out there, but if you're a good one, then I hope you know what I'm referring to)
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392947</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28398319</id>
	<title>Re:US School System compared to Europes School Sys</title>
	<author>oclawgeek</author>
	<datestamp>1245422220000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>That's not even remotely true.  Most major metropolitan school districts in my state (California) cater mostly to the mediocre, and offer advanced classes to some kids who are better at following instructions, and minimal training to problem kids.  The control ought to be more fine-grained than this.  The problem kids, for example, are all just lumped together, even if no rational person would think that prudent.  For example, at one school I know of, the mentally disabled kids are placed with kids who are just too far behind other kids of the same age, and both groups are blended with kids who are just disciplinary issues, with no ability on the part of the teacher to deal with each situation in an appropriate way.


Thanks, standardized testing!</htmltext>
<tokenext>That 's not even remotely true .
Most major metropolitan school districts in my state ( California ) cater mostly to the mediocre , and offer advanced classes to some kids who are better at following instructions , and minimal training to problem kids .
The control ought to be more fine-grained than this .
The problem kids , for example , are all just lumped together , even if no rational person would think that prudent .
For example , at one school I know of , the mentally disabled kids are placed with kids who are just too far behind other kids of the same age , and both groups are blended with kids who are just disciplinary issues , with no ability on the part of the teacher to deal with each situation in an appropriate way .
Thanks , standardized testing !</tokentext>
<sentencetext>That's not even remotely true.
Most major metropolitan school districts in my state (California) cater mostly to the mediocre, and offer advanced classes to some kids who are better at following instructions, and minimal training to problem kids.
The control ought to be more fine-grained than this.
The problem kids, for example, are all just lumped together, even if no rational person would think that prudent.
For example, at one school I know of, the mentally disabled kids are placed with kids who are just too far behind other kids of the same age, and both groups are blended with kids who are just disciplinary issues, with no ability on the part of the teacher to deal with each situation in an appropriate way.
Thanks, standardized testing!</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393241</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393491</id>
	<title>Re:Cue the other subjects</title>
	<author>mh1997</author>
	<datestamp>1245441120000</datestamp>
	<modclass>Interestin</modclass>
	<modscore>3</modscore>
	<htmltext><blockquote><div><p> and most of them can be traced to certain groups (*cough*fundamentalists*cough*) waging a 30 year war on public education, and people refusing to see and treat education as what it is: an investment in the future national security and economic stability of the united states.</p></div></blockquote><p>

American education was designed to fail. Read the book (it's free online) The Underground History of American Education by John Taylor Gatto. He is a former New York State and New York City Teacher of the Year </p><p>http://www.johntaylorgatto.com/underground/</p></div>
	</htmltext>
<tokenext>and most of them can be traced to certain groups ( * cough * fundamentalists * cough * ) waging a 30 year war on public education , and people refusing to see and treat education as what it is : an investment in the future national security and economic stability of the united states .
American education was designed to fail .
Read the book ( it 's free online ) The Underground History of American Education by John Taylor Gatto .
He is a former New York State and New York City Teacher of the Year http : //www.johntaylorgatto.com/underground/</tokentext>
<sentencetext> and most of them can be traced to certain groups (*cough*fundamentalists*cough*) waging a 30 year war on public education, and people refusing to see and treat education as what it is: an investment in the future national security and economic stability of the united states.
American education was designed to fail.
Read the book (it's free online) The Underground History of American Education by John Taylor Gatto.
He is a former New York State and New York City Teacher of the Year http://www.johntaylorgatto.com/underground/
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393083</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394409</id>
	<title>Re:True story ....</title>
	<author>rkit</author>
	<datestamp>1245444360000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>
Obvious question: what is 95\% confidence supposed to mean? How is it different from say 94\%?
</p><p>
As long as the student cannot come up with something like "there is a chance of 5 in 100 that the result was caused by the sampling process" he has no idea what he is talking about.
</p><p>
Speaking of critical thinking, the student should also understand that one in twenty results with 95\% confidence will be wrong.
</p></htmltext>
<tokenext>Obvious question : what is 95 \ % confidence supposed to mean ?
How is it different from say 94 \ % ?
As long as the student can not come up with something like " there is a chance of 5 in 100 that the result was caused by the sampling process " he has no idea what he is talking about .
Speaking of critical thinking , the student should also understand that one in twenty results with 95 \ % confidence will be wrong .</tokentext>
<sentencetext>
Obvious question: what is 95\% confidence supposed to mean?
How is it different from say 94\%?
As long as the student cannot come up with something like "there is a chance of 5 in 100 that the result was caused by the sampling process" he has no idea what he is talking about.
Speaking of critical thinking, the student should also understand that one in twenty results with 95\% confidence will be wrong.
</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392947</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28396879</id>
	<title>Re:The way math is structured is disconnected from</title>
	<author>Anonymous</author>
	<datestamp>1245411180000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>You've missed the point: it isn't mathematicians who've made it overly complicated. It is people responsible for<nobr> <wbr></nobr>/teaching/ math.

Mathematicians have made it exactly as complicated as it needs to be, no more and no less. But many textbook authors have taken that complicatedness and introduced it into areas where it isn't needed, out of a lack of understanding as to why it was needed in the first place.

An example from TFA: mathematicians prefer "|x-5|2" over "x is between 3 and 7" because the former generalizes naturally to arbitrary metric spaces (like R^n). But until somebody is ready to talk about distance in R^2, and circles and such, the latter should be preferred. It uses less notation, and requires less thought to really grok.</htmltext>
<tokenext>You 've missed the point : it is n't mathematicians who 've made it overly complicated .
It is people responsible for /teaching/ math .
Mathematicians have made it exactly as complicated as it needs to be , no more and no less .
But many textbook authors have taken that complicatedness and introduced it into areas where it is n't needed , out of a lack of understanding as to why it was needed in the first place .
An example from TFA : mathematicians prefer " | x-5 | 2 " over " x is between 3 and 7 " because the former generalizes naturally to arbitrary metric spaces ( like R ^ n ) .
But until somebody is ready to talk about distance in R ^ 2 , and circles and such , the latter should be preferred .
It uses less notation , and requires less thought to really grok .</tokentext>
<sentencetext>You've missed the point: it isn't mathematicians who've made it overly complicated.
It is people responsible for /teaching/ math.
Mathematicians have made it exactly as complicated as it needs to be, no more and no less.
But many textbook authors have taken that complicatedness and introduced it into areas where it isn't needed, out of a lack of understanding as to why it was needed in the first place.
An example from TFA: mathematicians prefer "|x-5|2" over "x is between 3 and 7" because the former generalizes naturally to arbitrary metric spaces (like R^n).
But until somebody is ready to talk about distance in R^2, and circles and such, the latter should be preferred.
It uses less notation, and requires less thought to really grok.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392921</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28405345</id>
	<title>Re:You can convince me</title>
	<author>ChaosDiscord</author>
	<datestamp>1245500040000</datestamp>
	<modclass>Insightful</modclass>
	<modscore>2</modscore>
	<htmltext><p>Part of his argument is that by focusing on "math as tool" via "math as rote memorization", you fail even at that.  Math at higher levels becomes cryptic symbols that you manipulate according to cryptic rules to make your teacher happy.  And a few years out of school you promptly forget the whole thing.  If they forget most of it, and for the overwhelming majority it never hurts them to have forgotten it, what was the point in having "taught" it in the first place?  He argues that it's such a waste of time that we might simply drop some math courses entirely and we would be better off.   (Indeed, I suspect that if you replace your average American's high school senior math courses with Spanish that society on the whole would benefit.  They're more likely to make use of the Spanish.)

</p><p>  The author believes that his proposal will lead to more students discovering that they actually like math, and more students as a whole actually retaining what they learned.  While they might learn less, they'll actually retain more in the long run, and be better armed to figure out things for themselves.</p></htmltext>
<tokenext>Part of his argument is that by focusing on " math as tool " via " math as rote memorization " , you fail even at that .
Math at higher levels becomes cryptic symbols that you manipulate according to cryptic rules to make your teacher happy .
And a few years out of school you promptly forget the whole thing .
If they forget most of it , and for the overwhelming majority it never hurts them to have forgotten it , what was the point in having " taught " it in the first place ?
He argues that it 's such a waste of time that we might simply drop some math courses entirely and we would be better off .
( Indeed , I suspect that if you replace your average American 's high school senior math courses with Spanish that society on the whole would benefit .
They 're more likely to make use of the Spanish .
) The author believes that his proposal will lead to more students discovering that they actually like math , and more students as a whole actually retaining what they learned .
While they might learn less , they 'll actually retain more in the long run , and be better armed to figure out things for themselves .</tokentext>
<sentencetext>Part of his argument is that by focusing on "math as tool" via "math as rote memorization", you fail even at that.
Math at higher levels becomes cryptic symbols that you manipulate according to cryptic rules to make your teacher happy.
And a few years out of school you promptly forget the whole thing.
If they forget most of it, and for the overwhelming majority it never hurts them to have forgotten it, what was the point in having "taught" it in the first place?
He argues that it's such a waste of time that we might simply drop some math courses entirely and we would be better off.
(Indeed, I suspect that if you replace your average American's high school senior math courses with Spanish that society on the whole would benefit.
They're more likely to make use of the Spanish.
)

  The author believes that his proposal will lead to more students discovering that they actually like math, and more students as a whole actually retaining what they learned.
While they might learn less, they'll actually retain more in the long run, and be better armed to figure out things for themselves.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393159</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28396383</id>
	<title>Re:tl;dr</title>
	<author>Anonymous</author>
	<datestamp>1245408900000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>Way to <em>completely miss the point</em> that the problem was disinclination, not gender. The stereotypical characterization of elementary school teachers as mathematically disinclined women is largely an acurrate one. Most elementary school teachers are women. Most elementary school teachers are mathematically disinclined.</p></htmltext>
<tokenext>Way to completely miss the point that the problem was disinclination , not gender .
The stereotypical characterization of elementary school teachers as mathematically disinclined women is largely an acurrate one .
Most elementary school teachers are women .
Most elementary school teachers are mathematically disinclined .</tokentext>
<sentencetext>Way to completely miss the point that the problem was disinclination, not gender.
The stereotypical characterization of elementary school teachers as mathematically disinclined women is largely an acurrate one.
Most elementary school teachers are women.
Most elementary school teachers are mathematically disinclined.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393055</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393877</id>
	<title>Math may be an art, but teaching math is not.</title>
	<author>NotPeteMcCabe</author>
	<datestamp>1245442500000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>Math may be an art, but a math teacher is not a mathematician. A math teacher is a teacher, and their expertise in math is second to their expertise in teaching. I would much rather my kids learn math from an expert teacher who knows only the math he or she is teaching than from a world-class mathematician with no knowledge of teaching.
<p>
This is the biggest misunderstanding most people have of teaching. The general view seems to be that if you know your subject, you're qualified to be a teacher. Nothing could be further from the truth. The most important qualification a teacher has is the ability to relate to their students; the relationship between student and teacher is the single most important factor in how much a student gets our of a class. Second is the teacher's ability to encourage students to do the work, since people only learn by doing. Third is the ability to design a series of activities that will, if give students the practice they need to learn what they're supposed to learn.
</p><p>
None of this presupposes a knowledge of the subject beyond what's being taught. Obviously, the more you know about the subject, the better. But there are half a dozen more important things.</p></htmltext>
<tokenext>Math may be an art , but a math teacher is not a mathematician .
A math teacher is a teacher , and their expertise in math is second to their expertise in teaching .
I would much rather my kids learn math from an expert teacher who knows only the math he or she is teaching than from a world-class mathematician with no knowledge of teaching .
This is the biggest misunderstanding most people have of teaching .
The general view seems to be that if you know your subject , you 're qualified to be a teacher .
Nothing could be further from the truth .
The most important qualification a teacher has is the ability to relate to their students ; the relationship between student and teacher is the single most important factor in how much a student gets our of a class .
Second is the teacher 's ability to encourage students to do the work , since people only learn by doing .
Third is the ability to design a series of activities that will , if give students the practice they need to learn what they 're supposed to learn .
None of this presupposes a knowledge of the subject beyond what 's being taught .
Obviously , the more you know about the subject , the better .
But there are half a dozen more important things .</tokentext>
<sentencetext>Math may be an art, but a math teacher is not a mathematician.
A math teacher is a teacher, and their expertise in math is second to their expertise in teaching.
I would much rather my kids learn math from an expert teacher who knows only the math he or she is teaching than from a world-class mathematician with no knowledge of teaching.
This is the biggest misunderstanding most people have of teaching.
The general view seems to be that if you know your subject, you're qualified to be a teacher.
Nothing could be further from the truth.
The most important qualification a teacher has is the ability to relate to their students; the relationship between student and teacher is the single most important factor in how much a student gets our of a class.
Second is the teacher's ability to encourage students to do the work, since people only learn by doing.
Third is the ability to design a series of activities that will, if give students the practice they need to learn what they're supposed to learn.
None of this presupposes a knowledge of the subject beyond what's being taught.
Obviously, the more you know about the subject, the better.
But there are half a dozen more important things.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28399103</id>
	<title>In Charlotte, we have a buffoon for a</title>
	<author>Anonymous</author>
	<datestamp>1245431340000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>Superintendent.  A perfect buffoon.  If you dont believe me, listen to him whine and cry like a girl, on the radio and on TV, as he "earns" 300K per year and has 5 assistants making 100K EACH per year - DOING NOTHING.   Not one damn thing, to further our city's education.  Meanwhile, he wonders where the good teachers are?   Yea, they want to earn 25K and put up with brats who curse them and hit them, and when the teachers complain, they get fired.  Sounds like a better job than 20K a year at Borders to me!   Not.</p><p>Math, my friends, is NOT the only problem with the US education.  Look deep within the system.   Is so far gone it needs to be replaced - top to bottom.</p></htmltext>
<tokenext>Superintendent .
A perfect buffoon .
If you dont believe me , listen to him whine and cry like a girl , on the radio and on TV , as he " earns " 300K per year and has 5 assistants making 100K EACH per year - DOING NOTHING .
Not one damn thing , to further our city 's education .
Meanwhile , he wonders where the good teachers are ?
Yea , they want to earn 25K and put up with brats who curse them and hit them , and when the teachers complain , they get fired .
Sounds like a better job than 20K a year at Borders to me !
Not.Math , my friends , is NOT the only problem with the US education .
Look deep within the system .
Is so far gone it needs to be replaced - top to bottom .</tokentext>
<sentencetext>Superintendent.
A perfect buffoon.
If you dont believe me, listen to him whine and cry like a girl, on the radio and on TV, as he "earns" 300K per year and has 5 assistants making 100K EACH per year - DOING NOTHING.
Not one damn thing, to further our city's education.
Meanwhile, he wonders where the good teachers are?
Yea, they want to earn 25K and put up with brats who curse them and hit them, and when the teachers complain, they get fired.
Sounds like a better job than 20K a year at Borders to me!
Not.Math, my friends, is NOT the only problem with the US education.
Look deep within the system.
Is so far gone it needs to be replaced - top to bottom.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393249</id>
	<title>Re:Several Proxies</title>
	<author>Gerzel</author>
	<datestamp>1245440280000</datestamp>
	<modclass>Troll</modclass>
	<modscore>0</modscore>
	<htmltext><p>2 + 2 = Jesus and that is all they need to know!</p></htmltext>
<tokenext>2 + 2 = Jesus and that is all they need to know !</tokentext>
<sentencetext>2 + 2 = Jesus and that is all they need to know!</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392769</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393517</id>
	<title>Re:US School System compared to Europes School Sys</title>
	<author>Anonymous</author>
	<datestamp>1245441180000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p><i>Most US schools have different courses based on skill level.</i></p><p>Um, no they don't, apart from a <i>very</i> limited portion of Honors/AP courses.  The rest are one-size-fits-all, based on some sort of misguided egalitarianism.</p></htmltext>
<tokenext>Most US schools have different courses based on skill level.Um , no they do n't , apart from a very limited portion of Honors/AP courses .
The rest are one-size-fits-all , based on some sort of misguided egalitarianism .</tokentext>
<sentencetext>Most US schools have different courses based on skill level.Um, no they don't, apart from a very limited portion of Honors/AP courses.
The rest are one-size-fits-all, based on some sort of misguided egalitarianism.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393241</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28399187</id>
	<title>Re:The way math is structured is disconnected from</title>
	<author>Anonymous</author>
	<datestamp>1245432120000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>Ugh...<br>
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; I defy you to rigorously prove -any- statement without the use of the "symbolic format" of mathematics. The great power of mathematics is to turn unclear intuitions into clean, precise symbolic statements, and to -understand- why these statements correspond to intuition. If you believe you can greatly simplify the notations currently used to do mathematics, then i believe you would be a runner up for the next field medal award.</p></htmltext>
<tokenext>Ugh.. .           I defy you to rigorously prove -any- statement without the use of the " symbolic format " of mathematics .
The great power of mathematics is to turn unclear intuitions into clean , precise symbolic statements , and to -understand- why these statements correspond to intuition .
If you believe you can greatly simplify the notations currently used to do mathematics , then i believe you would be a runner up for the next field medal award .</tokentext>
<sentencetext>Ugh...
          I defy you to rigorously prove -any- statement without the use of the "symbolic format" of mathematics.
The great power of mathematics is to turn unclear intuitions into clean, precise symbolic statements, and to -understand- why these statements correspond to intuition.
If you believe you can greatly simplify the notations currently used to do mathematics, then i believe you would be a runner up for the next field medal award.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392921</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394451</id>
	<title>Old habits die hard</title>
	<author>SloppyElvis</author>
	<datestamp>1245444480000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>Excellent argument on the frustrating habits of culture... and well written too.</p><p>
You could substitute nearly any area of study into this analysis, and find a great deal of truth in the result, and in this, The Lamenting Mathematician has uncovered a very subtle and elegant habit of culture.  The fact is that there are a great many musical technicians, incapable of creating the art of music, just as there are a great many mathematical technicians, who will never contribute to The Masterpiece.  Software, Politics, History, Leadership...  All have their share of artists and technicians alike.  The key element is that the cultural perception of mathematics is that there is no art; that it is but a technical discipline.
</p><p>
The truth is that all disciplines are both artistic and technical in nature, and that society would do well to discover this and promote this duality through education.
</p><p>
The first advanced math course I took in college consisted entirely of proofs and abstract discoveries such as described in the article, and it was eye-opening.  The clever approaches and solutions discussed gave that intuitive appreciation... no less artful than capturing a feeling with a photograph or instilling instant familiarity with a speech.</p></htmltext>
<tokenext>Excellent argument on the frustrating habits of culture... and well written too .
You could substitute nearly any area of study into this analysis , and find a great deal of truth in the result , and in this , The Lamenting Mathematician has uncovered a very subtle and elegant habit of culture .
The fact is that there are a great many musical technicians , incapable of creating the art of music , just as there are a great many mathematical technicians , who will never contribute to The Masterpiece .
Software , Politics , History , Leadership... All have their share of artists and technicians alike .
The key element is that the cultural perception of mathematics is that there is no art ; that it is but a technical discipline .
The truth is that all disciplines are both artistic and technical in nature , and that society would do well to discover this and promote this duality through education .
The first advanced math course I took in college consisted entirely of proofs and abstract discoveries such as described in the article , and it was eye-opening .
The clever approaches and solutions discussed gave that intuitive appreciation... no less artful than capturing a feeling with a photograph or instilling instant familiarity with a speech .</tokentext>
<sentencetext>Excellent argument on the frustrating habits of culture... and well written too.
You could substitute nearly any area of study into this analysis, and find a great deal of truth in the result, and in this, The Lamenting Mathematician has uncovered a very subtle and elegant habit of culture.
The fact is that there are a great many musical technicians, incapable of creating the art of music, just as there are a great many mathematical technicians, who will never contribute to The Masterpiece.
Software, Politics, History, Leadership...  All have their share of artists and technicians alike.
The key element is that the cultural perception of mathematics is that there is no art; that it is but a technical discipline.
The truth is that all disciplines are both artistic and technical in nature, and that society would do well to discover this and promote this duality through education.
The first advanced math course I took in college consisted entirely of proofs and abstract discoveries such as described in the article, and it was eye-opening.
The clever approaches and solutions discussed gave that intuitive appreciation... no less artful than capturing a feeling with a photograph or instilling instant familiarity with a speech.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393353</id>
	<title>Re:tl;dr</title>
	<author>superwiz</author>
	<datestamp>1245440580000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>Why did you slip the word "women" in there?  My best math teachers/professors were women.  They tended to be less self-absorbed and when they showed the love for the subject it was love of the subject rather than plain narcissism that's so common to men teaching math (I am guilty of it too, btw).</htmltext>
<tokenext>Why did you slip the word " women " in there ?
My best math teachers/professors were women .
They tended to be less self-absorbed and when they showed the love for the subject it was love of the subject rather than plain narcissism that 's so common to men teaching math ( I am guilty of it too , btw ) .</tokentext>
<sentencetext>Why did you slip the word "women" in there?
My best math teachers/professors were women.
They tended to be less self-absorbed and when they showed the love for the subject it was love of the subject rather than plain narcissism that's so common to men teaching math (I am guilty of it too, btw).</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392895</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28395845</id>
	<title>Re:Cue the other subjects</title>
	<author>Anonymous</author>
	<datestamp>1245406320000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p> <em>and most of them can be traced to certain groups (*cough*fundamentalists*cough*) waging a 30 year war on public education</em> </p><p>Yeah, it's all the fault of those bitter, gun-clinging church-goin' folks.  Nothing to do with <a href="http://www.google.com/search?hl=en&amp;safe=off&amp;q=teachers+unions&amp;aq=f&amp;oq=&amp;aqi=" title="google.com" rel="nofollow">one of the most entrenched, self-interested political bodies of the hard-left</a> [google.com].</p><p>Yeah, yeah.  -1 Flame bait.  Also +1 True.</p></htmltext>
<tokenext>and most of them can be traced to certain groups ( * cough * fundamentalists * cough * ) waging a 30 year war on public education Yeah , it 's all the fault of those bitter , gun-clinging church-goin ' folks .
Nothing to do with one of the most entrenched , self-interested political bodies of the hard-left [ google.com ] .Yeah , yeah .
-1 Flame bait .
Also + 1 True .</tokentext>
<sentencetext> and most of them can be traced to certain groups (*cough*fundamentalists*cough*) waging a 30 year war on public education Yeah, it's all the fault of those bitter, gun-clinging church-goin' folks.
Nothing to do with one of the most entrenched, self-interested political bodies of the hard-left [google.com].Yeah, yeah.
-1 Flame bait.
Also +1 True.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393083</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393717</id>
	<title>Re:Eh.</title>
	<author>jayme0227</author>
	<datestamp>1245441960000</datestamp>
	<modclass>Insightful</modclass>
	<modscore>4</modscore>
	<htmltext><p>I read as much of the essay as I could before I realized that the guy doesn't understand that his experience doesn't apply to everyone else. I understand where he's coming from because I tell the worst stories imaginable. I will go on talking about little, highly interesting details, until I realize that I'm the only one who finds them interesting. It took me a long time to realize that, just because I find it interesting, that doesn't mean that other people will.</p><p>To say that mathematics should be taught in the way that he likes the most is silly, at best. Most people will be able to pass through life with a rudimentary, at best, understanding of mathematics. Most jobs in this world do not require 90\% of the theorems and principles that people are forced to learn through high school. I agree with the essay 100\% on that point.</p><p>The key to math education, though, is not memorizing these principles, but rather learning how to solve problems. If someone can logically plan their way through a calculus problem, almost anything that they have to figure out at their job would be well within reason.</p><p>I never have understood the concept of math as an art, yet I enjoy math. I enjoy solving problems, enough so that I earned my BS in Mathematics, but this guy takes it to a whole new level. If not even all mathematicians think like he does, why does he expect that the general population will?</p></htmltext>
<tokenext>I read as much of the essay as I could before I realized that the guy does n't understand that his experience does n't apply to everyone else .
I understand where he 's coming from because I tell the worst stories imaginable .
I will go on talking about little , highly interesting details , until I realize that I 'm the only one who finds them interesting .
It took me a long time to realize that , just because I find it interesting , that does n't mean that other people will.To say that mathematics should be taught in the way that he likes the most is silly , at best .
Most people will be able to pass through life with a rudimentary , at best , understanding of mathematics .
Most jobs in this world do not require 90 \ % of the theorems and principles that people are forced to learn through high school .
I agree with the essay 100 \ % on that point.The key to math education , though , is not memorizing these principles , but rather learning how to solve problems .
If someone can logically plan their way through a calculus problem , almost anything that they have to figure out at their job would be well within reason.I never have understood the concept of math as an art , yet I enjoy math .
I enjoy solving problems , enough so that I earned my BS in Mathematics , but this guy takes it to a whole new level .
If not even all mathematicians think like he does , why does he expect that the general population will ?</tokentext>
<sentencetext>I read as much of the essay as I could before I realized that the guy doesn't understand that his experience doesn't apply to everyone else.
I understand where he's coming from because I tell the worst stories imaginable.
I will go on talking about little, highly interesting details, until I realize that I'm the only one who finds them interesting.
It took me a long time to realize that, just because I find it interesting, that doesn't mean that other people will.To say that mathematics should be taught in the way that he likes the most is silly, at best.
Most people will be able to pass through life with a rudimentary, at best, understanding of mathematics.
Most jobs in this world do not require 90\% of the theorems and principles that people are forced to learn through high school.
I agree with the essay 100\% on that point.The key to math education, though, is not memorizing these principles, but rather learning how to solve problems.
If someone can logically plan their way through a calculus problem, almost anything that they have to figure out at their job would be well within reason.I never have understood the concept of math as an art, yet I enjoy math.
I enjoy solving problems, enough so that I earned my BS in Mathematics, but this guy takes it to a whole new level.
If not even all mathematicians think like he does, why does he expect that the general population will?</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392961</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393789</id>
	<title>Re:I Sympathize With Him But Too Idyllic</title>
	<author>immcintosh</author>
	<datestamp>1245442200000</datestamp>
	<modclass>Insightful</modclass>
	<modscore>4</modscore>
	<htmltext><p>To be honest, I thoroughly disagree with you, because I <i>DID HAVE</i> just such a teacher.  She wasn't some kind of superwoman either, she was just very competent at math (no advanced degrees, but good enough to teach basic calculus, algebra, and geometry in a way that made pretty much all the students at my school respect her).  More importantly, she was passionate about giving students a fundamental understanding of the subject matter.  She didn't want to just cross her T's and dot her I's and be done with it, she wanted us to learn what it was all about.  She was a hard teacher, but she was almost remarkable in that nearly the entire student body had a great deal of respect for her.</p><p>I think the author's whole POINT was that it's claims like yours--that this is some kind of unreasonable expectation--that are entirely the problem with the situation we have.  The simple fact is, <i>it is not unreasonable</i>.  My personal experience has shown me that there ARE such teachers out there; mine as well as others I've known.</p><p>My own personal take is that our society simply doesn't give educators the respect they deserve.  There's very little motivation for the kind of intelligent, competent, passionate people to go into to lower tiers of the world of education.  We pay them peanuts and there's not nearly the kind of appreciation and respect out there for them to want to do those jobs.  I happened to go to a private Catholic school, where neither of those things are true, and let me tell you the difference was obvious.</p></htmltext>
<tokenext>To be honest , I thoroughly disagree with you , because I DID HAVE just such a teacher .
She was n't some kind of superwoman either , she was just very competent at math ( no advanced degrees , but good enough to teach basic calculus , algebra , and geometry in a way that made pretty much all the students at my school respect her ) .
More importantly , she was passionate about giving students a fundamental understanding of the subject matter .
She did n't want to just cross her T 's and dot her I 's and be done with it , she wanted us to learn what it was all about .
She was a hard teacher , but she was almost remarkable in that nearly the entire student body had a great deal of respect for her.I think the author 's whole POINT was that it 's claims like yours--that this is some kind of unreasonable expectation--that are entirely the problem with the situation we have .
The simple fact is , it is not unreasonable .
My personal experience has shown me that there ARE such teachers out there ; mine as well as others I 've known.My own personal take is that our society simply does n't give educators the respect they deserve .
There 's very little motivation for the kind of intelligent , competent , passionate people to go into to lower tiers of the world of education .
We pay them peanuts and there 's not nearly the kind of appreciation and respect out there for them to want to do those jobs .
I happened to go to a private Catholic school , where neither of those things are true , and let me tell you the difference was obvious .</tokentext>
<sentencetext>To be honest, I thoroughly disagree with you, because I DID HAVE just such a teacher.
She wasn't some kind of superwoman either, she was just very competent at math (no advanced degrees, but good enough to teach basic calculus, algebra, and geometry in a way that made pretty much all the students at my school respect her).
More importantly, she was passionate about giving students a fundamental understanding of the subject matter.
She didn't want to just cross her T's and dot her I's and be done with it, she wanted us to learn what it was all about.
She was a hard teacher, but she was almost remarkable in that nearly the entire student body had a great deal of respect for her.I think the author's whole POINT was that it's claims like yours--that this is some kind of unreasonable expectation--that are entirely the problem with the situation we have.
The simple fact is, it is not unreasonable.
My personal experience has shown me that there ARE such teachers out there; mine as well as others I've known.My own personal take is that our society simply doesn't give educators the respect they deserve.
There's very little motivation for the kind of intelligent, competent, passionate people to go into to lower tiers of the world of education.
We pay them peanuts and there's not nearly the kind of appreciation and respect out there for them to want to do those jobs.
I happened to go to a private Catholic school, where neither of those things are true, and let me tell you the difference was obvious.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392903</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393185</id>
	<title>As an old codger....</title>
	<author>John Hasler</author>
	<datestamp>1245440040000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>...I know I'm supposed to say "Things ain't like they used to be!" but the fact is, they never were.  K12 in the fifties and sixties tried hard to convince me that I was to hate math and science and treated me as wierdo when I didn't.  Instead I learned to despise classroom education, which did me incalculable harm at university.</p><p>Basically, public education sucks.</p></htmltext>
<tokenext>...I know I 'm supposed to say " Things ai n't like they used to be !
" but the fact is , they never were .
K12 in the fifties and sixties tried hard to convince me that I was to hate math and science and treated me as wierdo when I did n't .
Instead I learned to despise classroom education , which did me incalculable harm at university.Basically , public education sucks .</tokentext>
<sentencetext>...I know I'm supposed to say "Things ain't like they used to be!
" but the fact is, they never were.
K12 in the fifties and sixties tried hard to convince me that I was to hate math and science and treated me as wierdo when I didn't.
Instead I learned to despise classroom education, which did me incalculable harm at university.Basically, public education sucks.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28397603</id>
	<title>Re:The way math is structured is disconnected from</title>
	<author>Anonymous</author>
	<datestamp>1245416640000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>This is certainly a generalization. The Singapore mathematics curriculum is very problem driven and not at all rote memorization. Singapore regularly appears in the highest places in the TIMSS. Indeed a study of student performance on statistics questions showed that the Singaporean students did better than the US counterparts despite the fact that the US curriculum contains statistics as a topic whilst the Singaporean curriculum does not.</p><p>I don't buy the "pressure to succeed" arguments either. I think that it is the system that is failing the students and not the other way around.</p></htmltext>
<tokenext>This is certainly a generalization .
The Singapore mathematics curriculum is very problem driven and not at all rote memorization .
Singapore regularly appears in the highest places in the TIMSS .
Indeed a study of student performance on statistics questions showed that the Singaporean students did better than the US counterparts despite the fact that the US curriculum contains statistics as a topic whilst the Singaporean curriculum does not.I do n't buy the " pressure to succeed " arguments either .
I think that it is the system that is failing the students and not the other way around .</tokentext>
<sentencetext>This is certainly a generalization.
The Singapore mathematics curriculum is very problem driven and not at all rote memorization.
Singapore regularly appears in the highest places in the TIMSS.
Indeed a study of student performance on statistics questions showed that the Singaporean students did better than the US counterparts despite the fact that the US curriculum contains statistics as a topic whilst the Singaporean curriculum does not.I don't buy the "pressure to succeed" arguments either.
I think that it is the system that is failing the students and not the other way around.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393115</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394493</id>
	<title>Re:Cue the other subjects</title>
	<author>johnlcallaway</author>
	<datestamp>1245444600000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>
Here<nobr> <wbr></nobr>... let me correct that for you<p><div class="quote"><p>Too many families are <b>under the mistaken believe they have to have a full-time two-income home</b> (for a variety of reasons) and simply can't/won't/don't spend the time needed with their children in the formative years.</p></div><p>The actual disposable income that a second income, full-time wage earner provides to a home is much lower than that second check.  Two income families often eat out more, require day care facilities for their kids when the kids are not in school, have a second car, lose vacation time due to 'half days' and child sick days, have less time to spend together and spend extravagantly when they do rather than finding simple and free things to do.
<br> <br>I'm not saying two incomes aren't necessary, but it's the amount and timing of the second income that is often not given enough thought.  My first wife didn't work the first two years after she had our first child, then went to work three evenings a week, two of which were alternating weekends, so that we didn't need day care. It wasn't a lot of pay, but it helped.
<br> <br>
During that time, she went to evening classes to get her RN license.  As our kids got older, she was able to work those three evenings as a nurse instead of a store clerk, doubling her salary.  Once the kids were old enough, and didn't really want to spend time with their parents anymore, she was able to work full time.
<br> <br>
A recent double income couple I know lamented about his working so much and not being able to quit because no one would pay him as much. After talking with him, I showed him how much money they were spending eating out, and how finding cheaper places to eat and forgoing the alcohol, appetizers, and desert and making inexpensive, quick meals at home would reduce his expenses enough that he could afford the other job at the lower pay. His only cost?? A happier family life.</p></div>
	</htmltext>
<tokenext>Here ... let me correct that for youToo many families are under the mistaken believe they have to have a full-time two-income home ( for a variety of reasons ) and simply ca n't/wo n't/do n't spend the time needed with their children in the formative years.The actual disposable income that a second income , full-time wage earner provides to a home is much lower than that second check .
Two income families often eat out more , require day care facilities for their kids when the kids are not in school , have a second car , lose vacation time due to 'half days ' and child sick days , have less time to spend together and spend extravagantly when they do rather than finding simple and free things to do .
I 'm not saying two incomes are n't necessary , but it 's the amount and timing of the second income that is often not given enough thought .
My first wife did n't work the first two years after she had our first child , then went to work three evenings a week , two of which were alternating weekends , so that we did n't need day care .
It was n't a lot of pay , but it helped .
During that time , she went to evening classes to get her RN license .
As our kids got older , she was able to work those three evenings as a nurse instead of a store clerk , doubling her salary .
Once the kids were old enough , and did n't really want to spend time with their parents anymore , she was able to work full time .
A recent double income couple I know lamented about his working so much and not being able to quit because no one would pay him as much .
After talking with him , I showed him how much money they were spending eating out , and how finding cheaper places to eat and forgoing the alcohol , appetizers , and desert and making inexpensive , quick meals at home would reduce his expenses enough that he could afford the other job at the lower pay .
His only cost ? ?
A happier family life .</tokentext>
<sentencetext>
Here ... let me correct that for youToo many families are under the mistaken believe they have to have a full-time two-income home (for a variety of reasons) and simply can't/won't/don't spend the time needed with their children in the formative years.The actual disposable income that a second income, full-time wage earner provides to a home is much lower than that second check.
Two income families often eat out more, require day care facilities for their kids when the kids are not in school, have a second car, lose vacation time due to 'half days' and child sick days, have less time to spend together and spend extravagantly when they do rather than finding simple and free things to do.
I'm not saying two incomes aren't necessary, but it's the amount and timing of the second income that is often not given enough thought.
My first wife didn't work the first two years after she had our first child, then went to work three evenings a week, two of which were alternating weekends, so that we didn't need day care.
It wasn't a lot of pay, but it helped.
During that time, she went to evening classes to get her RN license.
As our kids got older, she was able to work those three evenings as a nurse instead of a store clerk, doubling her salary.
Once the kids were old enough, and didn't really want to spend time with their parents anymore, she was able to work full time.
A recent double income couple I know lamented about his working so much and not being able to quit because no one would pay him as much.
After talking with him, I showed him how much money they were spending eating out, and how finding cheaper places to eat and forgoing the alcohol, appetizers, and desert and making inexpensive, quick meals at home would reduce his expenses enough that he could afford the other job at the lower pay.
His only cost??
A happier family life.
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393137</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394119</id>
	<title>Re:I Sympathize With Him But Too Idyllic</title>
	<author>nine-times</author>
	<datestamp>1245443340000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p><div class="quote"><p>Well if you're not asking for teachers needing to be professional published mathematicians, what was that paragraph about?</p> </div><p>I think he's asking for teachers to know about and care about the subjects they teach.  I think you do need to understand and care about a topic in order to teach it well, so he's at least on the right track there.
</p><p>You may be right that expecting that much from teachers seems unrealistic.  However, if expecting our teachers to teach well is an unreasonably high expectation, then it might just be a sign of how screwed our education system is.</p></div>
	</htmltext>
<tokenext>Well if you 're not asking for teachers needing to be professional published mathematicians , what was that paragraph about ?
I think he 's asking for teachers to know about and care about the subjects they teach .
I think you do need to understand and care about a topic in order to teach it well , so he 's at least on the right track there .
You may be right that expecting that much from teachers seems unrealistic .
However , if expecting our teachers to teach well is an unreasonably high expectation , then it might just be a sign of how screwed our education system is .</tokentext>
<sentencetext>Well if you're not asking for teachers needing to be professional published mathematicians, what was that paragraph about?
I think he's asking for teachers to know about and care about the subjects they teach.
I think you do need to understand and care about a topic in order to teach it well, so he's at least on the right track there.
You may be right that expecting that much from teachers seems unrealistic.
However, if expecting our teachers to teach well is an unreasonably high expectation, then it might just be a sign of how screwed our education system is.
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392903</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392889</id>
	<title>Cue the other subjects</title>
	<author>b0r1s</author>
	<datestamp>1245438900000</datestamp>
	<modclass>Insightful</modclass>
	<modscore>4</modscore>
	<htmltext><p>The problems with K-12 education go WAY BEYOND mathematics.</p></htmltext>
<tokenext>The problems with K-12 education go WAY BEYOND mathematics .</tokentext>
<sentencetext>The problems with K-12 education go WAY BEYOND mathematics.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28396275</id>
	<title>Re:Eh.</title>
	<author>Anonymous</author>
	<datestamp>1245408300000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>No, actually what is taught in schools is the useful part of math. It's basically the same debate as Computer Science vs. using a computer. Schools teach to use math to solve problems that arise in at least some professions.</p></htmltext>
<tokenext>No , actually what is taught in schools is the useful part of math .
It 's basically the same debate as Computer Science vs. using a computer .
Schools teach to use math to solve problems that arise in at least some professions .</tokentext>
<sentencetext>No, actually what is taught in schools is the useful part of math.
It's basically the same debate as Computer Science vs. using a computer.
Schools teach to use math to solve problems that arise in at least some professions.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393427</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28395015</id>
	<title>Re:Wrong tool for the job</title>
	<author>geekoid</author>
	<datestamp>1245403140000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>That is completly wrong.</p></htmltext>
<tokenext>That is completly wrong .</tokentext>
<sentencetext>That is completly wrong.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393389</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393035</id>
	<title>US School System compared to Europes School System</title>
	<author>0x000000</author>
	<datestamp>1245439500000</datestamp>
	<modclass>Informativ</modclass>
	<modscore>5</modscore>
	<htmltext><p>I myself have gone through the US school system starting at grade 7 (lived in Switzerland and The Netherlands before then), I am currently in uni for a software engineering degree. While I have read only part of the article (the blog post) I wanted to post my experience compared to that of my cousin who went through school in The Netherlands.</p><p>Math at the schools I went to was catered to the lowest common denominator, the slowest person in the class, the person who would just not get it got the most attention and the rest of the class was stuck at that level until that person tagged along and finally got moving. Whereas in Europe and other places they place those students in various levels of math dependent on their skill level so that those that don't need the extra time are able to get to the higher level maths faster. This creates a gap between the math that is considered required at age 18 in the US and The Netherlands. My cousin was going for a degree in hotel management and food preparation (chef). He at the age of 18 had a better understanding of math, and had more knowledge of high level math (Linear Algebra, Calculus and others) than I did when I graduated High School, and the classes he were in were considered the slower less demanding classes since it was not as much of a requirement for the degree he was going to be pursuing.</p><p>This is the same with a lot of the classes though, history, english, and science classes. Especially for English, you don't get to think for yourself anymore, you have to follow exactly what the teacher told you. If the teacher says this is important for this reason, and you attempt to argue it differently in a paper you fail, everyone coming out of high school has been passed through a cookie cutter, there is no innovation left, there is no real thinking for oneself anymore.</p><p>It is sad, and the state the US educational system is currently in will not allow it to compete in the global market, it will not allow it to be innovate and provide new ideas, but what it will provide is people who are like sheep and are more than willing to follow the crowd and just do it because everyone does. These people will be easy to govern and control since they won't ask questions and least of all will they rebel and fight for their beliefs. In other words, the US education system as it currently stands is making zombies.</p></htmltext>
<tokenext>I myself have gone through the US school system starting at grade 7 ( lived in Switzerland and The Netherlands before then ) , I am currently in uni for a software engineering degree .
While I have read only part of the article ( the blog post ) I wanted to post my experience compared to that of my cousin who went through school in The Netherlands.Math at the schools I went to was catered to the lowest common denominator , the slowest person in the class , the person who would just not get it got the most attention and the rest of the class was stuck at that level until that person tagged along and finally got moving .
Whereas in Europe and other places they place those students in various levels of math dependent on their skill level so that those that do n't need the extra time are able to get to the higher level maths faster .
This creates a gap between the math that is considered required at age 18 in the US and The Netherlands .
My cousin was going for a degree in hotel management and food preparation ( chef ) .
He at the age of 18 had a better understanding of math , and had more knowledge of high level math ( Linear Algebra , Calculus and others ) than I did when I graduated High School , and the classes he were in were considered the slower less demanding classes since it was not as much of a requirement for the degree he was going to be pursuing.This is the same with a lot of the classes though , history , english , and science classes .
Especially for English , you do n't get to think for yourself anymore , you have to follow exactly what the teacher told you .
If the teacher says this is important for this reason , and you attempt to argue it differently in a paper you fail , everyone coming out of high school has been passed through a cookie cutter , there is no innovation left , there is no real thinking for oneself anymore.It is sad , and the state the US educational system is currently in will not allow it to compete in the global market , it will not allow it to be innovate and provide new ideas , but what it will provide is people who are like sheep and are more than willing to follow the crowd and just do it because everyone does .
These people will be easy to govern and control since they wo n't ask questions and least of all will they rebel and fight for their beliefs .
In other words , the US education system as it currently stands is making zombies .</tokentext>
<sentencetext>I myself have gone through the US school system starting at grade 7 (lived in Switzerland and The Netherlands before then), I am currently in uni for a software engineering degree.
While I have read only part of the article (the blog post) I wanted to post my experience compared to that of my cousin who went through school in The Netherlands.Math at the schools I went to was catered to the lowest common denominator, the slowest person in the class, the person who would just not get it got the most attention and the rest of the class was stuck at that level until that person tagged along and finally got moving.
Whereas in Europe and other places they place those students in various levels of math dependent on their skill level so that those that don't need the extra time are able to get to the higher level maths faster.
This creates a gap between the math that is considered required at age 18 in the US and The Netherlands.
My cousin was going for a degree in hotel management and food preparation (chef).
He at the age of 18 had a better understanding of math, and had more knowledge of high level math (Linear Algebra, Calculus and others) than I did when I graduated High School, and the classes he were in were considered the slower less demanding classes since it was not as much of a requirement for the degree he was going to be pursuing.This is the same with a lot of the classes though, history, english, and science classes.
Especially for English, you don't get to think for yourself anymore, you have to follow exactly what the teacher told you.
If the teacher says this is important for this reason, and you attempt to argue it differently in a paper you fail, everyone coming out of high school has been passed through a cookie cutter, there is no innovation left, there is no real thinking for oneself anymore.It is sad, and the state the US educational system is currently in will not allow it to compete in the global market, it will not allow it to be innovate and provide new ideas, but what it will provide is people who are like sheep and are more than willing to follow the crowd and just do it because everyone does.
These people will be easy to govern and control since they won't ask questions and least of all will they rebel and fight for their beliefs.
In other words, the US education system as it currently stands is making zombies.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393083</id>
	<title>Re:Cue the other subjects</title>
	<author>Anonymous</author>
	<datestamp>1245439680000</datestamp>
	<modclass>Insightful</modclass>
	<modscore>4</modscore>
	<htmltext><p>and most of them can be traced to certain groups (*cough*fundamentalists*cough*) waging a 30 year war on public education, and people refusing to see and treat education as what it is: an investment in the future national security and economic stability of the united states.</p></htmltext>
<tokenext>and most of them can be traced to certain groups ( * cough * fundamentalists * cough * ) waging a 30 year war on public education , and people refusing to see and treat education as what it is : an investment in the future national security and economic stability of the united states .</tokentext>
<sentencetext>and most of them can be traced to certain groups (*cough*fundamentalists*cough*) waging a 30 year war on public education, and people refusing to see and treat education as what it is: an investment in the future national security and economic stability of the united states.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392889</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28396541</id>
	<title>Re:Two mathematicians</title>
	<author>SilverEyes</author>
	<datestamp>1245409620000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>You know... I've never thought that joke was funny.</htmltext>
<tokenext>You know... I 've never thought that joke was funny .</tokentext>
<sentencetext>You know... I've never thought that joke was funny.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393275</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394717</id>
	<title>Challenge Accepted</title>
	<author>Anonymous</author>
	<datestamp>1245402120000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>Rant time. From the original post: "I defy you to read and find a single sentence that isn't permeated, suffused, soaked, and encrusted with truth."</p><p>Challenge accepted, for example, from the article:</p><p>"The area of a triangle is equal to one-half its base times its height." Students are asked tomemorize this formula and then "apply" it over and over in the "exercises." Gone is the thrill, the joy, even the pain and frustration of the creative act. There is not even a problem anymore. The question has been asked and answered at the same time--there is nothing left for the student to do."</p><p>Item (1) I have an MA in math and teach at a community college in NYC (previously Boston; algebra, trigonometry, statistics, etc.) (2) As an academic, when you start teaching, you are in for a <i>rude shock</i>. All throughout school, I was engaged, getting "A"'s almost all the time, and considered a "B" to be a signal of failure. The shock is to discover that the majority of people in most classes (including, unknown to you, all of your prior classmates) are unengaged, and are more-or-less comfortable with doing C/D/F work. (3) The problem discussed here (exercising area of a triangle) is, yes, trivial to someone who "gets it". However, it is <i>very difficult</i> to the majority of community college students that I see. For students who fundamentally can't grasp the concept of a variable, repeating algebra for years and years, and who can't "get" the idea of substitution, it's possibly overwhelmingly difficult.</p><p>Yes, to you and me, "there is nothing left for the student to do", I agree fully. But what I've learned since starting as a teacher is that the exercises are an ongoing attempt to prove mastery of the "substitution" concept, and it's actually an enormous struggle for most people who aren't posting on Slashdot.</p><p>I've learned that I can hand out a complete "practice test" in advance of an exam (passingly similar to this proposed exercise), and give an <i>exact duplicate</i> of that test in the next class, with <i>only the numbers changed</i>, and still have the <i>majority of a class fail the test</i>.</p><p>Now, that's not all I do, but I do include examples of this just to check my own sanity all the time. What I also do now is to always include one or two "concept questions" requiring actual analysis of ideas, and the level of frustration and aggravation from the students for those is far, far more enormous. Frequently people just stop trying those by the end of a semester, leaving them blank, and are happy to walk away with a "B" or "C" from the rest of their tests.</p><p>In summary: I now consider my #1 job in all my classes to be an effort to <i>make students comfortable with abstraction</i>. Give me or you a formula and then, indeed, "there is nothing left... to do". But for most students, whose brains fundamentally cannot abstract enough to grasp substitution, there is an enormous skyscraper-sized obstacle still standing in front of them. That is in fact the fundamental goal of most math classes for most students, and they certainly can't do creative exploration or problem-solving until they at least "get" that, and are able to express patterns coherently when they see them.</p><p>Unlike mathematicians like these, my claim is that mathematics is <i>not</i> art; it is a desperate battle. For your consideration, the AngryMath Manifesto: <a href="http://angrymath.blogspot.com/2009/01/angrymath-manifesto.html" title="blogspot.com">http://angrymath.blogspot.com/2009/01/angrymath-manifesto.html</a> [blogspot.com]</p></htmltext>
<tokenext>Rant time .
From the original post : " I defy you to read and find a single sentence that is n't permeated , suffused , soaked , and encrusted with truth .
" Challenge accepted , for example , from the article : " The area of a triangle is equal to one-half its base times its height .
" Students are asked tomemorize this formula and then " apply " it over and over in the " exercises .
" Gone is the thrill , the joy , even the pain and frustration of the creative act .
There is not even a problem anymore .
The question has been asked and answered at the same time--there is nothing left for the student to do .
" Item ( 1 ) I have an MA in math and teach at a community college in NYC ( previously Boston ; algebra , trigonometry , statistics , etc .
) ( 2 ) As an academic , when you start teaching , you are in for a rude shock .
All throughout school , I was engaged , getting " A " 's almost all the time , and considered a " B " to be a signal of failure .
The shock is to discover that the majority of people in most classes ( including , unknown to you , all of your prior classmates ) are unengaged , and are more-or-less comfortable with doing C/D/F work .
( 3 ) The problem discussed here ( exercising area of a triangle ) is , yes , trivial to someone who " gets it " .
However , it is very difficult to the majority of community college students that I see .
For students who fundamentally ca n't grasp the concept of a variable , repeating algebra for years and years , and who ca n't " get " the idea of substitution , it 's possibly overwhelmingly difficult.Yes , to you and me , " there is nothing left for the student to do " , I agree fully .
But what I 've learned since starting as a teacher is that the exercises are an ongoing attempt to prove mastery of the " substitution " concept , and it 's actually an enormous struggle for most people who are n't posting on Slashdot.I 've learned that I can hand out a complete " practice test " in advance of an exam ( passingly similar to this proposed exercise ) , and give an exact duplicate of that test in the next class , with only the numbers changed , and still have the majority of a class fail the test.Now , that 's not all I do , but I do include examples of this just to check my own sanity all the time .
What I also do now is to always include one or two " concept questions " requiring actual analysis of ideas , and the level of frustration and aggravation from the students for those is far , far more enormous .
Frequently people just stop trying those by the end of a semester , leaving them blank , and are happy to walk away with a " B " or " C " from the rest of their tests.In summary : I now consider my # 1 job in all my classes to be an effort to make students comfortable with abstraction .
Give me or you a formula and then , indeed , " there is nothing left... to do " .
But for most students , whose brains fundamentally can not abstract enough to grasp substitution , there is an enormous skyscraper-sized obstacle still standing in front of them .
That is in fact the fundamental goal of most math classes for most students , and they certainly ca n't do creative exploration or problem-solving until they at least " get " that , and are able to express patterns coherently when they see them.Unlike mathematicians like these , my claim is that mathematics is not art ; it is a desperate battle .
For your consideration , the AngryMath Manifesto : http : //angrymath.blogspot.com/2009/01/angrymath-manifesto.html [ blogspot.com ]</tokentext>
<sentencetext>Rant time.
From the original post: "I defy you to read and find a single sentence that isn't permeated, suffused, soaked, and encrusted with truth.
"Challenge accepted, for example, from the article:"The area of a triangle is equal to one-half its base times its height.
" Students are asked tomemorize this formula and then "apply" it over and over in the "exercises.
" Gone is the thrill, the joy, even the pain and frustration of the creative act.
There is not even a problem anymore.
The question has been asked and answered at the same time--there is nothing left for the student to do.
"Item (1) I have an MA in math and teach at a community college in NYC (previously Boston; algebra, trigonometry, statistics, etc.
) (2) As an academic, when you start teaching, you are in for a rude shock.
All throughout school, I was engaged, getting "A"'s almost all the time, and considered a "B" to be a signal of failure.
The shock is to discover that the majority of people in most classes (including, unknown to you, all of your prior classmates) are unengaged, and are more-or-less comfortable with doing C/D/F work.
(3) The problem discussed here (exercising area of a triangle) is, yes, trivial to someone who "gets it".
However, it is very difficult to the majority of community college students that I see.
For students who fundamentally can't grasp the concept of a variable, repeating algebra for years and years, and who can't "get" the idea of substitution, it's possibly overwhelmingly difficult.Yes, to you and me, "there is nothing left for the student to do", I agree fully.
But what I've learned since starting as a teacher is that the exercises are an ongoing attempt to prove mastery of the "substitution" concept, and it's actually an enormous struggle for most people who aren't posting on Slashdot.I've learned that I can hand out a complete "practice test" in advance of an exam (passingly similar to this proposed exercise), and give an exact duplicate of that test in the next class, with only the numbers changed, and still have the majority of a class fail the test.Now, that's not all I do, but I do include examples of this just to check my own sanity all the time.
What I also do now is to always include one or two "concept questions" requiring actual analysis of ideas, and the level of frustration and aggravation from the students for those is far, far more enormous.
Frequently people just stop trying those by the end of a semester, leaving them blank, and are happy to walk away with a "B" or "C" from the rest of their tests.In summary: I now consider my #1 job in all my classes to be an effort to make students comfortable with abstraction.
Give me or you a formula and then, indeed, "there is nothing left... to do".
But for most students, whose brains fundamentally cannot abstract enough to grasp substitution, there is an enormous skyscraper-sized obstacle still standing in front of them.
That is in fact the fundamental goal of most math classes for most students, and they certainly can't do creative exploration or problem-solving until they at least "get" that, and are able to express patterns coherently when they see them.Unlike mathematicians like these, my claim is that mathematics is not art; it is a desperate battle.
For your consideration, the AngryMath Manifesto: http://angrymath.blogspot.com/2009/01/angrymath-manifesto.html [blogspot.com]</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28395213</id>
	<title>Re:Cue the other subjects</title>
	<author>CajunArson</author>
	<datestamp>1245403800000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>In your "fundamentalists" group I sincerely hope you are also adding in all the left-wing teachers unions and academics who REALLY run the school system.<br>Modern educators hate things like objective tests since not everybody does equally well, and they desperately want to eliminate competition from schools since it is considered to promote terrible things like capitalism.  When your math teacher only cares about "feelings" and not objective laws of mathematics, it doesn't matter that he followed his Union leader's instructions to vote for Obama, you'll still get morons coming out of the school system.</p></htmltext>
<tokenext>In your " fundamentalists " group I sincerely hope you are also adding in all the left-wing teachers unions and academics who REALLY run the school system.Modern educators hate things like objective tests since not everybody does equally well , and they desperately want to eliminate competition from schools since it is considered to promote terrible things like capitalism .
When your math teacher only cares about " feelings " and not objective laws of mathematics , it does n't matter that he followed his Union leader 's instructions to vote for Obama , you 'll still get morons coming out of the school system .</tokentext>
<sentencetext>In your "fundamentalists" group I sincerely hope you are also adding in all the left-wing teachers unions and academics who REALLY run the school system.Modern educators hate things like objective tests since not everybody does equally well, and they desperately want to eliminate competition from schools since it is considered to promote terrible things like capitalism.
When your math teacher only cares about "feelings" and not objective laws of mathematics, it doesn't matter that he followed his Union leader's instructions to vote for Obama, you'll still get morons coming out of the school system.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393083</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28395071</id>
	<title>Re:True story ....</title>
	<author>PearsSoap</author>
	<datestamp>1245403260000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p><div class="quote"><p>No, that's just indicative of lazy teachers. Since most humans are lazy and all teachers are human, this is to be expected.</p></div><p>Let's check that with a tableau.</p><p>1.  &#226;fx (H(x) -&gt; L(x)) </p><p>
               |
</p><p>2.  &#226;x  (T(x) -&gt; H(x)) </p><p>
               |
</p><p>3.  ~&#226;fx (H(x) -&gt; L(x)) </p><p>
               |
</p><p>4.  (H(a) -&gt; L(a))                (1. &#226;f) </p><p>
               |
</p><p>5.  &#226;x~(H(x) -&gt; L(x))           (3. ~&#226;f) </p><p>
               |
</p><p>6.  ~(H(a) -&gt; L(a))              (4.  &#226;x) </p><p>Yep, your argument appears valid. (Of course, the conclusion won't be true unless the premises are).</p></div>
	</htmltext>
<tokenext>No , that 's just indicative of lazy teachers .
Since most humans are lazy and all teachers are human , this is to be expected.Let 's check that with a tableau.1 .
  fx ( H ( x ) - &gt; L ( x ) ) | 2 .
  x ( T ( x ) - &gt; H ( x ) ) | 3 .
~   fx ( H ( x ) - &gt; L ( x ) ) | 4 .
( H ( a ) - &gt; L ( a ) ) ( 1 .
  f ) | 5 .
  x ~ ( H ( x ) - &gt; L ( x ) ) ( 3 .
~   f ) | 6 .
~ ( H ( a ) - &gt; L ( a ) ) ( 4 .
  x ) Yep , your argument appears valid .
( Of course , the conclusion wo n't be true unless the premises are ) .</tokentext>
<sentencetext>No, that's just indicative of lazy teachers.
Since most humans are lazy and all teachers are human, this is to be expected.Let's check that with a tableau.1.
âfx (H(x) -&gt; L(x)) 
               |
2.
âx  (T(x) -&gt; H(x)) 
               |
3.
~âfx (H(x) -&gt; L(x)) 
               |
4.
(H(a) -&gt; L(a))                (1.
âf) 
               |
5.
âx~(H(x) -&gt; L(x))           (3.
~âf) 
               |
6.
~(H(a) -&gt; L(a))              (4.
âx) Yep, your argument appears valid.
(Of course, the conclusion won't be true unless the premises are).
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393199</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28426787</id>
	<title>Re:In defense of notation</title>
	<author>Tetsujin</author>
	<datestamp>1245701640000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p><div class="quote"><p>What I took away from Lockhart's essay was that the concept is more important than the notation - not that the notation isn't valuable at all, just that it isn't necessary for simple problems, and by sharing the joy of the simple problems, you can get students to think.</p></div><p>For simple problems, this may be true.  For moderately complex problems, I think the weight of the less compact representation outweighs the cost of learning to work in a more compact representation.</p><p>The problem is that many of the concepts that come into play in these problems <em>aren't</em> readily represented in everyday language.  So the first time you introduce the concept, of course, you have to provide a full explanation of the concept in terms the reader can understand - thereafter, if you've introduced <em>notation</em> to represent the concept, you can rely upon that.  Otherwise, each time you <em>use</em> the concept, you need to represent it using language that evokes that original explanation.</p><p>Imagine, for instance, using the concept "square root" without introducing symbols or language which would encapsulate that concept.  Thus, every time you use the concept "square root" you would have to say something like "that which, when multiplied by itself, equals this".  Or picture trying to represent moderately complex equations in written form without the use of parentheses or any other notation which "contains" parts of the expression - this would really hurt the expressive power of the notation.</p><p>These seem like extreme examples, but it's basically the same thing.  The students are being introduced to a concept which is, to some extent, <em>alien</em> to them.  To work with that concept, they need to put some kind of <em>handle</em> on it, something that conveniently and unambiguously refers to "that thing we learned about last week".  Whether it's a word they've never seen before, or a symbol they've never seen before makes little difference - but I really think it's sensible to include this right from the start.</p></div>
	</htmltext>
<tokenext>What I took away from Lockhart 's essay was that the concept is more important than the notation - not that the notation is n't valuable at all , just that it is n't necessary for simple problems , and by sharing the joy of the simple problems , you can get students to think.For simple problems , this may be true .
For moderately complex problems , I think the weight of the less compact representation outweighs the cost of learning to work in a more compact representation.The problem is that many of the concepts that come into play in these problems are n't readily represented in everyday language .
So the first time you introduce the concept , of course , you have to provide a full explanation of the concept in terms the reader can understand - thereafter , if you 've introduced notation to represent the concept , you can rely upon that .
Otherwise , each time you use the concept , you need to represent it using language that evokes that original explanation.Imagine , for instance , using the concept " square root " without introducing symbols or language which would encapsulate that concept .
Thus , every time you use the concept " square root " you would have to say something like " that which , when multiplied by itself , equals this " .
Or picture trying to represent moderately complex equations in written form without the use of parentheses or any other notation which " contains " parts of the expression - this would really hurt the expressive power of the notation.These seem like extreme examples , but it 's basically the same thing .
The students are being introduced to a concept which is , to some extent , alien to them .
To work with that concept , they need to put some kind of handle on it , something that conveniently and unambiguously refers to " that thing we learned about last week " .
Whether it 's a word they 've never seen before , or a symbol they 've never seen before makes little difference - but I really think it 's sensible to include this right from the start .</tokentext>
<sentencetext>What I took away from Lockhart's essay was that the concept is more important than the notation - not that the notation isn't valuable at all, just that it isn't necessary for simple problems, and by sharing the joy of the simple problems, you can get students to think.For simple problems, this may be true.
For moderately complex problems, I think the weight of the less compact representation outweighs the cost of learning to work in a more compact representation.The problem is that many of the concepts that come into play in these problems aren't readily represented in everyday language.
So the first time you introduce the concept, of course, you have to provide a full explanation of the concept in terms the reader can understand - thereafter, if you've introduced notation to represent the concept, you can rely upon that.
Otherwise, each time you use the concept, you need to represent it using language that evokes that original explanation.Imagine, for instance, using the concept "square root" without introducing symbols or language which would encapsulate that concept.
Thus, every time you use the concept "square root" you would have to say something like "that which, when multiplied by itself, equals this".
Or picture trying to represent moderately complex equations in written form without the use of parentheses or any other notation which "contains" parts of the expression - this would really hurt the expressive power of the notation.These seem like extreme examples, but it's basically the same thing.
The students are being introduced to a concept which is, to some extent, alien to them.
To work with that concept, they need to put some kind of handle on it, something that conveniently and unambiguously refers to "that thing we learned about last week".
Whether it's a word they've never seen before, or a symbol they've never seen before makes little difference - but I really think it's sensible to include this right from the start.
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28403825</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28407901</id>
	<title>Gentle Revolution</title>
	<author>Anonymous</author>
	<datestamp>1245521100000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>Read about it, it states (with clinical research going back to early 60's), that math is best learned before 3 years old.  So all you old morons can't benefit but for the few of you that will reproduce, you can make your children into geniuses.</p></htmltext>
<tokenext>Read about it , it states ( with clinical research going back to early 60 's ) , that math is best learned before 3 years old .
So all you old morons ca n't benefit but for the few of you that will reproduce , you can make your children into geniuses .</tokentext>
<sentencetext>Read about it, it states (with clinical research going back to early 60's), that math is best learned before 3 years old.
So all you old morons can't benefit but for the few of you that will reproduce, you can make your children into geniuses.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392969</id>
	<title>It's a problem</title>
	<author>SEWilco</author>
	<datestamp>1245439200000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><blockquote><div><p>K-12 'education'</p></div>
</blockquote><p>
Solve for education.</p></div>
	</htmltext>
<tokenext>K-12 'education ' Solve for education .</tokentext>
<sentencetext>K-12 'education'

Solve for education.
	</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394595</id>
	<title>Re:Oh give it a rest</title>
	<author>phantomfive</author>
	<datestamp>1245444960000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>It's actually not that hard.  I have a friend who is working teaching people who never learned anything in school.  As in, they some how managed to graduate without ever knowing how to subtract.  That alone indicates that something is wrong with the educational system, but it's besides the point.<br> <br>
He takes these people, the dumbest of the dumb, and he teaches them all the math they need to know to pass the asvab, which includes geometry and algebra, and he does it in 8-12 weeks.  This is enough to pass the California exit exam (and more), by the way.<br> <br>
Now, it's true these guys are adults, and they are getting tutored in small groups, and my friend doesn't have to deal with many problems of the classroom, BUT: if it is possible to condense 12 years of math into four months, and teachers are still having trouble teaching students, then something is clearly wrong with the schooling system.<br> <br>
And actually no one is denying that.  It's obvious that there are problems, everyone can see it.  But what is the solution?  That is the hard part.  How do you make schools better?  This guy doesn't really have an answer either, he just names a bunch of things that are wrong.  Great.  Add your complaints to the list.  There must be a mile long list of problems with schools, so adding a few more can't hurt.  Wake me up when he gets an answer.<br> <br>
Oh, and his nightmare scenario at the beginning, the one about music?  That situation pretty much described my experience learning music theory.  So it's not just math......</htmltext>
<tokenext>It 's actually not that hard .
I have a friend who is working teaching people who never learned anything in school .
As in , they some how managed to graduate without ever knowing how to subtract .
That alone indicates that something is wrong with the educational system , but it 's besides the point .
He takes these people , the dumbest of the dumb , and he teaches them all the math they need to know to pass the asvab , which includes geometry and algebra , and he does it in 8-12 weeks .
This is enough to pass the California exit exam ( and more ) , by the way .
Now , it 's true these guys are adults , and they are getting tutored in small groups , and my friend does n't have to deal with many problems of the classroom , BUT : if it is possible to condense 12 years of math into four months , and teachers are still having trouble teaching students , then something is clearly wrong with the schooling system .
And actually no one is denying that .
It 's obvious that there are problems , everyone can see it .
But what is the solution ?
That is the hard part .
How do you make schools better ?
This guy does n't really have an answer either , he just names a bunch of things that are wrong .
Great. Add your complaints to the list .
There must be a mile long list of problems with schools , so adding a few more ca n't hurt .
Wake me up when he gets an answer .
Oh , and his nightmare scenario at the beginning , the one about music ?
That situation pretty much described my experience learning music theory .
So it 's not just math..... .</tokentext>
<sentencetext>It's actually not that hard.
I have a friend who is working teaching people who never learned anything in school.
As in, they some how managed to graduate without ever knowing how to subtract.
That alone indicates that something is wrong with the educational system, but it's besides the point.
He takes these people, the dumbest of the dumb, and he teaches them all the math they need to know to pass the asvab, which includes geometry and algebra, and he does it in 8-12 weeks.
This is enough to pass the California exit exam (and more), by the way.
Now, it's true these guys are adults, and they are getting tutored in small groups, and my friend doesn't have to deal with many problems of the classroom, BUT: if it is possible to condense 12 years of math into four months, and teachers are still having trouble teaching students, then something is clearly wrong with the schooling system.
And actually no one is denying that.
It's obvious that there are problems, everyone can see it.
But what is the solution?
That is the hard part.
How do you make schools better?
This guy doesn't really have an answer either, he just names a bunch of things that are wrong.
Great.  Add your complaints to the list.
There must be a mile long list of problems with schools, so adding a few more can't hurt.
Wake me up when he gets an answer.
Oh, and his nightmare scenario at the beginning, the one about music?
That situation pretty much described my experience learning music theory.
So it's not just math......</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392993</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28395007</id>
	<title>Math isn't useful for getting a job</title>
	<author>Anonymous</author>
	<datestamp>1245403080000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>I have a PhD in Math from a top school.<br>I was unemployed for a few months after graduating.<br>Employers were far more interested in my BS in CS.</p></htmltext>
<tokenext>I have a PhD in Math from a top school.I was unemployed for a few months after graduating.Employers were far more interested in my BS in CS .</tokentext>
<sentencetext>I have a PhD in Math from a top school.I was unemployed for a few months after graduating.Employers were far more interested in my BS in CS.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28395397</id>
	<title>Re:Eh.</title>
	<author>Anonymous</author>
	<datestamp>1245404400000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>I don't think you read the essay.</p></htmltext>
<tokenext>I do n't think you read the essay .</tokentext>
<sentencetext>I don't think you read the essay.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392961</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394271</id>
	<title>A teachers take</title>
	<author>Anonymous</author>
	<datestamp>1245443880000</datestamp>
	<modclass>Insightful</modclass>
	<modscore>4</modscore>
	<htmltext>I am a teacher, albeit not a a math teacher but teaching in general has a lot of problems in the U.S.  The largest problem that I see in America is that we have a system of education that is largely based on talent.  We recognize it, reward it, and care for it like a price flower.  Effort on the other hand is culturally unappreciated and that cultural attitude is reflected in education.  The talented students have the opportunity to shine, and they always have.<br> <br>Would our culture demand effort from our students instead of recognizing talent we'd be much further along.<br> <br>I'm not suggesting that talent should go un-nurtured but, at least from an educators point of view, the effort of the students should be the focus of rewards.</htmltext>
<tokenext>I am a teacher , albeit not a a math teacher but teaching in general has a lot of problems in the U.S. The largest problem that I see in America is that we have a system of education that is largely based on talent .
We recognize it , reward it , and care for it like a price flower .
Effort on the other hand is culturally unappreciated and that cultural attitude is reflected in education .
The talented students have the opportunity to shine , and they always have .
Would our culture demand effort from our students instead of recognizing talent we 'd be much further along .
I 'm not suggesting that talent should go un-nurtured but , at least from an educators point of view , the effort of the students should be the focus of rewards .</tokentext>
<sentencetext>I am a teacher, albeit not a a math teacher but teaching in general has a lot of problems in the U.S.  The largest problem that I see in America is that we have a system of education that is largely based on talent.
We recognize it, reward it, and care for it like a price flower.
Effort on the other hand is culturally unappreciated and that cultural attitude is reflected in education.
The talented students have the opportunity to shine, and they always have.
Would our culture demand effort from our students instead of recognizing talent we'd be much further along.
I'm not suggesting that talent should go un-nurtured but, at least from an educators point of view, the effort of the students should be the focus of rewards.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28401195</id>
	<title>Re:US School System compared to Europes School Sys</title>
	<author>gatkinso</author>
	<datestamp>1245507480000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>The public schools I attended in the US were set up very similarly to the way you describe European schools - sections based on performance levels.</p><p>Incidentally, they stopped this about two years after I graduated high school.</p><p>I come from a small rural town in western Maryland.  Redneck city.  Many of the kids I graduated with left town, went to college are all over the world doing all kinds of things.  I currently design airborne hyperspectral sensors for instance.</p><p>The kids afterward?  Much lower college attendance.  Many of them still living with their parents.  A lot of unemployment in that group.</p><p>Oh well.</p></htmltext>
<tokenext>The public schools I attended in the US were set up very similarly to the way you describe European schools - sections based on performance levels.Incidentally , they stopped this about two years after I graduated high school.I come from a small rural town in western Maryland .
Redneck city .
Many of the kids I graduated with left town , went to college are all over the world doing all kinds of things .
I currently design airborne hyperspectral sensors for instance.The kids afterward ?
Much lower college attendance .
Many of them still living with their parents .
A lot of unemployment in that group.Oh well .</tokentext>
<sentencetext>The public schools I attended in the US were set up very similarly to the way you describe European schools - sections based on performance levels.Incidentally, they stopped this about two years after I graduated high school.I come from a small rural town in western Maryland.
Redneck city.
Many of the kids I graduated with left town, went to college are all over the world doing all kinds of things.
I currently design airborne hyperspectral sensors for instance.The kids afterward?
Much lower college attendance.
Many of them still living with their parents.
A lot of unemployment in that group.Oh well.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393035</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394953</id>
	<title>Re:True story ....</title>
	<author>bograt</author>
	<datestamp>1245402900000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>Your professor also seems to have the whole concept of "statistical significance" wrong.  A significance level of 0.05 doesn't mean you have "95\% confidence" in the results, it means there would be a 5\% chance of the observed data being generated if the null hypothesis was true.</htmltext>
<tokenext>Your professor also seems to have the whole concept of " statistical significance " wrong .
A significance level of 0.05 does n't mean you have " 95 \ % confidence " in the results , it means there would be a 5 \ % chance of the observed data being generated if the null hypothesis was true .</tokentext>
<sentencetext>Your professor also seems to have the whole concept of "statistical significance" wrong.
A significance level of 0.05 doesn't mean you have "95\% confidence" in the results, it means there would be a 5\% chance of the observed data being generated if the null hypothesis was true.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392947</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393389</id>
	<title>Wrong tool for the job</title>
	<author>tyrione</author>
	<datestamp>1245440760000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>Stop hiring Education Majors to teach The Hard Sciences. Unless you include Historical Curriculum of famous and infamous Scientists into your early days of learning the Hard Sciences will forever be a mystery.</p><p>If you want a kid to know Euclidean Plane Geometry you better make ``The Elements Books I-XIII'', by Euclid part of the curriculum early on and gradually bring into view the history of its making followed by the actually application.</p><p>The same goes for Physics with Newton, Robert Boyle, Euler, etc.</p><p>Hell, I'm just getting all the backlog history of these giants and I'm a M.E. It would have made my days far more enriching to know how they came up with this crap outside of the Calculus derived explanations. I love Mathematics and it's endless Engineering Applications [mainly because I could always visualize their application--something innate and not taught] but reading the greats memoirs and more makes it come together.</p><p>Instead of just History over political events we need History over Mathematics, Physics, Chemistry, EE, ME, CE, etc.</p><p>You don't suddenly become educated in Paleontology without first knowing it's foundation, heavily grounded in History. Hell even Fine Arts requires a massive background in the history of the fields pioneers.</p></htmltext>
<tokenext>Stop hiring Education Majors to teach The Hard Sciences .
Unless you include Historical Curriculum of famous and infamous Scientists into your early days of learning the Hard Sciences will forever be a mystery.If you want a kid to know Euclidean Plane Geometry you better make ` ` The Elements Books I-XIII' ' , by Euclid part of the curriculum early on and gradually bring into view the history of its making followed by the actually application.The same goes for Physics with Newton , Robert Boyle , Euler , etc.Hell , I 'm just getting all the backlog history of these giants and I 'm a M.E .
It would have made my days far more enriching to know how they came up with this crap outside of the Calculus derived explanations .
I love Mathematics and it 's endless Engineering Applications [ mainly because I could always visualize their application--something innate and not taught ] but reading the greats memoirs and more makes it come together.Instead of just History over political events we need History over Mathematics , Physics , Chemistry , EE , ME , CE , etc.You do n't suddenly become educated in Paleontology without first knowing it 's foundation , heavily grounded in History .
Hell even Fine Arts requires a massive background in the history of the fields pioneers .</tokentext>
<sentencetext>Stop hiring Education Majors to teach The Hard Sciences.
Unless you include Historical Curriculum of famous and infamous Scientists into your early days of learning the Hard Sciences will forever be a mystery.If you want a kid to know Euclidean Plane Geometry you better make ``The Elements Books I-XIII'', by Euclid part of the curriculum early on and gradually bring into view the history of its making followed by the actually application.The same goes for Physics with Newton, Robert Boyle, Euler, etc.Hell, I'm just getting all the backlog history of these giants and I'm a M.E.
It would have made my days far more enriching to know how they came up with this crap outside of the Calculus derived explanations.
I love Mathematics and it's endless Engineering Applications [mainly because I could always visualize their application--something innate and not taught] but reading the greats memoirs and more makes it come together.Instead of just History over political events we need History over Mathematics, Physics, Chemistry, EE, ME, CE, etc.You don't suddenly become educated in Paleontology without first knowing it's foundation, heavily grounded in History.
Hell even Fine Arts requires a massive background in the history of the fields pioneers.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28395997</id>
	<title>Another valid point</title>
	<author>Locke2005</author>
	<datestamp>1245406980000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>Why aren't all textbooks open sourced already? Allowing teachers to take educational texts, modify them for their own needs, and distribute the changes makes even more sense than open source software does. And yet it rarely happens. Case in point: Beaverton School District wants to start a new math curiculum; with 32,000 students they will be spending $70,000/year on new text books for the next 12 years... I want to know the name of the teacher they are firing so that they can afford this!</htmltext>
<tokenext>Why are n't all textbooks open sourced already ?
Allowing teachers to take educational texts , modify them for their own needs , and distribute the changes makes even more sense than open source software does .
And yet it rarely happens .
Case in point : Beaverton School District wants to start a new math curiculum ; with 32,000 students they will be spending $ 70,000/year on new text books for the next 12 years... I want to know the name of the teacher they are firing so that they can afford this !</tokentext>
<sentencetext>Why aren't all textbooks open sourced already?
Allowing teachers to take educational texts, modify them for their own needs, and distribute the changes makes even more sense than open source software does.
And yet it rarely happens.
Case in point: Beaverton School District wants to start a new math curiculum; with 32,000 students they will be spending $70,000/year on new text books for the next 12 years... I want to know the name of the teacher they are firing so that they can afford this!</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28397685</id>
	<title>My POV</title>
	<author>Anonymous</author>
	<datestamp>1245417180000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>As a high school math teacher (who has a BA in Math and MSEd in Educational Psych - by the way, Masters are NOT required for teaching HS, at least not in most states - and I did find the MSEd valuable in helping me learn how to teach math, probably more valuable than an additional degree in math, as at that level, I would not be using it in HS), I believe there is a lot of validity to the article and the comments made here. But I think it is important to recognize additional problems (which may be listed in some of the 400 comments I didn't have a chance to read)...<br>1) Though I would ideally love to teach the history and art of math, we are limited by time and curriculum. We are held slave to standardized tests that require we focus on required material in a limited amount of time.  I do my best to incorporate history and passion, but sometimes it is lost due to other constraints, but not by lack of desire.<br>2) One of the absolute largest problems is that our grade level standards are absurd. While the top performing countries will focus on 10 or less standards per year (thus allowing them to go into more detail, understanding, passion/art/history and mastery and thereby requiring less review each subsequent year), there are several grade/math levels in the US that have 20 or more standards to be covered.  What that usually results in is the need for LOTS of review each year because it is not resonable for us to expect students to really "get" something if they spend 9 days on a topic, where as their international counterparts are spending 2 times that on the same material. And the more we review, the less time we have for new learning. If we, as simple teachers, cogs in the machine, could narrow those standards down so that we could really internalize the material, the students would better learn, understand and maybe even love the subject.  Unfortunately, we cannot make that decision on our own - we answer to many other people.  Ideally, we could revamp the entire system starting with Kindergarten.<br>There are many other things to consider as well, but what we can do right now is NOT demoralize the teachers that are working their tails off to help their students learn and succeed and instead, find ways to bring this important educational deficit to the front of government minds.  We do need change, and it has to start at the very beginning.</p></htmltext>
<tokenext>As a high school math teacher ( who has a BA in Math and MSEd in Educational Psych - by the way , Masters are NOT required for teaching HS , at least not in most states - and I did find the MSEd valuable in helping me learn how to teach math , probably more valuable than an additional degree in math , as at that level , I would not be using it in HS ) , I believe there is a lot of validity to the article and the comments made here .
But I think it is important to recognize additional problems ( which may be listed in some of the 400 comments I did n't have a chance to read ) ...1 ) Though I would ideally love to teach the history and art of math , we are limited by time and curriculum .
We are held slave to standardized tests that require we focus on required material in a limited amount of time .
I do my best to incorporate history and passion , but sometimes it is lost due to other constraints , but not by lack of desire.2 ) One of the absolute largest problems is that our grade level standards are absurd .
While the top performing countries will focus on 10 or less standards per year ( thus allowing them to go into more detail , understanding , passion/art/history and mastery and thereby requiring less review each subsequent year ) , there are several grade/math levels in the US that have 20 or more standards to be covered .
What that usually results in is the need for LOTS of review each year because it is not resonable for us to expect students to really " get " something if they spend 9 days on a topic , where as their international counterparts are spending 2 times that on the same material .
And the more we review , the less time we have for new learning .
If we , as simple teachers , cogs in the machine , could narrow those standards down so that we could really internalize the material , the students would better learn , understand and maybe even love the subject .
Unfortunately , we can not make that decision on our own - we answer to many other people .
Ideally , we could revamp the entire system starting with Kindergarten.There are many other things to consider as well , but what we can do right now is NOT demoralize the teachers that are working their tails off to help their students learn and succeed and instead , find ways to bring this important educational deficit to the front of government minds .
We do need change , and it has to start at the very beginning .</tokentext>
<sentencetext>As a high school math teacher (who has a BA in Math and MSEd in Educational Psych - by the way, Masters are NOT required for teaching HS, at least not in most states - and I did find the MSEd valuable in helping me learn how to teach math, probably more valuable than an additional degree in math, as at that level, I would not be using it in HS), I believe there is a lot of validity to the article and the comments made here.
But I think it is important to recognize additional problems (which may be listed in some of the 400 comments I didn't have a chance to read)...1) Though I would ideally love to teach the history and art of math, we are limited by time and curriculum.
We are held slave to standardized tests that require we focus on required material in a limited amount of time.
I do my best to incorporate history and passion, but sometimes it is lost due to other constraints, but not by lack of desire.2) One of the absolute largest problems is that our grade level standards are absurd.
While the top performing countries will focus on 10 or less standards per year (thus allowing them to go into more detail, understanding, passion/art/history and mastery and thereby requiring less review each subsequent year), there are several grade/math levels in the US that have 20 or more standards to be covered.
What that usually results in is the need for LOTS of review each year because it is not resonable for us to expect students to really "get" something if they spend 9 days on a topic, where as their international counterparts are spending 2 times that on the same material.
And the more we review, the less time we have for new learning.
If we, as simple teachers, cogs in the machine, could narrow those standards down so that we could really internalize the material, the students would better learn, understand and maybe even love the subject.
Unfortunately, we cannot make that decision on our own - we answer to many other people.
Ideally, we could revamp the entire system starting with Kindergarten.There are many other things to consider as well, but what we can do right now is NOT demoralize the teachers that are working their tails off to help their students learn and succeed and instead, find ways to bring this important educational deficit to the front of government minds.
We do need change, and it has to start at the very beginning.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394151</id>
	<title>Re:You can convince me</title>
	<author>Anonymous</author>
	<datestamp>1245443460000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>You have missed the point. The problem solving toolkit that is mathematics isn't tied to all of the notions taught in school. To continue with the idea of painting, The current teaching of mathematics would be like teaching a student that a brush goes into the paint and then up once, down once, and then back into the paint. Then forcing the student to do that several thousand times. The student doesn't really understand what he is doing, why he is doing it or why its important that he does it in this particular way. What does the student do if he has to paint something above him? Unfortunately he hasn't drilled on that and will not be able to solve the problem.</p><p>The art is the tool. There is no separation, thinking there is is the problem. For example a bridge painter is restricted to only using his painting skills for work, he can paint for pleasure using the same techniques. The only difference is the outcome.</p></htmltext>
<tokenext>You have missed the point .
The problem solving toolkit that is mathematics is n't tied to all of the notions taught in school .
To continue with the idea of painting , The current teaching of mathematics would be like teaching a student that a brush goes into the paint and then up once , down once , and then back into the paint .
Then forcing the student to do that several thousand times .
The student does n't really understand what he is doing , why he is doing it or why its important that he does it in this particular way .
What does the student do if he has to paint something above him ?
Unfortunately he has n't drilled on that and will not be able to solve the problem.The art is the tool .
There is no separation , thinking there is is the problem .
For example a bridge painter is restricted to only using his painting skills for work , he can paint for pleasure using the same techniques .
The only difference is the outcome .</tokentext>
<sentencetext>You have missed the point.
The problem solving toolkit that is mathematics isn't tied to all of the notions taught in school.
To continue with the idea of painting, The current teaching of mathematics would be like teaching a student that a brush goes into the paint and then up once, down once, and then back into the paint.
Then forcing the student to do that several thousand times.
The student doesn't really understand what he is doing, why he is doing it or why its important that he does it in this particular way.
What does the student do if he has to paint something above him?
Unfortunately he hasn't drilled on that and will not be able to solve the problem.The art is the tool.
There is no separation, thinking there is is the problem.
For example a bridge painter is restricted to only using his painting skills for work, he can paint for pleasure using the same techniques.
The only difference is the outcome.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393159</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28400679</id>
	<title>You Can't Teach Around The Economics!</title>
	<author>logicnazi</author>
	<datestamp>1245498660000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>As a working mathematician I had a great deal of sympathy for many things Lockhardt had to say. In particular he couldn't be more right about the total uselessness of most of the math curriculum to most students. Go ask a working professional (doctor, lawyer, etc..) to solve a system of linear equations in 2 unknowns and it's immediately apparent they got no direct practical benefit from their math classes.<br><br>I quibble with his ragging on epsilon-delta and other precise definitions. I finally realized math was elegant and exciting precisely because I was so disgusted with (ugly) intuitive arguments about smoothness I went and found a book that taught me the elegant formal definitions that made calculus all fit together. Not that I would recommend this for everyone but I personally find it one of the most aesthetically aspects of analysis.<br><br>-----<br><br>However, where he really totally blows it is when he assumes that math can be a fun exploratory intellectual adventure for everyone. Yes, virtually everyone has the innate intelligence to do this but no matter what you do math is going to make some people feel dumb and frustrated. There are right and wrong answers in math and not everyone can be above average.<br><br>Sure, everyone might be lackadaisical in HS art class but that's because few (no?) people's future depends on their ability to do well in the class. On the other hand the best and the brightest signal their ability by performing well in math. Sure, these students succeed because they are curious and interested but all the other students will struggle to look like the mathematically advanced kids and those who fail will feel bad about themselves for it.  No matter how you teach you can't eliminate the economic pressure on the students to appear as if they are good at math.<br><br>People don't like doing things that make them feel stupid or frustrated and learning real math requires genuine curiosity and thought. You just can't force people who resent the subject to think.<br><br>Perhaps we should simply accept that math is going to be like literature or art. A small percent will have the desire and interest to pursue it in highschool and we should just try to avoid turning off the rest enough they might return in their own time.</htmltext>
<tokenext>As a working mathematician I had a great deal of sympathy for many things Lockhardt had to say .
In particular he could n't be more right about the total uselessness of most of the math curriculum to most students .
Go ask a working professional ( doctor , lawyer , etc.. ) to solve a system of linear equations in 2 unknowns and it 's immediately apparent they got no direct practical benefit from their math classes.I quibble with his ragging on epsilon-delta and other precise definitions .
I finally realized math was elegant and exciting precisely because I was so disgusted with ( ugly ) intuitive arguments about smoothness I went and found a book that taught me the elegant formal definitions that made calculus all fit together .
Not that I would recommend this for everyone but I personally find it one of the most aesthetically aspects of analysis.-----However , where he really totally blows it is when he assumes that math can be a fun exploratory intellectual adventure for everyone .
Yes , virtually everyone has the innate intelligence to do this but no matter what you do math is going to make some people feel dumb and frustrated .
There are right and wrong answers in math and not everyone can be above average.Sure , everyone might be lackadaisical in HS art class but that 's because few ( no ?
) people 's future depends on their ability to do well in the class .
On the other hand the best and the brightest signal their ability by performing well in math .
Sure , these students succeed because they are curious and interested but all the other students will struggle to look like the mathematically advanced kids and those who fail will feel bad about themselves for it .
No matter how you teach you ca n't eliminate the economic pressure on the students to appear as if they are good at math.People do n't like doing things that make them feel stupid or frustrated and learning real math requires genuine curiosity and thought .
You just ca n't force people who resent the subject to think.Perhaps we should simply accept that math is going to be like literature or art .
A small percent will have the desire and interest to pursue it in highschool and we should just try to avoid turning off the rest enough they might return in their own time .</tokentext>
<sentencetext>As a working mathematician I had a great deal of sympathy for many things Lockhardt had to say.
In particular he couldn't be more right about the total uselessness of most of the math curriculum to most students.
Go ask a working professional (doctor, lawyer, etc..) to solve a system of linear equations in 2 unknowns and it's immediately apparent they got no direct practical benefit from their math classes.I quibble with his ragging on epsilon-delta and other precise definitions.
I finally realized math was elegant and exciting precisely because I was so disgusted with (ugly) intuitive arguments about smoothness I went and found a book that taught me the elegant formal definitions that made calculus all fit together.
Not that I would recommend this for everyone but I personally find it one of the most aesthetically aspects of analysis.-----However, where he really totally blows it is when he assumes that math can be a fun exploratory intellectual adventure for everyone.
Yes, virtually everyone has the innate intelligence to do this but no matter what you do math is going to make some people feel dumb and frustrated.
There are right and wrong answers in math and not everyone can be above average.Sure, everyone might be lackadaisical in HS art class but that's because few (no?
) people's future depends on their ability to do well in the class.
On the other hand the best and the brightest signal their ability by performing well in math.
Sure, these students succeed because they are curious and interested but all the other students will struggle to look like the mathematically advanced kids and those who fail will feel bad about themselves for it.
No matter how you teach you can't eliminate the economic pressure on the students to appear as if they are good at math.People don't like doing things that make them feel stupid or frustrated and learning real math requires genuine curiosity and thought.
You just can't force people who resent the subject to think.Perhaps we should simply accept that math is going to be like literature or art.
A small percent will have the desire and interest to pursue it in highschool and we should just try to avoid turning off the rest enough they might return in their own time.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393347</id>
	<title>Re:Cue the other subjects</title>
	<author>b0r1s</author>
	<datestamp>1245440580000</datestamp>
	<modclass>Interestin</modclass>
	<modscore>2</modscore>
	<htmltext><p>Personally, I put the blame less on fundamentalists and more on decreasing importance of education in the home.</p><p>There are dozens of examples (single mothers with multiple jobs and multiple kids who just don't have time to parent, illegal immigrants raising kids that accept no-skill jobs as manual labor as sufficient for a lifetime instead of working to get an education and work in a skilled field), but the basic problem is that kids don't believe that they need a real education to live.</p></htmltext>
<tokenext>Personally , I put the blame less on fundamentalists and more on decreasing importance of education in the home.There are dozens of examples ( single mothers with multiple jobs and multiple kids who just do n't have time to parent , illegal immigrants raising kids that accept no-skill jobs as manual labor as sufficient for a lifetime instead of working to get an education and work in a skilled field ) , but the basic problem is that kids do n't believe that they need a real education to live .</tokentext>
<sentencetext>Personally, I put the blame less on fundamentalists and more on decreasing importance of education in the home.There are dozens of examples (single mothers with multiple jobs and multiple kids who just don't have time to parent, illegal immigrants raising kids that accept no-skill jobs as manual labor as sufficient for a lifetime instead of working to get an education and work in a skilled field), but the basic problem is that kids don't believe that they need a real education to live.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393083</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28397753</id>
	<title>Re:I Sympathize With Him But Too Idyllic</title>
	<author>Anonymous</author>
	<datestamp>1245417600000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p><i>The public school system is more worried about getting someone that actualy cares about the students at all. They can't even find those people let alone people who care about the students and live/eat/sleep/bleed math.</i> </p><p>I'm one such person, with an MS in mathematics. I can't be found because of the rotten system that is in place that completely strips the educator of any autonomy. Too bad for the students.</p></htmltext>
<tokenext>The public school system is more worried about getting someone that actualy cares about the students at all .
They ca n't even find those people let alone people who care about the students and live/eat/sleep/bleed math .
I 'm one such person , with an MS in mathematics .
I ca n't be found because of the rotten system that is in place that completely strips the educator of any autonomy .
Too bad for the students .</tokentext>
<sentencetext>The public school system is more worried about getting someone that actualy cares about the students at all.
They can't even find those people let alone people who care about the students and live/eat/sleep/bleed math.
I'm one such person, with an MS in mathematics.
I can't be found because of the rotten system that is in place that completely strips the educator of any autonomy.
Too bad for the students.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392903</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28396519</id>
	<title>Re:Vulcans are doing it right</title>
	<author>SilverEyes</author>
	<datestamp>1245409560000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p><nobr> <wbr></nobr></p><div class="quote"><p>...Kind of like leveling up in an RPG.. would make things fun.</p></div><p>The only problem is that some people would then become addicted to this so-called "life MMORPG" and neglect their own lives<nobr> <wbr></nobr>:P</p></div>
	</htmltext>
<tokenext>...Kind of like leveling up in an RPG.. would make things fun.The only problem is that some people would then become addicted to this so-called " life MMORPG " and neglect their own lives : P</tokentext>
<sentencetext> ...Kind of like leveling up in an RPG.. would make things fun.The only problem is that some people would then become addicted to this so-called "life MMORPG" and neglect their own lives :P
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393253</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28397199</id>
	<title>Re:Two mathematicians</title>
	<author>Anonymous</author>
	<datestamp>1245413220000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>Killer!!! Mod up funny<nobr> <wbr></nobr>:-)</p></htmltext>
<tokenext>Killer ! ! !
Mod up funny : - )</tokentext>
<sentencetext>Killer!!!
Mod up funny :-)</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393275</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393339</id>
	<title>Re:it's really bad</title>
	<author>Anonymous</author>
	<datestamp>1245440520000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>So I shouldn't have enjoyed all those proofs in geometry and trig, then?  Dammit, why doesn't anybody tell me these things--here I was growing up without knowing there's only one proper order in which to learn things!</p></htmltext>
<tokenext>So I should n't have enjoyed all those proofs in geometry and trig , then ?
Dammit , why does n't anybody tell me these things--here I was growing up without knowing there 's only one proper order in which to learn things !</tokentext>
<sentencetext>So I shouldn't have enjoyed all those proofs in geometry and trig, then?
Dammit, why doesn't anybody tell me these things--here I was growing up without knowing there's only one proper order in which to learn things!</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392911</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394487</id>
	<title>Re:tl;dr</title>
	<author>Grishnakh</author>
	<datestamp>1245444600000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>It's because he was talking about elementary teachers, not high school or above.  I had both good and horrible female math teachers in high school; of course it has nothing to do with sex.</p><p>What does have to do with sex, however, is elementary education: elementary teachers are almost always women.  This is for two reasons: 1) women are generally more interested in teaching and being around small children than men, and 2) men who are interested in being around small children are viewed as pedophiles in our society, so men who genuinely like being around small children, but not molesting them, tend to avoid this profession.  Oh yeah: 3) elementary teachers aren't paid very well, so it's ok for women who have a husband's larger primary income to live on, but not for a man.</p><p>So the OP, speaking from his personal experience with elementary teachers, said "women" because that's what all his elementary teachers were.  Mine were all women too.  If you had any male teachers in the K-5 grades, then you are a statistical anomaly I believe.</p></htmltext>
<tokenext>It 's because he was talking about elementary teachers , not high school or above .
I had both good and horrible female math teachers in high school ; of course it has nothing to do with sex.What does have to do with sex , however , is elementary education : elementary teachers are almost always women .
This is for two reasons : 1 ) women are generally more interested in teaching and being around small children than men , and 2 ) men who are interested in being around small children are viewed as pedophiles in our society , so men who genuinely like being around small children , but not molesting them , tend to avoid this profession .
Oh yeah : 3 ) elementary teachers are n't paid very well , so it 's ok for women who have a husband 's larger primary income to live on , but not for a man.So the OP , speaking from his personal experience with elementary teachers , said " women " because that 's what all his elementary teachers were .
Mine were all women too .
If you had any male teachers in the K-5 grades , then you are a statistical anomaly I believe .</tokentext>
<sentencetext>It's because he was talking about elementary teachers, not high school or above.
I had both good and horrible female math teachers in high school; of course it has nothing to do with sex.What does have to do with sex, however, is elementary education: elementary teachers are almost always women.
This is for two reasons: 1) women are generally more interested in teaching and being around small children than men, and 2) men who are interested in being around small children are viewed as pedophiles in our society, so men who genuinely like being around small children, but not molesting them, tend to avoid this profession.
Oh yeah: 3) elementary teachers aren't paid very well, so it's ok for women who have a husband's larger primary income to live on, but not for a man.So the OP, speaking from his personal experience with elementary teachers, said "women" because that's what all his elementary teachers were.
Mine were all women too.
If you had any male teachers in the K-5 grades, then you are a statistical anomaly I believe.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393353</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393585</id>
	<title>Re:it's really bad</title>
	<author>Sage Gaspar</author>
	<datestamp>1245441480000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>I think that logic and, more broadly, philosophy would be absolutely excellent additions to the high school curriculum, but you really do not need any formal knowledge of mathematical logic to do Euclidean geometry. It's a great introduction to the basic idea of math, starting with a set of facts and deducing a conclusion. People have intuition about geometry in the plane, and introducing more formalism would just obscure everything.<br> <br>The temptation once you know a lot of math is that math should be a sequential subject where you build up from axioms. If you actually try to teach using this method, by which I mean heaping formalism on students before they need it, you'll find out that it just doesn't stick. That isn't even really how mathematicians do math. Usually the intuition leads to the formalism. People were working with the natural numbers for thousands of years before we decided to nail it down with ZFC.</htmltext>
<tokenext>I think that logic and , more broadly , philosophy would be absolutely excellent additions to the high school curriculum , but you really do not need any formal knowledge of mathematical logic to do Euclidean geometry .
It 's a great introduction to the basic idea of math , starting with a set of facts and deducing a conclusion .
People have intuition about geometry in the plane , and introducing more formalism would just obscure everything .
The temptation once you know a lot of math is that math should be a sequential subject where you build up from axioms .
If you actually try to teach using this method , by which I mean heaping formalism on students before they need it , you 'll find out that it just does n't stick .
That is n't even really how mathematicians do math .
Usually the intuition leads to the formalism .
People were working with the natural numbers for thousands of years before we decided to nail it down with ZFC .</tokentext>
<sentencetext>I think that logic and, more broadly, philosophy would be absolutely excellent additions to the high school curriculum, but you really do not need any formal knowledge of mathematical logic to do Euclidean geometry.
It's a great introduction to the basic idea of math, starting with a set of facts and deducing a conclusion.
People have intuition about geometry in the plane, and introducing more formalism would just obscure everything.
The temptation once you know a lot of math is that math should be a sequential subject where you build up from axioms.
If you actually try to teach using this method, by which I mean heaping formalism on students before they need it, you'll find out that it just doesn't stick.
That isn't even really how mathematicians do math.
Usually the intuition leads to the formalism.
People were working with the natural numbers for thousands of years before we decided to nail it down with ZFC.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392911</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392769</id>
	<title>Several Proxies</title>
	<author>eldavojohn</author>
	<datestamp>1245438420000</datestamp>
	<modclass>Informativ</modclass>
	<modscore>5</modscore>
	<htmltext>

I couldn't get this PDF from the frontpage link so via <a href="http://scholar.google.com/scholar?hl=en&amp;lr=&amp;cluster=10492339539540996751&amp;um=1&amp;ie=UTF-8&amp;ei=sM87SvOUG4u6M56cwLEO&amp;sa=X&amp;oi=science\_links&amp;resnum=1&amp;ct=sl-allversions" title="google.com" rel="nofollow">Google Scholar</a> [google.com], here's some help:


<ul>
<li>
The original source linked <a href="http://66.102.1.104/scholar?hl=en&amp;lr=&amp;q=cache:j3IgbThHnJEJ:www.maa.org/devlin/LockhartsLament.pdf+" title="66.102.1.104" rel="nofollow">PDF turned HTML by Google Scholar</a> [66.102.1.104] (actually does a fine job!)
</li><li>
<a href="http://plato.asu.edu/LockhartsLament.pdf" title="asu.edu" rel="nofollow">A Mathematician's Lament</a> [asu.edu]
</li><li>
<a href="http://finkelitis.googlepages.com/LockhartsLament.pdf" title="googlepages.com" rel="nofollow">A Mathematician's Lament</a> [googlepages.com]
</li><li>
<a href="http://www.mathteacherctk.com/blog/wp-content/uploads/2008/03/lockhartslament.pdf" title="mathteacherctk.com" rel="nofollow">A Mathematician's Lament</a> [mathteacherctk.com]
</li><li>
<a href="http://www.geocities.com/Athens/Delphi/5136/LockhartsLament.pdf" title="geocities.com" rel="nofollow">A Mathematician's Lament</a> [geocities.com]
</li><li>
<a href="http://radian.org/~krstic/LockhartsLament.pdf" title="radian.org" rel="nofollow">A Mathematician's Lament</a> [radian.org]
</li></ul><p>

From what I can tell, they all look to be the same length and size and hopefully are not older revisions of this paper.</p></htmltext>
<tokenext>I could n't get this PDF from the frontpage link so via Google Scholar [ google.com ] , here 's some help : The original source linked PDF turned HTML by Google Scholar [ 66.102.1.104 ] ( actually does a fine job !
) A Mathematician 's Lament [ asu.edu ] A Mathematician 's Lament [ googlepages.com ] A Mathematician 's Lament [ mathteacherctk.com ] A Mathematician 's Lament [ geocities.com ] A Mathematician 's Lament [ radian.org ] From what I can tell , they all look to be the same length and size and hopefully are not older revisions of this paper .</tokentext>
<sentencetext>

I couldn't get this PDF from the frontpage link so via Google Scholar [google.com], here's some help:




The original source linked PDF turned HTML by Google Scholar [66.102.1.104] (actually does a fine job!
)

A Mathematician's Lament [asu.edu]

A Mathematician's Lament [googlepages.com]

A Mathematician's Lament [mathteacherctk.com]

A Mathematician's Lament [geocities.com]

A Mathematician's Lament [radian.org]


From what I can tell, they all look to be the same length and size and hopefully are not older revisions of this paper.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393275</id>
	<title>Two mathematicians</title>
	<author>Conspiracy\_Of\_Doves</author>
	<datestamp>1245440340000</datestamp>
	<modclass>Funny</modclass>
	<modscore>4</modscore>
	<htmltext><p>Two mathematics professors are having lunch at a restaurant. The first mathematician keeps complaining about how ignorant the typical American is and how he's suprised that the average person in this country has enough mathematical prowess to balance a checkbook.</p><p>The second mathematician says, "Don't you think you're being a little harsh? The average person surely has more mathematical ability than you give them credit for."</p><p>The first mathematician responds, "Absolutely not! I'm sure if you asked the first person you met on the street to solve a basic algebra problem, they would have no idea where to start."</p><p>The second mathematician says, "Okay, I'll make a bet with you. At the end of the meal, I'll ask our waitress to solve a calculus problem. If she can solve it, you pay for lunch. If she can't, I'll pay."</p><p>"Thanks in advance for lunch!" the first mathematician says confidently.</p><p>Later, while the first mathematician is in the bathroom, the second mathematician flags the waitress down and says, "Listen, when you bring us our check I'm going to ask you a math question. I want you to answer, &#226;one-half x-squared.' Can you remember that? If you do, I'll leave an extra big tip." He encourages her to write it down phonetically and practice it so that it seems natural.</p><p>At the end of the meal, after the waitress puts the bill on the table, the second mathematician says, "Oh, could you answer a little question for me? What's the integral of x with respect to x?"</p><p>The waitress looks unsure at first, but says, "One-half x-squared."</p><p>With a grin, the second mathematician slides the bill over to the first mathematician.</p><p>As the waitress is walking away, she turns back and says over her shoulder "plus a constant!"</p></htmltext>
<tokenext>Two mathematics professors are having lunch at a restaurant .
The first mathematician keeps complaining about how ignorant the typical American is and how he 's suprised that the average person in this country has enough mathematical prowess to balance a checkbook.The second mathematician says , " Do n't you think you 're being a little harsh ?
The average person surely has more mathematical ability than you give them credit for .
" The first mathematician responds , " Absolutely not !
I 'm sure if you asked the first person you met on the street to solve a basic algebra problem , they would have no idea where to start .
" The second mathematician says , " Okay , I 'll make a bet with you .
At the end of the meal , I 'll ask our waitress to solve a calculus problem .
If she can solve it , you pay for lunch .
If she ca n't , I 'll pay .
" " Thanks in advance for lunch !
" the first mathematician says confidently.Later , while the first mathematician is in the bathroom , the second mathematician flags the waitress down and says , " Listen , when you bring us our check I 'm going to ask you a math question .
I want you to answer ,   one-half x-squared .
' Can you remember that ?
If you do , I 'll leave an extra big tip .
" He encourages her to write it down phonetically and practice it so that it seems natural.At the end of the meal , after the waitress puts the bill on the table , the second mathematician says , " Oh , could you answer a little question for me ?
What 's the integral of x with respect to x ?
" The waitress looks unsure at first , but says , " One-half x-squared .
" With a grin , the second mathematician slides the bill over to the first mathematician.As the waitress is walking away , she turns back and says over her shoulder " plus a constant !
"</tokentext>
<sentencetext>Two mathematics professors are having lunch at a restaurant.
The first mathematician keeps complaining about how ignorant the typical American is and how he's suprised that the average person in this country has enough mathematical prowess to balance a checkbook.The second mathematician says, "Don't you think you're being a little harsh?
The average person surely has more mathematical ability than you give them credit for.
"The first mathematician responds, "Absolutely not!
I'm sure if you asked the first person you met on the street to solve a basic algebra problem, they would have no idea where to start.
"The second mathematician says, "Okay, I'll make a bet with you.
At the end of the meal, I'll ask our waitress to solve a calculus problem.
If she can solve it, you pay for lunch.
If she can't, I'll pay.
""Thanks in advance for lunch!
" the first mathematician says confidently.Later, while the first mathematician is in the bathroom, the second mathematician flags the waitress down and says, "Listen, when you bring us our check I'm going to ask you a math question.
I want you to answer, âone-half x-squared.
' Can you remember that?
If you do, I'll leave an extra big tip.
" He encourages her to write it down phonetically and practice it so that it seems natural.At the end of the meal, after the waitress puts the bill on the table, the second mathematician says, "Oh, could you answer a little question for me?
What's the integral of x with respect to x?
"The waitress looks unsure at first, but says, "One-half x-squared.
"With a grin, the second mathematician slides the bill over to the first mathematician.As the waitress is walking away, she turns back and says over her shoulder "plus a constant!
"</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393397</id>
	<title>Re:The way math is structured is disconnected from</title>
	<author>mario\_grgic</author>
	<datestamp>1245440760000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>You are not truly a mathematician until you learn to abstract. Symbols are ultimate abstractions. Yes, you can invent your own symbols, but you will still have symbols.</p><p>Think about how children learn to count. They first count concrete objects, one finger, two fingers,<nobr> <wbr></nobr>... one apple, two apples, etc. and then we abstract. Remove the object being counted and just have one, two. This is where the big abstraction happens. We arrive to the concept of oneness, without thinking about 1 something. Now add symbols for those abstractions 1, 2 and now you can do some neat things with symbols that translate into concrete objects when applied. This is the essence of math.</p><p>Yes, symbolism introduced is standardized so that we can talk to each other and exchange ideas. Otherwise, it would take a lot of time for you to explain all your symbols to me before we could have any meaningful conversation.</p></htmltext>
<tokenext>You are not truly a mathematician until you learn to abstract .
Symbols are ultimate abstractions .
Yes , you can invent your own symbols , but you will still have symbols.Think about how children learn to count .
They first count concrete objects , one finger , two fingers , ... one apple , two apples , etc .
and then we abstract .
Remove the object being counted and just have one , two .
This is where the big abstraction happens .
We arrive to the concept of oneness , without thinking about 1 something .
Now add symbols for those abstractions 1 , 2 and now you can do some neat things with symbols that translate into concrete objects when applied .
This is the essence of math.Yes , symbolism introduced is standardized so that we can talk to each other and exchange ideas .
Otherwise , it would take a lot of time for you to explain all your symbols to me before we could have any meaningful conversation .</tokentext>
<sentencetext>You are not truly a mathematician until you learn to abstract.
Symbols are ultimate abstractions.
Yes, you can invent your own symbols, but you will still have symbols.Think about how children learn to count.
They first count concrete objects, one finger, two fingers, ... one apple, two apples, etc.
and then we abstract.
Remove the object being counted and just have one, two.
This is where the big abstraction happens.
We arrive to the concept of oneness, without thinking about 1 something.
Now add symbols for those abstractions 1, 2 and now you can do some neat things with symbols that translate into concrete objects when applied.
This is the essence of math.Yes, symbolism introduced is standardized so that we can talk to each other and exchange ideas.
Otherwise, it would take a lot of time for you to explain all your symbols to me before we could have any meaningful conversation.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392921</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392981</id>
	<title>Hmm</title>
	<author>Anonymous</author>
	<datestamp>1245439320000</datestamp>
	<modclass>Funny</modclass>
	<modscore>4</modscore>
	<htmltext><p><div class="quote"><p>I implore you to read his essay with every atom of my being.</p></div><p>Well, OK, seeing as I can use *your* atoms.</p></div>
	</htmltext>
<tokenext>I implore you to read his essay with every atom of my being.Well , OK , seeing as I can use * your * atoms .</tokentext>
<sentencetext>I implore you to read his essay with every atom of my being.Well, OK, seeing as I can use *your* atoms.
	</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394561</id>
	<title>Re:The way math is structured is disconnected from</title>
	<author>Anonymous</author>
	<datestamp>1245444840000</datestamp>
	<modclass>Interestin</modclass>
	<modscore>1</modscore>
	<htmltext><p>People, people, people.  If there's one thing outsourcing has taught us in the United States is that we don't have to invest in educating our children.   We can always recruit the "best and the brightest" from around the world.   They want to come to this country, right?  Let the other countries do the heavy lifting and we'll all get jobs waiting tables using government paid health care.  Listen to corporate America.  Don't raise taxes on the idle rich, er, most productive segment of our country just to educate our children.  We have foreign cars to buy.  Professional sports stadiums to build (someone say something about bread and circuses?).</p><p>The sad part about being outclassed by other countries isn't that we can't afford to educate our children, it's that we simply refuse to do it.   The culture in the U.S.A. simply doesn't value education or it's children anymore.</p></htmltext>
<tokenext>People , people , people .
If there 's one thing outsourcing has taught us in the United States is that we do n't have to invest in educating our children .
We can always recruit the " best and the brightest " from around the world .
They want to come to this country , right ?
Let the other countries do the heavy lifting and we 'll all get jobs waiting tables using government paid health care .
Listen to corporate America .
Do n't raise taxes on the idle rich , er , most productive segment of our country just to educate our children .
We have foreign cars to buy .
Professional sports stadiums to build ( someone say something about bread and circuses ?
) .The sad part about being outclassed by other countries is n't that we ca n't afford to educate our children , it 's that we simply refuse to do it .
The culture in the U.S.A. simply does n't value education or it 's children anymore .</tokentext>
<sentencetext>People, people, people.
If there's one thing outsourcing has taught us in the United States is that we don't have to invest in educating our children.
We can always recruit the "best and the brightest" from around the world.
They want to come to this country, right?
Let the other countries do the heavy lifting and we'll all get jobs waiting tables using government paid health care.
Listen to corporate America.
Don't raise taxes on the idle rich, er, most productive segment of our country just to educate our children.
We have foreign cars to buy.
Professional sports stadiums to build (someone say something about bread and circuses?
).The sad part about being outclassed by other countries isn't that we can't afford to educate our children, it's that we simply refuse to do it.
The culture in the U.S.A. simply doesn't value education or it's children anymore.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393115</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394641</id>
	<title>Re:US School System compared to Europes School Sys</title>
	<author>Skadet</author>
	<datestamp>1245445080000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>I lol because you're making the same type of generalization that you're looking down your nose upon.</htmltext>
<tokenext>I lol because you 're making the same type of generalization that you 're looking down your nose upon .</tokentext>
<sentencetext>I lol because you're making the same type of generalization that you're looking down your nose upon.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393241</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393543</id>
	<title>Re:it's really bad</title>
	<author>Anonymous</author>
	<datestamp>1245441300000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>For the mathematically uninclined such as myself, would someone care to explain what proofs are?</p><p>I'm led to believe that it's the equivalent of "show your work". A lot of kids - damn, most kids - hate "showing their work". I think this largely has to do with the fact that math seems to be taught as the means to an end, when its really an exercise in logic.</p><p>Also, do proofs have to be heavy in the details, or can they be light? For instance, if you had 10 x 20 as a problem, many of us remember the trick we were taught when multiplying numbers with zeroes at the end: set aside the zeroes, multiply the remaining integers, and then append all of the zeroes to the end. (So 10 x 20 would be 1 x 2 = 2, and then append the two zeroes at the end for 200.) So, in the case of proofs, would simply using such a trick be acceptable, or would you have to write out the whole process (carrying numbers if need be, etc.)?</p><p>Largely I'm interested in knowing what they are so I can understand what the hell Rodney McKay was making such a big deal about. d:</p></htmltext>
<tokenext>For the mathematically uninclined such as myself , would someone care to explain what proofs are ? I 'm led to believe that it 's the equivalent of " show your work " .
A lot of kids - damn , most kids - hate " showing their work " .
I think this largely has to do with the fact that math seems to be taught as the means to an end , when its really an exercise in logic.Also , do proofs have to be heavy in the details , or can they be light ?
For instance , if you had 10 x 20 as a problem , many of us remember the trick we were taught when multiplying numbers with zeroes at the end : set aside the zeroes , multiply the remaining integers , and then append all of the zeroes to the end .
( So 10 x 20 would be 1 x 2 = 2 , and then append the two zeroes at the end for 200 .
) So , in the case of proofs , would simply using such a trick be acceptable , or would you have to write out the whole process ( carrying numbers if need be , etc .
) ? Largely I 'm interested in knowing what they are so I can understand what the hell Rodney McKay was making such a big deal about .
d :</tokentext>
<sentencetext>For the mathematically uninclined such as myself, would someone care to explain what proofs are?I'm led to believe that it's the equivalent of "show your work".
A lot of kids - damn, most kids - hate "showing their work".
I think this largely has to do with the fact that math seems to be taught as the means to an end, when its really an exercise in logic.Also, do proofs have to be heavy in the details, or can they be light?
For instance, if you had 10 x 20 as a problem, many of us remember the trick we were taught when multiplying numbers with zeroes at the end: set aside the zeroes, multiply the remaining integers, and then append all of the zeroes to the end.
(So 10 x 20 would be 1 x 2 = 2, and then append the two zeroes at the end for 200.
) So, in the case of proofs, would simply using such a trick be acceptable, or would you have to write out the whole process (carrying numbers if need be, etc.
)?Largely I'm interested in knowing what they are so I can understand what the hell Rodney McKay was making such a big deal about.
d:</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392911</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28405797</id>
	<title>Re:You can convince me</title>
	<author>Anonymous</author>
	<datestamp>1245502680000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>I don't think he is saying that math is only for the elite, but just the opposite. He makes several arguments against using cumbersome formal terminology and symbols.</p></htmltext>
<tokenext>I do n't think he is saying that math is only for the elite , but just the opposite .
He makes several arguments against using cumbersome formal terminology and symbols .</tokentext>
<sentencetext>I don't think he is saying that math is only for the elite, but just the opposite.
He makes several arguments against using cumbersome formal terminology and symbols.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393159</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28397471</id>
	<title>Re:True story ....</title>
	<author>Deadstick</author>
	<datestamp>1245415380000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>Did you challenge the crackpo^H^H^Hfacilitator to produce a set of scores that would NOT come up with 100?</p><p>rj</p></htmltext>
<tokenext>Did you challenge the crackpo ^ H ^ H ^ Hfacilitator to produce a set of scores that would NOT come up with 100 ? rj</tokentext>
<sentencetext>Did you challenge the crackpo^H^H^Hfacilitator to produce a set of scores that would NOT come up with 100?rj</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394633</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393233</id>
	<title>Re:US K-12 MATH = Real world fail.</title>
	<author>DragonWriter</author>
	<datestamp>1245440220000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><blockquote><div><p>And a 24 year long high school teacher didn't know what the sign for factorial means. Choices where along the lines of : ! &amp; \%</p></div></blockquote><p>&lt;pedantic&gt;<br>Well, from those choices, I would know that "!" was probably intended, but that's as much skill at dealing with improperly-posed questions as anything else.</p><p>In fact, though, none of the options are correct as you have related the question: what the sign for factorial means is "factorial", just as a stop sign (or "sign for stop") means "stop", not "red octagon with a white border".<br>&lt;/pedantic&gt;</p></div>
	</htmltext>
<tokenext>And a 24 year long high school teacher did n't know what the sign for factorial means .
Choices where along the lines of : !
&amp; \ % Well , from those choices , I would know that " !
" was probably intended , but that 's as much skill at dealing with improperly-posed questions as anything else.In fact , though , none of the options are correct as you have related the question : what the sign for factorial means is " factorial " , just as a stop sign ( or " sign for stop " ) means " stop " , not " red octagon with a white border " .</tokentext>
<sentencetext>And a 24 year long high school teacher didn't know what the sign for factorial means.
Choices where along the lines of : !
&amp; \%Well, from those choices, I would know that "!
" was probably intended, but that's as much skill at dealing with improperly-posed questions as anything else.In fact, though, none of the options are correct as you have related the question: what the sign for factorial means is "factorial", just as a stop sign (or "sign for stop") means "stop", not "red octagon with a white border".
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392991</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393305</id>
	<title>Half Steps</title>
	<author>sampson7</author>
	<datestamp>1245440400000</datestamp>
	<modclass>Insightful</modclass>
	<modscore>3</modscore>
	<htmltext>This man is a beautiful dreamer.  I don't think his rather Platonic vision of the perfect math class will ever be acheivable.  But there are a bunch of half steps that I think would really help math and address his fundamental point that math, as it's currently taught, is boring as all heck and does nothing for the vast majority of us who don't use calculus or even algebra in our day-to-day lives.  I mean really, the last time I did anything more than basic algebra was tutoring others!  And while learning math so that you can help someone elses' kids study for a test is a fine goal, I'm not sure it's really worth the thousands of hours I spent taking math!<br> <br>
First, *use* math to solve real problems and explain real scientific principles.  Radio Lab (THE official National Public Radio show for geeks everywhere) had a great little episode where some student "discovers" that the periodicity of a pendulum forms a parabola when charted on a graph.  Wow!  That's heady stuff.  (It's the first story of <a href="http://www.wnyc.org/shows/radiolab/episodes/2008/12/12" title="wnyc.org">this episode</a> [wnyc.org].)  Understanding the interaction of science and math -- the universe, really -- is something that we can teach.  Integration of math and science gets us part of the way there.<br> <br>Second, incorporate the history of math into math class.  Math advances all occur because of some historical context.  Combining the two is a half-step that will get students to understand "why" we created this math, even if they never quite get the quadratic formula down.  Combine these two principles, and it would go a long way.</htmltext>
<tokenext>This man is a beautiful dreamer .
I do n't think his rather Platonic vision of the perfect math class will ever be acheivable .
But there are a bunch of half steps that I think would really help math and address his fundamental point that math , as it 's currently taught , is boring as all heck and does nothing for the vast majority of us who do n't use calculus or even algebra in our day-to-day lives .
I mean really , the last time I did anything more than basic algebra was tutoring others !
And while learning math so that you can help someone elses ' kids study for a test is a fine goal , I 'm not sure it 's really worth the thousands of hours I spent taking math !
First , * use * math to solve real problems and explain real scientific principles .
Radio Lab ( THE official National Public Radio show for geeks everywhere ) had a great little episode where some student " discovers " that the periodicity of a pendulum forms a parabola when charted on a graph .
Wow ! That 's heady stuff .
( It 's the first story of this episode [ wnyc.org ] .
) Understanding the interaction of science and math -- the universe , really -- is something that we can teach .
Integration of math and science gets us part of the way there .
Second , incorporate the history of math into math class .
Math advances all occur because of some historical context .
Combining the two is a half-step that will get students to understand " why " we created this math , even if they never quite get the quadratic formula down .
Combine these two principles , and it would go a long way .</tokentext>
<sentencetext>This man is a beautiful dreamer.
I don't think his rather Platonic vision of the perfect math class will ever be acheivable.
But there are a bunch of half steps that I think would really help math and address his fundamental point that math, as it's currently taught, is boring as all heck and does nothing for the vast majority of us who don't use calculus or even algebra in our day-to-day lives.
I mean really, the last time I did anything more than basic algebra was tutoring others!
And while learning math so that you can help someone elses' kids study for a test is a fine goal, I'm not sure it's really worth the thousands of hours I spent taking math!
First, *use* math to solve real problems and explain real scientific principles.
Radio Lab (THE official National Public Radio show for geeks everywhere) had a great little episode where some student "discovers" that the periodicity of a pendulum forms a parabola when charted on a graph.
Wow!  That's heady stuff.
(It's the first story of this episode [wnyc.org].
)  Understanding the interaction of science and math -- the universe, really -- is something that we can teach.
Integration of math and science gets us part of the way there.
Second, incorporate the history of math into math class.
Math advances all occur because of some historical context.
Combining the two is a half-step that will get students to understand "why" we created this math, even if they never quite get the quadratic formula down.
Combine these two principles, and it would go a long way.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28395847</id>
	<title>Re:The way math is structured is disconnected from</title>
	<author>exploder</author>
	<datestamp>1245406320000</datestamp>
	<modclass>Flamebait</modclass>
	<modscore>0</modscore>
	<htmltext><p>Do you hold any degree in mathematics, i.e. are you qualified to make the criticisms in your post?  Or are you a crank?</p></htmltext>
<tokenext>Do you hold any degree in mathematics , i.e .
are you qualified to make the criticisms in your post ?
Or are you a crank ?</tokentext>
<sentencetext>Do you hold any degree in mathematics, i.e.
are you qualified to make the criticisms in your post?
Or are you a crank?</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392921</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28404339</id>
	<title>You missed the point</title>
	<author>trveler</author>
	<datestamp>1245492720000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>The author doesn't claim that the point is to get everyone to love it. The author claims that the point is to get everyone to realize what mathematics really is.<br>
From TFA:
<br>
SALVIATI: If everyone were exposed to mathematics in its natural state, with all
the challenging fun and surprises that that entails, I think we would
see a dramatic change both in the attitude of students toward
mathematics, and in our conception of what it means to be "good at
math."  We are losing so many potentially gifted mathematicians --
creative, intelligent people who rightly reject what appears to be a
meaningless and sterile subject.  They are simply too smart to waste
their time on such piffle.
<br>
SIMPLICIO: But don't you think that if math class were made more like art class
that a lot of kids just wouldn't learn anything?
<br>
SALVIATI: They're not learning anything now!  Better to not have math classes at
all than to do what is currently being done.  At least some people
might have a chance to discover something beautiful on their own.
<br>
SIMPLICIO: So you would remove mathematics from the school curriculum?
<br>
SALVIATI: The mathematics has already been removed!  The only question is
what to do with the vapid, hollow shell that remains.  Of course I
would prefer to replace it with an active and joyful engagement with
mathematical ideas.</htmltext>
<tokenext>The author does n't claim that the point is to get everyone to love it .
The author claims that the point is to get everyone to realize what mathematics really is .
From TFA : SALVIATI : If everyone were exposed to mathematics in its natural state , with all the challenging fun and surprises that that entails , I think we would see a dramatic change both in the attitude of students toward mathematics , and in our conception of what it means to be " good at math .
" We are losing so many potentially gifted mathematicians -- creative , intelligent people who rightly reject what appears to be a meaningless and sterile subject .
They are simply too smart to waste their time on such piffle .
SIMPLICIO : But do n't you think that if math class were made more like art class that a lot of kids just would n't learn anything ?
SALVIATI : They 're not learning anything now !
Better to not have math classes at all than to do what is currently being done .
At least some people might have a chance to discover something beautiful on their own .
SIMPLICIO : So you would remove mathematics from the school curriculum ?
SALVIATI : The mathematics has already been removed !
The only question is what to do with the vapid , hollow shell that remains .
Of course I would prefer to replace it with an active and joyful engagement with mathematical ideas .</tokentext>
<sentencetext>The author doesn't claim that the point is to get everyone to love it.
The author claims that the point is to get everyone to realize what mathematics really is.
From TFA:

SALVIATI: If everyone were exposed to mathematics in its natural state, with all
the challenging fun and surprises that that entails, I think we would
see a dramatic change both in the attitude of students toward
mathematics, and in our conception of what it means to be "good at
math.
"  We are losing so many potentially gifted mathematicians --
creative, intelligent people who rightly reject what appears to be a
meaningless and sterile subject.
They are simply too smart to waste
their time on such piffle.
SIMPLICIO: But don't you think that if math class were made more like art class
that a lot of kids just wouldn't learn anything?
SALVIATI: They're not learning anything now!
Better to not have math classes at
all than to do what is currently being done.
At least some people
might have a chance to discover something beautiful on their own.
SIMPLICIO: So you would remove mathematics from the school curriculum?
SALVIATI: The mathematics has already been removed!
The only question is
what to do with the vapid, hollow shell that remains.
Of course I
would prefer to replace it with an active and joyful engagement with
mathematical ideas.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394309</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28403825</id>
	<title>Re:In defense of notation</title>
	<author>$pace6host</author>
	<datestamp>1245530640000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>What I took away from Lockhart's essay was that the concept is more important than the notation - not that the notation isn't valuable at all, just that it isn't necessary for simple problems, and by sharing the joy of the simple problems, you can get students to think. Learning the notation can come along a little later when you need it's compactness. Forcing the notation and letting the students experience little or none of the joy associated with the insights behind solving the problems is what he is was decrying. I think it's true, though, that there are some students that are intrigued by the symbolic language, and get drawn in that way - we are all individuals! (except me)</htmltext>
<tokenext>What I took away from Lockhart 's essay was that the concept is more important than the notation - not that the notation is n't valuable at all , just that it is n't necessary for simple problems , and by sharing the joy of the simple problems , you can get students to think .
Learning the notation can come along a little later when you need it 's compactness .
Forcing the notation and letting the students experience little or none of the joy associated with the insights behind solving the problems is what he is was decrying .
I think it 's true , though , that there are some students that are intrigued by the symbolic language , and get drawn in that way - we are all individuals !
( except me )</tokentext>
<sentencetext>What I took away from Lockhart's essay was that the concept is more important than the notation - not that the notation isn't valuable at all, just that it isn't necessary for simple problems, and by sharing the joy of the simple problems, you can get students to think.
Learning the notation can come along a little later when you need it's compactness.
Forcing the notation and letting the students experience little or none of the joy associated with the insights behind solving the problems is what he is was decrying.
I think it's true, though, that there are some students that are intrigued by the symbolic language, and get drawn in that way - we are all individuals!
(except me)</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28395275</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28396569</id>
	<title>Re:US School System compared to Europes School Sys</title>
	<author>Anonymous</author>
	<datestamp>1245409800000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>Sounds like *YOU* were the "lowest common denominator" or you might've been in a higher level class.  There's no limit to what math you can take in school here.  AP and honors classes are common and many students take college courses for high school credit.  Hell, I studied group theory (just a rough overview really, but still) in the 5th grade.  More recently, I took a graduate university course on non-linear dynamical systems (aka "chaos theory") with a high school student.</p><p>Success in American academics is achieved the same as everything else here: work hard at it and the sky is the limit but you can always just "get by".</p></htmltext>
<tokenext>Sounds like * YOU * were the " lowest common denominator " or you might 've been in a higher level class .
There 's no limit to what math you can take in school here .
AP and honors classes are common and many students take college courses for high school credit .
Hell , I studied group theory ( just a rough overview really , but still ) in the 5th grade .
More recently , I took a graduate university course on non-linear dynamical systems ( aka " chaos theory " ) with a high school student.Success in American academics is achieved the same as everything else here : work hard at it and the sky is the limit but you can always just " get by " .</tokentext>
<sentencetext>Sounds like *YOU* were the "lowest common denominator" or you might've been in a higher level class.
There's no limit to what math you can take in school here.
AP and honors classes are common and many students take college courses for high school credit.
Hell, I studied group theory (just a rough overview really, but still) in the 5th grade.
More recently, I took a graduate university course on non-linear dynamical systems (aka "chaos theory") with a high school student.Success in American academics is achieved the same as everything else here: work hard at it and the sky is the limit but you can always just "get by".</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393035</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28397969</id>
	<title>Re:Cue the other subjects</title>
	<author>deander2</author>
	<datestamp>1245419460000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>of course, people often forget *why* the war started 30-40 years ago:  forced desegregation</p></htmltext>
<tokenext>of course , people often forget * why * the war started 30-40 years ago : forced desegregation</tokentext>
<sentencetext>of course, people often forget *why* the war started 30-40 years ago:  forced desegregation</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393083</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28405259</id>
	<title>Re:Oh give it a rest</title>
	<author>ChaosDiscord</author>
	<datestamp>1245499560000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>Original author: The current curriculum sucks and standardized testing sucks.  We should replace them with something better.

</p><p>You: But we need to teach the curriculum, and we need to pass the standardized tests!

</p><p>That's not a counter argument.  That's a sad affirmation of what he's saying.

</p><p>He has realistic and implementable ideas.  While he paints in broad strokes, that's an appropriate level for an essay of that length.  In short: teach math like you teach english, or art.  Sure, teach some basics, but rote memorization is usually counterproductive.  Instead hand the child some tools and an unsolved problem and ask them to solve it.  An art teacher puts a chair at the front of the class and asks the kids to draw it.  Yeah, they'll suck, but they'll learn.  When he provides suggestions for improvements, it's grounded in their own experimentation.  An english teacher says, "Read this book, then write an essay on the themes."  The english teacher (hopefully) doesn't just say, "The themes of this this chapter are X, Y, and Z," but instead asks the class, "What are the themes?  You think X?  Okay, what in the chapter says X to you?  Sure, that makes sense.  What about when the main character did A?  Did that support the theme X?"  <em>Ask the children to think and reason, not just apply cryptic rules in a sad implementation of the Chinese Room.</em></p></htmltext>
<tokenext>Original author : The current curriculum sucks and standardized testing sucks .
We should replace them with something better .
You : But we need to teach the curriculum , and we need to pass the standardized tests !
That 's not a counter argument .
That 's a sad affirmation of what he 's saying .
He has realistic and implementable ideas .
While he paints in broad strokes , that 's an appropriate level for an essay of that length .
In short : teach math like you teach english , or art .
Sure , teach some basics , but rote memorization is usually counterproductive .
Instead hand the child some tools and an unsolved problem and ask them to solve it .
An art teacher puts a chair at the front of the class and asks the kids to draw it .
Yeah , they 'll suck , but they 'll learn .
When he provides suggestions for improvements , it 's grounded in their own experimentation .
An english teacher says , " Read this book , then write an essay on the themes .
" The english teacher ( hopefully ) does n't just say , " The themes of this this chapter are X , Y , and Z , " but instead asks the class , " What are the themes ?
You think X ?
Okay , what in the chapter says X to you ?
Sure , that makes sense .
What about when the main character did A ?
Did that support the theme X ?
" Ask the children to think and reason , not just apply cryptic rules in a sad implementation of the Chinese Room .</tokentext>
<sentencetext>Original author: The current curriculum sucks and standardized testing sucks.
We should replace them with something better.
You: But we need to teach the curriculum, and we need to pass the standardized tests!
That's not a counter argument.
That's a sad affirmation of what he's saying.
He has realistic and implementable ideas.
While he paints in broad strokes, that's an appropriate level for an essay of that length.
In short: teach math like you teach english, or art.
Sure, teach some basics, but rote memorization is usually counterproductive.
Instead hand the child some tools and an unsolved problem and ask them to solve it.
An art teacher puts a chair at the front of the class and asks the kids to draw it.
Yeah, they'll suck, but they'll learn.
When he provides suggestions for improvements, it's grounded in their own experimentation.
An english teacher says, "Read this book, then write an essay on the themes.
"  The english teacher (hopefully) doesn't just say, "The themes of this this chapter are X, Y, and Z," but instead asks the class, "What are the themes?
You think X?
Okay, what in the chapter says X to you?
Sure, that makes sense.
What about when the main character did A?
Did that support the theme X?
"  Ask the children to think and reason, not just apply cryptic rules in a sad implementation of the Chinese Room.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392993</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393895</id>
	<title>Re:I Sympathize With Him But Too Idyllic</title>
	<author>EEBaum</author>
	<datestamp>1245442560000</datestamp>
	<modclass>Interestin</modclass>
	<modscore>2</modscore>
	<htmltext><i>The public school system is more worried about getting someone that actualy cares about the students at all. </i> <br>
<br>
Now who's being the idealist?  The public school system rarely has such concerns, or they wouldn't do everything possible to scare away the best teachers, and even moderately good ones.  Standardized testing, nonsensical state mandates, psychotic district administrators, requirements to use ghastly textbooks, etc.  So many headaches are thrust upon our public teachers that have nothing to do with teaching, that it's a wonder anyone sticks with it.  I've known people who would have been excellent teachers (including one who was the "perfect" math teacher you speak of) who were scared off by the horrors of the system and ended up pursuing other fields.<br>
<br>
The last thing our system is geared toward is finding good teachers, or ones who care about the students.  It's geared toward finding teachers who are willing to put up with all the crap that our public school system shovels their way.  Some do it because they love teaching or care about the students and will put up with the suffering.  Some do it because the job offers an awesome 3 months off per year.  Some do it because they were able to get tenure and love the job security.  Some do it because that's the career path they started in and they don't want to make a change.</htmltext>
<tokenext>The public school system is more worried about getting someone that actualy cares about the students at all .
Now who 's being the idealist ?
The public school system rarely has such concerns , or they would n't do everything possible to scare away the best teachers , and even moderately good ones .
Standardized testing , nonsensical state mandates , psychotic district administrators , requirements to use ghastly textbooks , etc .
So many headaches are thrust upon our public teachers that have nothing to do with teaching , that it 's a wonder anyone sticks with it .
I 've known people who would have been excellent teachers ( including one who was the " perfect " math teacher you speak of ) who were scared off by the horrors of the system and ended up pursuing other fields .
The last thing our system is geared toward is finding good teachers , or ones who care about the students .
It 's geared toward finding teachers who are willing to put up with all the crap that our public school system shovels their way .
Some do it because they love teaching or care about the students and will put up with the suffering .
Some do it because the job offers an awesome 3 months off per year .
Some do it because they were able to get tenure and love the job security .
Some do it because that 's the career path they started in and they do n't want to make a change .</tokentext>
<sentencetext>The public school system is more worried about getting someone that actualy cares about the students at all.
Now who's being the idealist?
The public school system rarely has such concerns, or they wouldn't do everything possible to scare away the best teachers, and even moderately good ones.
Standardized testing, nonsensical state mandates, psychotic district administrators, requirements to use ghastly textbooks, etc.
So many headaches are thrust upon our public teachers that have nothing to do with teaching, that it's a wonder anyone sticks with it.
I've known people who would have been excellent teachers (including one who was the "perfect" math teacher you speak of) who were scared off by the horrors of the system and ended up pursuing other fields.
The last thing our system is geared toward is finding good teachers, or ones who care about the students.
It's geared toward finding teachers who are willing to put up with all the crap that our public school system shovels their way.
Some do it because they love teaching or care about the students and will put up with the suffering.
Some do it because the job offers an awesome 3 months off per year.
Some do it because they were able to get tenure and love the job security.
Some do it because that's the career path they started in and they don't want to make a change.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392903</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393137</id>
	<title>Re:Cue the other subjects</title>
	<author>Em Emalb</author>
	<datestamp>1245439860000</datestamp>
	<modclass>Insightful</modclass>
	<modscore>4</modscore>
	<htmltext><p><i>The problems with K-12 education go WAY BEYOND mathematics.</i></p><p>Amen to this.</p><p>I'd say the majority of the issues, though, start at home.</p><p>Too many families are stuck running a two-income home (for a variety of reasons) and simply can't/won't/don't spend the time needed with their children in the formative years.</p><p>A lot of the rest, IMO, can be traced to schools not teaching children how to think critically, just to memorize stuff.</p><p>And that sucks.</p></htmltext>
<tokenext>The problems with K-12 education go WAY BEYOND mathematics.Amen to this.I 'd say the majority of the issues , though , start at home.Too many families are stuck running a two-income home ( for a variety of reasons ) and simply ca n't/wo n't/do n't spend the time needed with their children in the formative years.A lot of the rest , IMO , can be traced to schools not teaching children how to think critically , just to memorize stuff.And that sucks .</tokentext>
<sentencetext>The problems with K-12 education go WAY BEYOND mathematics.Amen to this.I'd say the majority of the issues, though, start at home.Too many families are stuck running a two-income home (for a variety of reasons) and simply can't/won't/don't spend the time needed with their children in the formative years.A lot of the rest, IMO, can be traced to schools not teaching children how to think critically, just to memorize stuff.And that sucks.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392889</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28396245</id>
	<title>Re:Cue the other subjects</title>
	<author>Belial6</author>
	<datestamp>1245408180000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>I have to disagree.  Maybe you come from a different part of the country than I do (California), but at least here, the fundamentalists have virtually no power, and our schools system is as much of a disgrace as any where.  The problems here are not fundamentalists.  It is that the nanny state realized that if you want to capture the minds of the people, it is best to indoctrinate them when they are young.  What we have is an orphanage state.  From the fact that most children spend more waking hours in the care of the state than their biological 'parents'.  To the fact that an increasing number of children are fed more meals by the state than by their 'parents'.  To the fact that social promotion is the standard.  The list of problems goes on and on.  Most of the end up surrounding the fact that the public education is a sacred cash cow.  Heck, just this week, people were defending my complain that schools who claim to be underfunded in my city can afford to maintain very fancy stadiums and one even has an amusement park style water slide.<br> <br>

Fundamentalist are not even on the radar with the problems here.</htmltext>
<tokenext>I have to disagree .
Maybe you come from a different part of the country than I do ( California ) , but at least here , the fundamentalists have virtually no power , and our schools system is as much of a disgrace as any where .
The problems here are not fundamentalists .
It is that the nanny state realized that if you want to capture the minds of the people , it is best to indoctrinate them when they are young .
What we have is an orphanage state .
From the fact that most children spend more waking hours in the care of the state than their biological 'parents' .
To the fact that an increasing number of children are fed more meals by the state than by their 'parents' .
To the fact that social promotion is the standard .
The list of problems goes on and on .
Most of the end up surrounding the fact that the public education is a sacred cash cow .
Heck , just this week , people were defending my complain that schools who claim to be underfunded in my city can afford to maintain very fancy stadiums and one even has an amusement park style water slide .
Fundamentalist are not even on the radar with the problems here .</tokentext>
<sentencetext>I have to disagree.
Maybe you come from a different part of the country than I do (California), but at least here, the fundamentalists have virtually no power, and our schools system is as much of a disgrace as any where.
The problems here are not fundamentalists.
It is that the nanny state realized that if you want to capture the minds of the people, it is best to indoctrinate them when they are young.
What we have is an orphanage state.
From the fact that most children spend more waking hours in the care of the state than their biological 'parents'.
To the fact that an increasing number of children are fed more meals by the state than by their 'parents'.
To the fact that social promotion is the standard.
The list of problems goes on and on.
Most of the end up surrounding the fact that the public education is a sacred cash cow.
Heck, just this week, people were defending my complain that schools who claim to be underfunded in my city can afford to maintain very fancy stadiums and one even has an amusement park style water slide.
Fundamentalist are not even on the radar with the problems here.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393083</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394633</id>
	<title>Re:True story ....</title>
	<author>EEBaum</author>
	<datestamp>1245445020000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>Ugh, that reminds me of this leadership retreat I went to (in college, mind you).<br>
<br>
We did one of those "rank the 40 things you would bring with you to a desert island" exercises, where you then compare your answers to an expert's.  We did a list on our own, then we did one as a group.<br>
<br>
We then got our group score, and did some seemingly unnecessary math to it, and voila!  The group got a perfect score!  "I don't know how it works, but it always does!  When we work together, we always get a superior score!  Teamwork is Awesome!" announced the retreat facilitator proudly.<br>
<br>
I immediately recognized that, to get the <i>group</i> score out of 100, the math we had just done was...<br>
<br>
score = a + (100 - a)<br>
<br>
So... If 100 = 100, then Teamwork is Awesome!<br>
<br>
Arguing until I was red in the face would not convince the lady that she had drawn a conclusion based on 1=1.  Insistence on "I've been doing this for 15 years, and it's always worked!" led me to believe that I'm the first attendee of that retreat in 15 years who could do math.  I about cried.  I remain highly skeptical about the value of teamwork to this day.</htmltext>
<tokenext>Ugh , that reminds me of this leadership retreat I went to ( in college , mind you ) .
We did one of those " rank the 40 things you would bring with you to a desert island " exercises , where you then compare your answers to an expert 's .
We did a list on our own , then we did one as a group .
We then got our group score , and did some seemingly unnecessary math to it , and voila !
The group got a perfect score !
" I do n't know how it works , but it always does !
When we work together , we always get a superior score !
Teamwork is Awesome !
" announced the retreat facilitator proudly .
I immediately recognized that , to get the group score out of 100 , the math we had just done was.. . score = a + ( 100 - a ) So... If 100 = 100 , then Teamwork is Awesome !
Arguing until I was red in the face would not convince the lady that she had drawn a conclusion based on 1 = 1 .
Insistence on " I 've been doing this for 15 years , and it 's always worked !
" led me to believe that I 'm the first attendee of that retreat in 15 years who could do math .
I about cried .
I remain highly skeptical about the value of teamwork to this day .</tokentext>
<sentencetext>Ugh, that reminds me of this leadership retreat I went to (in college, mind you).
We did one of those "rank the 40 things you would bring with you to a desert island" exercises, where you then compare your answers to an expert's.
We did a list on our own, then we did one as a group.
We then got our group score, and did some seemingly unnecessary math to it, and voila!
The group got a perfect score!
"I don't know how it works, but it always does!
When we work together, we always get a superior score!
Teamwork is Awesome!
" announced the retreat facilitator proudly.
I immediately recognized that, to get the group score out of 100, the math we had just done was...

score = a + (100 - a)

So... If 100 = 100, then Teamwork is Awesome!
Arguing until I was red in the face would not convince the lady that she had drawn a conclusion based on 1=1.
Insistence on "I've been doing this for 15 years, and it's always worked!
" led me to believe that I'm the first attendee of that retreat in 15 years who could do math.
I about cried.
I remain highly skeptical about the value of teamwork to this day.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392947</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393535</id>
	<title>Re:The way math is structured is disconnected from</title>
	<author>maraist</author>
	<datestamp>1245441240000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p><b>The failure of American pupils is probably not due to the way the subject is taught, but rather because they don't feel the pressure to excel like students in other cultures.</b></p><p>Huh?  Getting into college isn't an extremely pressing/taxing/competitive ordeal?</p><p>I'll tell you why US students are degrading in test-worthy performance: Grade-inflation forced down the throats of schools by bitchy parents who can't believe their kid got a C when in prior years they'd gotten an A (most likely due to grade-inflation having to slowly work it's way up and through college).  This does a tremendous disservice to the children, as they are less and less prepared for each successive year, until the overwhelming feeling completely puts them off of any subject that has prerequisites (like math/science).</p></htmltext>
<tokenext>The failure of American pupils is probably not due to the way the subject is taught , but rather because they do n't feel the pressure to excel like students in other cultures.Huh ?
Getting into college is n't an extremely pressing/taxing/competitive ordeal ? I 'll tell you why US students are degrading in test-worthy performance : Grade-inflation forced down the throats of schools by bitchy parents who ca n't believe their kid got a C when in prior years they 'd gotten an A ( most likely due to grade-inflation having to slowly work it 's way up and through college ) .
This does a tremendous disservice to the children , as they are less and less prepared for each successive year , until the overwhelming feeling completely puts them off of any subject that has prerequisites ( like math/science ) .</tokentext>
<sentencetext>The failure of American pupils is probably not due to the way the subject is taught, but rather because they don't feel the pressure to excel like students in other cultures.Huh?
Getting into college isn't an extremely pressing/taxing/competitive ordeal?I'll tell you why US students are degrading in test-worthy performance: Grade-inflation forced down the throats of schools by bitchy parents who can't believe their kid got a C when in prior years they'd gotten an A (most likely due to grade-inflation having to slowly work it's way up and through college).
This does a tremendous disservice to the children, as they are less and less prepared for each successive year, until the overwhelming feeling completely puts them off of any subject that has prerequisites (like math/science).</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393115</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394503</id>
	<title>Re:US School System compared to Europes School Sys</title>
	<author>Anonymous</author>
	<datestamp>1245444660000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p> <i>It is sad, and the state the US educational system is currently in will not allow it to compete in the global market, it will not allow it to be innovate and provide new ideas, but what it will provide is people who are like sheep and are more than willing to follow the crowd and just do it because everyone does. These people will be easy to govern and control since they won't ask questions and least of all will they rebel and fight for their beliefs. In other words, the US education system as it currently stands is making zombies.</i> </p><p>I am sorry to say, but this is very much <a href="http://www.johntaylorgatto.com/chapters/index.htm" title="johntaylorgatto.com">by design.</a> [johntaylorgatto.com]  The system was designed to by the powerful to perpetuate their own interests, not those of children.  It is designed not to teach children how to think, but to prevent them, insofar as possible, from ever doing so, or even realizing that they can.  After all, the easiest way to enslave people is to keep them so ignorant that they don't even realize that they are slaves.  And, sad to say, that is exactly what they have done.  It is probably among the greatest crimes of all of human history.</p></htmltext>
<tokenext>It is sad , and the state the US educational system is currently in will not allow it to compete in the global market , it will not allow it to be innovate and provide new ideas , but what it will provide is people who are like sheep and are more than willing to follow the crowd and just do it because everyone does .
These people will be easy to govern and control since they wo n't ask questions and least of all will they rebel and fight for their beliefs .
In other words , the US education system as it currently stands is making zombies .
I am sorry to say , but this is very much by design .
[ johntaylorgatto.com ] The system was designed to by the powerful to perpetuate their own interests , not those of children .
It is designed not to teach children how to think , but to prevent them , insofar as possible , from ever doing so , or even realizing that they can .
After all , the easiest way to enslave people is to keep them so ignorant that they do n't even realize that they are slaves .
And , sad to say , that is exactly what they have done .
It is probably among the greatest crimes of all of human history .</tokentext>
<sentencetext> It is sad, and the state the US educational system is currently in will not allow it to compete in the global market, it will not allow it to be innovate and provide new ideas, but what it will provide is people who are like sheep and are more than willing to follow the crowd and just do it because everyone does.
These people will be easy to govern and control since they won't ask questions and least of all will they rebel and fight for their beliefs.
In other words, the US education system as it currently stands is making zombies.
I am sorry to say, but this is very much by design.
[johntaylorgatto.com]  The system was designed to by the powerful to perpetuate their own interests, not those of children.
It is designed not to teach children how to think, but to prevent them, insofar as possible, from ever doing so, or even realizing that they can.
After all, the easiest way to enslave people is to keep them so ignorant that they don't even realize that they are slaves.
And, sad to say, that is exactly what they have done.
It is probably among the greatest crimes of all of human history.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393035</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28425681</id>
	<title>Re:Cue the other subjects</title>
	<author>Anonymous</author>
	<datestamp>1245697440000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>I don't know what other peoples reasons for doing so are, but I won't be involved in a single parent family for precisely the reasons this article discusses. I am a female and also a scientist and refuse to give up my career or love of learning because of my gender. Two-income homes are not the problem. Both parents are entitled to career satisfaction, should they desire it.</p></htmltext>
<tokenext>I do n't know what other peoples reasons for doing so are , but I wo n't be involved in a single parent family for precisely the reasons this article discusses .
I am a female and also a scientist and refuse to give up my career or love of learning because of my gender .
Two-income homes are not the problem .
Both parents are entitled to career satisfaction , should they desire it .</tokentext>
<sentencetext>I don't know what other peoples reasons for doing so are, but I won't be involved in a single parent family for precisely the reasons this article discusses.
I am a female and also a scientist and refuse to give up my career or love of learning because of my gender.
Two-income homes are not the problem.
Both parents are entitled to career satisfaction, should they desire it.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393137</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28397109</id>
	<title>Re:Cue the other subjects</title>
	<author>uncqual</author>
	<datestamp>1245412500000</datestamp>
	<modclass>Insightful</modclass>
	<modscore>2</modscore>
	<htmltext>Agreed...
<br> <br>
However, I think it's unfair to specifically single out these groups without including what seems to me to be a "lax" attitude by parents (including college educated parents) in middle-class homes where the kid's great-grandparents (or earlier) lived in the US (having immigrated or having been born in the US). In the public middle-class schools these kids go to, parents complain that poor Jason just doesn't have enough time after school for all his activities and his life is so stressful so the schools should cut back on expectations (including the amount of homework). Or, when their sweet Heather is called out at school for behavior problems, her parents raise a ruckus about how the teacher picks on poor Heather (when I was a kid [get off my lawn] it was assumed it was <i>me</i> who had the problem, not the teacher -- unless a lot of parents were complaining bitterly about one particular teacher).
<br> <br>
Of course, all this has given us public school teachers who are willing to accept this lax attitude and have low achievement expectations -- which results in a vicious cycle.
<br> <br>
From a practical standpoint, the primary source of effective practicing engineers and scientists is going to be middle class households with educated parents -- unfortunately, many of these families are/have raised soft kids who feel entitled to get whatever they want just because "I want it" and don't expect to "work" for it.
<br> <br>
At this point, I fear the US's only hope is the legal immigrants from India and China (in particular, due to their numbers) whose parents actually believe that their childrens' main "job" is getting a good education and don't mind that the kids sometimes feel some stress about it. This is not a terrible thing except that as the US builds up more and more deadwood (all of whom get to vote, but most of whom will pay few taxes due to their limited income producing potential) we cross the tipping point where 5\% are paying the other 95\% to exist - and the 95\% keep trying to get more from the 5\% until it all collapses when a few of the 5\% say "screw it, I'm not going to work this hard to give most of my earnings to someone else. Don't oppose generous issuance of H1Bs to well educated individuals - we need them to help keep Medicare (and the whole government bubble) propped up for a few more years - we need to keep this Ponzi scheme afloat...</htmltext>
<tokenext>Agreed.. . However , I think it 's unfair to specifically single out these groups without including what seems to me to be a " lax " attitude by parents ( including college educated parents ) in middle-class homes where the kid 's great-grandparents ( or earlier ) lived in the US ( having immigrated or having been born in the US ) .
In the public middle-class schools these kids go to , parents complain that poor Jason just does n't have enough time after school for all his activities and his life is so stressful so the schools should cut back on expectations ( including the amount of homework ) .
Or , when their sweet Heather is called out at school for behavior problems , her parents raise a ruckus about how the teacher picks on poor Heather ( when I was a kid [ get off my lawn ] it was assumed it was me who had the problem , not the teacher -- unless a lot of parents were complaining bitterly about one particular teacher ) .
Of course , all this has given us public school teachers who are willing to accept this lax attitude and have low achievement expectations -- which results in a vicious cycle .
From a practical standpoint , the primary source of effective practicing engineers and scientists is going to be middle class households with educated parents -- unfortunately , many of these families are/have raised soft kids who feel entitled to get whatever they want just because " I want it " and do n't expect to " work " for it .
At this point , I fear the US 's only hope is the legal immigrants from India and China ( in particular , due to their numbers ) whose parents actually believe that their childrens ' main " job " is getting a good education and do n't mind that the kids sometimes feel some stress about it .
This is not a terrible thing except that as the US builds up more and more deadwood ( all of whom get to vote , but most of whom will pay few taxes due to their limited income producing potential ) we cross the tipping point where 5 \ % are paying the other 95 \ % to exist - and the 95 \ % keep trying to get more from the 5 \ % until it all collapses when a few of the 5 \ % say " screw it , I 'm not going to work this hard to give most of my earnings to someone else .
Do n't oppose generous issuance of H1Bs to well educated individuals - we need them to help keep Medicare ( and the whole government bubble ) propped up for a few more years - we need to keep this Ponzi scheme afloat.. .</tokentext>
<sentencetext>Agreed...
 
However, I think it's unfair to specifically single out these groups without including what seems to me to be a "lax" attitude by parents (including college educated parents) in middle-class homes where the kid's great-grandparents (or earlier) lived in the US (having immigrated or having been born in the US).
In the public middle-class schools these kids go to, parents complain that poor Jason just doesn't have enough time after school for all his activities and his life is so stressful so the schools should cut back on expectations (including the amount of homework).
Or, when their sweet Heather is called out at school for behavior problems, her parents raise a ruckus about how the teacher picks on poor Heather (when I was a kid [get off my lawn] it was assumed it was me who had the problem, not the teacher -- unless a lot of parents were complaining bitterly about one particular teacher).
Of course, all this has given us public school teachers who are willing to accept this lax attitude and have low achievement expectations -- which results in a vicious cycle.
From a practical standpoint, the primary source of effective practicing engineers and scientists is going to be middle class households with educated parents -- unfortunately, many of these families are/have raised soft kids who feel entitled to get whatever they want just because "I want it" and don't expect to "work" for it.
At this point, I fear the US's only hope is the legal immigrants from India and China (in particular, due to their numbers) whose parents actually believe that their childrens' main "job" is getting a good education and don't mind that the kids sometimes feel some stress about it.
This is not a terrible thing except that as the US builds up more and more deadwood (all of whom get to vote, but most of whom will pay few taxes due to their limited income producing potential) we cross the tipping point where 5\% are paying the other 95\% to exist - and the 95\% keep trying to get more from the 5\% until it all collapses when a few of the 5\% say "screw it, I'm not going to work this hard to give most of my earnings to someone else.
Don't oppose generous issuance of H1Bs to well educated individuals - we need them to help keep Medicare (and the whole government bubble) propped up for a few more years - we need to keep this Ponzi scheme afloat...</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393347</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393427</id>
	<title>Re:Eh.</title>
	<author>AnotherBlackHat</author>
	<datestamp>1245440880000</datestamp>
	<modclass>Informativ</modclass>
	<modscore>2</modscore>
	<htmltext><p><div class="quote"><p>The whole idea behind his essay is that he liked playing with numbers and shapes as if it's an art, but he doesn't seem to realize most people don't share this love for math, like pretty much 90\% of any student population. This is me speaking as a just-graduated senior: the things he suggests is beyond the ability of most math students in high school.</p></div><p>I think you missed the point.<br>His point IMO, is what we are teaching as "math" in school is totally useless and should be scrapped completely, because it's not even close to what math is.<br>We don't need to teach math to 100\% of the students, just as we don't insist that 100\% of the students can paint landscapes, or bake brownies.</p></div>
	</htmltext>
<tokenext>The whole idea behind his essay is that he liked playing with numbers and shapes as if it 's an art , but he does n't seem to realize most people do n't share this love for math , like pretty much 90 \ % of any student population .
This is me speaking as a just-graduated senior : the things he suggests is beyond the ability of most math students in high school.I think you missed the point.His point IMO , is what we are teaching as " math " in school is totally useless and should be scrapped completely , because it 's not even close to what math is.We do n't need to teach math to 100 \ % of the students , just as we do n't insist that 100 \ % of the students can paint landscapes , or bake brownies .</tokentext>
<sentencetext>The whole idea behind his essay is that he liked playing with numbers and shapes as if it's an art, but he doesn't seem to realize most people don't share this love for math, like pretty much 90\% of any student population.
This is me speaking as a just-graduated senior: the things he suggests is beyond the ability of most math students in high school.I think you missed the point.His point IMO, is what we are teaching as "math" in school is totally useless and should be scrapped completely, because it's not even close to what math is.We don't need to teach math to 100\% of the students, just as we don't insist that 100\% of the students can paint landscapes, or bake brownies.
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392961</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394495</id>
	<title>Re:Cue the other subjects</title>
	<author>Anonymous</author>
	<datestamp>1245444600000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>and most of them can be traced to certain groups (*cough*progressives*cough*) waging a 50 year war on public education, and people refusing to see and treat education as what they think it is: an investment in the future new world order, which requires a compliant and ignorant populace.</htmltext>
<tokenext>and most of them can be traced to certain groups ( * cough * progressives * cough * ) waging a 50 year war on public education , and people refusing to see and treat education as what they think it is : an investment in the future new world order , which requires a compliant and ignorant populace .</tokentext>
<sentencetext>and most of them can be traced to certain groups (*cough*progressives*cough*) waging a 50 year war on public education, and people refusing to see and treat education as what they think it is: an investment in the future new world order, which requires a compliant and ignorant populace.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393083</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28399613</id>
	<title>The Argument is Seriously Flawed</title>
	<author>Borg Bucolic</author>
	<datestamp>1245438540000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>I agree with a few things stated, but...... just because you have experienced something does not make you an expert on it. <p>


On the other hand, he wrote an essay/article based upon his reasoned judgments about subject he was taught poorly by people </p><p>
that didn't know anything about it while claiming that this education provided no means of making the argument he just made.</p><p>
If you only knew what really happens in the classrooms today.....</p></htmltext>
<tokenext>I agree with a few things stated , but...... just because you have experienced something does not make you an expert on it .
On the other hand , he wrote an essay/article based upon his reasoned judgments about subject he was taught poorly by people that did n't know anything about it while claiming that this education provided no means of making the argument he just made .
If you only knew what really happens in the classrooms today.... .</tokentext>
<sentencetext>I agree with a few things stated, but...... just because you have experienced something does not make you an expert on it.
On the other hand, he wrote an essay/article based upon his reasoned judgments about subject he was taught poorly by people 
that didn't know anything about it while claiming that this education provided no means of making the argument he just made.
If you only knew what really happens in the classrooms today.....</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393953</id>
	<title>Re:it's really bad</title>
	<author>chebucto</author>
	<datestamp>1245442800000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>I'm just becoming reacquainted with math, and here is a proof I encoutered recently, showing that the square root (sqrt()) of 2 is not a rational number:</p><p>Proof of sqrt(2) != rational number:</p><p>suppose sqrt(2) = rational number:</p><p>then, sqrt(2) = m/n, where m = integer, n = non-zero integer (see definition of rational number), where n is the lowest common denominator</p><p>thus,<br>sqrt(2) = m/n<br>2 = m^2/n^2<br>2n^2 = m^2</p><p>we now know that m is an even number, for squares of even numbers are always even, and squares of odd numbers are always odd; if m^2 can be expressed as double the square of an integer, it must be even.</p><p>then, knowing m is even, we can create a new number q, which is m/2. Thus, m = 2q, m^2 = 4q^2<br>so</p><p>2n^2 = 4q^2<br>n^2 = 2q^2</p><p>thus, n is an even number (see reasoning for m being an even number)</p><p>so, if m and n must be even numbers, m/n cannot be a fraction at the lowest common denominator</p><p>thus sqrt(2) cannot be expressed as a rational number</p><p>thus sqrt(2) is not a rational number, thus sqrt(2) is an irrational number.</p><p>This is the proof as I understand it - starting from axioms (definition of a rational number, algrebraic rules), and arriving at a conclusion.</p><p>And yes, as I understand it, you have to write out every step to show the proof - though at times you are relying on assmptions taken as read (ig the properties of squares).</p><p>It's a lot to take in, but it is very rule-based, and, if broken down into small bits, can be digestible (I hope!)</p><p>-- Soon-to-be student of 1st year calc</p></htmltext>
<tokenext>I 'm just becoming reacquainted with math , and here is a proof I encoutered recently , showing that the square root ( sqrt ( ) ) of 2 is not a rational number : Proof of sqrt ( 2 ) ! = rational number : suppose sqrt ( 2 ) = rational number : then , sqrt ( 2 ) = m/n , where m = integer , n = non-zero integer ( see definition of rational number ) , where n is the lowest common denominatorthus,sqrt ( 2 ) = m/n2 = m ^ 2/n ^ 22n ^ 2 = m ^ 2we now know that m is an even number , for squares of even numbers are always even , and squares of odd numbers are always odd ; if m ^ 2 can be expressed as double the square of an integer , it must be even.then , knowing m is even , we can create a new number q , which is m/2 .
Thus , m = 2q , m ^ 2 = 4q ^ 2so2n ^ 2 = 4q ^ 2n ^ 2 = 2q ^ 2thus , n is an even number ( see reasoning for m being an even number ) so , if m and n must be even numbers , m/n can not be a fraction at the lowest common denominatorthus sqrt ( 2 ) can not be expressed as a rational numberthus sqrt ( 2 ) is not a rational number , thus sqrt ( 2 ) is an irrational number.This is the proof as I understand it - starting from axioms ( definition of a rational number , algrebraic rules ) , and arriving at a conclusion.And yes , as I understand it , you have to write out every step to show the proof - though at times you are relying on assmptions taken as read ( ig the properties of squares ) .It 's a lot to take in , but it is very rule-based , and , if broken down into small bits , can be digestible ( I hope !
) -- Soon-to-be student of 1st year calc</tokentext>
<sentencetext>I'm just becoming reacquainted with math, and here is a proof I encoutered recently, showing that the square root (sqrt()) of 2 is not a rational number:Proof of sqrt(2) != rational number:suppose sqrt(2) = rational number:then, sqrt(2) = m/n, where m = integer, n = non-zero integer (see definition of rational number), where n is the lowest common denominatorthus,sqrt(2) = m/n2 = m^2/n^22n^2 = m^2we now know that m is an even number, for squares of even numbers are always even, and squares of odd numbers are always odd; if m^2 can be expressed as double the square of an integer, it must be even.then, knowing m is even, we can create a new number q, which is m/2.
Thus, m = 2q, m^2 = 4q^2so2n^2 = 4q^2n^2 = 2q^2thus, n is an even number (see reasoning for m being an even number)so, if m and n must be even numbers, m/n cannot be a fraction at the lowest common denominatorthus sqrt(2) cannot be expressed as a rational numberthus sqrt(2) is not a rational number, thus sqrt(2) is an irrational number.This is the proof as I understand it - starting from axioms (definition of a rational number, algrebraic rules), and arriving at a conclusion.And yes, as I understand it, you have to write out every step to show the proof - though at times you are relying on assmptions taken as read (ig the properties of squares).It's a lot to take in, but it is very rule-based, and, if broken down into small bits, can be digestible (I hope!
)-- Soon-to-be student of 1st year calc</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393543</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28405117</id>
	<title>Re:Eh.</title>
	<author>ChaosDiscord</author>
	<datestamp>1245498720000</datestamp>
	<modclass>Insightful</modclass>
	<modscore>2</modscore>
	<htmltext><p>You overlooked the absolute core of his argument: a lot of high school students think they don't like math because they've been presented with a pale shadow of math for the previous eight years.  Of course a high school student couldn't handle what he's describing; all of their previous schooling has emphasized rote memorization, blind pattern matching, and robotic application of rules.  He thinks we need to rethink things all the way back to first grade.

</p><p>By odd coincidence, I had an english literature teacher in high school who taught english the same way math is frequently taught.  You read the book, and during class he lectured on the details of the story, the author's background, and the context of the world in which the story was written.  While this might sound interesting, it was presented as a serious facts.  Indeed, a few days before a test, he helpfully gave a study session that amounted to listing 100 or so facts from the book and his lectures.  You memorized them, then regurgitated 20 or so back on the multiple choice test.  It was mindless.   It was admittedly very easy, at least if you could memorize a list of 100 or so facts, but it did crap all for my appreciation for literature in the english language.  (At the time I liked his class.  I found it trivially easy.  But looking back on it in hindsight, especially after reading that essay, what a massive waste of time.  What a terrible teacher.)

</p><p>In english class in high school you can ask students to read a work, then write an essay on the themes.  In the process they will have to learn to actually pay attention to what they're reading, to consider it on a level beyond a simple telling of events.  Maybe the student will hate reading, writing, or both, but the overwhelming majority can manage to write that essay.  The original author argues that the same model can work for mathematics and that the idea that it will be too hard for many students is a false one created a system that already fails.</p></htmltext>
<tokenext>You overlooked the absolute core of his argument : a lot of high school students think they do n't like math because they 've been presented with a pale shadow of math for the previous eight years .
Of course a high school student could n't handle what he 's describing ; all of their previous schooling has emphasized rote memorization , blind pattern matching , and robotic application of rules .
He thinks we need to rethink things all the way back to first grade .
By odd coincidence , I had an english literature teacher in high school who taught english the same way math is frequently taught .
You read the book , and during class he lectured on the details of the story , the author 's background , and the context of the world in which the story was written .
While this might sound interesting , it was presented as a serious facts .
Indeed , a few days before a test , he helpfully gave a study session that amounted to listing 100 or so facts from the book and his lectures .
You memorized them , then regurgitated 20 or so back on the multiple choice test .
It was mindless .
It was admittedly very easy , at least if you could memorize a list of 100 or so facts , but it did crap all for my appreciation for literature in the english language .
( At the time I liked his class .
I found it trivially easy .
But looking back on it in hindsight , especially after reading that essay , what a massive waste of time .
What a terrible teacher .
) In english class in high school you can ask students to read a work , then write an essay on the themes .
In the process they will have to learn to actually pay attention to what they 're reading , to consider it on a level beyond a simple telling of events .
Maybe the student will hate reading , writing , or both , but the overwhelming majority can manage to write that essay .
The original author argues that the same model can work for mathematics and that the idea that it will be too hard for many students is a false one created a system that already fails .</tokentext>
<sentencetext>You overlooked the absolute core of his argument: a lot of high school students think they don't like math because they've been presented with a pale shadow of math for the previous eight years.
Of course a high school student couldn't handle what he's describing; all of their previous schooling has emphasized rote memorization, blind pattern matching, and robotic application of rules.
He thinks we need to rethink things all the way back to first grade.
By odd coincidence, I had an english literature teacher in high school who taught english the same way math is frequently taught.
You read the book, and during class he lectured on the details of the story, the author's background, and the context of the world in which the story was written.
While this might sound interesting, it was presented as a serious facts.
Indeed, a few days before a test, he helpfully gave a study session that amounted to listing 100 or so facts from the book and his lectures.
You memorized them, then regurgitated 20 or so back on the multiple choice test.
It was mindless.
It was admittedly very easy, at least if you could memorize a list of 100 or so facts, but it did crap all for my appreciation for literature in the english language.
(At the time I liked his class.
I found it trivially easy.
But looking back on it in hindsight, especially after reading that essay, what a massive waste of time.
What a terrible teacher.
)

In english class in high school you can ask students to read a work, then write an essay on the themes.
In the process they will have to learn to actually pay attention to what they're reading, to consider it on a level beyond a simple telling of events.
Maybe the student will hate reading, writing, or both, but the overwhelming majority can manage to write that essay.
The original author argues that the same model can work for mathematics and that the idea that it will be too hard for many students is a false one created a system that already fails.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392961</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28402011</id>
	<title>Re:Cue the other subjects</title>
	<author>iggymanz</author>
	<datestamp>1245514380000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>that is utter bullshit.  The decline happened while system became more and more under control of progressive leftist/socialist liberal leadership.

I have much against the religious fundamentalists, but the sad state of our educational system is very much the fault of another group.</htmltext>
<tokenext>that is utter bullshit .
The decline happened while system became more and more under control of progressive leftist/socialist liberal leadership .
I have much against the religious fundamentalists , but the sad state of our educational system is very much the fault of another group .</tokentext>
<sentencetext>that is utter bullshit.
The decline happened while system became more and more under control of progressive leftist/socialist liberal leadership.
I have much against the religious fundamentalists, but the sad state of our educational system is very much the fault of another group.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393083</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28396157</id>
	<title>Math For America.</title>
	<author>ammorris</author>
	<datestamp>1245407700000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>Sounds like Lockhart isn't the only one with this lament. This problem has been recognized by some , and some are in fact, Actively working to improve math education in our schools.
<p>
Math For America does exactly this. If you want better math education, the solution starts with retaining better math teachers. How do you do this? Simple.. Pay them a competitive salary.
</p><p>
Those who excel at math, rarely stay to teach it because it's more lucrative for them to take higher paying positions in the private sector.
</p><p>
Read more at <a href="http://www.mathforamerica.org/home" title="mathforamerica.org" rel="nofollow">http://www.mathforamerica.org/home</a> [mathforamerica.org]
</p><p>
From the MFA Website "We are a nonprofit organization with a mission to improve math education in secondary public schools in the United States by recruiting, training, and retaining outstanding mathematics teachers."</p></htmltext>
<tokenext>Sounds like Lockhart is n't the only one with this lament .
This problem has been recognized by some , and some are in fact , Actively working to improve math education in our schools .
Math For America does exactly this .
If you want better math education , the solution starts with retaining better math teachers .
How do you do this ?
Simple.. Pay them a competitive salary .
Those who excel at math , rarely stay to teach it because it 's more lucrative for them to take higher paying positions in the private sector .
Read more at http : //www.mathforamerica.org/home [ mathforamerica.org ] From the MFA Website " We are a nonprofit organization with a mission to improve math education in secondary public schools in the United States by recruiting , training , and retaining outstanding mathematics teachers .
"</tokentext>
<sentencetext>Sounds like Lockhart isn't the only one with this lament.
This problem has been recognized by some , and some are in fact, Actively working to improve math education in our schools.
Math For America does exactly this.
If you want better math education, the solution starts with retaining better math teachers.
How do you do this?
Simple.. Pay them a competitive salary.
Those who excel at math, rarely stay to teach it because it's more lucrative for them to take higher paying positions in the private sector.
Read more at http://www.mathforamerica.org/home [mathforamerica.org]

From the MFA Website "We are a nonprofit organization with a mission to improve math education in secondary public schools in the United States by recruiting, training, and retaining outstanding mathematics teachers.
"</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28399197</id>
	<title>Why are we still teaching classic plane geometry?</title>
	<author>Animats</author>
	<datestamp>1245432300000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>
I've done some rather math-heavy programming.  I'm one of the people who made ragdoll physics work, a painful exercise in geometry, differential equations, and error control.  (If you're not real serious about the error control, your ragdolls will fly apart or launch themselves into space for no reason visible to the end user.  This gets you nasty writeups in game magazines.)
</p><p>
I've also done proof of correctness work, using and working on automatic theorem provers.  And I've done some work on sensor fusion for inertial navigation systems.
</p><p>
Despite this, I've <i>never</i> had to do a classic high-school type geometric proof since high school.  High school geometry is taught that way because Euclid taught it that way two millennia ago.  (A century ago, schools were still using Euclid's <i>Elements</i> as a textbook.)  It's only taught because it's locked into college entrance exams like the SAT.
</p><p>
If you want to teach mathematical reasoning, that's fine.  But there's no reason to teach it in the geometric domain.  It's a skill that's used very, very seldom.</p></htmltext>
<tokenext>I 've done some rather math-heavy programming .
I 'm one of the people who made ragdoll physics work , a painful exercise in geometry , differential equations , and error control .
( If you 're not real serious about the error control , your ragdolls will fly apart or launch themselves into space for no reason visible to the end user .
This gets you nasty writeups in game magazines .
) I 've also done proof of correctness work , using and working on automatic theorem provers .
And I 've done some work on sensor fusion for inertial navigation systems .
Despite this , I 've never had to do a classic high-school type geometric proof since high school .
High school geometry is taught that way because Euclid taught it that way two millennia ago .
( A century ago , schools were still using Euclid 's Elements as a textbook .
) It 's only taught because it 's locked into college entrance exams like the SAT .
If you want to teach mathematical reasoning , that 's fine .
But there 's no reason to teach it in the geometric domain .
It 's a skill that 's used very , very seldom .</tokentext>
<sentencetext>
I've done some rather math-heavy programming.
I'm one of the people who made ragdoll physics work, a painful exercise in geometry, differential equations, and error control.
(If you're not real serious about the error control, your ragdolls will fly apart or launch themselves into space for no reason visible to the end user.
This gets you nasty writeups in game magazines.
)

I've also done proof of correctness work, using and working on automatic theorem provers.
And I've done some work on sensor fusion for inertial navigation systems.
Despite this, I've never had to do a classic high-school type geometric proof since high school.
High school geometry is taught that way because Euclid taught it that way two millennia ago.
(A century ago, schools were still using Euclid's Elements as a textbook.
)  It's only taught because it's locked into college entrance exams like the SAT.
If you want to teach mathematical reasoning, that's fine.
But there's no reason to teach it in the geometric domain.
It's a skill that's used very, very seldom.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28395413</id>
	<title>Re:Could be worse...</title>
	<author>Anonymous</author>
	<datestamp>1245404460000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>Yes, because the thousands of repeatable experiments done using the scientific method by people with PhD's is the complete antithesis of science.  Oh, and evolution and the big bang are perfect and cannot be challenged by anyone.  If they are, it's not science.</p><p>If you want to criticize Creation Science, fine.  But all I ask is that you <a href="http://www.answersingenesis.org/get-answers" title="answersingenesis.org">read some of it first</a> [answersingenesis.org], since, by your statements, you clearly never have.</p></htmltext>
<tokenext>Yes , because the thousands of repeatable experiments done using the scientific method by people with PhD 's is the complete antithesis of science .
Oh , and evolution and the big bang are perfect and can not be challenged by anyone .
If they are , it 's not science.If you want to criticize Creation Science , fine .
But all I ask is that you read some of it first [ answersingenesis.org ] , since , by your statements , you clearly never have .</tokentext>
<sentencetext>Yes, because the thousands of repeatable experiments done using the scientific method by people with PhD's is the complete antithesis of science.
Oh, and evolution and the big bang are perfect and cannot be challenged by anyone.
If they are, it's not science.If you want to criticize Creation Science, fine.
But all I ask is that you read some of it first [answersingenesis.org], since, by your statements, you clearly never have.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392957</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393241</id>
	<title>Re:US School System compared to Europes School Sys</title>
	<author>Lord Ender</author>
	<datestamp>1245440280000</datestamp>
	<modclass>Insightful</modclass>
	<modscore>3</modscore>
	<htmltext><p>You must have attended a very very small school. Most US schools have different courses based on skill level. Your conclusions about the US school system are therefore wrong. They are merely conclusions about very small schools.</p></htmltext>
<tokenext>You must have attended a very very small school .
Most US schools have different courses based on skill level .
Your conclusions about the US school system are therefore wrong .
They are merely conclusions about very small schools .</tokentext>
<sentencetext>You must have attended a very very small school.
Most US schools have different courses based on skill level.
Your conclusions about the US school system are therefore wrong.
They are merely conclusions about very small schools.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393035</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394075</id>
	<title>Re:it's really bad</title>
	<author>Anonymous</author>
	<datestamp>1245443220000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>Were you? I'm asking because you fail to understand the premises. You're required to understand logic to write proofs. Even if I believed you actually learned logic, stating that you didn't enjoy it even if you were taught logic, has nothing to do with the first statement.</p></htmltext>
<tokenext>Were you ?
I 'm asking because you fail to understand the premises .
You 're required to understand logic to write proofs .
Even if I believed you actually learned logic , stating that you did n't enjoy it even if you were taught logic , has nothing to do with the first statement .</tokentext>
<sentencetext>Were you?
I'm asking because you fail to understand the premises.
You're required to understand logic to write proofs.
Even if I believed you actually learned logic, stating that you didn't enjoy it even if you were taught logic, has nothing to do with the first statement.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393127</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393443</id>
	<title>Re:True story ....</title>
	<author>Neil Blender</author>
	<datestamp>1245440940000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>"No, that's just indicative of lazy teachers. Since most humans are lazy and all teachers are human, this is to be expected."</p><p>In college, I found it's more likely that profs refuse to admit they are wrong. I got dinged more than once for typos/errors in books that the professor wrote for the class.</p></htmltext>
<tokenext>" No , that 's just indicative of lazy teachers .
Since most humans are lazy and all teachers are human , this is to be expected .
" In college , I found it 's more likely that profs refuse to admit they are wrong .
I got dinged more than once for typos/errors in books that the professor wrote for the class .</tokentext>
<sentencetext>"No, that's just indicative of lazy teachers.
Since most humans are lazy and all teachers are human, this is to be expected.
"In college, I found it's more likely that profs refuse to admit they are wrong.
I got dinged more than once for typos/errors in books that the professor wrote for the class.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393199</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394781</id>
	<title>Re:You can convince me</title>
	<author>jweller</author>
	<datestamp>1245402360000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>IMHO the purpose of math in public schools is to make sure that upon release into the real world, students can do things like balance their checkbook, calculate a tip or a discount without a calculator, make change, and understand the concept of compounding interest. Sadly, it appears that they are failing miserably at that simple task.</p></htmltext>
<tokenext>IMHO the purpose of math in public schools is to make sure that upon release into the real world , students can do things like balance their checkbook , calculate a tip or a discount without a calculator , make change , and understand the concept of compounding interest .
Sadly , it appears that they are failing miserably at that simple task .</tokentext>
<sentencetext>IMHO the purpose of math in public schools is to make sure that upon release into the real world, students can do things like balance their checkbook, calculate a tip or a discount without a calculator, make change, and understand the concept of compounding interest.
Sadly, it appears that they are failing miserably at that simple task.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393159</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393725</id>
	<title>Re:it's really bad</title>
	<author>sumdumass</author>
	<datestamp>1245442020000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>I don't know. I think maybe you are falling for the because I saw it, it must be true logic problem. Education is actually controlled by each state and the territories by the federal government. Some states write broads guidelines and leave it to the counties to fill in the gaps. This is something the NCLBA was supposed to address by creating a guideline of what should be expected for a student to know after each grade level and supposedly if the states created a standard similar enough, tested the student's abilities and then showed progress when they didn't meet that, they were going to get a certain amount of federal funding to be used. Of course this was met with mass resistance when the <a href="http://www.boston.com/news/local/massachusetts/articles/2009/05/15/ex\_teachers\_sue\_over\_licensing\_exam/" title="boston.com">teachers</a> [boston.com] <a href="http://www.heartland.org/publications/school\%20reform/article/13202/Storm\_Erupts\_Over\_Mass\_Teacher\_Tests.html" title="heartland.org">couldn't pass</a> [heartland.org] the <a href="http://www.freerepublic.com/focus/f-news/1369069/posts" title="freerepublic.com">performance tests.</a> [freerepublic.com]</p><p>The problem is that I do remember getting an overview on the rules of logic in the course before advanced geometry. We had to take pre-algebra for half a year and intro to geometry the other half in 7th or 8th grade, then two algebra courses, then an advanced geometry course another algebra course, pre-calculus and if you were advanced enough you moved on to calculus and AP courses. Of course there was other math course options like Statistics and what they called integrated math which focused generic math skills until you got to career tech integrated math that focused more on specific aspects and formulas for various industries like carpentry and house building, electronics, drafting, auto repair, and so on. So the problem isn't the HS math curriculum in the US, it's the HS math Curriculum in certain states or counties within the US.</p><p>There is no one place to make any change to the schools procedures or curriculum.</p></htmltext>
<tokenext>I do n't know .
I think maybe you are falling for the because I saw it , it must be true logic problem .
Education is actually controlled by each state and the territories by the federal government .
Some states write broads guidelines and leave it to the counties to fill in the gaps .
This is something the NCLBA was supposed to address by creating a guideline of what should be expected for a student to know after each grade level and supposedly if the states created a standard similar enough , tested the student 's abilities and then showed progress when they did n't meet that , they were going to get a certain amount of federal funding to be used .
Of course this was met with mass resistance when the teachers [ boston.com ] could n't pass [ heartland.org ] the performance tests .
[ freerepublic.com ] The problem is that I do remember getting an overview on the rules of logic in the course before advanced geometry .
We had to take pre-algebra for half a year and intro to geometry the other half in 7th or 8th grade , then two algebra courses , then an advanced geometry course another algebra course , pre-calculus and if you were advanced enough you moved on to calculus and AP courses .
Of course there was other math course options like Statistics and what they called integrated math which focused generic math skills until you got to career tech integrated math that focused more on specific aspects and formulas for various industries like carpentry and house building , electronics , drafting , auto repair , and so on .
So the problem is n't the HS math curriculum in the US , it 's the HS math Curriculum in certain states or counties within the US.There is no one place to make any change to the schools procedures or curriculum .</tokentext>
<sentencetext>I don't know.
I think maybe you are falling for the because I saw it, it must be true logic problem.
Education is actually controlled by each state and the territories by the federal government.
Some states write broads guidelines and leave it to the counties to fill in the gaps.
This is something the NCLBA was supposed to address by creating a guideline of what should be expected for a student to know after each grade level and supposedly if the states created a standard similar enough, tested the student's abilities and then showed progress when they didn't meet that, they were going to get a certain amount of federal funding to be used.
Of course this was met with mass resistance when the teachers [boston.com] couldn't pass [heartland.org] the performance tests.
[freerepublic.com]The problem is that I do remember getting an overview on the rules of logic in the course before advanced geometry.
We had to take pre-algebra for half a year and intro to geometry the other half in 7th or 8th grade, then two algebra courses, then an advanced geometry course another algebra course, pre-calculus and if you were advanced enough you moved on to calculus and AP courses.
Of course there was other math course options like Statistics and what they called integrated math which focused generic math skills until you got to career tech integrated math that focused more on specific aspects and formulas for various industries like carpentry and house building, electronics, drafting, auto repair, and so on.
So the problem isn't the HS math curriculum in the US, it's the HS math Curriculum in certain states or counties within the US.There is no one place to make any change to the schools procedures or curriculum.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392911</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28395257</id>
	<title>Re:I Sympathize With Him But Too Idyllic</title>
	<author>Have Brain Will Rent</author>
	<datestamp>1245403860000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p> <i>Well if you're not asking for teachers needing to be professional published mathematicians, what was that paragraph about? </i> </p><p>
He is simply asking for someone who appreciates and understands math. Now I'm not a mathematician and while I've published papers in CS involving the use of math I don't consider them math papers (and I'm pretty sure math faculty would agree lol)... but I understand what math is and I appreciate it.</p><p>
A few years back there was a letter in one of the city newspapers from a professor in one of the humanities departments at one of the local universities. I cannot remember what prompted the letter but in it he opined that people would be better off spending their time studying the beauty found in art and not the dry sterile material of mathematics. In one sentence he showed himself to be completely ignorant of what math is and the phenomenal beauty it contains. It was astounding to "hear" someone with a Ph.D. being so phenomenally ignorant and so arrogant in his ignorance. Well maybe the latter goes hand in hand with the former.
</p><p>
Almost all my math teachers had an understanding and appreciation of math that was typical of an arts student forced to take something like "Intro to Math for Arts Students" to get their B.A. and teaching credentials. More than once I had "discussions" with teachers only to realize part way in that there was no point because they actually didn't understand the conceptual issue I was raising. It is amazingly discouraging to have the people are supposed to be teaching you a subject mark an answer as wrong because they are too ignorant of the subject they purport to teach to be able to understand the answer presented by a student. In grade 10 I had a math teacher who did in fact have a Ph.D. in math... it was a totally different experience from any other math class,or science class for that matter, that I'd ever had to that point.</p><p> <i>The paragraph I quote is not the truth, it's wishing for the impossible.</i> </p><p>
Well even if it is impossible, wishing for the impossible does not make it any less true. These are not mutually exclusive properties. That's something you learn along the way in math btw. </p></div>
	</htmltext>
<tokenext>Well if you 're not asking for teachers needing to be professional published mathematicians , what was that paragraph about ?
He is simply asking for someone who appreciates and understands math .
Now I 'm not a mathematician and while I 've published papers in CS involving the use of math I do n't consider them math papers ( and I 'm pretty sure math faculty would agree lol ) ... but I understand what math is and I appreciate it .
A few years back there was a letter in one of the city newspapers from a professor in one of the humanities departments at one of the local universities .
I can not remember what prompted the letter but in it he opined that people would be better off spending their time studying the beauty found in art and not the dry sterile material of mathematics .
In one sentence he showed himself to be completely ignorant of what math is and the phenomenal beauty it contains .
It was astounding to " hear " someone with a Ph.D. being so phenomenally ignorant and so arrogant in his ignorance .
Well maybe the latter goes hand in hand with the former .
Almost all my math teachers had an understanding and appreciation of math that was typical of an arts student forced to take something like " Intro to Math for Arts Students " to get their B.A .
and teaching credentials .
More than once I had " discussions " with teachers only to realize part way in that there was no point because they actually did n't understand the conceptual issue I was raising .
It is amazingly discouraging to have the people are supposed to be teaching you a subject mark an answer as wrong because they are too ignorant of the subject they purport to teach to be able to understand the answer presented by a student .
In grade 10 I had a math teacher who did in fact have a Ph.D. in math... it was a totally different experience from any other math class,or science class for that matter , that I 'd ever had to that point .
The paragraph I quote is not the truth , it 's wishing for the impossible .
Well even if it is impossible , wishing for the impossible does not make it any less true .
These are not mutually exclusive properties .
That 's something you learn along the way in math btw .</tokentext>
<sentencetext> Well if you're not asking for teachers needing to be professional published mathematicians, what was that paragraph about?
He is simply asking for someone who appreciates and understands math.
Now I'm not a mathematician and while I've published papers in CS involving the use of math I don't consider them math papers (and I'm pretty sure math faculty would agree lol)... but I understand what math is and I appreciate it.
A few years back there was a letter in one of the city newspapers from a professor in one of the humanities departments at one of the local universities.
I cannot remember what prompted the letter but in it he opined that people would be better off spending their time studying the beauty found in art and not the dry sterile material of mathematics.
In one sentence he showed himself to be completely ignorant of what math is and the phenomenal beauty it contains.
It was astounding to "hear" someone with a Ph.D. being so phenomenally ignorant and so arrogant in his ignorance.
Well maybe the latter goes hand in hand with the former.
Almost all my math teachers had an understanding and appreciation of math that was typical of an arts student forced to take something like "Intro to Math for Arts Students" to get their B.A.
and teaching credentials.
More than once I had "discussions" with teachers only to realize part way in that there was no point because they actually didn't understand the conceptual issue I was raising.
It is amazingly discouraging to have the people are supposed to be teaching you a subject mark an answer as wrong because they are too ignorant of the subject they purport to teach to be able to understand the answer presented by a student.
In grade 10 I had a math teacher who did in fact have a Ph.D. in math... it was a totally different experience from any other math class,or science class for that matter, that I'd ever had to that point.
The paragraph I quote is not the truth, it's wishing for the impossible.
Well even if it is impossible, wishing for the impossible does not make it any less true.
These are not mutually exclusive properties.
That's something you learn along the way in math btw. 
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392903</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393195</id>
	<title>There's lots to disagree with...</title>
	<author>twistedcubic</author>
	<datestamp>1245440100000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>From his critique of Algebra II:<br>
<br>
<i>Students will learn to rewrite quadratic forms in a variety of standard formats for no reason whatsoever.</i> <br>
<br>

I guess he's exaggerating, since he must be aware of the deep connection between algebra and geometry which is realized via manipulating equations.  And this provides lots of approaches for a good teacher.  I dunno, he just comes off as a garden-variety teacher with strong opinions.</htmltext>
<tokenext>From his critique of Algebra II : Students will learn to rewrite quadratic forms in a variety of standard formats for no reason whatsoever .
I guess he 's exaggerating , since he must be aware of the deep connection between algebra and geometry which is realized via manipulating equations .
And this provides lots of approaches for a good teacher .
I dunno , he just comes off as a garden-variety teacher with strong opinions .</tokentext>
<sentencetext>From his critique of Algebra II:

Students will learn to rewrite quadratic forms in a variety of standard formats for no reason whatsoever.
I guess he's exaggerating, since he must be aware of the deep connection between algebra and geometry which is realized via manipulating equations.
And this provides lots of approaches for a good teacher.
I dunno, he just comes off as a garden-variety teacher with strong opinions.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392903</id>
	<title>I Sympathize With Him But Too Idyllic</title>
	<author>eldavojohn</author>
	<datestamp>1245439020000</datestamp>
	<modclass>Insightful</modclass>
	<modscore>4</modscore>
	<htmltext>

I really do sympathize with Lockhart.  But what he's asking for is the perfect math teacher in the perfect math world with kids and their parents being tantalized by mathematics--not captain of the football team or even high achieving speech/band nerd.  <br> <br>

From the blog:<p><div class="quote"><p>I defy you to read and find a single sentence that isn't permeated, suffused, soaked, and encrusted with truth.</p></div><p>Very well, here is an excerpt from the PDF:</p><p><div class="quote"><p>Mathematics is an art, and art should be taught by working artists, or if not, at least by people who appreciate the art form and can recognize it when they see it. It is not necessary that you learn music from a professional composer, but would you want yourself or your child to be taught by someone who doesn't even play an instrument, and has never listened to a piece of music in their lives? Would you accept as an art teacher someone who has never picked up a pencil or stepped foot in a museum? Why is it that we accept math teachers who have never produced an original piece of mathematics, know nothing of the history and philosophy of the subject, nothing about recent developments, nothing in fact beyond what they are expected to present to their unfortunate students? What kind of a teacher is that? How can someone teach something that they themselves don't do? I can't dance, and consequently I would never presume to think that I could teach a dance class (I could try, but it wouldn't be pretty). The difference is I know I can't dance. I don't have anyone telling me I'm good at dancing just because I know a bunch of dance words.<br> <br>
Now I'm not saying that math teachers need to be professional mathematicians--far from it. But shouldn't they at least understand what mathematics is, be good at it, and enjoy doing it?</p></div><p>Well if you're not asking for teachers needing to be professional published mathematicians, what was that paragraph about?  <br> <br>

I'm sorry man, you're asking for the perfect math teacher.  You know Robin William's character from the movie <i>The Dead Poet's Society</i>?  You want a guy like that for math<nobr> <wbr></nobr>... everywhere.  That art teacher that actually made you think about what 'art' is?  Not going to find many of them in the political science department, are you?  Of course, for any subject, someone who puts their heart and soul into the subject is the best teacher!  In this respect, math is not special.  <br> <br>

The paragraph I quote is not the truth, it's wishing for the impossible.  I wish I had a math teacher like this all my life but come on.  The public school system is more worried about getting someone that actualy cares about the students at all.  They can't even find those people let alone people who care about the students <i>and</i> live/eat/sleep/bleed math.  <br> <br>

I'm right their with you in wishing for this but the expectation is unrealistic.  Passions come to people unexpectedly.  We should deal with the fact that more people are passionate about topics like Art and Humanities than Math and Computer Science.  It's just the reality of academia right now.</p></div>
	</htmltext>
<tokenext>I really do sympathize with Lockhart .
But what he 's asking for is the perfect math teacher in the perfect math world with kids and their parents being tantalized by mathematics--not captain of the football team or even high achieving speech/band nerd .
From the blog : I defy you to read and find a single sentence that is n't permeated , suffused , soaked , and encrusted with truth.Very well , here is an excerpt from the PDF : Mathematics is an art , and art should be taught by working artists , or if not , at least by people who appreciate the art form and can recognize it when they see it .
It is not necessary that you learn music from a professional composer , but would you want yourself or your child to be taught by someone who does n't even play an instrument , and has never listened to a piece of music in their lives ?
Would you accept as an art teacher someone who has never picked up a pencil or stepped foot in a museum ?
Why is it that we accept math teachers who have never produced an original piece of mathematics , know nothing of the history and philosophy of the subject , nothing about recent developments , nothing in fact beyond what they are expected to present to their unfortunate students ?
What kind of a teacher is that ?
How can someone teach something that they themselves do n't do ?
I ca n't dance , and consequently I would never presume to think that I could teach a dance class ( I could try , but it would n't be pretty ) .
The difference is I know I ca n't dance .
I do n't have anyone telling me I 'm good at dancing just because I know a bunch of dance words .
Now I 'm not saying that math teachers need to be professional mathematicians--far from it .
But should n't they at least understand what mathematics is , be good at it , and enjoy doing it ? Well if you 're not asking for teachers needing to be professional published mathematicians , what was that paragraph about ?
I 'm sorry man , you 're asking for the perfect math teacher .
You know Robin William 's character from the movie The Dead Poet 's Society ?
You want a guy like that for math ... everywhere. That art teacher that actually made you think about what 'art ' is ?
Not going to find many of them in the political science department , are you ?
Of course , for any subject , someone who puts their heart and soul into the subject is the best teacher !
In this respect , math is not special .
The paragraph I quote is not the truth , it 's wishing for the impossible .
I wish I had a math teacher like this all my life but come on .
The public school system is more worried about getting someone that actualy cares about the students at all .
They ca n't even find those people let alone people who care about the students and live/eat/sleep/bleed math .
I 'm right their with you in wishing for this but the expectation is unrealistic .
Passions come to people unexpectedly .
We should deal with the fact that more people are passionate about topics like Art and Humanities than Math and Computer Science .
It 's just the reality of academia right now .</tokentext>
<sentencetext>

I really do sympathize with Lockhart.
But what he's asking for is the perfect math teacher in the perfect math world with kids and their parents being tantalized by mathematics--not captain of the football team or even high achieving speech/band nerd.
From the blog:I defy you to read and find a single sentence that isn't permeated, suffused, soaked, and encrusted with truth.Very well, here is an excerpt from the PDF:Mathematics is an art, and art should be taught by working artists, or if not, at least by people who appreciate the art form and can recognize it when they see it.
It is not necessary that you learn music from a professional composer, but would you want yourself or your child to be taught by someone who doesn't even play an instrument, and has never listened to a piece of music in their lives?
Would you accept as an art teacher someone who has never picked up a pencil or stepped foot in a museum?
Why is it that we accept math teachers who have never produced an original piece of mathematics, know nothing of the history and philosophy of the subject, nothing about recent developments, nothing in fact beyond what they are expected to present to their unfortunate students?
What kind of a teacher is that?
How can someone teach something that they themselves don't do?
I can't dance, and consequently I would never presume to think that I could teach a dance class (I could try, but it wouldn't be pretty).
The difference is I know I can't dance.
I don't have anyone telling me I'm good at dancing just because I know a bunch of dance words.
Now I'm not saying that math teachers need to be professional mathematicians--far from it.
But shouldn't they at least understand what mathematics is, be good at it, and enjoy doing it?Well if you're not asking for teachers needing to be professional published mathematicians, what was that paragraph about?
I'm sorry man, you're asking for the perfect math teacher.
You know Robin William's character from the movie The Dead Poet's Society?
You want a guy like that for math ... everywhere.  That art teacher that actually made you think about what 'art' is?
Not going to find many of them in the political science department, are you?
Of course, for any subject, someone who puts their heart and soul into the subject is the best teacher!
In this respect, math is not special.
The paragraph I quote is not the truth, it's wishing for the impossible.
I wish I had a math teacher like this all my life but come on.
The public school system is more worried about getting someone that actualy cares about the students at all.
They can't even find those people let alone people who care about the students and live/eat/sleep/bleed math.
I'm right their with you in wishing for this but the expectation is unrealistic.
Passions come to people unexpectedly.
We should deal with the fact that more people are passionate about topics like Art and Humanities than Math and Computer Science.
It's just the reality of academia right now.
	</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394955</id>
	<title>Re:US School System compared to Europes School Sys</title>
	<author>Anonymous</author>
	<datestamp>1245402900000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>I know towards the end of my school career in high school, the school system I was going through was getting rid of the lower end of most of the classes.  My best guess is they were doing it for funding reasons.  So while it may not be overly indicative of the entire country, the lack of different levels of classes for different skill levels is definitely not something to be taken for granted in the US.</p></htmltext>
<tokenext>I know towards the end of my school career in high school , the school system I was going through was getting rid of the lower end of most of the classes .
My best guess is they were doing it for funding reasons .
So while it may not be overly indicative of the entire country , the lack of different levels of classes for different skill levels is definitely not something to be taken for granted in the US .</tokentext>
<sentencetext>I know towards the end of my school career in high school, the school system I was going through was getting rid of the lower end of most of the classes.
My best guess is they were doing it for funding reasons.
So while it may not be overly indicative of the entire country, the lack of different levels of classes for different skill levels is definitely not something to be taken for granted in the US.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393241</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394259</id>
	<title>Re:it's really bad</title>
	<author>ewenix</author>
	<datestamp>1245443820000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>If we taught logic in schools, pretty soon we wouldn't have anyone left who was "qualified" to be a politician.</htmltext>
<tokenext>If we taught logic in schools , pretty soon we would n't have anyone left who was " qualified " to be a politician .</tokentext>
<sentencetext>If we taught logic in schools, pretty soon we wouldn't have anyone left who was "qualified" to be a politician.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392911</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28397801</id>
	<title>Oh, my word.</title>
	<author>orngjce223</author>
	<datestamp>1245417840000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>I'd like to just spin off some sort of society where the "best practices" can be pursued, current government be damned.</p><p>Problem 1: You can't get a society of 1 person.  Who's going with me?<br>Problem 2: Easiest way out is to pilot a ship into international waters and then ground it, Sealand-style, but nobody makes that sort of platform that *I* know of.<br>Problem 3: Internet connectivity is a must.  Attracting the attention of one of those big fiber-optic-cable-laying companies will be nigh impossible for a micronation.<br>Problem 4: How do you make a sea platform expandable?</p><p>tl;dr: I want to fork society.  Who's with me?</p></htmltext>
<tokenext>I 'd like to just spin off some sort of society where the " best practices " can be pursued , current government be damned.Problem 1 : You ca n't get a society of 1 person .
Who 's going with me ? Problem 2 : Easiest way out is to pilot a ship into international waters and then ground it , Sealand-style , but nobody makes that sort of platform that * I * know of.Problem 3 : Internet connectivity is a must .
Attracting the attention of one of those big fiber-optic-cable-laying companies will be nigh impossible for a micronation.Problem 4 : How do you make a sea platform expandable ? tl ; dr : I want to fork society .
Who 's with me ?</tokentext>
<sentencetext>I'd like to just spin off some sort of society where the "best practices" can be pursued, current government be damned.Problem 1: You can't get a society of 1 person.
Who's going with me?Problem 2: Easiest way out is to pilot a ship into international waters and then ground it, Sealand-style, but nobody makes that sort of platform that *I* know of.Problem 3: Internet connectivity is a must.
Attracting the attention of one of those big fiber-optic-cable-laying companies will be nigh impossible for a micronation.Problem 4: How do you make a sea platform expandable?tl;dr: I want to fork society.
Who's with me?</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28397851</id>
	<title>That mathematician is clueless :-)</title>
	<author>Paul Fernhout</author>
	<datestamp>1245418260000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>Now, that is a very inflammatory subject title, so let me explain what I mean.</p><p>I was glad to see a previous comment referencing John Taylor Gatto. I do not see Gatto's name in the PDF document. Neither do I see John Holt's name. The fact is, the purpose of "schooling" (which is not the same as "education", and you would expect a mathematician to be more precise in a use of terms) is precisely to do what the mathematician decries at the end: "And there you have it.  A complete prescription for permanently disabling young minds-- a proven cure for curiosity.  What have they done to mathematics! There is such breathtaking depth and heartbreaking beauty in this ancient art form. How ironic that people dismiss mathematics as the antithesis of creativity.  They are missing out on an art form older than any book, more profound than any poem, and more abstract than any abstract. And it is school that has done this!  What a sad endless cycle of innocent teachers inflicting damage upon innocent students.  We could all be having so much more fun."</p><p>Education in the USA will not improve until people like this mathematician accept that what he said is the intentional purpose of schooling in all subjects for almost all children. See things like:<br>
&nbsp; &nbsp; "The 7-Lesson Schoolteacher" by John Taylor Gatto, NYS Teacher of the Year<br>
&nbsp; &nbsp; <a href="http://www.newciv.org/whole/schoolteacher.txt" title="newciv.org">http://www.newciv.org/whole/schoolteacher.txt</a> [newciv.org]<br>or:<br>
&nbsp; &nbsp; "The Big Crunch" by Dr. David Goodstein, Vice Provost Caltech<br>
&nbsp; &nbsp; <a href="http://www.its.caltech.edu/~dg/crunch\_art.html" title="caltech.edu">http://www.its.caltech.edu/~dg/crunch\_art.html</a> [caltech.edu]<br>or:<br>
&nbsp; &nbsp; "Growing Without Schooling" about John Holt's work, including failed attempts to reform schools<br>
&nbsp; &nbsp; <a href="http://www.holtgws.com/" title="holtgws.com">http://www.holtgws.com/</a> [holtgws.com]</p><p>At this point, it is people like Paul Lockhart who are the problem. People who think school is about education, when it is about socialization in a certain way intended for the most part to produce compliant workers, obedient soldiers, and mindless consumers. School is for fish. Curriculums are race tracks. And "class rooms" are literally to build social classes through selective breeding by genetics. Those are the origins of all those terms, at least according to Gatto, and, again, you would expect a mathematician to be precise about the origins and use of terminology.</p><p>With all that said, of course Paul Lockhart is right about how to improve mathematics education. But, it will never work within a Prussian-derived school system with no interest in truly educating children, despite every person who works at a school calling themselves an educator, and despite the truth that most of the people in schools might be fine educators if given the chance and a few years of untraining of their bad habits.<br>
&nbsp; &nbsp; "The Emergence of Compulsory Schooling and<nobr> <wbr></nobr>... Resistance"<br>
&nbsp; &nbsp; <a href="http://web.archive.org/web/20071014123355/http://www.social-ecology.org/article.php?story=20031028151034651" title="archive.org">http://web.archive.org/web/20071014123355/http://www.social-ecology.org/article.php?story=20031028151034651</a> [archive.org]</p><p>Anyway, sorry to be so harsh on you, Paul. Read "Disciplined Minds" and start building a social network to help you and them and others break out of the prison around you:<br>
&nbsp; &nbsp; "Disciplined Minds: A Critical Look at Salaried Professionals and the Soul-Battering System That Shapes Their Lives"<br>
&nbsp; &nbsp; <a href="http://www.disciplined-minds.com/" title="disciplined-minds.com">http://www.disciplined-minds.com/</a> [disciplined-minds.com]</p><p>The good news is, you have already taken the first step of getting out of the prison others have forced you to build for yourself.</p></htmltext>
<tokenext>Now , that is a very inflammatory subject title , so let me explain what I mean.I was glad to see a previous comment referencing John Taylor Gatto .
I do not see Gatto 's name in the PDF document .
Neither do I see John Holt 's name .
The fact is , the purpose of " schooling " ( which is not the same as " education " , and you would expect a mathematician to be more precise in a use of terms ) is precisely to do what the mathematician decries at the end : " And there you have it .
A complete prescription for permanently disabling young minds-- a proven cure for curiosity .
What have they done to mathematics !
There is such breathtaking depth and heartbreaking beauty in this ancient art form .
How ironic that people dismiss mathematics as the antithesis of creativity .
They are missing out on an art form older than any book , more profound than any poem , and more abstract than any abstract .
And it is school that has done this !
What a sad endless cycle of innocent teachers inflicting damage upon innocent students .
We could all be having so much more fun .
" Education in the USA will not improve until people like this mathematician accept that what he said is the intentional purpose of schooling in all subjects for almost all children .
See things like :     " The 7-Lesson Schoolteacher " by John Taylor Gatto , NYS Teacher of the Year     http : //www.newciv.org/whole/schoolteacher.txt [ newciv.org ] or :     " The Big Crunch " by Dr. David Goodstein , Vice Provost Caltech     http : //www.its.caltech.edu/ ~ dg/crunch \ _art.html [ caltech.edu ] or :     " Growing Without Schooling " about John Holt 's work , including failed attempts to reform schools     http : //www.holtgws.com/ [ holtgws.com ] At this point , it is people like Paul Lockhart who are the problem .
People who think school is about education , when it is about socialization in a certain way intended for the most part to produce compliant workers , obedient soldiers , and mindless consumers .
School is for fish .
Curriculums are race tracks .
And " class rooms " are literally to build social classes through selective breeding by genetics .
Those are the origins of all those terms , at least according to Gatto , and , again , you would expect a mathematician to be precise about the origins and use of terminology.With all that said , of course Paul Lockhart is right about how to improve mathematics education .
But , it will never work within a Prussian-derived school system with no interest in truly educating children , despite every person who works at a school calling themselves an educator , and despite the truth that most of the people in schools might be fine educators if given the chance and a few years of untraining of their bad habits .
    " The Emergence of Compulsory Schooling and ... Resistance "     http : //web.archive.org/web/20071014123355/http : //www.social-ecology.org/article.php ? story = 20031028151034651 [ archive.org ] Anyway , sorry to be so harsh on you , Paul .
Read " Disciplined Minds " and start building a social network to help you and them and others break out of the prison around you :     " Disciplined Minds : A Critical Look at Salaried Professionals and the Soul-Battering System That Shapes Their Lives "     http : //www.disciplined-minds.com/ [ disciplined-minds.com ] The good news is , you have already taken the first step of getting out of the prison others have forced you to build for yourself .</tokentext>
<sentencetext>Now, that is a very inflammatory subject title, so let me explain what I mean.I was glad to see a previous comment referencing John Taylor Gatto.
I do not see Gatto's name in the PDF document.
Neither do I see John Holt's name.
The fact is, the purpose of "schooling" (which is not the same as "education", and you would expect a mathematician to be more precise in a use of terms) is precisely to do what the mathematician decries at the end: "And there you have it.
A complete prescription for permanently disabling young minds-- a proven cure for curiosity.
What have they done to mathematics!
There is such breathtaking depth and heartbreaking beauty in this ancient art form.
How ironic that people dismiss mathematics as the antithesis of creativity.
They are missing out on an art form older than any book, more profound than any poem, and more abstract than any abstract.
And it is school that has done this!
What a sad endless cycle of innocent teachers inflicting damage upon innocent students.
We could all be having so much more fun.
"Education in the USA will not improve until people like this mathematician accept that what he said is the intentional purpose of schooling in all subjects for almost all children.
See things like:
    "The 7-Lesson Schoolteacher" by John Taylor Gatto, NYS Teacher of the Year
    http://www.newciv.org/whole/schoolteacher.txt [newciv.org]or:
    "The Big Crunch" by Dr. David Goodstein, Vice Provost Caltech
    http://www.its.caltech.edu/~dg/crunch\_art.html [caltech.edu]or:
    "Growing Without Schooling" about John Holt's work, including failed attempts to reform schools
    http://www.holtgws.com/ [holtgws.com]At this point, it is people like Paul Lockhart who are the problem.
People who think school is about education, when it is about socialization in a certain way intended for the most part to produce compliant workers, obedient soldiers, and mindless consumers.
School is for fish.
Curriculums are race tracks.
And "class rooms" are literally to build social classes through selective breeding by genetics.
Those are the origins of all those terms, at least according to Gatto, and, again, you would expect a mathematician to be precise about the origins and use of terminology.With all that said, of course Paul Lockhart is right about how to improve mathematics education.
But, it will never work within a Prussian-derived school system with no interest in truly educating children, despite every person who works at a school calling themselves an educator, and despite the truth that most of the people in schools might be fine educators if given the chance and a few years of untraining of their bad habits.
    "The Emergence of Compulsory Schooling and ... Resistance"
    http://web.archive.org/web/20071014123355/http://www.social-ecology.org/article.php?story=20031028151034651 [archive.org]Anyway, sorry to be so harsh on you, Paul.
Read "Disciplined Minds" and start building a social network to help you and them and others break out of the prison around you:
    "Disciplined Minds: A Critical Look at Salaried Professionals and the Soul-Battering System That Shapes Their Lives"
    http://www.disciplined-minds.com/ [disciplined-minds.com]The good news is, you have already taken the first step of getting out of the prison others have forced you to build for yourself.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393349</id>
	<title>Re:Cue the other subjects</title>
	<author>Anonymous</author>
	<datestamp>1245440580000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>
Really?  Fundamentalists?  The kind of people that home school their kids?  They're to blame?  Not teacher's unions?  Not parents who treat school like a babysitter?  Not the kids who graduate high school unable to read?
</p></htmltext>
<tokenext>Really ?
Fundamentalists ? The kind of people that home school their kids ?
They 're to blame ?
Not teacher 's unions ?
Not parents who treat school like a babysitter ?
Not the kids who graduate high school unable to read ?</tokentext>
<sentencetext>
Really?
Fundamentalists?  The kind of people that home school their kids?
They're to blame?
Not teacher's unions?
Not parents who treat school like a babysitter?
Not the kids who graduate high school unable to read?
</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393083</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28395249</id>
	<title>Re:US School System compared to Europes School Sys</title>
	<author>bADlOGIN</author>
	<datestamp>1245403860000</datestamp>
	<modclass>Informativ</modclass>
	<modscore>2</modscore>
	<htmltext>You must have attended a private or EXTREMELY large school.  Most US schools are nowhere near the described Netherlands system.  At best, you've got three tracks - "honors" which targets the cookie-cutter wrote memory college tracked kids, standard for those who aren't fighting or don't care about math scores WRT university applications, and "essentials" for poor suffering masses who are not picking up or don't care to do the work.  This is the situation in Washington State, Kent School district which is the 4th largest district in a High School with over 2600 students.  Even this delineation of "skill" is still cranked through the un-inspired compulsory  process Lockhart complains about.  If you want to know why, check out John Taylor Gatto's "The Underground History of American Education" (http://www.johntaylorgatto.com/underground/).<br><br>Saying knowledge comes from a schooling about as correct as saying milk comes from a store.  When you understand in both cases it's just simple packaging and processing, you can start asking questions about what it is, why it is, and how you can get it on your own, and how to evaluate the quality of the sources you get it from.</htmltext>
<tokenext>You must have attended a private or EXTREMELY large school .
Most US schools are nowhere near the described Netherlands system .
At best , you 've got three tracks - " honors " which targets the cookie-cutter wrote memory college tracked kids , standard for those who are n't fighting or do n't care about math scores WRT university applications , and " essentials " for poor suffering masses who are not picking up or do n't care to do the work .
This is the situation in Washington State , Kent School district which is the 4th largest district in a High School with over 2600 students .
Even this delineation of " skill " is still cranked through the un-inspired compulsory process Lockhart complains about .
If you want to know why , check out John Taylor Gatto 's " The Underground History of American Education " ( http : //www.johntaylorgatto.com/underground/ ) .Saying knowledge comes from a schooling about as correct as saying milk comes from a store .
When you understand in both cases it 's just simple packaging and processing , you can start asking questions about what it is , why it is , and how you can get it on your own , and how to evaluate the quality of the sources you get it from .</tokentext>
<sentencetext>You must have attended a private or EXTREMELY large school.
Most US schools are nowhere near the described Netherlands system.
At best, you've got three tracks - "honors" which targets the cookie-cutter wrote memory college tracked kids, standard for those who aren't fighting or don't care about math scores WRT university applications, and "essentials" for poor suffering masses who are not picking up or don't care to do the work.
This is the situation in Washington State, Kent School district which is the 4th largest district in a High School with over 2600 students.
Even this delineation of "skill" is still cranked through the un-inspired compulsory  process Lockhart complains about.
If you want to know why, check out John Taylor Gatto's "The Underground History of American Education" (http://www.johntaylorgatto.com/underground/).Saying knowledge comes from a schooling about as correct as saying milk comes from a store.
When you understand in both cases it's just simple packaging and processing, you can start asking questions about what it is, why it is, and how you can get it on your own, and how to evaluate the quality of the sources you get it from.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393241</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28397645</id>
	<title>Re:You can convince me</title>
	<author>Anonymous</author>
	<datestamp>1245416940000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>I profoundly thank you for introducing me to the word 'arrogation'.</p></htmltext>
<tokenext>I profoundly thank you for introducing me to the word 'arrogation' .</tokentext>
<sentencetext>I profoundly thank you for introducing me to the word 'arrogation'.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393159</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28397499</id>
	<title>Re:The way math is structured is disconnected from</title>
	<author>Anonymous</author>
	<datestamp>1245415680000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>It's worth noting that this type of creative math education would be extremely helpful in coding and development of all kinds. The process of writing a program to perform a task is very similar to devising a proper mental solution to a mathematical problem -- at least that's how I've always felt.</p></htmltext>
<tokenext>It 's worth noting that this type of creative math education would be extremely helpful in coding and development of all kinds .
The process of writing a program to perform a task is very similar to devising a proper mental solution to a mathematical problem -- at least that 's how I 've always felt .</tokentext>
<sentencetext>It's worth noting that this type of creative math education would be extremely helpful in coding and development of all kinds.
The process of writing a program to perform a task is very similar to devising a proper mental solution to a mathematical problem -- at least that's how I've always felt.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392921</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28396023</id>
	<title>Re:Single Best Fix: Introducing Discrete Mathemati</title>
	<author>Gospodin</author>
	<datestamp>1245407160000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>I don't dispute the premise that US math education sucks, or that it would be useful to add Discrete Math to the list. However, your assertion that all those courses are "just plug and chug" is just absurd. Geometry is generally centered around proofs - this is the first class most students ever have in which they are expected to learn a set of axioms and theorems, and construct new theorems from them. Trigonometry places some emphasis, at least, on trig identities, e.g. prove that tanx sinx = secx - cosx. Not extremely hard, but it's not just plugging numbers into formulas.</p><p>Calculus is similar: you work on limits, learning symbol manipulation rules like the chain rule and integration by parts, etc. Heck, even in algebra I you learn factoring polynomials, which is not at all plug and chug.</p><p>Again, don't get me wrong: I'm all in favor of more proofs and reasoning about math. But you're still mischaracterizing the rest of high-school math.</p></htmltext>
<tokenext>I do n't dispute the premise that US math education sucks , or that it would be useful to add Discrete Math to the list .
However , your assertion that all those courses are " just plug and chug " is just absurd .
Geometry is generally centered around proofs - this is the first class most students ever have in which they are expected to learn a set of axioms and theorems , and construct new theorems from them .
Trigonometry places some emphasis , at least , on trig identities , e.g .
prove that tanx sinx = secx - cosx .
Not extremely hard , but it 's not just plugging numbers into formulas.Calculus is similar : you work on limits , learning symbol manipulation rules like the chain rule and integration by parts , etc .
Heck , even in algebra I you learn factoring polynomials , which is not at all plug and chug.Again , do n't get me wrong : I 'm all in favor of more proofs and reasoning about math .
But you 're still mischaracterizing the rest of high-school math .</tokentext>
<sentencetext>I don't dispute the premise that US math education sucks, or that it would be useful to add Discrete Math to the list.
However, your assertion that all those courses are "just plug and chug" is just absurd.
Geometry is generally centered around proofs - this is the first class most students ever have in which they are expected to learn a set of axioms and theorems, and construct new theorems from them.
Trigonometry places some emphasis, at least, on trig identities, e.g.
prove that tanx sinx = secx - cosx.
Not extremely hard, but it's not just plugging numbers into formulas.Calculus is similar: you work on limits, learning symbol manipulation rules like the chain rule and integration by parts, etc.
Heck, even in algebra I you learn factoring polynomials, which is not at all plug and chug.Again, don't get me wrong: I'm all in favor of more proofs and reasoning about math.
But you're still mischaracterizing the rest of high-school math.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394873</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28397885</id>
	<title>Re:Two mathematicians</title>
	<author>juancnuno</author>
	<datestamp>1245418560000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>An exponential function and a constant function are walking down the street. In the distance they spot a differential operator. The constant function goes, "Oh no! A differential operator! If he gets to me I'm screwed!"</p><p>The exponential function confidently responds, "I'm not afraid! I'm e^x!"</p><p>The constant function says, "Well, I'm not sticking around to see what happens."</p><p>The exponential function and the constant function part ways. The exponential function reaches the differential operator and boasts, "I'm not afraid of you! I'm e^x!"</p><p>And the differential operator answers, "I'm d/dy."</p><p> <a href="http://instantrimshot.com/" title="instantrimshot.com" rel="nofollow">http://instantrimshot.com/</a> [instantrimshot.com] </p></htmltext>
<tokenext>An exponential function and a constant function are walking down the street .
In the distance they spot a differential operator .
The constant function goes , " Oh no !
A differential operator !
If he gets to me I 'm screwed !
" The exponential function confidently responds , " I 'm not afraid !
I 'm e ^ x !
" The constant function says , " Well , I 'm not sticking around to see what happens .
" The exponential function and the constant function part ways .
The exponential function reaches the differential operator and boasts , " I 'm not afraid of you !
I 'm e ^ x !
" And the differential operator answers , " I 'm d/dy .
" http : //instantrimshot.com/ [ instantrimshot.com ]</tokentext>
<sentencetext>An exponential function and a constant function are walking down the street.
In the distance they spot a differential operator.
The constant function goes, "Oh no!
A differential operator!
If he gets to me I'm screwed!
"The exponential function confidently responds, "I'm not afraid!
I'm e^x!
"The constant function says, "Well, I'm not sticking around to see what happens.
"The exponential function and the constant function part ways.
The exponential function reaches the differential operator and boasts, "I'm not afraid of you!
I'm e^x!
"And the differential operator answers, "I'm d/dy.
" http://instantrimshot.com/ [instantrimshot.com] </sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393275</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392881</id>
	<title>Slashdotted</title>
	<author>PPH</author>
	<datestamp>1245438840000</datestamp>
	<modclass>Funny</modclass>
	<modscore>3</modscore>
	<htmltext>Evidently, someone didn't do the server math.</htmltext>
<tokenext>Evidently , someone did n't do the server math .</tokentext>
<sentencetext>Evidently, someone didn't do the server math.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393633</id>
	<title>Re:True story ....</title>
	<author>Anonymous</author>
	<datestamp>1245441600000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p><div class="quote"><p>If that's indicative of how math is taught nowadays, we're all hosed.<nobr> <wbr></nobr>:-P</p></div><p>It is. Public Schools are all about regurgitating back what the teacher said in class on a piece of paper, regardless of what the question/numbers actually say.</p><p>It's sickening.</p></div>
	</htmltext>
<tokenext>If that 's indicative of how math is taught nowadays , we 're all hosed .
: -PIt is .
Public Schools are all about regurgitating back what the teacher said in class on a piece of paper , regardless of what the question/numbers actually say.It 's sickening .</tokentext>
<sentencetext>If that's indicative of how math is taught nowadays, we're all hosed.
:-PIt is.
Public Schools are all about regurgitating back what the teacher said in class on a piece of paper, regardless of what the question/numbers actually say.It's sickening.
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392947</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393503</id>
	<title>Re:US School System compared to Europes School Sys</title>
	<author>PeanutButterBreath</author>
	<datestamp>1245441180000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>US schools have Advanced Placement classes.  Oh yeah, and there is no reason motivated students can't move at their own pace outside of the classroom (or inside).</p><p>All you are calling for is a system that offers more than one sized spoon with which to feed students.  That's just a better version of a fundamentally flawed educational philosophy.  Or rather, it stretches a fine philosophy beyond its logical limit and makes it flawed.  A chef can get by just fine with a US HS level understanding of math, for example.  More math won't make better chefs (the opposite, potentially).</p><p>If a person's excuse for having less education than they wanted (or than Europenas might have) is that the US school system only caters to the lowest common denominator, they are lazy, not deprived.</p></htmltext>
<tokenext>US schools have Advanced Placement classes .
Oh yeah , and there is no reason motivated students ca n't move at their own pace outside of the classroom ( or inside ) .All you are calling for is a system that offers more than one sized spoon with which to feed students .
That 's just a better version of a fundamentally flawed educational philosophy .
Or rather , it stretches a fine philosophy beyond its logical limit and makes it flawed .
A chef can get by just fine with a US HS level understanding of math , for example .
More math wo n't make better chefs ( the opposite , potentially ) .If a person 's excuse for having less education than they wanted ( or than Europenas might have ) is that the US school system only caters to the lowest common denominator , they are lazy , not deprived .</tokentext>
<sentencetext>US schools have Advanced Placement classes.
Oh yeah, and there is no reason motivated students can't move at their own pace outside of the classroom (or inside).All you are calling for is a system that offers more than one sized spoon with which to feed students.
That's just a better version of a fundamentally flawed educational philosophy.
Or rather, it stretches a fine philosophy beyond its logical limit and makes it flawed.
A chef can get by just fine with a US HS level understanding of math, for example.
More math won't make better chefs (the opposite, potentially).If a person's excuse for having less education than they wanted (or than Europenas might have) is that the US school system only caters to the lowest common denominator, they are lazy, not deprived.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393035</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392991</id>
	<title>US K-12 MATH = Real world fail.</title>
	<author>Anonymous</author>
	<datestamp>1245439320000</datestamp>
	<modclass>Interestin</modclass>
	<modscore>1</modscore>
	<htmltext><p>Just the other day, I was watching "Who wants to be a Millionare?" And a 24 year long high school teacher didn't know what the sign for factorial means. Choices where along the lines of : ! &amp; \%</p></htmltext>
<tokenext>Just the other day , I was watching " Who wants to be a Millionare ?
" And a 24 year long high school teacher did n't know what the sign for factorial means .
Choices where along the lines of : !
&amp; \ %</tokentext>
<sentencetext>Just the other day, I was watching "Who wants to be a Millionare?
" And a 24 year long high school teacher didn't know what the sign for factorial means.
Choices where along the lines of : !
&amp; \%</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28402089</id>
	<title>Re:Eh.</title>
	<author>Lost Engineer</author>
	<datestamp>1245515040000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p><div class="quote"><p>Most jobs in this world do not require 90\% of the theorems and principles that people are forced to learn through high school.</p></div><p>Herein lies the problem:  certainly 90\% of high school students don't need to learn those theorems in high school but our future math grad students certainly do.  Some people would argue it would be a shame to segregate those students at such an early level, but it seems that successful schools abroad are already doing this.  To some extent this happens in good schools in the US via the AP Calculus program.</p><p>Actually my one beef with the US AP Calc program is that colleges accept the credits and dump freshmen into something like Differential Equations.  I know on some level that is supposed to a be a crucible, but it would not have killed me to have some sort of transition between "ok I can solve calculus problems" to "I can solve problems where understanding of calculus is necessary and taken for granted."</p></div>
	</htmltext>
<tokenext>Most jobs in this world do not require 90 \ % of the theorems and principles that people are forced to learn through high school.Herein lies the problem : certainly 90 \ % of high school students do n't need to learn those theorems in high school but our future math grad students certainly do .
Some people would argue it would be a shame to segregate those students at such an early level , but it seems that successful schools abroad are already doing this .
To some extent this happens in good schools in the US via the AP Calculus program.Actually my one beef with the US AP Calc program is that colleges accept the credits and dump freshmen into something like Differential Equations .
I know on some level that is supposed to a be a crucible , but it would not have killed me to have some sort of transition between " ok I can solve calculus problems " to " I can solve problems where understanding of calculus is necessary and taken for granted .
"</tokentext>
<sentencetext>Most jobs in this world do not require 90\% of the theorems and principles that people are forced to learn through high school.Herein lies the problem:  certainly 90\% of high school students don't need to learn those theorems in high school but our future math grad students certainly do.
Some people would argue it would be a shame to segregate those students at such an early level, but it seems that successful schools abroad are already doing this.
To some extent this happens in good schools in the US via the AP Calculus program.Actually my one beef with the US AP Calc program is that colleges accept the credits and dump freshmen into something like Differential Equations.
I know on some level that is supposed to a be a crucible, but it would not have killed me to have some sort of transition between "ok I can solve calculus problems" to "I can solve problems where understanding of calculus is necessary and taken for granted.
"
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393717</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394145</id>
	<title>Re:Oh give it a rest</title>
	<author>JumpDrive</author>
	<datestamp>1245443460000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>I would at least hope that they could reach a middle ground.<br>
In the past the state of Texas chose Physics text books without anyone having a physics background.  The same for the curriculum.  I saw some of the original tests which were going to be used for standardized performance examinations and the questions appeared to come from electrician tests.  A number of graduate students were asked to peruse the examination, I think basically all of us sat there and looked over the exam for about 5 minutes and said WTF.  We then thought that, well we hadn't read through it enough and started looking for anything about electro-magnetic fields.  We found one question.  It seemed obvious to us that there intention was to turn the second semester of Physics into a vocational school for electricians.  <br>
I have since met a number of graduates from high school here and somewhere this apparently got turned back around.  But it really kind of worried me that they were even considering this.</htmltext>
<tokenext>I would at least hope that they could reach a middle ground .
In the past the state of Texas chose Physics text books without anyone having a physics background .
The same for the curriculum .
I saw some of the original tests which were going to be used for standardized performance examinations and the questions appeared to come from electrician tests .
A number of graduate students were asked to peruse the examination , I think basically all of us sat there and looked over the exam for about 5 minutes and said WTF .
We then thought that , well we had n't read through it enough and started looking for anything about electro-magnetic fields .
We found one question .
It seemed obvious to us that there intention was to turn the second semester of Physics into a vocational school for electricians .
I have since met a number of graduates from high school here and somewhere this apparently got turned back around .
But it really kind of worried me that they were even considering this .</tokentext>
<sentencetext>I would at least hope that they could reach a middle ground.
In the past the state of Texas chose Physics text books without anyone having a physics background.
The same for the curriculum.
I saw some of the original tests which were going to be used for standardized performance examinations and the questions appeared to come from electrician tests.
A number of graduate students were asked to peruse the examination, I think basically all of us sat there and looked over the exam for about 5 minutes and said WTF.
We then thought that, well we hadn't read through it enough and started looking for anything about electro-magnetic fields.
We found one question.
It seemed obvious to us that there intention was to turn the second semester of Physics into a vocational school for electricians.
I have since met a number of graduates from high school here and somewhere this apparently got turned back around.
But it really kind of worried me that they were even considering this.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392993</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28397713</id>
	<title>Re:US School System compared to Europes School Sys</title>
	<author>Anonymous</author>
	<datestamp>1245417360000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>Well, sorry but I have to disagree with you here.</p><p>Personally, I am 16 and currently at High School in the UK. What you have described is exactly the same situation we have here.</p><p>Also, I have spent this week at a trial event for what is a section of the proposed new physics course for the whole of scotland. Easy, does not even begin to explain it. If you cannot, at my age, or even a few years prior to it understand that course then you deserve to spend your life cleaning bins I personally feel. The worst part is that it is for the new "Higher" course which is regarded as one of the highest levels that can be achieved in High School here. Maths is the same.</p><p>Maths at my School is taught as a series of completely useless garbage that has absolutely no relation to anything in the real world. I think the following conversation with another boy in my class last year about sums this up. This was during a lesson on Quadratic Formula:<br><b>Pupil:</b> Miss, what exactly are we EVER going to use this for?<br><b>Teacher:</b> To pass your exams!<br><b>Pupil:</b> No, I mean like, actually use it when we get a job or something?<br><b>Teacher:</b> You will need to pass your exams to get a job.</p><p>Very, very sad in my opinion. The only teacher Ive ever found to go against this was a previous English teacher of mines, fantastic guy. He realised that being the top english class, it would take a fraction of the time to actually learn the course than the time we had. So he would bassically spend a very small amount of time doing "lessons" and then the rest of period debating things, class discussions. REAL interesting topics where we weren't learning anything by the stats definition, but I certainly learned far more in that time than any other subjects in that school. Physics was similar but I think Physics teachers tend to be the most laid back, anti-disestablishmentarian type of teachers around.</p></htmltext>
<tokenext>Well , sorry but I have to disagree with you here.Personally , I am 16 and currently at High School in the UK .
What you have described is exactly the same situation we have here.Also , I have spent this week at a trial event for what is a section of the proposed new physics course for the whole of scotland .
Easy , does not even begin to explain it .
If you can not , at my age , or even a few years prior to it understand that course then you deserve to spend your life cleaning bins I personally feel .
The worst part is that it is for the new " Higher " course which is regarded as one of the highest levels that can be achieved in High School here .
Maths is the same.Maths at my School is taught as a series of completely useless garbage that has absolutely no relation to anything in the real world .
I think the following conversation with another boy in my class last year about sums this up .
This was during a lesson on Quadratic Formula : Pupil : Miss , what exactly are we EVER going to use this for ? Teacher : To pass your exams ! Pupil : No , I mean like , actually use it when we get a job or something ? Teacher : You will need to pass your exams to get a job.Very , very sad in my opinion .
The only teacher Ive ever found to go against this was a previous English teacher of mines , fantastic guy .
He realised that being the top english class , it would take a fraction of the time to actually learn the course than the time we had .
So he would bassically spend a very small amount of time doing " lessons " and then the rest of period debating things , class discussions .
REAL interesting topics where we were n't learning anything by the stats definition , but I certainly learned far more in that time than any other subjects in that school .
Physics was similar but I think Physics teachers tend to be the most laid back , anti-disestablishmentarian type of teachers around .</tokentext>
<sentencetext>Well, sorry but I have to disagree with you here.Personally, I am 16 and currently at High School in the UK.
What you have described is exactly the same situation we have here.Also, I have spent this week at a trial event for what is a section of the proposed new physics course for the whole of scotland.
Easy, does not even begin to explain it.
If you cannot, at my age, or even a few years prior to it understand that course then you deserve to spend your life cleaning bins I personally feel.
The worst part is that it is for the new "Higher" course which is regarded as one of the highest levels that can be achieved in High School here.
Maths is the same.Maths at my School is taught as a series of completely useless garbage that has absolutely no relation to anything in the real world.
I think the following conversation with another boy in my class last year about sums this up.
This was during a lesson on Quadratic Formula:Pupil: Miss, what exactly are we EVER going to use this for?Teacher: To pass your exams!Pupil: No, I mean like, actually use it when we get a job or something?Teacher: You will need to pass your exams to get a job.Very, very sad in my opinion.
The only teacher Ive ever found to go against this was a previous English teacher of mines, fantastic guy.
He realised that being the top english class, it would take a fraction of the time to actually learn the course than the time we had.
So he would bassically spend a very small amount of time doing "lessons" and then the rest of period debating things, class discussions.
REAL interesting topics where we weren't learning anything by the stats definition, but I certainly learned far more in that time than any other subjects in that school.
Physics was similar but I think Physics teachers tend to be the most laid back, anti-disestablishmentarian type of teachers around.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393035</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393495</id>
	<title>Re:US School System compared to Europes School Sys</title>
	<author>Fallingcow</author>
	<datestamp>1245441120000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>The big buzz word/trendy strategy in elementary-level teaching right now is "differentiated instruction".  What it means is teaching a single concept at several levels of difficulty simultaneously.  It's sort of like ability grouping into different classes like you talk about, but all in one classroom and with one teacher (and maybe a TA or Para or some such).</p><p>It's actually pretty good when it's done right, but as far as I can tell most elementary school teachers are <i>awful</i> at coming up with effective differentiated lesson plans.  Many just think it's impossible and refuse to even try.  I expect it to go away in a few years, just like most of the other trendy teaching ideas since, well, <i>forever</i> ago.  Maybe we'll move toward having separate ability-grouped classes after it fails.</p></htmltext>
<tokenext>The big buzz word/trendy strategy in elementary-level teaching right now is " differentiated instruction " .
What it means is teaching a single concept at several levels of difficulty simultaneously .
It 's sort of like ability grouping into different classes like you talk about , but all in one classroom and with one teacher ( and maybe a TA or Para or some such ) .It 's actually pretty good when it 's done right , but as far as I can tell most elementary school teachers are awful at coming up with effective differentiated lesson plans .
Many just think it 's impossible and refuse to even try .
I expect it to go away in a few years , just like most of the other trendy teaching ideas since , well , forever ago .
Maybe we 'll move toward having separate ability-grouped classes after it fails .</tokentext>
<sentencetext>The big buzz word/trendy strategy in elementary-level teaching right now is "differentiated instruction".
What it means is teaching a single concept at several levels of difficulty simultaneously.
It's sort of like ability grouping into different classes like you talk about, but all in one classroom and with one teacher (and maybe a TA or Para or some such).It's actually pretty good when it's done right, but as far as I can tell most elementary school teachers are awful at coming up with effective differentiated lesson plans.
Many just think it's impossible and refuse to even try.
I expect it to go away in a few years, just like most of the other trendy teaching ideas since, well, forever ago.
Maybe we'll move toward having separate ability-grouped classes after it fails.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393035</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394463</id>
	<title>Re:US School System compared to Europes School Sys</title>
	<author>gbarules2999</author>
	<datestamp>1245444540000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>Honor classes are pretty widespread nowadays, and offered to whoever wants to get in.</htmltext>
<tokenext>Honor classes are pretty widespread nowadays , and offered to whoever wants to get in .</tokentext>
<sentencetext>Honor classes are pretty widespread nowadays, and offered to whoever wants to get in.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393751</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394309</id>
	<title>Housecats</title>
	<author>MikeURL</author>
	<datestamp>1245444000000</datestamp>
	<modclass>Insightful</modclass>
	<modscore>2</modscore>
	<htmltext>I think the author misses the point.  The effort behind teaching math should not try to get everyone to love it.  It is, at least partially, twofold:
<ol>
<li>1) Try to keep humans a little bit above the level of a potted plant</li>
<li>2) Offer the opportunity for the inclined to learn a subject they will grow to love.</li>
</ol><p>
The author wants to a priori assume that everyone will love math if only the beauty of it is shown to them.  This is mistaken.  There are many beautiful things in the world that lots of people have absolutely no interest in.  If you tried to force the beauty on everyone then you'd cheapen the entire meaning of beauty.  Yes, in the lower grades math is a pretty mechanical thing that just equips human beings with the basics but that is OK.  The Einsteins take to that like a fish to water and do their amazing work because they see the beauty without anyone saying "HEY, appreciate!"</p></htmltext>
<tokenext>I think the author misses the point .
The effort behind teaching math should not try to get everyone to love it .
It is , at least partially , twofold : 1 ) Try to keep humans a little bit above the level of a potted plant 2 ) Offer the opportunity for the inclined to learn a subject they will grow to love .
The author wants to a priori assume that everyone will love math if only the beauty of it is shown to them .
This is mistaken .
There are many beautiful things in the world that lots of people have absolutely no interest in .
If you tried to force the beauty on everyone then you 'd cheapen the entire meaning of beauty .
Yes , in the lower grades math is a pretty mechanical thing that just equips human beings with the basics but that is OK. The Einsteins take to that like a fish to water and do their amazing work because they see the beauty without anyone saying " HEY , appreciate !
"</tokentext>
<sentencetext>I think the author misses the point.
The effort behind teaching math should not try to get everyone to love it.
It is, at least partially, twofold:

1) Try to keep humans a little bit above the level of a potted plant
2) Offer the opportunity for the inclined to learn a subject they will grow to love.
The author wants to a priori assume that everyone will love math if only the beauty of it is shown to them.
This is mistaken.
There are many beautiful things in the world that lots of people have absolutely no interest in.
If you tried to force the beauty on everyone then you'd cheapen the entire meaning of beauty.
Yes, in the lower grades math is a pretty mechanical thing that just equips human beings with the basics but that is OK.  The Einsteins take to that like a fish to water and do their amazing work because they see the beauty without anyone saying "HEY, appreciate!
"</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28397417</id>
	<title>Re:The way math is structured is disconnected from</title>
	<author>Anonymous</author>
	<datestamp>1245414900000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext>From <a href="http://www.symmetryperfect.com/" title="symmetryperfect.com" rel="nofollow">http://www.symmetryperfect.com/</a> [symmetryperfect.com]:<p><div class="quote"><p>This unconventional work initially involves the creation of a revised multiplication in which the revised product of two negative factors equals a negative real number, contrary to conventional multiplication.  This precludes the existence of the unit imaginary number and thus, the complex number system.</p></div><p>Takes mathematics back at least 300 years, if not a couple thousand, and prevents the development of most modern technology: useful alternating current circuits (complex impedance), GPS (relativity), solid-state memory (quantum mechanics), etc. Complex numbers made these advances possible, and you'd throw them out because "mathematicians have made them hard to understand."  Fantastic.</p><p><div class="quote"><p>In revised algebra, a binomial, linear equation to the nth (any) degree is solvable since after revised cross-multiplication, it is reducible to the original, first degree equation.  In conventional algebra, a binomial, linear equation to the fifth degree or higher is generally impossible to derive solutions for.</p></div><p>For every n &gt; 4 there are polynomials of degree n which are <a href="http://en.wikipedia.org/wiki/Solvable\_group" title="wikipedia.org" rel="nofollow">not solvable</a> [wikipedia.org] by radicals.  If this person has discovered otherwise, I'd like to see a concrete example.  Give me a root of f(x)=x^5-x-1 using only radicals. If you can, I know a few awards committees that would like to speak with you.
</p><p>
To the parent poster: you have a valid point that math should be taught with a stronger connection to the real world. I agree 100\% with you.
</p><p>
However, real science is damned hard, and demands results, not complaints.  If you've got a better way of thinking about math that will make it easier to do real science, by all means, let the scientific community know, they'll love you for it.  But you aren't going to convince people by linking to quacks.  When you come at the problem with "throw out complex numbers" and "the Mayans were way smart", you need to back that up with "here's why science is better without complex numbers -- because I can predict X" or "thinking about numbers using shapes has these advantages..."  Otherwise, you have no credibility, you're just whinging.</p></div>
	</htmltext>
<tokenext>From http : //www.symmetryperfect.com/ [ symmetryperfect.com ] : This unconventional work initially involves the creation of a revised multiplication in which the revised product of two negative factors equals a negative real number , contrary to conventional multiplication .
This precludes the existence of the unit imaginary number and thus , the complex number system.Takes mathematics back at least 300 years , if not a couple thousand , and prevents the development of most modern technology : useful alternating current circuits ( complex impedance ) , GPS ( relativity ) , solid-state memory ( quantum mechanics ) , etc .
Complex numbers made these advances possible , and you 'd throw them out because " mathematicians have made them hard to understand .
" Fantastic.In revised algebra , a binomial , linear equation to the nth ( any ) degree is solvable since after revised cross-multiplication , it is reducible to the original , first degree equation .
In conventional algebra , a binomial , linear equation to the fifth degree or higher is generally impossible to derive solutions for.For every n &gt; 4 there are polynomials of degree n which are not solvable [ wikipedia.org ] by radicals .
If this person has discovered otherwise , I 'd like to see a concrete example .
Give me a root of f ( x ) = x ^ 5-x-1 using only radicals .
If you can , I know a few awards committees that would like to speak with you .
To the parent poster : you have a valid point that math should be taught with a stronger connection to the real world .
I agree 100 \ % with you .
However , real science is damned hard , and demands results , not complaints .
If you 've got a better way of thinking about math that will make it easier to do real science , by all means , let the scientific community know , they 'll love you for it .
But you are n't going to convince people by linking to quacks .
When you come at the problem with " throw out complex numbers " and " the Mayans were way smart " , you need to back that up with " here 's why science is better without complex numbers -- because I can predict X " or " thinking about numbers using shapes has these advantages... " Otherwise , you have no credibility , you 're just whinging .</tokentext>
<sentencetext>From http://www.symmetryperfect.com/ [symmetryperfect.com]:This unconventional work initially involves the creation of a revised multiplication in which the revised product of two negative factors equals a negative real number, contrary to conventional multiplication.
This precludes the existence of the unit imaginary number and thus, the complex number system.Takes mathematics back at least 300 years, if not a couple thousand, and prevents the development of most modern technology: useful alternating current circuits (complex impedance), GPS (relativity), solid-state memory (quantum mechanics), etc.
Complex numbers made these advances possible, and you'd throw them out because "mathematicians have made them hard to understand.
"  Fantastic.In revised algebra, a binomial, linear equation to the nth (any) degree is solvable since after revised cross-multiplication, it is reducible to the original, first degree equation.
In conventional algebra, a binomial, linear equation to the fifth degree or higher is generally impossible to derive solutions for.For every n &gt; 4 there are polynomials of degree n which are not solvable [wikipedia.org] by radicals.
If this person has discovered otherwise, I'd like to see a concrete example.
Give me a root of f(x)=x^5-x-1 using only radicals.
If you can, I know a few awards committees that would like to speak with you.
To the parent poster: you have a valid point that math should be taught with a stronger connection to the real world.
I agree 100\% with you.
However, real science is damned hard, and demands results, not complaints.
If you've got a better way of thinking about math that will make it easier to do real science, by all means, let the scientific community know, they'll love you for it.
But you aren't going to convince people by linking to quacks.
When you come at the problem with "throw out complex numbers" and "the Mayans were way smart", you need to back that up with "here's why science is better without complex numbers -- because I can predict X" or "thinking about numbers using shapes has these advantages..."  Otherwise, you have no credibility, you're just whinging.
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392921</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394037</id>
	<title>Re:Oh give it a rest</title>
	<author>mcgrew</author>
	<datestamp>1245443100000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>The problem is they have math majors teaching English, English majors teaching science, and horticulture majors teaching physics.</p><p>The bigger problem is the teachers aren't paid well enough to attract good ones.</p></htmltext>
<tokenext>The problem is they have math majors teaching English , English majors teaching science , and horticulture majors teaching physics.The bigger problem is the teachers are n't paid well enough to attract good ones .</tokentext>
<sentencetext>The problem is they have math majors teaching English, English majors teaching science, and horticulture majors teaching physics.The bigger problem is the teachers aren't paid well enough to attract good ones.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392993</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28398261</id>
	<title>Re:US School System compared to Europes School Sys</title>
	<author>Anonymous</author>
	<datestamp>1245421680000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>Your cousin took linear algebra in high school?</p></htmltext>
<tokenext>Your cousin took linear algebra in high school ?</tokentext>
<sentencetext>Your cousin took linear algebra in high school?</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393035</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28398943</id>
	<title>Stop blaming our education system</title>
	<author>Tablizer</author>
	<datestamp>1245429300000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><blockquote><div><p>The United States is being outclassed in math and science education by a host of other nations.</p></div></blockquote><p>Because:</p><p>A. The US has only about 5\% of the world's population; thus we have only about 5\% of all math whizzes.</p><p>B. Compared to other fields in a given nation, math pays poorly in the US.</p><p>Those who keep blaming it on our education system ignore these facts.<br>
&nbsp; &nbsp; &nbsp;</p></div>
	</htmltext>
<tokenext>The United States is being outclassed in math and science education by a host of other nations.Because : A. The US has only about 5 \ % of the world 's population ; thus we have only about 5 \ % of all math whizzes.B .
Compared to other fields in a given nation , math pays poorly in the US.Those who keep blaming it on our education system ignore these facts .
     </tokentext>
<sentencetext>The United States is being outclassed in math and science education by a host of other nations.Because:A. The US has only about 5\% of the world's population; thus we have only about 5\% of all math whizzes.B.
Compared to other fields in a given nation, math pays poorly in the US.Those who keep blaming it on our education system ignore these facts.
     
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393115</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394963</id>
	<title>Re:I Sympathize With Him But Too Idyllic</title>
	<author>debest</author>
	<datestamp>1245402900000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p><div class="quote"><p>The paragraph I quote is not the truth, it's wishing for the impossible.  I wish I had a math teacher like this all my life but come on.  The public school system is more worried about getting someone that actualy cares about the students at all.  They can't even find those people let alone people who care about the students <i>and</i> live/eat/sleep/bleed math.</p> </div><p>As someone who went through teacher's college but realized that I was not capable of surviving the stresses of teaching in the public schools, I agree with this wholeheartedly.  After my experience in school and in practicum classrooms, I feel that there are two kinds of teachers that can survive the system:</p><ul><li>the brilliant, enthusiastic, respected "perfect" teacher: you know them when you see them, and there are a few of them in every school,</li><li>the less-than-perfect teacher who inevitably cannot stop students from falling through the cracks, and who really doesn't care (ie: it's just a job)</li></ul><p>Unfortunately for my potential career, I fell into the third category: the imperfect teacher who cared too much to be able to just forge ahead regardless of the failure to reach and inspire some students.  I found the stress of lesson planning and instruction overwhelming, because I was hung up on trying to accommodate the students who had different needs and learning styles, as well as the different levels of ability.  I believe that I was a fairly good teacher overall (and yes, I do love mathematics), but caring about the students really weighs heavily on you when you know you're not able to teach to everyone well.</p></div>
	</htmltext>
<tokenext>The paragraph I quote is not the truth , it 's wishing for the impossible .
I wish I had a math teacher like this all my life but come on .
The public school system is more worried about getting someone that actualy cares about the students at all .
They ca n't even find those people let alone people who care about the students and live/eat/sleep/bleed math .
As someone who went through teacher 's college but realized that I was not capable of surviving the stresses of teaching in the public schools , I agree with this wholeheartedly .
After my experience in school and in practicum classrooms , I feel that there are two kinds of teachers that can survive the system : the brilliant , enthusiastic , respected " perfect " teacher : you know them when you see them , and there are a few of them in every school,the less-than-perfect teacher who inevitably can not stop students from falling through the cracks , and who really does n't care ( ie : it 's just a job ) Unfortunately for my potential career , I fell into the third category : the imperfect teacher who cared too much to be able to just forge ahead regardless of the failure to reach and inspire some students .
I found the stress of lesson planning and instruction overwhelming , because I was hung up on trying to accommodate the students who had different needs and learning styles , as well as the different levels of ability .
I believe that I was a fairly good teacher overall ( and yes , I do love mathematics ) , but caring about the students really weighs heavily on you when you know you 're not able to teach to everyone well .</tokentext>
<sentencetext>The paragraph I quote is not the truth, it's wishing for the impossible.
I wish I had a math teacher like this all my life but come on.
The public school system is more worried about getting someone that actualy cares about the students at all.
They can't even find those people let alone people who care about the students and live/eat/sleep/bleed math.
As someone who went through teacher's college but realized that I was not capable of surviving the stresses of teaching in the public schools, I agree with this wholeheartedly.
After my experience in school and in practicum classrooms, I feel that there are two kinds of teachers that can survive the system:the brilliant, enthusiastic, respected "perfect" teacher: you know them when you see them, and there are a few of them in every school,the less-than-perfect teacher who inevitably cannot stop students from falling through the cracks, and who really doesn't care (ie: it's just a job)Unfortunately for my potential career, I fell into the third category: the imperfect teacher who cared too much to be able to just forge ahead regardless of the failure to reach and inspire some students.
I found the stress of lesson planning and instruction overwhelming, because I was hung up on trying to accommodate the students who had different needs and learning styles, as well as the different levels of ability.
I believe that I was a fairly good teacher overall (and yes, I do love mathematics), but caring about the students really weighs heavily on you when you know you're not able to teach to everyone well.
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392903</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393595</id>
	<title>Re:Cue the other subjects</title>
	<author>Anonymous</author>
	<datestamp>1245441480000</datestamp>
	<modclass>Informativ</modclass>
	<modscore>4</modscore>
	<htmltext><p>Before you troll and bash "fundamentalists" with no proof you should read a few books on why education in the US is in the state we now see.</p><p><a href="http://www.deliberatedumbingdown.com/" title="deliberate...ngdown.com">The Deliberate Dumbing Down of America</a> [deliberate...ngdown.com] By Charlotte Iserbyt</p><p><a href="http://www.johntaylorgatto.com/underground/" title="johntaylorgatto.com">An Underground History of Education</a> [johntaylorgatto.com] by John Gatto</p><p>Or read the <a href="http://www.scribd.com/doc/3768227/Dodd-Report-to-the-Reece-Committee-on-Foundations-1954" title="scribd.com">Dodd Report</a> [scribd.com] to the Reece Committee which investigated Tax Free Foundations in the early 1950's.</p></htmltext>
<tokenext>Before you troll and bash " fundamentalists " with no proof you should read a few books on why education in the US is in the state we now see.The Deliberate Dumbing Down of America [ deliberate...ngdown.com ] By Charlotte IserbytAn Underground History of Education [ johntaylorgatto.com ] by John GattoOr read the Dodd Report [ scribd.com ] to the Reece Committee which investigated Tax Free Foundations in the early 1950 's .</tokentext>
<sentencetext>Before you troll and bash "fundamentalists" with no proof you should read a few books on why education in the US is in the state we now see.The Deliberate Dumbing Down of America [deliberate...ngdown.com] By Charlotte IserbytAn Underground History of Education [johntaylorgatto.com] by John GattoOr read the Dodd Report [scribd.com] to the Reece Committee which investigated Tax Free Foundations in the early 1950's.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393083</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28397615</id>
	<title>Re:Eh.</title>
	<author>Anonymous</author>
	<datestamp>1245416700000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>I second that he missed the point.</p><p>Another part about it that he missed is this: How would the poster have any idea if people did have the ability or did like doing that? We aren't given the chance to find out in our current system.</p></htmltext>
<tokenext>I second that he missed the point.Another part about it that he missed is this : How would the poster have any idea if people did have the ability or did like doing that ?
We are n't given the chance to find out in our current system .</tokentext>
<sentencetext>I second that he missed the point.Another part about it that he missed is this: How would the poster have any idea if people did have the ability or did like doing that?
We aren't given the chance to find out in our current system.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393427</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394959</id>
	<title>Wrong on so many levels</title>
	<author>Locke2005</author>
	<datestamp>1245402900000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>Creativity can neither be taught nor guided. The analogy with painting and music is flawed; there are an infinite number of ways to create a painting or musical composition, but relatively few ways to create a logically consistent mathematical system. While discovering mathematical truths on your own may be fun for the author (it was for me as a child), allowing everybody to write their own Principia Mathematica is simply unpractical and would result in mathematicians being unable to communicate their precious ideas to each other. Learning math is more like learning english; while the author is correct that we shouldn't confuse the language with the beautiful ideas the language is intended to express, it is also true that we can't discuss Shakespeare without a common language for communicating the abstract ideas contained within. I feel the same way about software that this guy feels about math (some programs are much more aesthetically pleasing than others), but his worst mistake is assuming that everybody else should feel the same way about math he does. Unlike art where you can just fake it until you make it, math actually does consist of many layers that build upon each other and must be learned in progression. (There are some notable exceptions to this, e.g. Set Theory has been successfully taught to 5 year olds. Binary Arithmetic is really just a trivial case of Set Theory where only null set and unity set exist; it could be taught more easily to children BEFORE they learn decimal arithmetic, but our culture has a decimal-centric bias (in The Simpsons cartoon universe, do they count in base 8?)) Where was I? Most of us can't even make it all the way through Godel, Escher, Bach. Just because you enjoyed it is no reason to assume everyone else in the world thinks the same way you do.</htmltext>
<tokenext>Creativity can neither be taught nor guided .
The analogy with painting and music is flawed ; there are an infinite number of ways to create a painting or musical composition , but relatively few ways to create a logically consistent mathematical system .
While discovering mathematical truths on your own may be fun for the author ( it was for me as a child ) , allowing everybody to write their own Principia Mathematica is simply unpractical and would result in mathematicians being unable to communicate their precious ideas to each other .
Learning math is more like learning english ; while the author is correct that we should n't confuse the language with the beautiful ideas the language is intended to express , it is also true that we ca n't discuss Shakespeare without a common language for communicating the abstract ideas contained within .
I feel the same way about software that this guy feels about math ( some programs are much more aesthetically pleasing than others ) , but his worst mistake is assuming that everybody else should feel the same way about math he does .
Unlike art where you can just fake it until you make it , math actually does consist of many layers that build upon each other and must be learned in progression .
( There are some notable exceptions to this , e.g .
Set Theory has been successfully taught to 5 year olds .
Binary Arithmetic is really just a trivial case of Set Theory where only null set and unity set exist ; it could be taught more easily to children BEFORE they learn decimal arithmetic , but our culture has a decimal-centric bias ( in The Simpsons cartoon universe , do they count in base 8 ?
) ) Where was I ?
Most of us ca n't even make it all the way through Godel , Escher , Bach .
Just because you enjoyed it is no reason to assume everyone else in the world thinks the same way you do .</tokentext>
<sentencetext>Creativity can neither be taught nor guided.
The analogy with painting and music is flawed; there are an infinite number of ways to create a painting or musical composition, but relatively few ways to create a logically consistent mathematical system.
While discovering mathematical truths on your own may be fun for the author (it was for me as a child), allowing everybody to write their own Principia Mathematica is simply unpractical and would result in mathematicians being unable to communicate their precious ideas to each other.
Learning math is more like learning english; while the author is correct that we shouldn't confuse the language with the beautiful ideas the language is intended to express, it is also true that we can't discuss Shakespeare without a common language for communicating the abstract ideas contained within.
I feel the same way about software that this guy feels about math (some programs are much more aesthetically pleasing than others), but his worst mistake is assuming that everybody else should feel the same way about math he does.
Unlike art where you can just fake it until you make it, math actually does consist of many layers that build upon each other and must be learned in progression.
(There are some notable exceptions to this, e.g.
Set Theory has been successfully taught to 5 year olds.
Binary Arithmetic is really just a trivial case of Set Theory where only null set and unity set exist; it could be taught more easily to children BEFORE they learn decimal arithmetic, but our culture has a decimal-centric bias (in The Simpsons cartoon universe, do they count in base 8?
)) Where was I?
Most of us can't even make it all the way through Godel, Escher, Bach.
Just because you enjoyed it is no reason to assume everyone else in the world thinks the same way you do.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28398361</id>
	<title>Re:A teachers take</title>
	<author>LurkerXD</author>
	<datestamp>1245422760000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>That's all well in good but...</p><p>I had a few teachers do the "reward effort" thing. In response, instead of actually putting a lot more effort in, my fellow students and I found it was much more efficient to simply fake it and simply make it look like we had put lots of "effort" into our assignments, even when we had it.</p><p>Furthermore, even if we students did honestly work harder as we should, that doesn't necessarily mean we are learning more.  Do you seriously expect a teacher to be like..."Oh, you got all your problems wrong and didn't show your work, and clearly still have no grasp of what you're doing, but you studied really hard, so I should give you an A"? No.</p><p>I do agree that talent is a bit over-rated; I have a vague feeling I was a victim of this sort of over-nuturing in my younger years. Yes I say victim, because I was lucky enough to learn math concepts with little effort, and of course my teachers tended to jump up and down over what a smart little child I was. However what this did do was teach the poor habits you find so reprehensible. I learned that things were supposed to come easy, and that I wasn't supposed to have to work hard to learn stuff. Now while I did shake that gross mis-conception toward the end of high school (just in time for college thank god), there is a distinct possibility others didn't.</p><p>To me its sounding like rewards can't be a function of a single variable; you can't pass out rewards for just effort or just talent. Ideally you could reward students for actually learning things, but given that determining whether a student is learning so is so difficult, I'm not holding my breath.</p></htmltext>
<tokenext>That 's all well in good but...I had a few teachers do the " reward effort " thing .
In response , instead of actually putting a lot more effort in , my fellow students and I found it was much more efficient to simply fake it and simply make it look like we had put lots of " effort " into our assignments , even when we had it.Furthermore , even if we students did honestly work harder as we should , that does n't necessarily mean we are learning more .
Do you seriously expect a teacher to be like... " Oh , you got all your problems wrong and did n't show your work , and clearly still have no grasp of what you 're doing , but you studied really hard , so I should give you an A " ?
No.I do agree that talent is a bit over-rated ; I have a vague feeling I was a victim of this sort of over-nuturing in my younger years .
Yes I say victim , because I was lucky enough to learn math concepts with little effort , and of course my teachers tended to jump up and down over what a smart little child I was .
However what this did do was teach the poor habits you find so reprehensible .
I learned that things were supposed to come easy , and that I was n't supposed to have to work hard to learn stuff .
Now while I did shake that gross mis-conception toward the end of high school ( just in time for college thank god ) , there is a distinct possibility others did n't.To me its sounding like rewards ca n't be a function of a single variable ; you ca n't pass out rewards for just effort or just talent .
Ideally you could reward students for actually learning things , but given that determining whether a student is learning so is so difficult , I 'm not holding my breath .</tokentext>
<sentencetext>That's all well in good but...I had a few teachers do the "reward effort" thing.
In response, instead of actually putting a lot more effort in, my fellow students and I found it was much more efficient to simply fake it and simply make it look like we had put lots of "effort" into our assignments, even when we had it.Furthermore, even if we students did honestly work harder as we should, that doesn't necessarily mean we are learning more.
Do you seriously expect a teacher to be like..."Oh, you got all your problems wrong and didn't show your work, and clearly still have no grasp of what you're doing, but you studied really hard, so I should give you an A"?
No.I do agree that talent is a bit over-rated; I have a vague feeling I was a victim of this sort of over-nuturing in my younger years.
Yes I say victim, because I was lucky enough to learn math concepts with little effort, and of course my teachers tended to jump up and down over what a smart little child I was.
However what this did do was teach the poor habits you find so reprehensible.
I learned that things were supposed to come easy, and that I wasn't supposed to have to work hard to learn stuff.
Now while I did shake that gross mis-conception toward the end of high school (just in time for college thank god), there is a distinct possibility others didn't.To me its sounding like rewards can't be a function of a single variable; you can't pass out rewards for just effort or just talent.
Ideally you could reward students for actually learning things, but given that determining whether a student is learning so is so difficult, I'm not holding my breath.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394271</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394921</id>
	<title>Re:US School System compared to Europes School Sys</title>
	<author>gknoy</author>
	<datestamp>1245402780000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>HIGH SCHOOLS (and some junion high ones) tend to have various levels of math courses. However, in grades 1-6 (and somewhat 7-8), there's really only one math course for everyone. SOME very few kids are allowed to take the next-grade-up's math course (my best friend was one, 'twas how I met him), but for the most part, nearly all third graders (at a school) are studying the same thing, a nearly all sixth graders are studying the same thing.</p><p>The trouble comes when, in your fifth or sixth grade class, the teacher is going over (yet again) how to do long division or multiplication <i>with one more digit than the previous year</i>.  The students who Don't Get It still don't get it, and are frustrated. The smart kids are bored stiff because it's months of crap that they learned two years ago, and thus they either screw off, are disruptive, or (some few) are lucky enough to have teachers who let them go out in the hall and doodle or read or work on homework while the rest of the class covers Yet More Long Division.</p><p>I learned how to multiply and divide in third grade.  In fourth, we did it a little bit more, with two and three digit numbers... that might be when we were introduced to long division.  We then repeated that for two more years, with the digits increasing.  More rote-work, rather than finding interesting ways to USE the math.  I realize that practice is important, but there are better ways than "OK, 50 more problems, this time with 4 digit divisors".  I was fortunate to have compassionate teachers that let me play Oregon Trail in the hall.<nobr> <wbr></nobr>;)</p></htmltext>
<tokenext>HIGH SCHOOLS ( and some junion high ones ) tend to have various levels of math courses .
However , in grades 1-6 ( and somewhat 7-8 ) , there 's really only one math course for everyone .
SOME very few kids are allowed to take the next-grade-up 's math course ( my best friend was one , 't was how I met him ) , but for the most part , nearly all third graders ( at a school ) are studying the same thing , a nearly all sixth graders are studying the same thing.The trouble comes when , in your fifth or sixth grade class , the teacher is going over ( yet again ) how to do long division or multiplication with one more digit than the previous year .
The students who Do n't Get It still do n't get it , and are frustrated .
The smart kids are bored stiff because it 's months of crap that they learned two years ago , and thus they either screw off , are disruptive , or ( some few ) are lucky enough to have teachers who let them go out in the hall and doodle or read or work on homework while the rest of the class covers Yet More Long Division.I learned how to multiply and divide in third grade .
In fourth , we did it a little bit more , with two and three digit numbers... that might be when we were introduced to long division .
We then repeated that for two more years , with the digits increasing .
More rote-work , rather than finding interesting ways to USE the math .
I realize that practice is important , but there are better ways than " OK , 50 more problems , this time with 4 digit divisors " .
I was fortunate to have compassionate teachers that let me play Oregon Trail in the hall .
; )</tokentext>
<sentencetext>HIGH SCHOOLS (and some junion high ones) tend to have various levels of math courses.
However, in grades 1-6 (and somewhat 7-8), there's really only one math course for everyone.
SOME very few kids are allowed to take the next-grade-up's math course (my best friend was one, 'twas how I met him), but for the most part, nearly all third graders (at a school) are studying the same thing, a nearly all sixth graders are studying the same thing.The trouble comes when, in your fifth or sixth grade class, the teacher is going over (yet again) how to do long division or multiplication with one more digit than the previous year.
The students who Don't Get It still don't get it, and are frustrated.
The smart kids are bored stiff because it's months of crap that they learned two years ago, and thus they either screw off, are disruptive, or (some few) are lucky enough to have teachers who let them go out in the hall and doodle or read or work on homework while the rest of the class covers Yet More Long Division.I learned how to multiply and divide in third grade.
In fourth, we did it a little bit more, with two and three digit numbers... that might be when we were introduced to long division.
We then repeated that for two more years, with the digits increasing.
More rote-work, rather than finding interesting ways to USE the math.
I realize that practice is important, but there are better ways than "OK, 50 more problems, this time with 4 digit divisors".
I was fortunate to have compassionate teachers that let me play Oregon Trail in the hall.
;)</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393241</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393579</id>
	<title>Re:I Sympathize With Him But Too Idyllic</title>
	<author>Anonymous</author>
	<datestamp>1245441420000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p><div class="quote"><p>I'm right their with you in wishing for this but the expectation is unrealistic.</p></div><p>Its 'I'm right THERE with you', not THEIR.</p><p>Now where is the outrage that we don't have decent english teachers?</p></div>
	</htmltext>
<tokenext>I 'm right their with you in wishing for this but the expectation is unrealistic.Its 'I 'm right THERE with you ' , not THEIR.Now where is the outrage that we do n't have decent english teachers ?</tokentext>
<sentencetext>I'm right their with you in wishing for this but the expectation is unrealistic.Its 'I'm right THERE with you', not THEIR.Now where is the outrage that we don't have decent english teachers?
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392903</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393307</id>
	<title>Re:I Sympathize With Him But Too Idyllic</title>
	<author>Anonymous</author>
	<datestamp>1245440400000</datestamp>
	<modclass>Interestin</modclass>
	<modscore>3</modscore>
	<htmltext><p><div class="quote"><p>Passions come to people unexpectedly. We should deal with the fact that more people are passionate about topics like Art and Humanities than Math and Computer Science. It's just the reality of academia right now.</p></div><p>Isn't his point that we don't really know if that's true, since math isn't taught in a way to inspire passion? That if more people were able to glimpse some of the beauty and creativity in it, there might be more interest in it?</p><p><div class="quote"><p>Well if you're not asking for teachers needing to be professional published mathematicians, what was that paragraph about?</p> </div><p>I agree we can't expect every teacher to be awe-inspiring; even getting (and retaining) enough marginally competent teachers is a challenge. However, you needn't be a university-level mathematics professor to know some of what he's suggested. For example, public school teachers are supposed to have Master's degrees, right? Now, isn't there something funny about the fact that teachers will go and get their BS in the subject they will teach, but get their Master's degree in "education"? Cue the "Philosophy of science is about as useful to scientists as ornithology is to birds" quotes. I'd think that teachers might be better served by a decent master's degree in their field of teaching, rather than "education". That would allow them the opportunity to study the history and philosophy of their subject, get a grasp of recent developments (maybe not in all subjects, but they could at least be able to pick up journals), etc. The really good ones could even get published (I just got my Master's degree, and was able to get a paper published, so yes, it's possible).</p></div>
	</htmltext>
<tokenext>Passions come to people unexpectedly .
We should deal with the fact that more people are passionate about topics like Art and Humanities than Math and Computer Science .
It 's just the reality of academia right now.Is n't his point that we do n't really know if that 's true , since math is n't taught in a way to inspire passion ?
That if more people were able to glimpse some of the beauty and creativity in it , there might be more interest in it ? Well if you 're not asking for teachers needing to be professional published mathematicians , what was that paragraph about ?
I agree we ca n't expect every teacher to be awe-inspiring ; even getting ( and retaining ) enough marginally competent teachers is a challenge .
However , you need n't be a university-level mathematics professor to know some of what he 's suggested .
For example , public school teachers are supposed to have Master 's degrees , right ?
Now , is n't there something funny about the fact that teachers will go and get their BS in the subject they will teach , but get their Master 's degree in " education " ?
Cue the " Philosophy of science is about as useful to scientists as ornithology is to birds " quotes .
I 'd think that teachers might be better served by a decent master 's degree in their field of teaching , rather than " education " .
That would allow them the opportunity to study the history and philosophy of their subject , get a grasp of recent developments ( maybe not in all subjects , but they could at least be able to pick up journals ) , etc .
The really good ones could even get published ( I just got my Master 's degree , and was able to get a paper published , so yes , it 's possible ) .</tokentext>
<sentencetext>Passions come to people unexpectedly.
We should deal with the fact that more people are passionate about topics like Art and Humanities than Math and Computer Science.
It's just the reality of academia right now.Isn't his point that we don't really know if that's true, since math isn't taught in a way to inspire passion?
That if more people were able to glimpse some of the beauty and creativity in it, there might be more interest in it?Well if you're not asking for teachers needing to be professional published mathematicians, what was that paragraph about?
I agree we can't expect every teacher to be awe-inspiring; even getting (and retaining) enough marginally competent teachers is a challenge.
However, you needn't be a university-level mathematics professor to know some of what he's suggested.
For example, public school teachers are supposed to have Master's degrees, right?
Now, isn't there something funny about the fact that teachers will go and get their BS in the subject they will teach, but get their Master's degree in "education"?
Cue the "Philosophy of science is about as useful to scientists as ornithology is to birds" quotes.
I'd think that teachers might be better served by a decent master's degree in their field of teaching, rather than "education".
That would allow them the opportunity to study the history and philosophy of their subject, get a grasp of recent developments (maybe not in all subjects, but they could at least be able to pick up journals), etc.
The really good ones could even get published (I just got my Master's degree, and was able to get a paper published, so yes, it's possible).
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392903</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393897</id>
	<title>Re:Wrong tool for the job</title>
	<author>TheRaven64</author>
	<datestamp>1245442620000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>I hope you're not serious.  Expecting teenagers to read Newton is a great way of putting them off physics for life.  He is quite possibly the most dull and convoluted writer ever to abuse the English language.  A grounding in the history of a subject is important, but reading Newton is a terrible idea.</htmltext>
<tokenext>I hope you 're not serious .
Expecting teenagers to read Newton is a great way of putting them off physics for life .
He is quite possibly the most dull and convoluted writer ever to abuse the English language .
A grounding in the history of a subject is important , but reading Newton is a terrible idea .</tokentext>
<sentencetext>I hope you're not serious.
Expecting teenagers to read Newton is a great way of putting them off physics for life.
He is quite possibly the most dull and convoluted writer ever to abuse the English language.
A grounding in the history of a subject is important, but reading Newton is a terrible idea.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393389</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28395831</id>
	<title>Re:Cue the other subjects</title>
	<author>hardwarejunkie9</author>
	<datestamp>1245406200000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p><div class="quote"><p>and most of them can be traced to certain groups (*cough*fundamentalists*cough*) waging a 30 year war on public education, and people refusing to see and treat education as what it is: an investment in the future national security and economic stability of the united states.</p></div><p>I think you're missing the point and wonder if it's possible that you haven't read the article fully. The state that education is in can't be simply blamed on one group and left to lie. Sure, some fundamentalist groups are busy fighting a nonsensical war on science and sexual education. However to claim that they have drug down math education is an outright red herring argument. Other groups may be just as much to blame. To quote "The Two Cultures of Mathematics" by W.T. Gowers, there was a cited cased from C.P. Snow as follows


"A good many times I have been present at gatherings of people who, by the standards
of the traditional culture, are thought highly educated and who have with considerable
gusto been expressing their incredulity at the illiteracy of scientists. Once or twice I
have been provoked and have asked the company how many of them could describe
the Second Law of Thermodynamics. The response was cold: it was also negative.
Yet I was asking something which is about the scientic equivalent of: Have you read
a work of Shakespeare's?"

Who is to say that the sort of ignorance demonstrated by these people is not also to blame? The case this particular article points out is that there is a particular cultural ignorance of mathematics in both conceptual and practical understanding.

I'm sorry, but the issue at hand cannot be simply addressed by setting up the<nobr> <wbr></nobr>/. whipping boy of the ignorant right wing fundamentalist stereotype and giving him a good flaying.</p></div>
	</htmltext>
<tokenext>and most of them can be traced to certain groups ( * cough * fundamentalists * cough * ) waging a 30 year war on public education , and people refusing to see and treat education as what it is : an investment in the future national security and economic stability of the united states.I think you 're missing the point and wonder if it 's possible that you have n't read the article fully .
The state that education is in ca n't be simply blamed on one group and left to lie .
Sure , some fundamentalist groups are busy fighting a nonsensical war on science and sexual education .
However to claim that they have drug down math education is an outright red herring argument .
Other groups may be just as much to blame .
To quote " The Two Cultures of Mathematics " by W.T .
Gowers , there was a cited cased from C.P .
Snow as follows " A good many times I have been present at gatherings of people who , by the standards of the traditional culture , are thought highly educated and who have with considerable gusto been expressing their incredulity at the illiteracy of scientists .
Once or twice I have been provoked and have asked the company how many of them could describe the Second Law of Thermodynamics .
The response was cold : it was also negative .
Yet I was asking something which is about the scientic equivalent of : Have you read a work of Shakespeare 's ?
" Who is to say that the sort of ignorance demonstrated by these people is not also to blame ?
The case this particular article points out is that there is a particular cultural ignorance of mathematics in both conceptual and practical understanding .
I 'm sorry , but the issue at hand can not be simply addressed by setting up the / .
whipping boy of the ignorant right wing fundamentalist stereotype and giving him a good flaying .</tokentext>
<sentencetext>and most of them can be traced to certain groups (*cough*fundamentalists*cough*) waging a 30 year war on public education, and people refusing to see and treat education as what it is: an investment in the future national security and economic stability of the united states.I think you're missing the point and wonder if it's possible that you haven't read the article fully.
The state that education is in can't be simply blamed on one group and left to lie.
Sure, some fundamentalist groups are busy fighting a nonsensical war on science and sexual education.
However to claim that they have drug down math education is an outright red herring argument.
Other groups may be just as much to blame.
To quote "The Two Cultures of Mathematics" by W.T.
Gowers, there was a cited cased from C.P.
Snow as follows


"A good many times I have been present at gatherings of people who, by the standards
of the traditional culture, are thought highly educated and who have with considerable
gusto been expressing their incredulity at the illiteracy of scientists.
Once or twice I
have been provoked and have asked the company how many of them could describe
the Second Law of Thermodynamics.
The response was cold: it was also negative.
Yet I was asking something which is about the scientic equivalent of: Have you read
a work of Shakespeare's?
"

Who is to say that the sort of ignorance demonstrated by these people is not also to blame?
The case this particular article points out is that there is a particular cultural ignorance of mathematics in both conceptual and practical understanding.
I'm sorry, but the issue at hand cannot be simply addressed by setting up the /.
whipping boy of the ignorant right wing fundamentalist stereotype and giving him a good flaying.
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393083</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28395141</id>
	<title>Re:US School System compared to Europes School Sys</title>
	<author>billius</author>
	<datestamp>1245403560000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>The US system is something of an anomaly in that we have a secondary schools that are supposed to cater to EVERYONE.  A person earning a high school diploma could be either on their way to MIT or an exciting career at McDonald's, whereas in many other places (like Europe), people are pretty well separated out by the time they hit high school or even middle school.  In Germany, for example, the students earn different types of "degrees" from different types of secondary schools and only the hardest one (abitur) will get you into a regular university.  It's not expected that everyone "goes to college" like they do here and in many cases people pick special areas of study early on.  If you have a classroom full of kids who are planning on becoming engineers, it's a lot easier to push them harder when it comes to math since they know that they need it and thus will be more responsive.  By the same token, if you're a teacher used to dealing with kids who don't have much interested in or aptitude for math, you will eventually become good at figuring out ways to get them to be more responsive and try harder.  Here everyone is mixed together and teachers have the challenge of having to teach kids with widely varying abilities and plans for the future and many simply give up and point to the university bound students and say "Look, the curriculum and my teacher methods are sound!" while the kids who are not as gifted slip through the cracks.</htmltext>
<tokenext>The US system is something of an anomaly in that we have a secondary schools that are supposed to cater to EVERYONE .
A person earning a high school diploma could be either on their way to MIT or an exciting career at McDonald 's , whereas in many other places ( like Europe ) , people are pretty well separated out by the time they hit high school or even middle school .
In Germany , for example , the students earn different types of " degrees " from different types of secondary schools and only the hardest one ( abitur ) will get you into a regular university .
It 's not expected that everyone " goes to college " like they do here and in many cases people pick special areas of study early on .
If you have a classroom full of kids who are planning on becoming engineers , it 's a lot easier to push them harder when it comes to math since they know that they need it and thus will be more responsive .
By the same token , if you 're a teacher used to dealing with kids who do n't have much interested in or aptitude for math , you will eventually become good at figuring out ways to get them to be more responsive and try harder .
Here everyone is mixed together and teachers have the challenge of having to teach kids with widely varying abilities and plans for the future and many simply give up and point to the university bound students and say " Look , the curriculum and my teacher methods are sound !
" while the kids who are not as gifted slip through the cracks .</tokentext>
<sentencetext>The US system is something of an anomaly in that we have a secondary schools that are supposed to cater to EVERYONE.
A person earning a high school diploma could be either on their way to MIT or an exciting career at McDonald's, whereas in many other places (like Europe), people are pretty well separated out by the time they hit high school or even middle school.
In Germany, for example, the students earn different types of "degrees" from different types of secondary schools and only the hardest one (abitur) will get you into a regular university.
It's not expected that everyone "goes to college" like they do here and in many cases people pick special areas of study early on.
If you have a classroom full of kids who are planning on becoming engineers, it's a lot easier to push them harder when it comes to math since they know that they need it and thus will be more responsive.
By the same token, if you're a teacher used to dealing with kids who don't have much interested in or aptitude for math, you will eventually become good at figuring out ways to get them to be more responsive and try harder.
Here everyone is mixed together and teachers have the challenge of having to teach kids with widely varying abilities and plans for the future and many simply give up and point to the university bound students and say "Look, the curriculum and my teacher methods are sound!
" while the kids who are not as gifted slip through the cracks.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393035</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28406699</id>
	<title>Re:it's really bad</title>
	<author>JBaustian</author>
	<datestamp>1245509580000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>I thought of mathematical proofs as a game, and I enjoyed working them. But there were only a handful of us who felt that way.</htmltext>
<tokenext>I thought of mathematical proofs as a game , and I enjoyed working them .
But there were only a handful of us who felt that way .</tokentext>
<sentencetext>I thought of mathematical proofs as a game, and I enjoyed working them.
But there were only a handful of us who felt that way.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393127</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28396659</id>
	<title>Foundation of Public Education in the USA</title>
	<author>fragMasterFlash</author>
	<datestamp>1245410160000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>The notion that public education should be provided to all in the USA came about during the industrial revolution. This system of education was designed not to stimulate intellect as much as it was to create a workforce with the basic skills required to work at repetitive, menial tasks day after day. While much improved over the years, public schools are still chartered with the same task of generating a pool of semi-skilled labor that simply cannot compete in the current global economy.</htmltext>
<tokenext>The notion that public education should be provided to all in the USA came about during the industrial revolution .
This system of education was designed not to stimulate intellect as much as it was to create a workforce with the basic skills required to work at repetitive , menial tasks day after day .
While much improved over the years , public schools are still chartered with the same task of generating a pool of semi-skilled labor that simply can not compete in the current global economy .</tokentext>
<sentencetext>The notion that public education should be provided to all in the USA came about during the industrial revolution.
This system of education was designed not to stimulate intellect as much as it was to create a workforce with the basic skills required to work at repetitive, menial tasks day after day.
While much improved over the years, public schools are still chartered with the same task of generating a pool of semi-skilled labor that simply cannot compete in the current global economy.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394011</id>
	<title>Re:US School System compared to Europes School Sys</title>
	<author>Anonymous</author>
	<datestamp>1245442980000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p><div class="quote"><p>You must have attended a very very small school. Most US schools have different courses based on skill level. Your conclusions about the US school system are therefore wrong. They are merely conclusions about very small schools.</p></div><p>Are there honestly any US high schools that teach beyond calculus? No curricula that I know of goes beyond the contents of AP Calculus BC in high school. That's single variable differential and integral calculus, with coverage of series/sequences, and some vectors.</p><p>I would very much like to hear of any US high school which teaches linear algebra.</p></div>
	</htmltext>
<tokenext>You must have attended a very very small school .
Most US schools have different courses based on skill level .
Your conclusions about the US school system are therefore wrong .
They are merely conclusions about very small schools.Are there honestly any US high schools that teach beyond calculus ?
No curricula that I know of goes beyond the contents of AP Calculus BC in high school .
That 's single variable differential and integral calculus , with coverage of series/sequences , and some vectors.I would very much like to hear of any US high school which teaches linear algebra .</tokentext>
<sentencetext>You must have attended a very very small school.
Most US schools have different courses based on skill level.
Your conclusions about the US school system are therefore wrong.
They are merely conclusions about very small schools.Are there honestly any US high schools that teach beyond calculus?
No curricula that I know of goes beyond the contents of AP Calculus BC in high school.
That's single variable differential and integral calculus, with coverage of series/sequences, and some vectors.I would very much like to hear of any US high school which teaches linear algebra.
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393241</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393855</id>
	<title>Re:it's really bad</title>
	<author>fermion</author>
	<datestamp>1245442440000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>Students are not machines.  Some students are going to build rules from examples.  Some are going to want the rules, then apply them to examples.  Some are going to want only to know how to solve the problem then mimic the process on similar problems.  Some are simply going to copy the proof from another student.
<p>
The challenge of US education is to meet the need of all these students.  When someone comes up with a complaint, it is normally that things are not being taught in the way that they learn.  The fallacy is that if one teaches to one student, then everyone else does not learn.  It is never acceptable to always teach to the same students.  A competent teacher is going to teach an subject from many different angles so that each student has at least on opportunity to learn in their style.  For instance, in a class of four students, I might have one that learns by reading, one that learns by working out the solution for themselves, one that likes lecture, and one that is just not to learn anything at a high level no matter what is done.  This is not a atypical situation.
</p><p>
How in such a class can I teach using a single method, such a problem based learning, constructive learning, or drill and kill.  Like how could any administrator  remove any tool from my case simply because someone who doesn't teach thinks it is a bad idea.  If it helps a student learn something, it is a good idea.
</p><p>
I hear complaints like the one posted all the time.  It normally comes from 'experts' how thinks that everyone is like them.  Well, everyone isn't.  The world is diverse.  Some students really do like math, and no matter what anyone does they will learn math.  A person in the jungle of Nigeria, with no light or proper books learns math simply because the love it.  Is a child in America with electricity and books and teachers who are willing to help any worse off?  for students who are just getting a diploma, the math classes provide a basis.  Then the teachers have to deal with the kids that don't want to learn.  We can't kick them out.  They are just kids.  They deserve an education.  Some might say it is unfair to the other kids, but I think it is unfair that I have to be late to work because someone does not know how to drive and gets into an accident, or I can't have explosives because some idiot killed themselves and others with them.  Life is unfair.
</p><p>
School is not the aesthetic environment that mathematicians tends to live, which is one reason why it is so hard to find good math teachers.  if one genuinely feels that math education sucks, and that you can do better, go teach.  I can guarantee you that good math teachers are so desperately needed that you can pretty do whatever you want, and if it works you will be rewarded.  The flip side of that is that a math teacher has to be honest enough to accept empirical evidence, and when something does not work to adjust the process or try something else.</p></htmltext>
<tokenext>Students are not machines .
Some students are going to build rules from examples .
Some are going to want the rules , then apply them to examples .
Some are going to want only to know how to solve the problem then mimic the process on similar problems .
Some are simply going to copy the proof from another student .
The challenge of US education is to meet the need of all these students .
When someone comes up with a complaint , it is normally that things are not being taught in the way that they learn .
The fallacy is that if one teaches to one student , then everyone else does not learn .
It is never acceptable to always teach to the same students .
A competent teacher is going to teach an subject from many different angles so that each student has at least on opportunity to learn in their style .
For instance , in a class of four students , I might have one that learns by reading , one that learns by working out the solution for themselves , one that likes lecture , and one that is just not to learn anything at a high level no matter what is done .
This is not a atypical situation .
How in such a class can I teach using a single method , such a problem based learning , constructive learning , or drill and kill .
Like how could any administrator remove any tool from my case simply because someone who does n't teach thinks it is a bad idea .
If it helps a student learn something , it is a good idea .
I hear complaints like the one posted all the time .
It normally comes from 'experts ' how thinks that everyone is like them .
Well , everyone is n't .
The world is diverse .
Some students really do like math , and no matter what anyone does they will learn math .
A person in the jungle of Nigeria , with no light or proper books learns math simply because the love it .
Is a child in America with electricity and books and teachers who are willing to help any worse off ?
for students who are just getting a diploma , the math classes provide a basis .
Then the teachers have to deal with the kids that do n't want to learn .
We ca n't kick them out .
They are just kids .
They deserve an education .
Some might say it is unfair to the other kids , but I think it is unfair that I have to be late to work because someone does not know how to drive and gets into an accident , or I ca n't have explosives because some idiot killed themselves and others with them .
Life is unfair .
School is not the aesthetic environment that mathematicians tends to live , which is one reason why it is so hard to find good math teachers .
if one genuinely feels that math education sucks , and that you can do better , go teach .
I can guarantee you that good math teachers are so desperately needed that you can pretty do whatever you want , and if it works you will be rewarded .
The flip side of that is that a math teacher has to be honest enough to accept empirical evidence , and when something does not work to adjust the process or try something else .</tokentext>
<sentencetext>Students are not machines.
Some students are going to build rules from examples.
Some are going to want the rules, then apply them to examples.
Some are going to want only to know how to solve the problem then mimic the process on similar problems.
Some are simply going to copy the proof from another student.
The challenge of US education is to meet the need of all these students.
When someone comes up with a complaint, it is normally that things are not being taught in the way that they learn.
The fallacy is that if one teaches to one student, then everyone else does not learn.
It is never acceptable to always teach to the same students.
A competent teacher is going to teach an subject from many different angles so that each student has at least on opportunity to learn in their style.
For instance, in a class of four students, I might have one that learns by reading, one that learns by working out the solution for themselves, one that likes lecture, and one that is just not to learn anything at a high level no matter what is done.
This is not a atypical situation.
How in such a class can I teach using a single method, such a problem based learning, constructive learning, or drill and kill.
Like how could any administrator  remove any tool from my case simply because someone who doesn't teach thinks it is a bad idea.
If it helps a student learn something, it is a good idea.
I hear complaints like the one posted all the time.
It normally comes from 'experts' how thinks that everyone is like them.
Well, everyone isn't.
The world is diverse.
Some students really do like math, and no matter what anyone does they will learn math.
A person in the jungle of Nigeria, with no light or proper books learns math simply because the love it.
Is a child in America with electricity and books and teachers who are willing to help any worse off?
for students who are just getting a diploma, the math classes provide a basis.
Then the teachers have to deal with the kids that don't want to learn.
We can't kick them out.
They are just kids.
They deserve an education.
Some might say it is unfair to the other kids, but I think it is unfair that I have to be late to work because someone does not know how to drive and gets into an accident, or I can't have explosives because some idiot killed themselves and others with them.
Life is unfair.
School is not the aesthetic environment that mathematicians tends to live, which is one reason why it is so hard to find good math teachers.
if one genuinely feels that math education sucks, and that you can do better, go teach.
I can guarantee you that good math teachers are so desperately needed that you can pretty do whatever you want, and if it works you will be rewarded.
The flip side of that is that a math teacher has to be honest enough to accept empirical evidence, and when something does not work to adjust the process or try something else.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392911</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393507</id>
	<title>Re:US K-12 MATH = Real world fail.</title>
	<author>Anonymous</author>
	<datestamp>1245441180000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>And you don't seem to know what the word means means.</p><p>The symbol for factorial <b>is</b> !.</p><p>! (the symbol for factorial) <b>means</b> the product of the series of integers all integers from 1 to the integer which precedes the factorial symbol.</p><p>See the difference?</p></htmltext>
<tokenext>And you do n't seem to know what the word means means.The symbol for factorial is ! . !
( the symbol for factorial ) means the product of the series of integers all integers from 1 to the integer which precedes the factorial symbol.See the difference ?</tokentext>
<sentencetext>And you don't seem to know what the word means means.The symbol for factorial is !.!
(the symbol for factorial) means the product of the series of integers all integers from 1 to the integer which precedes the factorial symbol.See the difference?</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392991</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28396205</id>
	<title>Woflram Alpha</title>
	<author>hardwarejunkie9</author>
	<datestamp>1245407940000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>This is interesting particularly coupled with a posting earlier about Wolfram Alpha and all of the trouble rising over its place in mathematical education.
Under the math system that this article seeks to indict the introduction of an accessible mathematical tool such as WolframAlpha would be poison to everything they're trying to teach. However, in the system that he tries to forward, such technology would be a great boon. In the general attitude of<nobr> <wbr></nobr>/. being "Technology giveth and technology taketh away" wouldn't this be simply another variation on the same theme? Mathematics education needs some revitalization and what better way than to put power to teach oneself into the hands of eager students?</htmltext>
<tokenext>This is interesting particularly coupled with a posting earlier about Wolfram Alpha and all of the trouble rising over its place in mathematical education .
Under the math system that this article seeks to indict the introduction of an accessible mathematical tool such as WolframAlpha would be poison to everything they 're trying to teach .
However , in the system that he tries to forward , such technology would be a great boon .
In the general attitude of / .
being " Technology giveth and technology taketh away " would n't this be simply another variation on the same theme ?
Mathematics education needs some revitalization and what better way than to put power to teach oneself into the hands of eager students ?</tokentext>
<sentencetext>This is interesting particularly coupled with a posting earlier about Wolfram Alpha and all of the trouble rising over its place in mathematical education.
Under the math system that this article seeks to indict the introduction of an accessible mathematical tool such as WolframAlpha would be poison to everything they're trying to teach.
However, in the system that he tries to forward, such technology would be a great boon.
In the general attitude of /.
being "Technology giveth and technology taketh away" wouldn't this be simply another variation on the same theme?
Mathematics education needs some revitalization and what better way than to put power to teach oneself into the hands of eager students?</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393889</id>
	<title>Re:True story ....</title>
	<author>JumpDrive</author>
	<datestamp>1245442560000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>We're hosed</htmltext>
<tokenext>We 're hosed</tokentext>
<sentencetext>We're hosed</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392947</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394521</id>
	<title>Depends on what you mean by fundamentalists</title>
	<author>weston</author>
	<datestamp>1245444720000</datestamp>
	<modclass>Informativ</modclass>
	<modscore>2</modscore>
	<htmltext><p><i>and most of them can be traced to certain groups (*cough*fundamentalists*cough*) waging a 30 year war on public education</i></p><p>Depends on what you mean by fundamentalists. Honestly, I have my doubts you can trace all our problems back to creationists and prudes. You'd have to get the market fundamentalists, the "one curriculum to bind them all" fundamentalists, the Fabians, the Rothschilds, the Rockafellers, and probably more in there to get a really good idea of why we've ended up so mixed up.</p><p>That said: I got a fantastic high school education. I learned quite a bit and could have gotten a lot more out of it if I'd had the inclination.</p></htmltext>
<tokenext>and most of them can be traced to certain groups ( * cough * fundamentalists * cough * ) waging a 30 year war on public educationDepends on what you mean by fundamentalists .
Honestly , I have my doubts you can trace all our problems back to creationists and prudes .
You 'd have to get the market fundamentalists , the " one curriculum to bind them all " fundamentalists , the Fabians , the Rothschilds , the Rockafellers , and probably more in there to get a really good idea of why we 've ended up so mixed up.That said : I got a fantastic high school education .
I learned quite a bit and could have gotten a lot more out of it if I 'd had the inclination .</tokentext>
<sentencetext>and most of them can be traced to certain groups (*cough*fundamentalists*cough*) waging a 30 year war on public educationDepends on what you mean by fundamentalists.
Honestly, I have my doubts you can trace all our problems back to creationists and prudes.
You'd have to get the market fundamentalists, the "one curriculum to bind them all" fundamentalists, the Fabians, the Rothschilds, the Rockafellers, and probably more in there to get a really good idea of why we've ended up so mixed up.That said: I got a fantastic high school education.
I learned quite a bit and could have gotten a lot more out of it if I'd had the inclination.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393083</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393445</id>
	<title>Re:it's really bad</title>
	<author>delphi125</author>
	<datestamp>1245440940000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>The problem with proofs has nothing to do with logic.</p><p>It is necessary to be able to understand proofs, but duplicating them under exam conditions means you have to memorize them by rote.</p><p>At a certain point (for me it was the Cambridge maths tripos part IB) you are going to get exposed to maths you have to do but don't fully understand.</p><p>People who can memorise the proofs but only understand them partially do better than people than those who understand the material better, but prefer to "solve a problem" and struggle to memorize a proof verbatim.</p></htmltext>
<tokenext>The problem with proofs has nothing to do with logic.It is necessary to be able to understand proofs , but duplicating them under exam conditions means you have to memorize them by rote.At a certain point ( for me it was the Cambridge maths tripos part IB ) you are going to get exposed to maths you have to do but do n't fully understand.People who can memorise the proofs but only understand them partially do better than people than those who understand the material better , but prefer to " solve a problem " and struggle to memorize a proof verbatim .</tokentext>
<sentencetext>The problem with proofs has nothing to do with logic.It is necessary to be able to understand proofs, but duplicating them under exam conditions means you have to memorize them by rote.At a certain point (for me it was the Cambridge maths tripos part IB) you are going to get exposed to maths you have to do but don't fully understand.People who can memorise the proofs but only understand them partially do better than people than those who understand the material better, but prefer to "solve a problem" and struggle to memorize a proof verbatim.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392911</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28396701</id>
	<title>Re:Cue the other subjects</title>
	<author>CorporateSuit</author>
	<datestamp>1245410340000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p><div class="quote"><p>and most of them can be traced to certain groups (*cough*fundamentalists*cough*)</p></div><p>Yes, because everyone knows that you cannot learn Math until you accept evolution as fact..?  Wait, what are you trying to say?<br> <br>
It's the "progressive" system that says that children cannot be graded and all children must be treated equally, as the least common denominator, that are screwing up the education system.  Ignoring the focuses of challenge and achievement lower test scores in boys and girls, respectively.  That's not even the cause of it -- just a symptom.  It's apathy, greed, selfishness, and laziness up the entire educational chain (to the very top) that has put education in its sorry state.  These are not consequences of fundamentalist ideals.  How on earth did you come up with "fundamentalists" as a reason?  Close your eyes and use a dartboard?  Do you just go about blaming bad happenings on random things you don't like?</p><p><div class="quote"><p>and the recession can be traced back to certain groups (*cough*Kids texting while driving*cough*)</p></div></div>
	</htmltext>
<tokenext>and most of them can be traced to certain groups ( * cough * fundamentalists * cough * ) Yes , because everyone knows that you can not learn Math until you accept evolution as fact.. ?
Wait , what are you trying to say ?
It 's the " progressive " system that says that children can not be graded and all children must be treated equally , as the least common denominator , that are screwing up the education system .
Ignoring the focuses of challenge and achievement lower test scores in boys and girls , respectively .
That 's not even the cause of it -- just a symptom .
It 's apathy , greed , selfishness , and laziness up the entire educational chain ( to the very top ) that has put education in its sorry state .
These are not consequences of fundamentalist ideals .
How on earth did you come up with " fundamentalists " as a reason ?
Close your eyes and use a dartboard ?
Do you just go about blaming bad happenings on random things you do n't like ? and the recession can be traced back to certain groups ( * cough * Kids texting while driving * cough * )</tokentext>
<sentencetext>and most of them can be traced to certain groups (*cough*fundamentalists*cough*)Yes, because everyone knows that you cannot learn Math until you accept evolution as fact..?
Wait, what are you trying to say?
It's the "progressive" system that says that children cannot be graded and all children must be treated equally, as the least common denominator, that are screwing up the education system.
Ignoring the focuses of challenge and achievement lower test scores in boys and girls, respectively.
That's not even the cause of it -- just a symptom.
It's apathy, greed, selfishness, and laziness up the entire educational chain (to the very top) that has put education in its sorry state.
These are not consequences of fundamentalist ideals.
How on earth did you come up with "fundamentalists" as a reason?
Close your eyes and use a dartboard?
Do you just go about blaming bad happenings on random things you don't like?and the recession can be traced back to certain groups (*cough*Kids texting while driving*cough*)
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393083</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28398041</id>
	<title>abstraction</title>
	<author>lexluther</author>
	<datestamp>1245420000000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>I think the pdf was quite good, albeit repetitive. In any case, in the end, I think he makes an interesting point about abstraction:
<br> <br>
<i>
On the surface this seems fairly innocuous; why not make some abbreviations so that
things can be said more economically? The problem is that definitions matter. They come from
aesthetic decisions about what distinctions you as an artist consider important. And they are
problem-generated.  To make a definition is to highlight and call attention to a feature or
structural property.
</i> <br> <br>
Learning to make good abstraction when programming is a difficult challenge, the right choice can have huge downstream consequences. An educational system which allowed students to get comfortable with the exploration of different abstractions, as well as, the forestalling of notation and rigour until the right rigour was appropriate would be a huge win to reasoning across the board.</htmltext>
<tokenext>I think the pdf was quite good , albeit repetitive .
In any case , in the end , I think he makes an interesting point about abstraction : On the surface this seems fairly innocuous ; why not make some abbreviations so that things can be said more economically ?
The problem is that definitions matter .
They come from aesthetic decisions about what distinctions you as an artist consider important .
And they are problem-generated .
To make a definition is to highlight and call attention to a feature or structural property .
Learning to make good abstraction when programming is a difficult challenge , the right choice can have huge downstream consequences .
An educational system which allowed students to get comfortable with the exploration of different abstractions , as well as , the forestalling of notation and rigour until the right rigour was appropriate would be a huge win to reasoning across the board .</tokentext>
<sentencetext>I think the pdf was quite good, albeit repetitive.
In any case, in the end, I think he makes an interesting point about abstraction:
 

On the surface this seems fairly innocuous; why not make some abbreviations so that
things can be said more economically?
The problem is that definitions matter.
They come from
aesthetic decisions about what distinctions you as an artist consider important.
And they are
problem-generated.
To make a definition is to highlight and call attention to a feature or
structural property.
Learning to make good abstraction when programming is a difficult challenge, the right choice can have huge downstream consequences.
An educational system which allowed students to get comfortable with the exploration of different abstractions, as well as, the forestalling of notation and rigour until the right rigour was appropriate would be a huge win to reasoning across the board.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393971</id>
	<title>Re:The way math is structured is disconnected from</title>
	<author>cptdondo</author>
	<datestamp>1245442860000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>When I was studying computer science I had a horrible time understanding recursion.  Now understand that this was a long time ago, and structured programming was just beginning to be developed, so recursion was something new, both conceptually and technically.</p><p>But a big problem was the way it was presented.  Basically we were thrown into a world of stacks, heaps, pointers, and so on, without a single word of why recursion was useful, and without any sort of introduction to recursion.</p><p>Years later, when I taught CS, I would take my students outside, have them pull a leaf off the tree, and trace the veins.  We'd talk about the self-replicating nature of the structure of the veins in the leaf, at smaller and smaller scales, and finally stopping at some point.</p><p>Once my students understood this self-replicating nature of nature, we'd start implementing it in the classroom on a computer.  And things like recursion, binary trees, and traversal became trivial.</p><p>It's all about tying real world observations to the science you're doing.</p></htmltext>
<tokenext>When I was studying computer science I had a horrible time understanding recursion .
Now understand that this was a long time ago , and structured programming was just beginning to be developed , so recursion was something new , both conceptually and technically.But a big problem was the way it was presented .
Basically we were thrown into a world of stacks , heaps , pointers , and so on , without a single word of why recursion was useful , and without any sort of introduction to recursion.Years later , when I taught CS , I would take my students outside , have them pull a leaf off the tree , and trace the veins .
We 'd talk about the self-replicating nature of the structure of the veins in the leaf , at smaller and smaller scales , and finally stopping at some point.Once my students understood this self-replicating nature of nature , we 'd start implementing it in the classroom on a computer .
And things like recursion , binary trees , and traversal became trivial.It 's all about tying real world observations to the science you 're doing .</tokentext>
<sentencetext>When I was studying computer science I had a horrible time understanding recursion.
Now understand that this was a long time ago, and structured programming was just beginning to be developed, so recursion was something new, both conceptually and technically.But a big problem was the way it was presented.
Basically we were thrown into a world of stacks, heaps, pointers, and so on, without a single word of why recursion was useful, and without any sort of introduction to recursion.Years later, when I taught CS, I would take my students outside, have them pull a leaf off the tree, and trace the veins.
We'd talk about the self-replicating nature of the structure of the veins in the leaf, at smaller and smaller scales, and finally stopping at some point.Once my students understood this self-replicating nature of nature, we'd start implementing it in the classroom on a computer.
And things like recursion, binary trees, and traversal became trivial.It's all about tying real world observations to the science you're doing.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392921</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393055</id>
	<title>Re:tl;dr</title>
	<author>CRCulver</author>
	<datestamp>1245439560000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><blockquote><div><p>Having not read the actual PDF, I wonder if having a bunch of mathematically disinclined women teaching math to young students would have something to do with it?</p></div> </blockquote><p>My high school algebra teacher was female, but had come to high school teaching after spending much of her time in university research rounds. Her qualifications were impeccable. That didn't make my classmates anymore successful with their studies than the average. I'm inclined to think it's a problem of unmotivated students in all fields of education in general.</p></div>
	</htmltext>
<tokenext>Having not read the actual PDF , I wonder if having a bunch of mathematically disinclined women teaching math to young students would have something to do with it ?
My high school algebra teacher was female , but had come to high school teaching after spending much of her time in university research rounds .
Her qualifications were impeccable .
That did n't make my classmates anymore successful with their studies than the average .
I 'm inclined to think it 's a problem of unmotivated students in all fields of education in general .</tokentext>
<sentencetext>Having not read the actual PDF, I wonder if having a bunch of mathematically disinclined women teaching math to young students would have something to do with it?
My high school algebra teacher was female, but had come to high school teaching after spending much of her time in university research rounds.
Her qualifications were impeccable.
That didn't make my classmates anymore successful with their studies than the average.
I'm inclined to think it's a problem of unmotivated students in all fields of education in general.
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392895</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28400247</id>
	<title>Re:The way math is structured is disconnected from</title>
	<author>oiron</author>
	<datestamp>1245492060000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>It's more because we in Asia (I can talk about India, at least) still have teachers who can take notice of the kid who's questioning that rote learning and guide him/her further. Unfortunately, that's being compromised too</p></htmltext>
<tokenext>It 's more because we in Asia ( I can talk about India , at least ) still have teachers who can take notice of the kid who 's questioning that rote learning and guide him/her further .
Unfortunately , that 's being compromised too</tokentext>
<sentencetext>It's more because we in Asia (I can talk about India, at least) still have teachers who can take notice of the kid who's questioning that rote learning and guide him/her further.
Unfortunately, that's being compromised too</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393115</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28400295</id>
	<title>Whoa! A nerd who writes!?</title>
	<author>Xylene2301</author>
	<datestamp>1245493200000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>The author of the paper is a math nerd who can actually write and communicate ideas; that's an oddity in itself.</htmltext>
<tokenext>The author of the paper is a math nerd who can actually write and communicate ideas ; that 's an oddity in itself .</tokentext>
<sentencetext>The author of the paper is a math nerd who can actually write and communicate ideas; that's an oddity in itself.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394285</id>
	<title>Math is communication</title>
	<author>cowdung</author>
	<datestamp>1245443940000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>The problem with math is that it is taught with no reward. Imagine if we studied the formulas of physics w/o ever hearing about the cool stuff like General Relativity, the Uncertanty Principle, etc.. Understanding those interesting paradoxes is what makes physics interesting. Now look at math. How many people know that math can limit the very scope of a scientific theorem (as expressed in a piece of paper), or the odd patterns of primes, or that there is knowledge in the universe that cannot be summarized, etc.. Nobody ever gets to see the cool stuff.. they are just burried under the mechanics.</p><p>I believe school should teach people to communicate effectively. Initially this implies imprecise communication like English and Spanish, reading and writing.</p><p>But later as we try to describe things more fully we may employ the language of math. For example, lets take a table and see how we can draw it, we can measure it and precisely define its attributes. In fact we can do so so precisely that we can end up telling how heavy it will be, how much room it will take, and how much it will cost.</p><p>As school advances and the need to describe things increases we can use math to describe chemical and biological proceses, physical processes, and sociological processes.</p><p>In fact, as people advance in their education they tend to need math to precisely describe what happened, their theories of what will happen, etc..</p><p>In this manner, students can enjoy the benefits of math in all fields as they advance in its study.</p><p>I know so many people that have studied Differential Equations or even basic Algebra and have no idea how that could ever be useful to them.</p></htmltext>
<tokenext>The problem with math is that it is taught with no reward .
Imagine if we studied the formulas of physics w/o ever hearing about the cool stuff like General Relativity , the Uncertanty Principle , etc.. Understanding those interesting paradoxes is what makes physics interesting .
Now look at math .
How many people know that math can limit the very scope of a scientific theorem ( as expressed in a piece of paper ) , or the odd patterns of primes , or that there is knowledge in the universe that can not be summarized , etc.. Nobody ever gets to see the cool stuff.. they are just burried under the mechanics.I believe school should teach people to communicate effectively .
Initially this implies imprecise communication like English and Spanish , reading and writing.But later as we try to describe things more fully we may employ the language of math .
For example , lets take a table and see how we can draw it , we can measure it and precisely define its attributes .
In fact we can do so so precisely that we can end up telling how heavy it will be , how much room it will take , and how much it will cost.As school advances and the need to describe things increases we can use math to describe chemical and biological proceses , physical processes , and sociological processes.In fact , as people advance in their education they tend to need math to precisely describe what happened , their theories of what will happen , etc..In this manner , students can enjoy the benefits of math in all fields as they advance in its study.I know so many people that have studied Differential Equations or even basic Algebra and have no idea how that could ever be useful to them .</tokentext>
<sentencetext>The problem with math is that it is taught with no reward.
Imagine if we studied the formulas of physics w/o ever hearing about the cool stuff like General Relativity, the Uncertanty Principle, etc.. Understanding those interesting paradoxes is what makes physics interesting.
Now look at math.
How many people know that math can limit the very scope of a scientific theorem (as expressed in a piece of paper), or the odd patterns of primes, or that there is knowledge in the universe that cannot be summarized, etc.. Nobody ever gets to see the cool stuff.. they are just burried under the mechanics.I believe school should teach people to communicate effectively.
Initially this implies imprecise communication like English and Spanish, reading and writing.But later as we try to describe things more fully we may employ the language of math.
For example, lets take a table and see how we can draw it, we can measure it and precisely define its attributes.
In fact we can do so so precisely that we can end up telling how heavy it will be, how much room it will take, and how much it will cost.As school advances and the need to describe things increases we can use math to describe chemical and biological proceses, physical processes, and sociological processes.In fact, as people advance in their education they tend to need math to precisely describe what happened, their theories of what will happen, etc..In this manner, students can enjoy the benefits of math in all fields as they advance in its study.I know so many people that have studied Differential Equations or even basic Algebra and have no idea how that could ever be useful to them.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28395103</id>
	<title>I thoroughly agree</title>
	<author>Anonymous</author>
	<datestamp>1245403440000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>Lockhart is dead on.<br>I have had one "mathematics" teacher in my life. The rest made me memorize crap. They never taught the essence of the subject, only the solutions.</p><p>In this teacher's class he would write a brand new problem on the board which I had never seen. By the time he was making the last stroke of the last variable, I would have the solution, and promptly raise my hand. My answers always correct. He would make me come up to the board and put what I did in my head on the board. At first he was astonished to see that I had done the problem in an entirely new way which he hadn't seen before and would validate that I had solved it correctly. Often the solutions I presented were extremely simple as well as being new to him.</p><p>He  inspired me to love math, which subsequent teachers promptly crushed.</p><p>Every other "teacher" I had made me do it their way, memorizing everything they did and would fail me if  presented the solution any other way but the way they expected. I'm convinced that very few mathematics teachers should be teaching this subject. Most are snotty pseudo intellectuals with 0 imagination. I would do my best to not be noticed by them.</p><p>I've only met one that understood what math was about.</p><p>That's why I'm a software engineer instead of a mathematician (or historian). I'm really really good at solving problems but am terrible at memorizing. I did what I had to to get by in the math classes I did have to take. Usually it involved "cheating". God forbid I should actually solve the problems because usually I was "wrong" when I did it my own way and produced the expected result. You can only take hearing "you can't do it that way" so many times when you CAN do it that way.</p><p>I'm no genius but I also don't need some teacher forcing my hand to "help" me solve a problem which I've already solved in my brain by the time I finish reading it. Coding seems to be a lot easier for most people to understand so the instructors give you more latitude. That was just fine with me.</p><p>-AC</p></htmltext>
<tokenext>Lockhart is dead on.I have had one " mathematics " teacher in my life .
The rest made me memorize crap .
They never taught the essence of the subject , only the solutions.In this teacher 's class he would write a brand new problem on the board which I had never seen .
By the time he was making the last stroke of the last variable , I would have the solution , and promptly raise my hand .
My answers always correct .
He would make me come up to the board and put what I did in my head on the board .
At first he was astonished to see that I had done the problem in an entirely new way which he had n't seen before and would validate that I had solved it correctly .
Often the solutions I presented were extremely simple as well as being new to him.He inspired me to love math , which subsequent teachers promptly crushed.Every other " teacher " I had made me do it their way , memorizing everything they did and would fail me if presented the solution any other way but the way they expected .
I 'm convinced that very few mathematics teachers should be teaching this subject .
Most are snotty pseudo intellectuals with 0 imagination .
I would do my best to not be noticed by them.I 've only met one that understood what math was about.That 's why I 'm a software engineer instead of a mathematician ( or historian ) .
I 'm really really good at solving problems but am terrible at memorizing .
I did what I had to to get by in the math classes I did have to take .
Usually it involved " cheating " .
God forbid I should actually solve the problems because usually I was " wrong " when I did it my own way and produced the expected result .
You can only take hearing " you ca n't do it that way " so many times when you CAN do it that way.I 'm no genius but I also do n't need some teacher forcing my hand to " help " me solve a problem which I 've already solved in my brain by the time I finish reading it .
Coding seems to be a lot easier for most people to understand so the instructors give you more latitude .
That was just fine with me.-AC</tokentext>
<sentencetext>Lockhart is dead on.I have had one "mathematics" teacher in my life.
The rest made me memorize crap.
They never taught the essence of the subject, only the solutions.In this teacher's class he would write a brand new problem on the board which I had never seen.
By the time he was making the last stroke of the last variable, I would have the solution, and promptly raise my hand.
My answers always correct.
He would make me come up to the board and put what I did in my head on the board.
At first he was astonished to see that I had done the problem in an entirely new way which he hadn't seen before and would validate that I had solved it correctly.
Often the solutions I presented were extremely simple as well as being new to him.He  inspired me to love math, which subsequent teachers promptly crushed.Every other "teacher" I had made me do it their way, memorizing everything they did and would fail me if  presented the solution any other way but the way they expected.
I'm convinced that very few mathematics teachers should be teaching this subject.
Most are snotty pseudo intellectuals with 0 imagination.
I would do my best to not be noticed by them.I've only met one that understood what math was about.That's why I'm a software engineer instead of a mathematician (or historian).
I'm really really good at solving problems but am terrible at memorizing.
I did what I had to to get by in the math classes I did have to take.
Usually it involved "cheating".
God forbid I should actually solve the problems because usually I was "wrong" when I did it my own way and produced the expected result.
You can only take hearing "you can't do it that way" so many times when you CAN do it that way.I'm no genius but I also don't need some teacher forcing my hand to "help" me solve a problem which I've already solved in my brain by the time I finish reading it.
Coding seems to be a lot easier for most people to understand so the instructors give you more latitude.
That was just fine with me.-AC</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28399397</id>
	<title>Re:it's really bad</title>
	<author>Lord Ender</author>
	<datestamp>1245435240000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>Perhaps you are right in that some learn by example (mimickers?) while others learn by applying the rules (thinkers?), and so the school decided to teach logical proofs without first teaching logic because they were catering to the mimickers.</p><p>Even so, that's a mistake! They should both! At least speed over the rules of logic before trying to teach proof-writing by example! Don't just give the finger to your thinkers.</p><p>I had sooooooo many moments in college where I thought, "why in the hell didn't they just tell is that in high school??" Maybe they were trying to dumb things down so much that only an idiot could understand?</p><p>If my criticism is too harsh, I apologize. But I lost a lot of respect for my HS teachers while in college. I really should have been allowed to just audit the college courses, I think. Perhaps HS teachers should be required to do so, too.</p></htmltext>
<tokenext>Perhaps you are right in that some learn by example ( mimickers ?
) while others learn by applying the rules ( thinkers ?
) , and so the school decided to teach logical proofs without first teaching logic because they were catering to the mimickers.Even so , that 's a mistake !
They should both !
At least speed over the rules of logic before trying to teach proof-writing by example !
Do n't just give the finger to your thinkers.I had sooooooo many moments in college where I thought , " why in the hell did n't they just tell is that in high school ? ?
" Maybe they were trying to dumb things down so much that only an idiot could understand ? If my criticism is too harsh , I apologize .
But I lost a lot of respect for my HS teachers while in college .
I really should have been allowed to just audit the college courses , I think .
Perhaps HS teachers should be required to do so , too .</tokentext>
<sentencetext>Perhaps you are right in that some learn by example (mimickers?
) while others learn by applying the rules (thinkers?
), and so the school decided to teach logical proofs without first teaching logic because they were catering to the mimickers.Even so, that's a mistake!
They should both!
At least speed over the rules of logic before trying to teach proof-writing by example!
Don't just give the finger to your thinkers.I had sooooooo many moments in college where I thought, "why in the hell didn't they just tell is that in high school??
" Maybe they were trying to dumb things down so much that only an idiot could understand?If my criticism is too harsh, I apologize.
But I lost a lot of respect for my HS teachers while in college.
I really should have been allowed to just audit the college courses, I think.
Perhaps HS teachers should be required to do so, too.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393855</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394051</id>
	<title>Re:I Sympathize With Him But Too Idyllic</title>
	<author>Anonymous</author>
	<datestamp>1245443100000</datestamp>
	<modclass>Insightful</modclass>
	<modscore>2</modscore>
	<htmltext>Honestly, it's the people who are really passionate about math who are the ones that are least capable of teaching it to other people.  The ones I've known appreciate the subject matter too much to see it be ruined by a class full of students who couldn't care less just how elegant this theory that you're teaching is.  They just want to get through the class and get back to stuff they care about. <br>
<br>
The only way this guy would get the class he wants is to only teach elective courses that aren't pre-reqs for anything.  That's the only way to make sure that your students actually care about the subject and aren't taking the class just because they were forced to.  In public education this does not exist until sometimes very very late in a child's development (when it's already too late).</htmltext>
<tokenext>Honestly , it 's the people who are really passionate about math who are the ones that are least capable of teaching it to other people .
The ones I 've known appreciate the subject matter too much to see it be ruined by a class full of students who could n't care less just how elegant this theory that you 're teaching is .
They just want to get through the class and get back to stuff they care about .
The only way this guy would get the class he wants is to only teach elective courses that are n't pre-reqs for anything .
That 's the only way to make sure that your students actually care about the subject and are n't taking the class just because they were forced to .
In public education this does not exist until sometimes very very late in a child 's development ( when it 's already too late ) .</tokentext>
<sentencetext>Honestly, it's the people who are really passionate about math who are the ones that are least capable of teaching it to other people.
The ones I've known appreciate the subject matter too much to see it be ruined by a class full of students who couldn't care less just how elegant this theory that you're teaching is.
They just want to get through the class and get back to stuff they care about.
The only way this guy would get the class he wants is to only teach elective courses that aren't pre-reqs for anything.
That's the only way to make sure that your students actually care about the subject and aren't taking the class just because they were forced to.
In public education this does not exist until sometimes very very late in a child's development (when it's already too late).</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392903</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28395687</id>
	<title>Re:Cue the other subjects</title>
	<author>jacoby</author>
	<datestamp>1245405600000</datestamp>
	<modclass>Interestin</modclass>
	<modscore>2</modscore>
	<htmltext><p>Of course, that group has a higher percentage than average of home-schoolers.</p><p>And those home-schoolers tend to get much more out of their education than average.</p><p>But go ahead with your beliefs.</p></htmltext>
<tokenext>Of course , that group has a higher percentage than average of home-schoolers.And those home-schoolers tend to get much more out of their education than average.But go ahead with your beliefs .</tokentext>
<sentencetext>Of course, that group has a higher percentage than average of home-schoolers.And those home-schoolers tend to get much more out of their education than average.But go ahead with your beliefs.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393083</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392947</id>
	<title>True story ....</title>
	<author>gstoddart</author>
	<datestamp>1245439080000</datestamp>
	<modclass>Insightful</modclass>
	<modscore>5</modscore>
	<htmltext><p>In university, I was taking an intro philosophy course on critical reasoning.</p><p>We had covered the concept of statistical significance.  The example we'd used was a case of "0.05" meaning we had 95\% confidence in the statistical results.  On the exam, the professor made a typo, and the question read "how much certainty with a statistical confidence of 0.5", to which the correct answer is 50\%.</p><p>I was marked as wrong, and when I complained, the professor indicated that since we'd never covered that example, and only covered 0.05 in class, it was assumed that was what she meant.</p><p>I informed her for someone teaching critical reasoning, she wasn't demonstrating any.  I also insisted I get the credit for giving the actual correct answer (which I and everyone who answered it correctly did).</p><p>If that's indicative of how math is taught nowadays, we're all hosed.<nobr> <wbr></nobr>:-P</p><p>Cheers</p></htmltext>
<tokenext>In university , I was taking an intro philosophy course on critical reasoning.We had covered the concept of statistical significance .
The example we 'd used was a case of " 0.05 " meaning we had 95 \ % confidence in the statistical results .
On the exam , the professor made a typo , and the question read " how much certainty with a statistical confidence of 0.5 " , to which the correct answer is 50 \ % .I was marked as wrong , and when I complained , the professor indicated that since we 'd never covered that example , and only covered 0.05 in class , it was assumed that was what she meant.I informed her for someone teaching critical reasoning , she was n't demonstrating any .
I also insisted I get the credit for giving the actual correct answer ( which I and everyone who answered it correctly did ) .If that 's indicative of how math is taught nowadays , we 're all hosed .
: -PCheers</tokentext>
<sentencetext>In university, I was taking an intro philosophy course on critical reasoning.We had covered the concept of statistical significance.
The example we'd used was a case of "0.05" meaning we had 95\% confidence in the statistical results.
On the exam, the professor made a typo, and the question read "how much certainty with a statistical confidence of 0.5", to which the correct answer is 50\%.I was marked as wrong, and when I complained, the professor indicated that since we'd never covered that example, and only covered 0.05 in class, it was assumed that was what she meant.I informed her for someone teaching critical reasoning, she wasn't demonstrating any.
I also insisted I get the credit for giving the actual correct answer (which I and everyone who answered it correctly did).If that's indicative of how math is taught nowadays, we're all hosed.
:-PCheers</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392993</id>
	<title>Oh give it a rest</title>
	<author>eln</author>
	<datestamp>1245439380000</datestamp>
	<modclass>Insightful</modclass>
	<modscore>5</modscore>
	<htmltext>Specialists in every field complain that educators get their field wrong or don't stir the passions of kids for their field as much as they ought to.  What they fail to understand is that they're coming at the whole problem from the perspective of someone who is obviously gifted at and highly passionate about the field.  They don't seem to get that most people don't pick up their field as easily as they do, and don't care enough to put in the effort it would take to get even half as good at it as the specialist.
<br> <br>

Instructors of just about every field at any level of compulsory education (K-12) have to battle against entrenched biases against their fields, and against education in general, that have been fostered for years before the student ever gets in their classroom.  Further, their task is to teach the curriculum provided.  If they inspire their kids to love the field, that's great, but if they spend so much time inspiring the kids that they don't have enough time to teach the kids what they need to pass the state-required tests, they're still going to lose their jobs.
<br> <br>
Teaching math, science, or anything else is HARD.  Teaching it to people who don't care and don't want to be there is even harder.  Teaching kids to love the field when the only metric used to judge your performance is pass rates on a standardized test is harder still.  It's all well and good for professional mathematicians to bitch and moan about the state of education, but until they're ready to step in with some realistic and implementable ideas that don't presuppose that all kids have some inherent interest in these things that just needs to be tapped into, it's not helpful in the least.</htmltext>
<tokenext>Specialists in every field complain that educators get their field wrong or do n't stir the passions of kids for their field as much as they ought to .
What they fail to understand is that they 're coming at the whole problem from the perspective of someone who is obviously gifted at and highly passionate about the field .
They do n't seem to get that most people do n't pick up their field as easily as they do , and do n't care enough to put in the effort it would take to get even half as good at it as the specialist .
Instructors of just about every field at any level of compulsory education ( K-12 ) have to battle against entrenched biases against their fields , and against education in general , that have been fostered for years before the student ever gets in their classroom .
Further , their task is to teach the curriculum provided .
If they inspire their kids to love the field , that 's great , but if they spend so much time inspiring the kids that they do n't have enough time to teach the kids what they need to pass the state-required tests , they 're still going to lose their jobs .
Teaching math , science , or anything else is HARD .
Teaching it to people who do n't care and do n't want to be there is even harder .
Teaching kids to love the field when the only metric used to judge your performance is pass rates on a standardized test is harder still .
It 's all well and good for professional mathematicians to bitch and moan about the state of education , but until they 're ready to step in with some realistic and implementable ideas that do n't presuppose that all kids have some inherent interest in these things that just needs to be tapped into , it 's not helpful in the least .</tokentext>
<sentencetext>Specialists in every field complain that educators get their field wrong or don't stir the passions of kids for their field as much as they ought to.
What they fail to understand is that they're coming at the whole problem from the perspective of someone who is obviously gifted at and highly passionate about the field.
They don't seem to get that most people don't pick up their field as easily as they do, and don't care enough to put in the effort it would take to get even half as good at it as the specialist.
Instructors of just about every field at any level of compulsory education (K-12) have to battle against entrenched biases against their fields, and against education in general, that have been fostered for years before the student ever gets in their classroom.
Further, their task is to teach the curriculum provided.
If they inspire their kids to love the field, that's great, but if they spend so much time inspiring the kids that they don't have enough time to teach the kids what they need to pass the state-required tests, they're still going to lose their jobs.
Teaching math, science, or anything else is HARD.
Teaching it to people who don't care and don't want to be there is even harder.
Teaching kids to love the field when the only metric used to judge your performance is pass rates on a standardized test is harder still.
It's all well and good for professional mathematicians to bitch and moan about the state of education, but until they're ready to step in with some realistic and implementable ideas that don't presuppose that all kids have some inherent interest in these things that just needs to be tapped into, it's not helpful in the least.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28400263</id>
	<title>Re:The way math is structured is disconnected from</title>
	<author>rekees</author>
	<datestamp>1245492360000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>American pupils feel the pressure to make money, which is done best by the American model through business or law schools. To get a business degree or MBA, one needs very basic algebra, even in 'good' business programs. We have a problem of culture obsessed with making money first, ahead of many other values including being creative. The MBAs and lawyers then go an run the country and promote their lifestyle: "I made it well without math or sciences, others can, too." Not sure when/how it will change, but this model puts us at great risk in a democracy: if the majority don't create any value, making money in itself is not creating value, then they'll run us into the ground. This was the very reason public schools were created; forgot what president in the 19th century figured this out. Pretty sad story we are living.</htmltext>
<tokenext>American pupils feel the pressure to make money , which is done best by the American model through business or law schools .
To get a business degree or MBA , one needs very basic algebra , even in 'good ' business programs .
We have a problem of culture obsessed with making money first , ahead of many other values including being creative .
The MBAs and lawyers then go an run the country and promote their lifestyle : " I made it well without math or sciences , others can , too .
" Not sure when/how it will change , but this model puts us at great risk in a democracy : if the majority do n't create any value , making money in itself is not creating value , then they 'll run us into the ground .
This was the very reason public schools were created ; forgot what president in the 19th century figured this out .
Pretty sad story we are living .</tokentext>
<sentencetext>American pupils feel the pressure to make money, which is done best by the American model through business or law schools.
To get a business degree or MBA, one needs very basic algebra, even in 'good' business programs.
We have a problem of culture obsessed with making money first, ahead of many other values including being creative.
The MBAs and lawyers then go an run the country and promote their lifestyle: "I made it well without math or sciences, others can, too.
" Not sure when/how it will change, but this model puts us at great risk in a democracy: if the majority don't create any value, making money in itself is not creating value, then they'll run us into the ground.
This was the very reason public schools were created; forgot what president in the 19th century figured this out.
Pretty sad story we are living.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393115</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28401231</id>
	<title>Re:I Sympathize With Him But Too Idyllic</title>
	<author>dzfoo</author>
	<datestamp>1245507840000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>&gt;&gt; <i>Well if you're not asking for teachers needing to be professional published mathematicians, what was that paragraph about? </i></p><p>You missed the point.  He wasn't talking about being professional or published; when he mentioned <i>"who have never produced an original piece of mathematics,"</i> he meant in the same creative and engaging thought games he wishes they taught the students.  He's point being that teachers are just regurgitating "facts" from a text-book, whose context and history they themselves never bothered to understand first hand.</p><p>
&nbsp; &nbsp; &nbsp; -dZ.</p></htmltext>
<tokenext>&gt; &gt; Well if you 're not asking for teachers needing to be professional published mathematicians , what was that paragraph about ?
You missed the point .
He was n't talking about being professional or published ; when he mentioned " who have never produced an original piece of mathematics , " he meant in the same creative and engaging thought games he wishes they taught the students .
He 's point being that teachers are just regurgitating " facts " from a text-book , whose context and history they themselves never bothered to understand first hand .
      -dZ .</tokentext>
<sentencetext>&gt;&gt; Well if you're not asking for teachers needing to be professional published mathematicians, what was that paragraph about?
You missed the point.
He wasn't talking about being professional or published; when he mentioned "who have never produced an original piece of mathematics," he meant in the same creative and engaging thought games he wishes they taught the students.
He's point being that teachers are just regurgitating "facts" from a text-book, whose context and history they themselves never bothered to understand first hand.
      -dZ.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392903</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28395083</id>
	<title>Re:You can convince me</title>
	<author>geekoid</author>
	<datestamp>1245403320000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>"It's a pretty common arrogation in the math culture"<br>yes, yes it is.<br>Math is a tool.<br>You sue it to get answers. It's cool that its a tool used to expand itself, but it's still a tool.</p></htmltext>
<tokenext>" It 's a pretty common arrogation in the math culture " yes , yes it is.Math is a tool.You sue it to get answers .
It 's cool that its a tool used to expand itself , but it 's still a tool .</tokentext>
<sentencetext>"It's a pretty common arrogation in the math culture"yes, yes it is.Math is a tool.You sue it to get answers.
It's cool that its a tool used to expand itself, but it's still a tool.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393159</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28402377</id>
	<title>Re:Cue the other subjects</title>
	<author>Anonymous</author>
	<datestamp>1245517440000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>I was going to say.. I'm not religious by any stretch of the imagination, but this country produced a lot of phenomenally good work when we were significantly more fundamentalist. If anything I'd say the 'everyone is a winner' attitude bought on by our weak 'modern' touchy-feely approach to children, education, and personal responsibility has contributed more to the degradation of K-12 learning than any 'fundamentalist ideas'. In fact I would argue that we are much more likely to see a resurgence of ignorance and the acceptance of things with 'god did it' explanations in the future, simply because we allow school systems and idiot parents who are unwilling to hurt little johnny's feelings ( which is of course a more modern approach ).</p><p>The education system needs to go back to basics, don't let stupid children in k-12 have a calculator that can do symbolic integration, root finding, and complex matrix operations... Kids don't need that crap. They need READING (if you can read, you can do whatever you want), writing, and arithmetic... and by arithmetic I mean geometry, algebra, and basic calc, with some intro abstract concepts for people who arn't retarded. Waves of kids finishing high school and taking basic algebra in college is a disgrace.</p></htmltext>
<tokenext>I was going to say.. I 'm not religious by any stretch of the imagination , but this country produced a lot of phenomenally good work when we were significantly more fundamentalist .
If anything I 'd say the 'everyone is a winner ' attitude bought on by our weak 'modern ' touchy-feely approach to children , education , and personal responsibility has contributed more to the degradation of K-12 learning than any 'fundamentalist ideas' .
In fact I would argue that we are much more likely to see a resurgence of ignorance and the acceptance of things with 'god did it ' explanations in the future , simply because we allow school systems and idiot parents who are unwilling to hurt little johnny 's feelings ( which is of course a more modern approach ) .The education system needs to go back to basics , do n't let stupid children in k-12 have a calculator that can do symbolic integration , root finding , and complex matrix operations... Kids do n't need that crap .
They need READING ( if you can read , you can do whatever you want ) , writing , and arithmetic... and by arithmetic I mean geometry , algebra , and basic calc , with some intro abstract concepts for people who ar n't retarded .
Waves of kids finishing high school and taking basic algebra in college is a disgrace .</tokentext>
<sentencetext>I was going to say.. I'm not religious by any stretch of the imagination, but this country produced a lot of phenomenally good work when we were significantly more fundamentalist.
If anything I'd say the 'everyone is a winner' attitude bought on by our weak 'modern' touchy-feely approach to children, education, and personal responsibility has contributed more to the degradation of K-12 learning than any 'fundamentalist ideas'.
In fact I would argue that we are much more likely to see a resurgence of ignorance and the acceptance of things with 'god did it' explanations in the future, simply because we allow school systems and idiot parents who are unwilling to hurt little johnny's feelings ( which is of course a more modern approach ).The education system needs to go back to basics, don't let stupid children in k-12 have a calculator that can do symbolic integration, root finding, and complex matrix operations... Kids don't need that crap.
They need READING (if you can read, you can do whatever you want), writing, and arithmetic... and by arithmetic I mean geometry, algebra, and basic calc, with some intro abstract concepts for people who arn't retarded.
Waves of kids finishing high school and taking basic algebra in college is a disgrace.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393595</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28395431</id>
	<title>Re:The way math is structured is disconnected from</title>
	<author>NoOneInParticular</author>
	<datestamp>1245404520000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>Interesting and creative summary of the article. You might want to read it...</htmltext>
<tokenext>Interesting and creative summary of the article .
You might want to read it.. .</tokentext>
<sentencetext>Interesting and creative summary of the article.
You might want to read it...</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392921</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28408419</id>
	<title>Re:The way math is structured is disconnected from</title>
	<author>Anonymous</author>
	<datestamp>1245526800000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>That's not true if you exclude Hispanics and Blacks. Exclude Hispanics and Blacks, and US White/Asian kids do the same or better as world leaders. As someone who's taught in barrio schools, most Hispanic kids (and I assume Blacks) have severe problems with the US educational system.</p><p>1. Single Motherhood -- this is the big one. Single motherhood is rampant in both these groups, increasing sadly in the White population, and it leads to low resources particularly time for parents, and kids acting out. Boys being hypermasculine or withdrawn, and girls being generally too interested in boys and not enough in school around puberty.</p><p>2. Negative cultural attitudes towards education, which is perceived as "White" and a "sell-out" to racial/ethnic values.</p><p>3. Lower median IQ. It's not very popular, but it is true, that every study ever done, shows consistently a lower median IQ for Blacks (around 85) than Whites (around 100) and Asians coming in around 105. Hispanics come in around 89. This does NOT mean all Blacks and Hispanics have low IQ, but enough of them do that they drag down instruction to their level, making most classes slow, boring and remedial. A huge frustration for the few bright kids, and really a huge drag on the US educational system.</p><p>Let's get real. Mostly White/Asian schools do well because the kids are mostly orderly, behaved, come from two-parent families where the parents are involved and care about the kids, and are committed to Education as a gateway to upward mobility. Mostly Black and Hispanic schools are pits, because the students don't care, gangs are rampant, their parent is a single mother (often chasing the neighborhood thugs), nobody cares, and no one views Education as a gateway to upward mobility. In Ghetto/Barrio schools, the only upward path is through athletics. Which is the only effort kids put forward (particularly for boys, being seen as a "schoolboy" equates to being less masculine, and unworthy of girls). White/Asian boys face this too, but it's not as strong. [Girls face little penalty for being "smart" -- they are either hot or not, it's purely physical.]</p><p>Shrug.</p><p>There have been a FEW schools that have done well with Black/Hispanic kids, they are outside the Public Schools and screen out troublemakers, and emphasize fairly strict discipline, rote memorization, and group identity. They are not replicable because they require highly dedicated and charismatic leaders, and are not "community friendly" i.e. featherbedding for local political machines, and swayed by parents demands. They don't allow gang members for example, require uniforms, and Marine Corps like group indoctrination/spirit. Few communities would stand still for that -- they want niceness rather than results. [Black/Hispanic kids probably can do far better, but it is not politically possible to construct strict discipline schools they need to perform at higher levels, which requires walling off in effect the dysfunctional outside community.]</p><p>But exclude Black/Hispanic schools and US White/Asian kids do in the top of nearly all categories, it's just impolitic and UN-PC to say it. Even though it is in fact true. This should shock no one. By and large, the society in Black/Hispanic communities is dysfunctional and a complete failure. In White/Asian communities, mostly successful. It would be shocking in fact if their schools did not reflect the failure and success of their wider communities.</p></htmltext>
<tokenext>That 's not true if you exclude Hispanics and Blacks .
Exclude Hispanics and Blacks , and US White/Asian kids do the same or better as world leaders .
As someone who 's taught in barrio schools , most Hispanic kids ( and I assume Blacks ) have severe problems with the US educational system.1 .
Single Motherhood -- this is the big one .
Single motherhood is rampant in both these groups , increasing sadly in the White population , and it leads to low resources particularly time for parents , and kids acting out .
Boys being hypermasculine or withdrawn , and girls being generally too interested in boys and not enough in school around puberty.2 .
Negative cultural attitudes towards education , which is perceived as " White " and a " sell-out " to racial/ethnic values.3 .
Lower median IQ .
It 's not very popular , but it is true , that every study ever done , shows consistently a lower median IQ for Blacks ( around 85 ) than Whites ( around 100 ) and Asians coming in around 105 .
Hispanics come in around 89 .
This does NOT mean all Blacks and Hispanics have low IQ , but enough of them do that they drag down instruction to their level , making most classes slow , boring and remedial .
A huge frustration for the few bright kids , and really a huge drag on the US educational system.Let 's get real .
Mostly White/Asian schools do well because the kids are mostly orderly , behaved , come from two-parent families where the parents are involved and care about the kids , and are committed to Education as a gateway to upward mobility .
Mostly Black and Hispanic schools are pits , because the students do n't care , gangs are rampant , their parent is a single mother ( often chasing the neighborhood thugs ) , nobody cares , and no one views Education as a gateway to upward mobility .
In Ghetto/Barrio schools , the only upward path is through athletics .
Which is the only effort kids put forward ( particularly for boys , being seen as a " schoolboy " equates to being less masculine , and unworthy of girls ) .
White/Asian boys face this too , but it 's not as strong .
[ Girls face little penalty for being " smart " -- they are either hot or not , it 's purely physical .
] Shrug.There have been a FEW schools that have done well with Black/Hispanic kids , they are outside the Public Schools and screen out troublemakers , and emphasize fairly strict discipline , rote memorization , and group identity .
They are not replicable because they require highly dedicated and charismatic leaders , and are not " community friendly " i.e .
featherbedding for local political machines , and swayed by parents demands .
They do n't allow gang members for example , require uniforms , and Marine Corps like group indoctrination/spirit .
Few communities would stand still for that -- they want niceness rather than results .
[ Black/Hispanic kids probably can do far better , but it is not politically possible to construct strict discipline schools they need to perform at higher levels , which requires walling off in effect the dysfunctional outside community .
] But exclude Black/Hispanic schools and US White/Asian kids do in the top of nearly all categories , it 's just impolitic and UN-PC to say it .
Even though it is in fact true .
This should shock no one .
By and large , the society in Black/Hispanic communities is dysfunctional and a complete failure .
In White/Asian communities , mostly successful .
It would be shocking in fact if their schools did not reflect the failure and success of their wider communities .</tokentext>
<sentencetext>That's not true if you exclude Hispanics and Blacks.
Exclude Hispanics and Blacks, and US White/Asian kids do the same or better as world leaders.
As someone who's taught in barrio schools, most Hispanic kids (and I assume Blacks) have severe problems with the US educational system.1.
Single Motherhood -- this is the big one.
Single motherhood is rampant in both these groups, increasing sadly in the White population, and it leads to low resources particularly time for parents, and kids acting out.
Boys being hypermasculine or withdrawn, and girls being generally too interested in boys and not enough in school around puberty.2.
Negative cultural attitudes towards education, which is perceived as "White" and a "sell-out" to racial/ethnic values.3.
Lower median IQ.
It's not very popular, but it is true, that every study ever done, shows consistently a lower median IQ for Blacks (around 85) than Whites (around 100) and Asians coming in around 105.
Hispanics come in around 89.
This does NOT mean all Blacks and Hispanics have low IQ, but enough of them do that they drag down instruction to their level, making most classes slow, boring and remedial.
A huge frustration for the few bright kids, and really a huge drag on the US educational system.Let's get real.
Mostly White/Asian schools do well because the kids are mostly orderly, behaved, come from two-parent families where the parents are involved and care about the kids, and are committed to Education as a gateway to upward mobility.
Mostly Black and Hispanic schools are pits, because the students don't care, gangs are rampant, their parent is a single mother (often chasing the neighborhood thugs), nobody cares, and no one views Education as a gateway to upward mobility.
In Ghetto/Barrio schools, the only upward path is through athletics.
Which is the only effort kids put forward (particularly for boys, being seen as a "schoolboy" equates to being less masculine, and unworthy of girls).
White/Asian boys face this too, but it's not as strong.
[Girls face little penalty for being "smart" -- they are either hot or not, it's purely physical.
]Shrug.There have been a FEW schools that have done well with Black/Hispanic kids, they are outside the Public Schools and screen out troublemakers, and emphasize fairly strict discipline, rote memorization, and group identity.
They are not replicable because they require highly dedicated and charismatic leaders, and are not "community friendly" i.e.
featherbedding for local political machines, and swayed by parents demands.
They don't allow gang members for example, require uniforms, and Marine Corps like group indoctrination/spirit.
Few communities would stand still for that -- they want niceness rather than results.
[Black/Hispanic kids probably can do far better, but it is not politically possible to construct strict discipline schools they need to perform at higher levels, which requires walling off in effect the dysfunctional outside community.
]But exclude Black/Hispanic schools and US White/Asian kids do in the top of nearly all categories, it's just impolitic and UN-PC to say it.
Even though it is in fact true.
This should shock no one.
By and large, the society in Black/Hispanic communities is dysfunctional and a complete failure.
In White/Asian communities, mostly successful.
It would be shocking in fact if their schools did not reflect the failure and success of their wider communities.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393115</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392911</id>
	<title>it's really bad</title>
	<author>Anonymous</author>
	<datestamp>1245439020000</datestamp>
	<modclass>Insightful</modclass>
	<modscore>4</modscore>
	<htmltext><p>High school students are forced to write proofs as part of geometry class. However, they are never taught the rules of logic before being asked to write these proofs. That is just one example of how horribly, horribly stupid the HS math curriculum is in the US.</p></htmltext>
<tokenext>High school students are forced to write proofs as part of geometry class .
However , they are never taught the rules of logic before being asked to write these proofs .
That is just one example of how horribly , horribly stupid the HS math curriculum is in the US .</tokentext>
<sentencetext>High school students are forced to write proofs as part of geometry class.
However, they are never taught the rules of logic before being asked to write these proofs.
That is just one example of how horribly, horribly stupid the HS math curriculum is in the US.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393279</id>
	<title>Re:Cue the other subjects</title>
	<author>superwiz</author>
	<datestamp>1245440340000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>Can you name one day in history that started that war?  (I am fairly certain that I can)</htmltext>
<tokenext>Can you name one day in history that started that war ?
( I am fairly certain that I can )</tokentext>
<sentencetext>Can you name one day in history that started that war?
(I am fairly certain that I can)</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393083</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393823</id>
	<title>Re:US School System compared to Europes School Sys</title>
	<author>kaiser423</author>
	<datestamp>1245442320000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>My large school got rid of all the courses based upon skill level shortly after I left because helicopter parents were too stressed out and causing too many administrative and political problems for the school when their children didn't qualify for the high skill level class.  That has happened across a large number of schools in the US.
<br> <br>
Also, the US tracking starts actually tracking kids in like 10th and 11th grade.  Great, they're tracked and get the benefits for two years...yippee!</htmltext>
<tokenext>My large school got rid of all the courses based upon skill level shortly after I left because helicopter parents were too stressed out and causing too many administrative and political problems for the school when their children did n't qualify for the high skill level class .
That has happened across a large number of schools in the US .
Also , the US tracking starts actually tracking kids in like 10th and 11th grade .
Great , they 're tracked and get the benefits for two years...yippee !</tokentext>
<sentencetext>My large school got rid of all the courses based upon skill level shortly after I left because helicopter parents were too stressed out and causing too many administrative and political problems for the school when their children didn't qualify for the high skill level class.
That has happened across a large number of schools in the US.
Also, the US tracking starts actually tracking kids in like 10th and 11th grade.
Great, they're tracked and get the benefits for two years...yippee!</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393241</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393149</id>
	<title>Meanwhile, the English teachers lament...</title>
	<author>scalpod</author>
	<datestamp>1245439920000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext>...that Roget ever compiled his damned, accursed, infernal, confounded thesaurus!</htmltext>
<tokenext>...that Roget ever compiled his damned , accursed , infernal , confounded thesaurus !</tokentext>
<sentencetext>...that Roget ever compiled his damned, accursed, infernal, confounded thesaurus!</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393677</id>
	<title>Re:it's really bad</title>
	<author>Anonymous</author>
	<datestamp>1245441780000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p><div class="quote"><p>It is necessary to be able to understand proofs, but duplicating them under exam conditions means you have to memorize them by rote.</p></div><p>When I intuitively understand why something is true I never have trouble formulating a proof.  For example, following a lazy three years at Oxford I spent the three weeks before my Maths finals learning all the <i>definitions</i> for the maths I was supposed to know.  I didn't learn any proofs.  And I got a first.</p></div>
	</htmltext>
<tokenext>It is necessary to be able to understand proofs , but duplicating them under exam conditions means you have to memorize them by rote.When I intuitively understand why something is true I never have trouble formulating a proof .
For example , following a lazy three years at Oxford I spent the three weeks before my Maths finals learning all the definitions for the maths I was supposed to know .
I did n't learn any proofs .
And I got a first .</tokentext>
<sentencetext>It is necessary to be able to understand proofs, but duplicating them under exam conditions means you have to memorize them by rote.When I intuitively understand why something is true I never have trouble formulating a proof.
For example, following a lazy three years at Oxford I spent the three weeks before my Maths finals learning all the definitions for the maths I was supposed to know.
I didn't learn any proofs.
And I got a first.
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393445</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394565</id>
	<title>Re:True story ....</title>
	<author>david\_thornley</author>
	<datestamp>1245444840000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>
Thank you for illustrating your point with a fallacious syllogism.</p></htmltext>
<tokenext>Thank you for illustrating your point with a fallacious syllogism .</tokentext>
<sentencetext>
Thank you for illustrating your point with a fallacious syllogism.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393199</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394391</id>
	<title>Re:True story ....</title>
	<author>ObsessiveMathsFreak</author>
	<datestamp>1245444300000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>You have just discovered the difference between philosophers and mathematicians.</p><p>Mathematicians find truths.<br>Philosophers "interpret" truths.</p></htmltext>
<tokenext>You have just discovered the difference between philosophers and mathematicians.Mathematicians find truths.Philosophers " interpret " truths .</tokentext>
<sentencetext>You have just discovered the difference between philosophers and mathematicians.Mathematicians find truths.Philosophers "interpret" truths.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392947</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28398297</id>
	<title>Re:The way math is structured is disconnected from</title>
	<author>Anonymous</author>
	<datestamp>1245422040000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>The U.S. is being outclassed in mathematics because the average IQ of Americans<br>is lower.  Period.  End of story.</p></htmltext>
<tokenext>The U.S. is being outclassed in mathematics because the average IQ of Americansis lower .
Period. End of story .</tokentext>
<sentencetext>The U.S. is being outclassed in mathematics because the average IQ of Americansis lower.
Period.  End of story.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393115</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28398363</id>
	<title>Re:Cue the other subjects</title>
	<author>Forrest Kyle</author>
	<datestamp>1245422760000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>If you honestly believe the quality of public education had declined because of groups advocating private education and freedom of choice for education, you have no idea how the public education system works at all.  My wife taught mathematics at a public elementary school, and I assure you our public schools are failing because of government policies, government inefficiency, government sponsored group-think, and horrible, irresponsible parents who are raising tv and sugar addicted monsters that don't care about anything and don't know how to behave.</htmltext>
<tokenext>If you honestly believe the quality of public education had declined because of groups advocating private education and freedom of choice for education , you have no idea how the public education system works at all .
My wife taught mathematics at a public elementary school , and I assure you our public schools are failing because of government policies , government inefficiency , government sponsored group-think , and horrible , irresponsible parents who are raising tv and sugar addicted monsters that do n't care about anything and do n't know how to behave .</tokentext>
<sentencetext>If you honestly believe the quality of public education had declined because of groups advocating private education and freedom of choice for education, you have no idea how the public education system works at all.
My wife taught mathematics at a public elementary school, and I assure you our public schools are failing because of government policies, government inefficiency, government sponsored group-think, and horrible, irresponsible parents who are raising tv and sugar addicted monsters that don't care about anything and don't know how to behave.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393083</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28399781</id>
	<title>Re:You can convince me</title>
	<author>DrEasy</author>
	<datestamp>1245441120000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>But is school a place for training or for education? If math is taught as a tool then the purpose is to train. I believe Lockhard is arguing that school is a place to awaken curiosity and interest, and therefore it is the art of maths that needs to be taught. I sit in the middle, I think the art part helps to capture the interest, so that they can suffer through the repetitive training part. You start a lecture by bringing up an interesting problem, then you provide the tool to solve the given problem as well as many other ones.</p></htmltext>
<tokenext>But is school a place for training or for education ?
If math is taught as a tool then the purpose is to train .
I believe Lockhard is arguing that school is a place to awaken curiosity and interest , and therefore it is the art of maths that needs to be taught .
I sit in the middle , I think the art part helps to capture the interest , so that they can suffer through the repetitive training part .
You start a lecture by bringing up an interesting problem , then you provide the tool to solve the given problem as well as many other ones .</tokentext>
<sentencetext>But is school a place for training or for education?
If math is taught as a tool then the purpose is to train.
I believe Lockhard is arguing that school is a place to awaken curiosity and interest, and therefore it is the art of maths that needs to be taught.
I sit in the middle, I think the art part helps to capture the interest, so that they can suffer through the repetitive training part.
You start a lecture by bringing up an interesting problem, then you provide the tool to solve the given problem as well as many other ones.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393159</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28400855</id>
	<title>News?</title>
	<author>PoliticalGamer</author>
	<datestamp>1245502200000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>Isn't this fairly old?
I know I have seen it before.</htmltext>
<tokenext>Is n't this fairly old ?
I know I have seen it before .</tokentext>
<sentencetext>Isn't this fairly old?
I know I have seen it before.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28398091</id>
	<title>Damn you!</title>
	<author>Anonymous</author>
	<datestamp>1245420180000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>Damn you! Damn you to hell! You made me like math again. Now I have to get Mathematica out again to get funny looks just like in high school.</p></htmltext>
<tokenext>Damn you !
Damn you to hell !
You made me like math again .
Now I have to get Mathematica out again to get funny looks just like in high school .</tokentext>
<sentencetext>Damn you!
Damn you to hell!
You made me like math again.
Now I have to get Mathematica out again to get funny looks just like in high school.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28442897</id>
	<title>Non-Truth-Suffused</title>
	<author>Anonymous</author>
	<datestamp>1245786480000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>Submitter's claim: "I defy you to read and find a single sentence that isn't permeated, suffused, soaked, and encrusted with truth."</p><p>Well, Scott Aaronson, your defiance is unsuccessful. I found one. Bottom of page 8:<br>"Here is a simple and elegant question, and it requires no effort to be made appealing."</p><p>I didn't find the question appealing, so it WOULD require some effort to make it so. The sentence is a claim based on the subjective experience of the reader and can't be truth.</p><p>So yeah, I'm being a pedantic ass, but Scott, DON'T BE A LYING SENSATIONALIST. Next time just say you agree with the entire essay and you think everyone else will too, which is what you tried to say, but FAILED due to wanting to sound cool.</p></htmltext>
<tokenext>Submitter 's claim : " I defy you to read and find a single sentence that is n't permeated , suffused , soaked , and encrusted with truth .
" Well , Scott Aaronson , your defiance is unsuccessful .
I found one .
Bottom of page 8 : " Here is a simple and elegant question , and it requires no effort to be made appealing .
" I did n't find the question appealing , so it WOULD require some effort to make it so .
The sentence is a claim based on the subjective experience of the reader and ca n't be truth.So yeah , I 'm being a pedantic ass , but Scott , DO N'T BE A LYING SENSATIONALIST .
Next time just say you agree with the entire essay and you think everyone else will too , which is what you tried to say , but FAILED due to wanting to sound cool .</tokentext>
<sentencetext>Submitter's claim: "I defy you to read and find a single sentence that isn't permeated, suffused, soaked, and encrusted with truth.
"Well, Scott Aaronson, your defiance is unsuccessful.
I found one.
Bottom of page 8:"Here is a simple and elegant question, and it requires no effort to be made appealing.
"I didn't find the question appealing, so it WOULD require some effort to make it so.
The sentence is a claim based on the subjective experience of the reader and can't be truth.So yeah, I'm being a pedantic ass, but Scott, DON'T BE A LYING SENSATIONALIST.
Next time just say you agree with the entire essay and you think everyone else will too, which is what you tried to say, but FAILED due to wanting to sound cool.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394121</id>
	<title>Re:Wrong tool for the job</title>
	<author>John Hasler</author>
	<datestamp>1245443340000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>&gt; Stop hiring Education Majors to teach The Hard Sciences.</p><p>The government won't license anyone else to teach (one of many examples of the perniciousness of the entire concept of licensing).</p></htmltext>
<tokenext>&gt; Stop hiring Education Majors to teach The Hard Sciences.The government wo n't license anyone else to teach ( one of many examples of the perniciousness of the entire concept of licensing ) .</tokentext>
<sentencetext>&gt; Stop hiring Education Majors to teach The Hard Sciences.The government won't license anyone else to teach (one of many examples of the perniciousness of the entire concept of licensing).</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393389</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28395833</id>
	<title>Re:A teachers take</title>
	<author>Anonymous</author>
	<datestamp>1245406260000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>recognizing effort is ok, I suppose... But as a talented and rather bright student I always found that completely insidious and hurtful to my education.</p><p>IE, I don't know how many advanced and AP classes I took where the other kids in the class were there because they "tried really hard" and so the teachers let them in... Well guess what? That just slowed down my education, cause now the advanced teacher is having to babysit, review, and in general spend all of the time in the class helping these remedial math students understand basic algebra before we can actually get into calculus.</p><p>Or the AP Chemistry class I had where a total of 2 (and yes I was one of them) (OUT OF 35) passed the AP test, because 33 of the 35 kids could barely handle algebra and they didn't have even a basic understanding of molecules, atoms, or anything else.</p><p>This is what rewarding effort gets you, it gets you a bunch of idiots who are good at hard work, not people that are actually smart, or able to learn.</p></htmltext>
<tokenext>recognizing effort is ok , I suppose... But as a talented and rather bright student I always found that completely insidious and hurtful to my education.IE , I do n't know how many advanced and AP classes I took where the other kids in the class were there because they " tried really hard " and so the teachers let them in... Well guess what ?
That just slowed down my education , cause now the advanced teacher is having to babysit , review , and in general spend all of the time in the class helping these remedial math students understand basic algebra before we can actually get into calculus.Or the AP Chemistry class I had where a total of 2 ( and yes I was one of them ) ( OUT OF 35 ) passed the AP test , because 33 of the 35 kids could barely handle algebra and they did n't have even a basic understanding of molecules , atoms , or anything else.This is what rewarding effort gets you , it gets you a bunch of idiots who are good at hard work , not people that are actually smart , or able to learn .</tokentext>
<sentencetext>recognizing effort is ok, I suppose... But as a talented and rather bright student I always found that completely insidious and hurtful to my education.IE, I don't know how many advanced and AP classes I took where the other kids in the class were there because they "tried really hard" and so the teachers let them in... Well guess what?
That just slowed down my education, cause now the advanced teacher is having to babysit, review, and in general spend all of the time in the class helping these remedial math students understand basic algebra before we can actually get into calculus.Or the AP Chemistry class I had where a total of 2 (and yes I was one of them) (OUT OF 35) passed the AP test, because 33 of the 35 kids could barely handle algebra and they didn't have even a basic understanding of molecules, atoms, or anything else.This is what rewarding effort gets you, it gets you a bunch of idiots who are good at hard work, not people that are actually smart, or able to learn.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394271</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28405741</id>
	<title>Re:Cue the other subjects</title>
	<author>rossifer</author>
	<datestamp>1245502320000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><blockquote><div><p>When your math teacher only cares about "feelings" and not objective laws of mathematics</p></div></blockquote><p>Oohhh...  you're really going to be disappointed if you ever RTFA.</p><p>BTW, I completely agree that teacher's unions are a huge part of the problem, but for a different set of reasons than you mention.  My issue is that unions strongly resist any effort to pay teachers differently based on ability and have successfully negotiated contracts that make teachers essentially impossible to fire once they've successfully completed two or three years of teaching.  The same contracts dictate pay scales based on degree level and seniority.  Being an excellent teacher pays no better than being a seatwarmer, and probably pays much worse, since most of the seatwarmers have seniority.</p><p>If you're looking for a completely screwed up incentive structure for educators, look no further than any school with a teacher's union contract.  Sadly, that's 99\% of public schools in the US.</p></div>
	</htmltext>
<tokenext>When your math teacher only cares about " feelings " and not objective laws of mathematicsOohhh... you 're really going to be disappointed if you ever RTFA.BTW , I completely agree that teacher 's unions are a huge part of the problem , but for a different set of reasons than you mention .
My issue is that unions strongly resist any effort to pay teachers differently based on ability and have successfully negotiated contracts that make teachers essentially impossible to fire once they 've successfully completed two or three years of teaching .
The same contracts dictate pay scales based on degree level and seniority .
Being an excellent teacher pays no better than being a seatwarmer , and probably pays much worse , since most of the seatwarmers have seniority.If you 're looking for a completely screwed up incentive structure for educators , look no further than any school with a teacher 's union contract .
Sadly , that 's 99 \ % of public schools in the US .</tokentext>
<sentencetext>When your math teacher only cares about "feelings" and not objective laws of mathematicsOohhh...  you're really going to be disappointed if you ever RTFA.BTW, I completely agree that teacher's unions are a huge part of the problem, but for a different set of reasons than you mention.
My issue is that unions strongly resist any effort to pay teachers differently based on ability and have successfully negotiated contracts that make teachers essentially impossible to fire once they've successfully completed two or three years of teaching.
The same contracts dictate pay scales based on degree level and seniority.
Being an excellent teacher pays no better than being a seatwarmer, and probably pays much worse, since most of the seatwarmers have seniority.If you're looking for a completely screwed up incentive structure for educators, look no further than any school with a teacher's union contract.
Sadly, that's 99\% of public schools in the US.
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28395213</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394013</id>
	<title>Re:it's really bad</title>
	<author>cbs4385</author>
	<datestamp>1245442980000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>Proofs are pretty simple, but they can be long.
Basically, for a proof, you start out with a set of axioms (things which are by definition true), and a pool of things like Laws, Theories, Postulates, and Lemmas.  Those are basically well known results of combining the axioms above (sort of like open source black boxes, you feed it the right inputs, and out the other end comes the output).  To do a proof, you start with your problem, and your toolkit from above.  Then you go set by set, just like in school where you had to show your work.  The difference is that for each set, you have to justify why something like (A + 5 = B) == (A = B - 5) by reference to the tools or something that you have in a previous step derived from the tools.  The prood shows you how to get from point A to B and guarentees that you never go off the path while doing it.</htmltext>
<tokenext>Proofs are pretty simple , but they can be long .
Basically , for a proof , you start out with a set of axioms ( things which are by definition true ) , and a pool of things like Laws , Theories , Postulates , and Lemmas .
Those are basically well known results of combining the axioms above ( sort of like open source black boxes , you feed it the right inputs , and out the other end comes the output ) .
To do a proof , you start with your problem , and your toolkit from above .
Then you go set by set , just like in school where you had to show your work .
The difference is that for each set , you have to justify why something like ( A + 5 = B ) = = ( A = B - 5 ) by reference to the tools or something that you have in a previous step derived from the tools .
The prood shows you how to get from point A to B and guarentees that you never go off the path while doing it .</tokentext>
<sentencetext>Proofs are pretty simple, but they can be long.
Basically, for a proof, you start out with a set of axioms (things which are by definition true), and a pool of things like Laws, Theories, Postulates, and Lemmas.
Those are basically well known results of combining the axioms above (sort of like open source black boxes, you feed it the right inputs, and out the other end comes the output).
To do a proof, you start with your problem, and your toolkit from above.
Then you go set by set, just like in school where you had to show your work.
The difference is that for each set, you have to justify why something like (A + 5 = B) == (A = B - 5) by reference to the tools or something that you have in a previous step derived from the tools.
The prood shows you how to get from point A to B and guarentees that you never go off the path while doing it.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393543</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393229</id>
	<title>There are 10 kinds of people.........</title>
	<author>i\_want\_you\_to\_throw\_</author>
	<datestamp>1245440160000</datestamp>
	<modclass>Redundant</modclass>
	<modscore>-1</modscore>
	<htmltext>There are 10 kinds of people in the world: Those who know binary and those who don't.</htmltext>
<tokenext>There are 10 kinds of people in the world : Those who know binary and those who do n't .</tokentext>
<sentencetext>There are 10 kinds of people in the world: Those who know binary and those who don't.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393253</id>
	<title>Vulcans are doing it right</title>
	<author>Anonymous</author>
	<datestamp>1245440280000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>The depiction of math education in Star Trek was great - you know, the scene where the youthful Spock is answering math questions prompted by a screen in front of him, instructors observing overhead. Something akin to this would be pretty sweet. Where you could whiteboard out stuff all day in a high fidelity environment that uses OCR and AI to keep testing you on your weak points until you become stronger in each particular subject area. Something like this would ensure that you truly do have an understanding of everything before moving on. It could also use this information collected about you to introduce you to new topics in other subjects like physics based on your current understanding. Concepts could be masterfully articulated and narrated by famous voice actors like Morgan Freeman ect. A taxononomy/hierachy of subjects and concepts could be traversed to create unique learning programs when achievement is unlocked through true understanding rather than letter grades. Kind of like leveling up in an RPG.. would make things fun.</htmltext>
<tokenext>The depiction of math education in Star Trek was great - you know , the scene where the youthful Spock is answering math questions prompted by a screen in front of him , instructors observing overhead .
Something akin to this would be pretty sweet .
Where you could whiteboard out stuff all day in a high fidelity environment that uses OCR and AI to keep testing you on your weak points until you become stronger in each particular subject area .
Something like this would ensure that you truly do have an understanding of everything before moving on .
It could also use this information collected about you to introduce you to new topics in other subjects like physics based on your current understanding .
Concepts could be masterfully articulated and narrated by famous voice actors like Morgan Freeman ect .
A taxononomy/hierachy of subjects and concepts could be traversed to create unique learning programs when achievement is unlocked through true understanding rather than letter grades .
Kind of like leveling up in an RPG.. would make things fun .</tokentext>
<sentencetext>The depiction of math education in Star Trek was great - you know, the scene where the youthful Spock is answering math questions prompted by a screen in front of him, instructors observing overhead.
Something akin to this would be pretty sweet.
Where you could whiteboard out stuff all day in a high fidelity environment that uses OCR and AI to keep testing you on your weak points until you become stronger in each particular subject area.
Something like this would ensure that you truly do have an understanding of everything before moving on.
It could also use this information collected about you to introduce you to new topics in other subjects like physics based on your current understanding.
Concepts could be masterfully articulated and narrated by famous voice actors like Morgan Freeman ect.
A taxononomy/hierachy of subjects and concepts could be traversed to create unique learning programs when achievement is unlocked through true understanding rather than letter grades.
Kind of like leveling up in an RPG.. would make things fun.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393123</id>
	<title>Re:Cue the other subjects</title>
	<author>Anonymous</author>
	<datestamp>1245439800000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>Queue.</p></htmltext>
<tokenext>Queue .</tokentext>
<sentencetext>Queue.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392889</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393651</id>
	<title>Re:US School System compared to Europes School Sys</title>
	<author>Anonymous</author>
	<datestamp>1245441660000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>Ah, well, you see, when I was in school 40 years ago, classes were broken out based on ability - those students that were slower to understand, shall we say (boneheads, my mother called them) were in one class, and those quick to catch on in another. Then in the very early '70s, such tracking came to be seen as evil, discriminatory, and just not fair. So, everyone was lumped into one group, so no one would feel stigmatized. The results were predictable - schools got into a race to the bottom.</p><p>Fortunately, that nonsense seems to be fading away. My son's high school has an honors track (I think most do, now), and he's in it. At first, he hated it, because it meant extra work, then he realized that the clowns who caused him so much aggravation weren't in the honors classes, but his friends were, and now he's all for that kind of separation.</p></htmltext>
<tokenext>Ah , well , you see , when I was in school 40 years ago , classes were broken out based on ability - those students that were slower to understand , shall we say ( boneheads , my mother called them ) were in one class , and those quick to catch on in another .
Then in the very early '70s , such tracking came to be seen as evil , discriminatory , and just not fair .
So , everyone was lumped into one group , so no one would feel stigmatized .
The results were predictable - schools got into a race to the bottom.Fortunately , that nonsense seems to be fading away .
My son 's high school has an honors track ( I think most do , now ) , and he 's in it .
At first , he hated it , because it meant extra work , then he realized that the clowns who caused him so much aggravation were n't in the honors classes , but his friends were , and now he 's all for that kind of separation .</tokentext>
<sentencetext>Ah, well, you see, when I was in school 40 years ago, classes were broken out based on ability - those students that were slower to understand, shall we say (boneheads, my mother called them) were in one class, and those quick to catch on in another.
Then in the very early '70s, such tracking came to be seen as evil, discriminatory, and just not fair.
So, everyone was lumped into one group, so no one would feel stigmatized.
The results were predictable - schools got into a race to the bottom.Fortunately, that nonsense seems to be fading away.
My son's high school has an honors track (I think most do, now), and he's in it.
At first, he hated it, because it meant extra work, then he realized that the clowns who caused him so much aggravation weren't in the honors classes, but his friends were, and now he's all for that kind of separation.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393035</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394473</id>
	<title>Re:US School System compared to Europes School Sys</title>
	<author>Anonymous</author>
	<datestamp>1245444540000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>You must not be in the Los Angeles Unified School District where there seems to be less willingness on the part of Admins. to seperate kids according to their abilities.  Pisses off the parents of the dumb kids.  Can't have that happen.</p></htmltext>
<tokenext>You must not be in the Los Angeles Unified School District where there seems to be less willingness on the part of Admins .
to seperate kids according to their abilities .
Pisses off the parents of the dumb kids .
Ca n't have that happen .</tokentext>
<sentencetext>You must not be in the Los Angeles Unified School District where there seems to be less willingness on the part of Admins.
to seperate kids according to their abilities.
Pisses off the parents of the dumb kids.
Can't have that happen.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393241</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28396711</id>
	<title>Re:Cue the other subjects</title>
	<author>Anonymous</author>
	<datestamp>1245410460000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>Absolutely positively false.  The problem started in the 1960's with liberal educational policy.  No fundamentalist supports Whole Language studies, or Multiculturalism, or Reduce, Reuse, Recycle programs, Alternative Family studies or the multitude of other experimental liberal educational programs that have been foisted on the public schools ad infinitum.  Real fundamentalists don't medal in the public school system, they pull their kids out and send them to private schools, and the liberals whine about this, harass the fundamentalists and try to outlaw alternatives like homeschooling or require private schools to use the same garbage as curriculum.  Your ignorance is absolutely profound and your view is positively bigoted and revisionist.</p></htmltext>
<tokenext>Absolutely positively false .
The problem started in the 1960 's with liberal educational policy .
No fundamentalist supports Whole Language studies , or Multiculturalism , or Reduce , Reuse , Recycle programs , Alternative Family studies or the multitude of other experimental liberal educational programs that have been foisted on the public schools ad infinitum .
Real fundamentalists do n't medal in the public school system , they pull their kids out and send them to private schools , and the liberals whine about this , harass the fundamentalists and try to outlaw alternatives like homeschooling or require private schools to use the same garbage as curriculum .
Your ignorance is absolutely profound and your view is positively bigoted and revisionist .</tokentext>
<sentencetext>Absolutely positively false.
The problem started in the 1960's with liberal educational policy.
No fundamentalist supports Whole Language studies, or Multiculturalism, or Reduce, Reuse, Recycle programs, Alternative Family studies or the multitude of other experimental liberal educational programs that have been foisted on the public schools ad infinitum.
Real fundamentalists don't medal in the public school system, they pull their kids out and send them to private schools, and the liberals whine about this, harass the fundamentalists and try to outlaw alternatives like homeschooling or require private schools to use the same garbage as curriculum.
Your ignorance is absolutely profound and your view is positively bigoted and revisionist.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393083</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28486333</id>
	<title>What do you suggest Kemosabe?</title>
	<author>jotaeleemeese</author>
	<datestamp>1246045260000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>That in order to avoid plug-and-chug we develop the corresponding mathematical theory to solve an equation or make an integral?</p><p>Once you are done and dusted with the theory behind a concept then you proceed to apply the concept as needed.</p></htmltext>
<tokenext>That in order to avoid plug-and-chug we develop the corresponding mathematical theory to solve an equation or make an integral ? Once you are done and dusted with the theory behind a concept then you proceed to apply the concept as needed .</tokentext>
<sentencetext>That in order to avoid plug-and-chug we develop the corresponding mathematical theory to solve an equation or make an integral?Once you are done and dusted with the theory behind a concept then you proceed to apply the concept as needed.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394873</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28397989</id>
	<title>Re:I Sympathize With Him But Too Idyllic</title>
	<author>Anonymous</author>
	<datestamp>1245419640000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>Or we could just admit that public school teachers do not need a Master's degree and do away with the useless "education" Master's degree in the first place, thus allowing already qualified people holding a BS degree to teach the subjects they love straight out of college - without loading them down with a lot of "educational theory".</p></htmltext>
<tokenext>Or we could just admit that public school teachers do not need a Master 's degree and do away with the useless " education " Master 's degree in the first place , thus allowing already qualified people holding a BS degree to teach the subjects they love straight out of college - without loading them down with a lot of " educational theory " .</tokentext>
<sentencetext>Or we could just admit that public school teachers do not need a Master's degree and do away with the useless "education" Master's degree in the first place, thus allowing already qualified people holding a BS degree to teach the subjects they love straight out of college - without loading them down with a lot of "educational theory".</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393307</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394831</id>
	<title>Why should the excel?</title>
	<author>Shivetya</author>
	<datestamp>1245402540000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>when there are so many people out there claiming that failure isn't their fault.  Let alone a government which essentially pats them on the back and tells them that the government will make it all right, the government will take care of them, the government will take money from other, more successful people, and give it to them?</p><p>When you have schools which decry any form of testing or proof of ability?  When schools and the unions fight tooth and nail to ignore or subvert proof of the schools upholding their education ability?</p><p>When you can pass kids because they tried...  because "trying" is so easy to prove.</p></htmltext>
<tokenext>when there are so many people out there claiming that failure is n't their fault .
Let alone a government which essentially pats them on the back and tells them that the government will make it all right , the government will take care of them , the government will take money from other , more successful people , and give it to them ? When you have schools which decry any form of testing or proof of ability ?
When schools and the unions fight tooth and nail to ignore or subvert proof of the schools upholding their education ability ? When you can pass kids because they tried... because " trying " is so easy to prove .</tokentext>
<sentencetext>when there are so many people out there claiming that failure isn't their fault.
Let alone a government which essentially pats them on the back and tells them that the government will make it all right, the government will take care of them, the government will take money from other, more successful people, and give it to them?When you have schools which decry any form of testing or proof of ability?
When schools and the unions fight tooth and nail to ignore or subvert proof of the schools upholding their education ability?When you can pass kids because they tried...  because "trying" is so easy to prove.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393115</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393903</id>
	<title>Re:I Sympathize With Him But Too Idyllic</title>
	<author>panthroman</author>
	<datestamp>1245442620000</datestamp>
	<modclass>Insightful</modclass>
	<modscore>3</modscore>
	<htmltext><p><div class="quote"><p>We should deal with the fact that more people are passionate about topics like Art and Humanities than Math and Computer Science.  It's just the reality of academia right now.</p></div><p>Of course it is, because we have these ridiculous stigmas:</p><p> <b>Art</b> is passionate, frivolous, and beautiful.<br>
<b>Math</b> is boring, uninspiring, and useful.</p><p>What?!  There is no such thing as frivolous beauty; no utility is uninspiring and cold.  Lockhart, I fear, misses this point.  I understand the frustration Lockhart feels at the 'math = boring' stigma, but countering that 'math = art' is just as damning in our obsessed-with-mutual-exclusion society.</p><p>Beauty and utility have long been a happy couple.  The false rumors of their divorce is, I think, the root of Lockhart's (and my) frustration.</p></div>
	</htmltext>
<tokenext>We should deal with the fact that more people are passionate about topics like Art and Humanities than Math and Computer Science .
It 's just the reality of academia right now.Of course it is , because we have these ridiculous stigmas : Art is passionate , frivolous , and beautiful .
Math is boring , uninspiring , and useful.What ? !
There is no such thing as frivolous beauty ; no utility is uninspiring and cold .
Lockhart , I fear , misses this point .
I understand the frustration Lockhart feels at the 'math = boring ' stigma , but countering that 'math = art ' is just as damning in our obsessed-with-mutual-exclusion society.Beauty and utility have long been a happy couple .
The false rumors of their divorce is , I think , the root of Lockhart 's ( and my ) frustration .</tokentext>
<sentencetext>We should deal with the fact that more people are passionate about topics like Art and Humanities than Math and Computer Science.
It's just the reality of academia right now.Of course it is, because we have these ridiculous stigmas: Art is passionate, frivolous, and beautiful.
Math is boring, uninspiring, and useful.What?!
There is no such thing as frivolous beauty; no utility is uninspiring and cold.
Lockhart, I fear, misses this point.
I understand the frustration Lockhart feels at the 'math = boring' stigma, but countering that 'math = art' is just as damning in our obsessed-with-mutual-exclusion society.Beauty and utility have long been a happy couple.
The false rumors of their divorce is, I think, the root of Lockhart's (and my) frustration.
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392903</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393413</id>
	<title>Re:True story ....</title>
	<author>Gunnut1124</author>
	<datestamp>1245440820000</datestamp>
	<modclass>Informativ</modclass>
	<modscore>2</modscore>
	<htmltext><p><div class="quote"><p>If that's indicative of how math is taught nowadays, we're all hosed.</p></div><p>
It is. We are.</p></div>
	</htmltext>
<tokenext>If that 's indicative of how math is taught nowadays , we 're all hosed .
It is .
We are .</tokentext>
<sentencetext>If that's indicative of how math is taught nowadays, we're all hosed.
It is.
We are.
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392947</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394431</id>
	<title>Story Familiar - Where are the dragons?</title>
	<author>Dareth</author>
	<datestamp>1245444480000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>I remember this story, only it had dragons, miniature and large, in it as well.</p></htmltext>
<tokenext>I remember this story , only it had dragons , miniature and large , in it as well .</tokentext>
<sentencetext>I remember this story, only it had dragons, miniature and large, in it as well.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394751</id>
	<title>Re:Eh.</title>
	<author>Anonymous</author>
	<datestamp>1245402240000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>I suspect that's exactly his point. As math is currently taught, it doesn't capture the interests of students.</p></htmltext>
<tokenext>I suspect that 's exactly his point .
As math is currently taught , it does n't capture the interests of students .</tokentext>
<sentencetext>I suspect that's exactly his point.
As math is currently taught, it doesn't capture the interests of students.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392961</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28401501</id>
	<title>Re:Single Best Fix: Introducing Discrete Mathemati</title>
	<author>michael\_cain</author>
	<datestamp>1245510060000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>Notice what the student is prepared for at the various points where they might leave this sequence: balance the checkbook, accounting/business planning, construction/design, medieval mechanical/civil engineering. Math in the public schools has never been about creating mathematicians, but creating crafts people of various sorts (just as the art program is not about creating real artists). Not math as an end to itself, but strictly math as a tool.  Even when I was an undergraduate at a public university 30 years ago, there were calculus sections for math majors (small, where I was) and calculus sections for engineers (large, where most of my friends were).  And we learned very different things in "calculus": they learned how to apply it, I learned how to prove it.
<p>
If I were going to change this sequence, I would drop geometry before I added anything.  I loved geometry, for all the reasons that the essay identifies: an opportunity to create something beautiful out of ideas alone. Frustrated when the teacher asked, "How would all this change if we were doing it on the surface of a sphere, instead of on a plane?" and then didn't pursue it. But it's simply boring as hell for most people, and at least from my anecdotal experience, chases more kids out of applied math than anything else in the curriculum.</p></htmltext>
<tokenext>Notice what the student is prepared for at the various points where they might leave this sequence : balance the checkbook , accounting/business planning , construction/design , medieval mechanical/civil engineering .
Math in the public schools has never been about creating mathematicians , but creating crafts people of various sorts ( just as the art program is not about creating real artists ) .
Not math as an end to itself , but strictly math as a tool .
Even when I was an undergraduate at a public university 30 years ago , there were calculus sections for math majors ( small , where I was ) and calculus sections for engineers ( large , where most of my friends were ) .
And we learned very different things in " calculus " : they learned how to apply it , I learned how to prove it .
If I were going to change this sequence , I would drop geometry before I added anything .
I loved geometry , for all the reasons that the essay identifies : an opportunity to create something beautiful out of ideas alone .
Frustrated when the teacher asked , " How would all this change if we were doing it on the surface of a sphere , instead of on a plane ?
" and then did n't pursue it .
But it 's simply boring as hell for most people , and at least from my anecdotal experience , chases more kids out of applied math than anything else in the curriculum .</tokentext>
<sentencetext>Notice what the student is prepared for at the various points where they might leave this sequence: balance the checkbook, accounting/business planning, construction/design, medieval mechanical/civil engineering.
Math in the public schools has never been about creating mathematicians, but creating crafts people of various sorts (just as the art program is not about creating real artists).
Not math as an end to itself, but strictly math as a tool.
Even when I was an undergraduate at a public university 30 years ago, there were calculus sections for math majors (small, where I was) and calculus sections for engineers (large, where most of my friends were).
And we learned very different things in "calculus": they learned how to apply it, I learned how to prove it.
If I were going to change this sequence, I would drop geometry before I added anything.
I loved geometry, for all the reasons that the essay identifies: an opportunity to create something beautiful out of ideas alone.
Frustrated when the teacher asked, "How would all this change if we were doing it on the surface of a sphere, instead of on a plane?
" and then didn't pursue it.
But it's simply boring as hell for most people, and at least from my anecdotal experience, chases more kids out of applied math than anything else in the curriculum.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394873</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28395417</id>
	<title>Re:Oh give it a rest</title>
	<author>Anonymous</author>
	<datestamp>1245404460000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>Actually it's not HARD it's DIFFICULT.</p></htmltext>
<tokenext>Actually it 's not HARD it 's DIFFICULT .</tokentext>
<sentencetext>Actually it's not HARD it's DIFFICULT.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392993</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28395275</id>
	<title>In defense of notation</title>
	<author>Tetsujin</author>
	<datestamp>1245403980000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>In the "High School Geometry" section, Lockhart talks about how a fairly simple idea - that when two lines cross, the angles on opposing sides of the crossing point will be equal - is turned into a complex and ugly chunk of notation...  Lines must be identified as "AB" (with a bar over the top), there's notation for identifying the angle formed by three points, and the whole, simple idea is then backed up with a hefty "proof" in place of a simple, natural-language explanation.</p><p>Now, I don't quite agree with all of this.  Maybe that's because it worked for me, and because I enjoy the idea of mathematics and logic having their own "language", and their own notation.  I mean, sure, back then I always used to wonder why they threw all those Greek letters at us - in some cases it seemed totally arbitrary.  Some of it is just long-standing tradition: like the capital Sigma or the long-s glyph used for summation and integration...</p><p>But what I enjoy about the use of these symbols is that they provide a <em>compact</em> way of identifying <em>precisely</em> what one is talking about.  That these characters aren't part of everyday English writing means that they can be set aside to encapsulate powerful, specialized ideas.</p><p>The whole "proofs" thing worked out just fine for me, too.  I think it makes sense: as part of teaching people how to build up simple ideas to form an argument in support of a more complicated idea, provide examples of how to do this: even with the simplest of ideas, the things that lend themselves most readily to intuitive understanding...  If a proof is provided for a problem people naturally understand to begin with, then it will help them to understand how the proof works.</p><p>With regard to line and angle notation I think Lockhart is dead wrong.  In the context of the "crossed lines" example he argues that the lines could be called "line a" and "line b" or something - and that the whole idea should be presented in a more conversational style.  This could work for certain problems - especially really simple problems like that one - but there are other problems with expressing things in a conversational style.  For starters, natural language is <em>imprecise</em> - at least the way most people use it.  <em>Precise</em> natural language is the domain, for instance, of lawyers and logicians.  It tends to be <em>very heavy</em>, often with its <em>own</em> specialized vocabulary that people don't readily understand on first exposure.  <em>Codifying</em> the problem makes it less accessible, but also much more precise and concise.</p><p>Now, if I'd learned "High school geometry" in high school instead of, you know, 5th grade or whatever, it's possible things would have played out differently...  As it stands, however, I'm a big fan of <em>taking advantage of</em> domain-specific vocabulary and symbols where they are available and useful.</p></htmltext>
<tokenext>In the " High School Geometry " section , Lockhart talks about how a fairly simple idea - that when two lines cross , the angles on opposing sides of the crossing point will be equal - is turned into a complex and ugly chunk of notation... Lines must be identified as " AB " ( with a bar over the top ) , there 's notation for identifying the angle formed by three points , and the whole , simple idea is then backed up with a hefty " proof " in place of a simple , natural-language explanation.Now , I do n't quite agree with all of this .
Maybe that 's because it worked for me , and because I enjoy the idea of mathematics and logic having their own " language " , and their own notation .
I mean , sure , back then I always used to wonder why they threw all those Greek letters at us - in some cases it seemed totally arbitrary .
Some of it is just long-standing tradition : like the capital Sigma or the long-s glyph used for summation and integration...But what I enjoy about the use of these symbols is that they provide a compact way of identifying precisely what one is talking about .
That these characters are n't part of everyday English writing means that they can be set aside to encapsulate powerful , specialized ideas.The whole " proofs " thing worked out just fine for me , too .
I think it makes sense : as part of teaching people how to build up simple ideas to form an argument in support of a more complicated idea , provide examples of how to do this : even with the simplest of ideas , the things that lend themselves most readily to intuitive understanding... If a proof is provided for a problem people naturally understand to begin with , then it will help them to understand how the proof works.With regard to line and angle notation I think Lockhart is dead wrong .
In the context of the " crossed lines " example he argues that the lines could be called " line a " and " line b " or something - and that the whole idea should be presented in a more conversational style .
This could work for certain problems - especially really simple problems like that one - but there are other problems with expressing things in a conversational style .
For starters , natural language is imprecise - at least the way most people use it .
Precise natural language is the domain , for instance , of lawyers and logicians .
It tends to be very heavy , often with its own specialized vocabulary that people do n't readily understand on first exposure .
Codifying the problem makes it less accessible , but also much more precise and concise.Now , if I 'd learned " High school geometry " in high school instead of , you know , 5th grade or whatever , it 's possible things would have played out differently... As it stands , however , I 'm a big fan of taking advantage of domain-specific vocabulary and symbols where they are available and useful .</tokentext>
<sentencetext>In the "High School Geometry" section, Lockhart talks about how a fairly simple idea - that when two lines cross, the angles on opposing sides of the crossing point will be equal - is turned into a complex and ugly chunk of notation...  Lines must be identified as "AB" (with a bar over the top), there's notation for identifying the angle formed by three points, and the whole, simple idea is then backed up with a hefty "proof" in place of a simple, natural-language explanation.Now, I don't quite agree with all of this.
Maybe that's because it worked for me, and because I enjoy the idea of mathematics and logic having their own "language", and their own notation.
I mean, sure, back then I always used to wonder why they threw all those Greek letters at us - in some cases it seemed totally arbitrary.
Some of it is just long-standing tradition: like the capital Sigma or the long-s glyph used for summation and integration...But what I enjoy about the use of these symbols is that they provide a compact way of identifying precisely what one is talking about.
That these characters aren't part of everyday English writing means that they can be set aside to encapsulate powerful, specialized ideas.The whole "proofs" thing worked out just fine for me, too.
I think it makes sense: as part of teaching people how to build up simple ideas to form an argument in support of a more complicated idea, provide examples of how to do this: even with the simplest of ideas, the things that lend themselves most readily to intuitive understanding...  If a proof is provided for a problem people naturally understand to begin with, then it will help them to understand how the proof works.With regard to line and angle notation I think Lockhart is dead wrong.
In the context of the "crossed lines" example he argues that the lines could be called "line a" and "line b" or something - and that the whole idea should be presented in a more conversational style.
This could work for certain problems - especially really simple problems like that one - but there are other problems with expressing things in a conversational style.
For starters, natural language is imprecise - at least the way most people use it.
Precise natural language is the domain, for instance, of lawyers and logicians.
It tends to be very heavy, often with its own specialized vocabulary that people don't readily understand on first exposure.
Codifying the problem makes it less accessible, but also much more precise and concise.Now, if I'd learned "High school geometry" in high school instead of, you know, 5th grade or whatever, it's possible things would have played out differently...  As it stands, however, I'm a big fan of taking advantage of domain-specific vocabulary and symbols where they are available and useful.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393115</id>
	<title>Re:The way math is structured is disconnected from</title>
	<author>CRCulver</author>
	<datestamp>1245439800000</datestamp>
	<modclass>Insightful</modclass>
	<modscore>4</modscore>
	<htmltext>The United States is being outclassed in math and science education by a host of other nations. Those nations, for the most part, teach the subject in an exceedingly traditional format. Asia, for example, is still really keen on rote learning. The failure of American pupils is probably not due to the way the subject is taught, but rather because they don't feel the pressure to excel like students in other cultures.</htmltext>
<tokenext>The United States is being outclassed in math and science education by a host of other nations .
Those nations , for the most part , teach the subject in an exceedingly traditional format .
Asia , for example , is still really keen on rote learning .
The failure of American pupils is probably not due to the way the subject is taught , but rather because they do n't feel the pressure to excel like students in other cultures .</tokentext>
<sentencetext>The United States is being outclassed in math and science education by a host of other nations.
Those nations, for the most part, teach the subject in an exceedingly traditional format.
Asia, for example, is still really keen on rote learning.
The failure of American pupils is probably not due to the way the subject is taught, but rather because they don't feel the pressure to excel like students in other cultures.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392921</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393643</id>
	<title>Re:Eh.</title>
	<author>egcagrac0</author>
	<datestamp>1245441660000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p><div class="quote"><p>the things he suggests is beyond the ability of most math students in high school.</p></div><p>Really.  The result of a broken system is that competent graduates who meet all the state requirements for conferment of a diploma are unable to grapple with these relatively basic concepts?</p><p>Is it the students who are incapable, or are they merely inexperienced?</p></div>
	</htmltext>
<tokenext>the things he suggests is beyond the ability of most math students in high school.Really .
The result of a broken system is that competent graduates who meet all the state requirements for conferment of a diploma are unable to grapple with these relatively basic concepts ? Is it the students who are incapable , or are they merely inexperienced ?</tokentext>
<sentencetext>the things he suggests is beyond the ability of most math students in high school.Really.
The result of a broken system is that competent graduates who meet all the state requirements for conferment of a diploma are unable to grapple with these relatively basic concepts?Is it the students who are incapable, or are they merely inexperienced?
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392961</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28397469</id>
	<title>I just wanna be loved!!!</title>
	<author>Sax Maniac</author>
	<datestamp>1245415380000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>This strikes as me as bricklayer who looks at the rock stars getting laid any saying "Hey! Bricklaying is an art too!  Why don't I get the girls?  Why don't people love what I do?  I just want to be loved!  IS THAT SO RAWWWNG?"</p><p>I read the entire paper, and I agree with most of the statements.  However the central thesis -- people don't like pure math because it's not taught properly in school -- is a load of bull.</p><p>Given no prompting at all, people <b>will</b> draw pictures.  It's fun.  They <b>will</b> sing and create music.  It's fun.  A three year will do it, and good luck stopping them, as it seems to be built-in to humans.</p><p>They <b>won't</b> look at a box and wonder whether a triangle takes up half the area and then carefully ruminate upon the chain of pure deductive reasoning towards the clever orgasmic bliss of enlightenment.   Otherwise, people would spontaneously get together and have math parties where they talk about hypercubes and whatever stuff mathematicians talk about.  No, instead they get together, have a couple of drinks and listen to music.</p><p>I love pure math, despite being terrible at it.  It's obviously a great thing, but not everyone's built that way.  The kind of thinking that he likes is just not as common as he would like it to be.</p></htmltext>
<tokenext>This strikes as me as bricklayer who looks at the rock stars getting laid any saying " Hey !
Bricklaying is an art too !
Why do n't I get the girls ?
Why do n't people love what I do ?
I just want to be loved !
IS THAT SO RAWWWNG ?
" I read the entire paper , and I agree with most of the statements .
However the central thesis -- people do n't like pure math because it 's not taught properly in school -- is a load of bull.Given no prompting at all , people will draw pictures .
It 's fun .
They will sing and create music .
It 's fun .
A three year will do it , and good luck stopping them , as it seems to be built-in to humans.They wo n't look at a box and wonder whether a triangle takes up half the area and then carefully ruminate upon the chain of pure deductive reasoning towards the clever orgasmic bliss of enlightenment .
Otherwise , people would spontaneously get together and have math parties where they talk about hypercubes and whatever stuff mathematicians talk about .
No , instead they get together , have a couple of drinks and listen to music.I love pure math , despite being terrible at it .
It 's obviously a great thing , but not everyone 's built that way .
The kind of thinking that he likes is just not as common as he would like it to be .</tokentext>
<sentencetext>This strikes as me as bricklayer who looks at the rock stars getting laid any saying "Hey!
Bricklaying is an art too!
Why don't I get the girls?
Why don't people love what I do?
I just want to be loved!
IS THAT SO RAWWWNG?
"I read the entire paper, and I agree with most of the statements.
However the central thesis -- people don't like pure math because it's not taught properly in school -- is a load of bull.Given no prompting at all, people will draw pictures.
It's fun.
They will sing and create music.
It's fun.
A three year will do it, and good luck stopping them, as it seems to be built-in to humans.They won't look at a box and wonder whether a triangle takes up half the area and then carefully ruminate upon the chain of pure deductive reasoning towards the clever orgasmic bliss of enlightenment.
Otherwise, people would spontaneously get together and have math parties where they talk about hypercubes and whatever stuff mathematicians talk about.
No, instead they get together, have a couple of drinks and listen to music.I love pure math, despite being terrible at it.
It's obviously a great thing, but not everyone's built that way.
The kind of thinking that he likes is just not as common as he would like it to be.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28397245</id>
	<title>Re:You can convince me</title>
	<author>Mao</author>
	<datestamp>1245413580000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p><div class="quote"><p>Seriously. Math is both an art and a tool. The best artists find their art by themselves.</p></div><p>Absolutely.  It is an art and a tool in not so different a way from how a language is an art and a tool.</p><p>And like learning a foreign language, learning Mathematics is not a straight path.  We would love to build up a sense of mathematics from first principles in a perfect, coherent way, but that is no more realistic than learning French by studying the etymology of every word from the get-go.  No, you learn French by listening to it, by speaking it, by making mistakes, without necessarily knowing how it evolved.  Later, once you are more fluent in it, you begin to read more sophisticated literature, you begin to be interested in the development of the language, and then you say, "Ah... so that's how things come to be."</p><p>A student may fully appreciate "the transcendental nature of the trigonometric functions", but what good would that do if he cannot bother to memorize (yes, MEMORIZE) the double angle formulas.  How would he understand later on a real life application of Calculus, where it is taken for granted that he is fluent in the language of trigonometry.</p><p>It's funny that Lockhart uses the practice of visual arts as a metaphor.  Fact is, there is a lot of dry, uninteresting stuff that went into the training of an artist.  The myth that Da Vinci started out painting eggs probably isn't too far from the truth. You think Picasso painted things in the style of Guernica when he first started?  Doing the dry non-interesting stuff allowed Picasso to express his artistic vision with technical facility.  So what if he had the "vision" of Guernica, if he can't even handle paint competently?</p><p>From my own experience as a pure mathematician, I can tell you that my own learning curve is far from linear.  When one learns topology, one has to learn all the formal definitions of open sets, compactness, and so on.  Of course, one tries to motivate these definitions with intuitive notions, but ultimately, a lot of my appreciation of "the language of topology" is obtained from seeing how it is applied.  One can talk about donuts and coffee cups all they want at the beginning, but that doesn't even begin to capture the beauty of it (Try talking about cups and donuts in the context of p-adic topology on a p-adic field).  It's a back and forth process.  Most often the person coming up with the definitions isn't him/herself fully aware of the full implications.  But that's the beauty of it.</p></div>
	</htmltext>
<tokenext>Seriously .
Math is both an art and a tool .
The best artists find their art by themselves.Absolutely .
It is an art and a tool in not so different a way from how a language is an art and a tool.And like learning a foreign language , learning Mathematics is not a straight path .
We would love to build up a sense of mathematics from first principles in a perfect , coherent way , but that is no more realistic than learning French by studying the etymology of every word from the get-go .
No , you learn French by listening to it , by speaking it , by making mistakes , without necessarily knowing how it evolved .
Later , once you are more fluent in it , you begin to read more sophisticated literature , you begin to be interested in the development of the language , and then you say , " Ah... so that 's how things come to be .
" A student may fully appreciate " the transcendental nature of the trigonometric functions " , but what good would that do if he can not bother to memorize ( yes , MEMORIZE ) the double angle formulas .
How would he understand later on a real life application of Calculus , where it is taken for granted that he is fluent in the language of trigonometry.It 's funny that Lockhart uses the practice of visual arts as a metaphor .
Fact is , there is a lot of dry , uninteresting stuff that went into the training of an artist .
The myth that Da Vinci started out painting eggs probably is n't too far from the truth .
You think Picasso painted things in the style of Guernica when he first started ?
Doing the dry non-interesting stuff allowed Picasso to express his artistic vision with technical facility .
So what if he had the " vision " of Guernica , if he ca n't even handle paint competently ? From my own experience as a pure mathematician , I can tell you that my own learning curve is far from linear .
When one learns topology , one has to learn all the formal definitions of open sets , compactness , and so on .
Of course , one tries to motivate these definitions with intuitive notions , but ultimately , a lot of my appreciation of " the language of topology " is obtained from seeing how it is applied .
One can talk about donuts and coffee cups all they want at the beginning , but that does n't even begin to capture the beauty of it ( Try talking about cups and donuts in the context of p-adic topology on a p-adic field ) .
It 's a back and forth process .
Most often the person coming up with the definitions is n't him/herself fully aware of the full implications .
But that 's the beauty of it .</tokentext>
<sentencetext>Seriously.
Math is both an art and a tool.
The best artists find their art by themselves.Absolutely.
It is an art and a tool in not so different a way from how a language is an art and a tool.And like learning a foreign language, learning Mathematics is not a straight path.
We would love to build up a sense of mathematics from first principles in a perfect, coherent way, but that is no more realistic than learning French by studying the etymology of every word from the get-go.
No, you learn French by listening to it, by speaking it, by making mistakes, without necessarily knowing how it evolved.
Later, once you are more fluent in it, you begin to read more sophisticated literature, you begin to be interested in the development of the language, and then you say, "Ah... so that's how things come to be.
"A student may fully appreciate "the transcendental nature of the trigonometric functions", but what good would that do if he cannot bother to memorize (yes, MEMORIZE) the double angle formulas.
How would he understand later on a real life application of Calculus, where it is taken for granted that he is fluent in the language of trigonometry.It's funny that Lockhart uses the practice of visual arts as a metaphor.
Fact is, there is a lot of dry, uninteresting stuff that went into the training of an artist.
The myth that Da Vinci started out painting eggs probably isn't too far from the truth.
You think Picasso painted things in the style of Guernica when he first started?
Doing the dry non-interesting stuff allowed Picasso to express his artistic vision with technical facility.
So what if he had the "vision" of Guernica, if he can't even handle paint competently?From my own experience as a pure mathematician, I can tell you that my own learning curve is far from linear.
When one learns topology, one has to learn all the formal definitions of open sets, compactness, and so on.
Of course, one tries to motivate these definitions with intuitive notions, but ultimately, a lot of my appreciation of "the language of topology" is obtained from seeing how it is applied.
One can talk about donuts and coffee cups all they want at the beginning, but that doesn't even begin to capture the beauty of it (Try talking about cups and donuts in the context of p-adic topology on a p-adic field).
It's a back and forth process.
Most often the person coming up with the definitions isn't him/herself fully aware of the full implications.
But that's the beauty of it.
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393159</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393973</id>
	<title>Actually, I'm surprised</title>
	<author>idontgno</author>
	<datestamp>1245442860000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>no one has cited <a href="http://xkcd.com/435/" title="xkcd.com">this</a> [xkcd.com] yet. This particular comic strip is the "smug" side of the mathematician mindset, whereas the essay cited in TFA is the "angry" side.</htmltext>
<tokenext>no one has cited this [ xkcd.com ] yet .
This particular comic strip is the " smug " side of the mathematician mindset , whereas the essay cited in TFA is the " angry " side .</tokentext>
<sentencetext>no one has cited this [xkcd.com] yet.
This particular comic strip is the "smug" side of the mathematician mindset, whereas the essay cited in TFA is the "angry" side.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28395517</id>
	<title>Ya</title>
	<author>Sycraft-fu</author>
	<datestamp>1245405000000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>I went to a rather small high school, graduating class of less than 300, in a smallish town and we still had multiple math tracks. Your senior year you could be taking any of the following: Calculus, Precalculus, Trigonometry, Advanced Algebra, Geometry, or Algebra 2. Which track you were on depended on how you'd done in previous years. It started in 6th grade where kids were tested in to either normal or advanced math. It then just continued diverging based on how you did. Algebra 2 was the second half of the Algebra that the most advanced kids took in 7th grade. So if you were particularly bad at math, you'd get some basic algebra before you graduated, and have it presented at a slower pace. If you were the best, you took a real calculus class, equivalent to about Calc 1 at a university, your senior year.</p><p>This sort of thing seems fairly common. Indeed our school did it not other for math but for many subjects. They weren't all a direct linear progression as math was, but there were choices based on your skill and interests. You could take normal English, College Prep English, or AP English your senior year, for example.</p><p>It wasn't a perfect system, but then nothing will ever be. However it did do a reasonable job of allowing those that were good at a subject and interested to progress, without denying those that needed a slower pace the opportunity to learn.</p><p>After all, I get a little tired of the idea that education should be targeted only at the top 10\% and all the "dumb" kids should just be left behind. No, I think the opposite is true. See if you are smart, you have the ability to learn on your own to a great deal. You can take the initiative to teach yourself. How many times have we heard geeks talk about their valuable self education in programming and such? However the lower performers don't have that option, they need more help. In particular, if they don't get help, they may not be able to be productive members of society. They can't just "learn it themselves."</p><p>So really I think education needs to be setup to help those with troubles first and foremost, and worry about the top achievers second. That doesn't mean ignore the top achievers, it just means their needs aren't the most paramount.</p><p>Now this is primary education, of course, university is different.</p></htmltext>
<tokenext>I went to a rather small high school , graduating class of less than 300 , in a smallish town and we still had multiple math tracks .
Your senior year you could be taking any of the following : Calculus , Precalculus , Trigonometry , Advanced Algebra , Geometry , or Algebra 2 .
Which track you were on depended on how you 'd done in previous years .
It started in 6th grade where kids were tested in to either normal or advanced math .
It then just continued diverging based on how you did .
Algebra 2 was the second half of the Algebra that the most advanced kids took in 7th grade .
So if you were particularly bad at math , you 'd get some basic algebra before you graduated , and have it presented at a slower pace .
If you were the best , you took a real calculus class , equivalent to about Calc 1 at a university , your senior year.This sort of thing seems fairly common .
Indeed our school did it not other for math but for many subjects .
They were n't all a direct linear progression as math was , but there were choices based on your skill and interests .
You could take normal English , College Prep English , or AP English your senior year , for example.It was n't a perfect system , but then nothing will ever be .
However it did do a reasonable job of allowing those that were good at a subject and interested to progress , without denying those that needed a slower pace the opportunity to learn.After all , I get a little tired of the idea that education should be targeted only at the top 10 \ % and all the " dumb " kids should just be left behind .
No , I think the opposite is true .
See if you are smart , you have the ability to learn on your own to a great deal .
You can take the initiative to teach yourself .
How many times have we heard geeks talk about their valuable self education in programming and such ?
However the lower performers do n't have that option , they need more help .
In particular , if they do n't get help , they may not be able to be productive members of society .
They ca n't just " learn it themselves .
" So really I think education needs to be setup to help those with troubles first and foremost , and worry about the top achievers second .
That does n't mean ignore the top achievers , it just means their needs are n't the most paramount.Now this is primary education , of course , university is different .</tokentext>
<sentencetext>I went to a rather small high school, graduating class of less than 300, in a smallish town and we still had multiple math tracks.
Your senior year you could be taking any of the following: Calculus, Precalculus, Trigonometry, Advanced Algebra, Geometry, or Algebra 2.
Which track you were on depended on how you'd done in previous years.
It started in 6th grade where kids were tested in to either normal or advanced math.
It then just continued diverging based on how you did.
Algebra 2 was the second half of the Algebra that the most advanced kids took in 7th grade.
So if you were particularly bad at math, you'd get some basic algebra before you graduated, and have it presented at a slower pace.
If you were the best, you took a real calculus class, equivalent to about Calc 1 at a university, your senior year.This sort of thing seems fairly common.
Indeed our school did it not other for math but for many subjects.
They weren't all a direct linear progression as math was, but there were choices based on your skill and interests.
You could take normal English, College Prep English, or AP English your senior year, for example.It wasn't a perfect system, but then nothing will ever be.
However it did do a reasonable job of allowing those that were good at a subject and interested to progress, without denying those that needed a slower pace the opportunity to learn.After all, I get a little tired of the idea that education should be targeted only at the top 10\% and all the "dumb" kids should just be left behind.
No, I think the opposite is true.
See if you are smart, you have the ability to learn on your own to a great deal.
You can take the initiative to teach yourself.
How many times have we heard geeks talk about their valuable self education in programming and such?
However the lower performers don't have that option, they need more help.
In particular, if they don't get help, they may not be able to be productive members of society.
They can't just "learn it themselves.
"So really I think education needs to be setup to help those with troubles first and foremost, and worry about the top achievers second.
That doesn't mean ignore the top achievers, it just means their needs aren't the most paramount.Now this is primary education, of course, university is different.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393241</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393941</id>
	<title>Re:I Sympathize With Him But Too Idyllic</title>
	<author>EEBaum</author>
	<datestamp>1245442740000</datestamp>
	<modclass>Informativ</modclass>
	<modscore>2</modscore>
	<htmltext>There's no requirement for public school teachers to have masters' degrees.  A Bachelor's degree and a credential are all that's required, at least in California.</htmltext>
<tokenext>There 's no requirement for public school teachers to have masters ' degrees .
A Bachelor 's degree and a credential are all that 's required , at least in California .</tokentext>
<sentencetext>There's no requirement for public school teachers to have masters' degrees.
A Bachelor's degree and a credential are all that's required, at least in California.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393307</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394873</id>
	<title>Single Best Fix:  Introducing Discrete Mathematics</title>
	<author>reporter</author>
	<datestamp>1245402660000</datestamp>
	<modclass>Interestin</modclass>
	<modscore>2</modscore>
	<htmltext>The mathematics education in K-12 in the USA typically includes the following sequence.
<p>
0.  arithmetic
</p><p>
1.  algebra I
</p><p>
2.  geometry
</p><p>
3.  algebra II
</p><p>
4.  trigonometry
</p><p>
5.  elementary analysis  (includes some probability and statistics)
</p><p>
6.  calculus
</p><p>
The above mathematics sequence is typically plug-and-chug:  plug some numbers into some formulas and produce a result.  No thinking is required.
</p><p>
What is sorely needed is a course in discrete mathematics between geometry and algebra II.  Discrete mathematics teaches the most fundamental mathematical concept:  methods of reasoning about mathematics.  Not surprisingly, discrete mathematics includes plenty of proofs.
</p><p>
Discrete mathematics is not only a foundation of math but is a foundation of computer science.  All the important ideas in data structures and finite automata require an understanding of discrete mathematics.</p></htmltext>
<tokenext>The mathematics education in K-12 in the USA typically includes the following sequence .
0. arithmetic 1. algebra I 2. geometry 3. algebra II 4. trigonometry 5. elementary analysis ( includes some probability and statistics ) 6. calculus The above mathematics sequence is typically plug-and-chug : plug some numbers into some formulas and produce a result .
No thinking is required .
What is sorely needed is a course in discrete mathematics between geometry and algebra II .
Discrete mathematics teaches the most fundamental mathematical concept : methods of reasoning about mathematics .
Not surprisingly , discrete mathematics includes plenty of proofs .
Discrete mathematics is not only a foundation of math but is a foundation of computer science .
All the important ideas in data structures and finite automata require an understanding of discrete mathematics .</tokentext>
<sentencetext>The mathematics education in K-12 in the USA typically includes the following sequence.
0.  arithmetic

1.  algebra I

2.  geometry

3.  algebra II

4.  trigonometry

5.  elementary analysis  (includes some probability and statistics)

6.  calculus

The above mathematics sequence is typically plug-and-chug:  plug some numbers into some formulas and produce a result.
No thinking is required.
What is sorely needed is a course in discrete mathematics between geometry and algebra II.
Discrete mathematics teaches the most fundamental mathematical concept:  methods of reasoning about mathematics.
Not surprisingly, discrete mathematics includes plenty of proofs.
Discrete mathematics is not only a foundation of math but is a foundation of computer science.
All the important ideas in data structures and finite automata require an understanding of discrete mathematics.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392769</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28395179</id>
	<title>Mathematician, Taught Public HS for 5 Years</title>
	<author>Hnice</author>
	<datestamp>1245403680000</datestamp>
	<modclass>Insightful</modclass>
	<modscore>2</modscore>
	<htmltext><p>Though I don't need the rhetoric, this hits it on the head, in every aspect.</p><p>I'd like to try teaching math like English -- Math 1, Math 2, Math 3, Math 4, with curriculum determined in part by such apparently meaningless factors as what might be useful in other classes or what's happening, you know, outside of my room.</p><p>The textbook comments are particularly right on -- step 1, burn them.  If teachers complain that they won't know what to teach, fire them on the spot.</p><p>Geometry is also a lousy place for proof.  Teach deduction all the time, in every topic -- and in classrooms other than math.  "Here's a bunch of fake stuff you don't know anything about that's hard to draw.  Now let's think really abstractly about how we're thinking about it!"  And induction doesn't get taught at all.</p><p>The practical deal-killer, the one that drove me out of the profession, is that the barrel full of math teachers is so close to empty that you're pretty much scraping bottom from day 1.  This kind of instruction -- and this kind of critique -- can only originate with someone who likes math, and is sort of good at it.  You'd be amazed (or maybe you wouldn't) at how few public high school math teachers this describes.</p><p>America has gotten the math teaching instruction it asked for when it decided to prop up bad teachers with lousy but easy-to-use texts, and to boot it got the benefit of not having to pay very well for people willing to go through these motions.  (It's not about money, but really, it's a little bit about money.  I doubled my salary when I left last year.)  It's a big, huge problem, and since you're going to have to convince parents that it needs the kind of dramatic overhaul this (great) article describes, and since parents were largely victimized by the existing system, I'm pretty sure it's a losing battle.</p></htmltext>
<tokenext>Though I do n't need the rhetoric , this hits it on the head , in every aspect.I 'd like to try teaching math like English -- Math 1 , Math 2 , Math 3 , Math 4 , with curriculum determined in part by such apparently meaningless factors as what might be useful in other classes or what 's happening , you know , outside of my room.The textbook comments are particularly right on -- step 1 , burn them .
If teachers complain that they wo n't know what to teach , fire them on the spot.Geometry is also a lousy place for proof .
Teach deduction all the time , in every topic -- and in classrooms other than math .
" Here 's a bunch of fake stuff you do n't know anything about that 's hard to draw .
Now let 's think really abstractly about how we 're thinking about it !
" And induction does n't get taught at all.The practical deal-killer , the one that drove me out of the profession , is that the barrel full of math teachers is so close to empty that you 're pretty much scraping bottom from day 1 .
This kind of instruction -- and this kind of critique -- can only originate with someone who likes math , and is sort of good at it .
You 'd be amazed ( or maybe you would n't ) at how few public high school math teachers this describes.America has gotten the math teaching instruction it asked for when it decided to prop up bad teachers with lousy but easy-to-use texts , and to boot it got the benefit of not having to pay very well for people willing to go through these motions .
( It 's not about money , but really , it 's a little bit about money .
I doubled my salary when I left last year .
) It 's a big , huge problem , and since you 're going to have to convince parents that it needs the kind of dramatic overhaul this ( great ) article describes , and since parents were largely victimized by the existing system , I 'm pretty sure it 's a losing battle .</tokentext>
<sentencetext>Though I don't need the rhetoric, this hits it on the head, in every aspect.I'd like to try teaching math like English -- Math 1, Math 2, Math 3, Math 4, with curriculum determined in part by such apparently meaningless factors as what might be useful in other classes or what's happening, you know, outside of my room.The textbook comments are particularly right on -- step 1, burn them.
If teachers complain that they won't know what to teach, fire them on the spot.Geometry is also a lousy place for proof.
Teach deduction all the time, in every topic -- and in classrooms other than math.
"Here's a bunch of fake stuff you don't know anything about that's hard to draw.
Now let's think really abstractly about how we're thinking about it!
"  And induction doesn't get taught at all.The practical deal-killer, the one that drove me out of the profession, is that the barrel full of math teachers is so close to empty that you're pretty much scraping bottom from day 1.
This kind of instruction -- and this kind of critique -- can only originate with someone who likes math, and is sort of good at it.
You'd be amazed (or maybe you wouldn't) at how few public high school math teachers this describes.America has gotten the math teaching instruction it asked for when it decided to prop up bad teachers with lousy but easy-to-use texts, and to boot it got the benefit of not having to pay very well for people willing to go through these motions.
(It's not about money, but really, it's a little bit about money.
I doubled my salary when I left last year.
)  It's a big, huge problem, and since you're going to have to convince parents that it needs the kind of dramatic overhaul this (great) article describes, and since parents were largely victimized by the existing system, I'm pretty sure it's a losing battle.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393199</id>
	<title>Re:True story ....</title>
	<author>Lord Ender</author>
	<datestamp>1245440100000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>No, that's just indicative of lazy teachers. Since most humans are lazy and all teachers are human, this is to be expected.</p></htmltext>
<tokenext>No , that 's just indicative of lazy teachers .
Since most humans are lazy and all teachers are human , this is to be expected .</tokentext>
<sentencetext>No, that's just indicative of lazy teachers.
Since most humans are lazy and all teachers are human, this is to be expected.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392947</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394171</id>
	<title>Re:Eh.</title>
	<author>Anonymous</author>
	<datestamp>1245443520000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>You are right it is beyond the ability of most high school students because they have never had to do it.  You see the same problems in the sciences.  You have to memorize things instead of understanding it.  When I graduated high school way back when the dinosaurs roamed the earth, math and science was boring because it was just a collection of facts.  The only thing worse was every other subject.  It wasn't until college that I started to actually do real science and it was fun and why I ended up with a ph.d in physics.<br>I am willing to bet that the majority of students would learn mathematics if they had that type of education starting with 1st grade.  Kids don't learn because they are told to but because they want to for what ever reason.  And yes I still consider high schoolers kids.</p></htmltext>
<tokenext>You are right it is beyond the ability of most high school students because they have never had to do it .
You see the same problems in the sciences .
You have to memorize things instead of understanding it .
When I graduated high school way back when the dinosaurs roamed the earth , math and science was boring because it was just a collection of facts .
The only thing worse was every other subject .
It was n't until college that I started to actually do real science and it was fun and why I ended up with a ph.d in physics.I am willing to bet that the majority of students would learn mathematics if they had that type of education starting with 1st grade .
Kids do n't learn because they are told to but because they want to for what ever reason .
And yes I still consider high schoolers kids .</tokentext>
<sentencetext>You are right it is beyond the ability of most high school students because they have never had to do it.
You see the same problems in the sciences.
You have to memorize things instead of understanding it.
When I graduated high school way back when the dinosaurs roamed the earth, math and science was boring because it was just a collection of facts.
The only thing worse was every other subject.
It wasn't until college that I started to actually do real science and it was fun and why I ended up with a ph.d in physics.I am willing to bet that the majority of students would learn mathematics if they had that type of education starting with 1st grade.
Kids don't learn because they are told to but because they want to for what ever reason.
And yes I still consider high schoolers kids.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392961</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393865</id>
	<title>Re:I Sympathize With Him But Too Idyllic</title>
	<author>Anonymous</author>
	<datestamp>1245442500000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>I agree. Hence a part of the solution is training students to also be teachers, whenever possible. Start at an early age having students tutor each other (or younger grades) and maybe those few students who end up being teachers will actually end up being good teachers. And those that don't will have learned the subject matter all the better (I believe that you haven't comprehended a concept until you can teach it)</p></htmltext>
<tokenext>I agree .
Hence a part of the solution is training students to also be teachers , whenever possible .
Start at an early age having students tutor each other ( or younger grades ) and maybe those few students who end up being teachers will actually end up being good teachers .
And those that do n't will have learned the subject matter all the better ( I believe that you have n't comprehended a concept until you can teach it )</tokentext>
<sentencetext>I agree.
Hence a part of the solution is training students to also be teachers, whenever possible.
Start at an early age having students tutor each other (or younger grades) and maybe those few students who end up being teachers will actually end up being good teachers.
And those that don't will have learned the subject matter all the better (I believe that you haven't comprehended a concept until you can teach it)</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392903</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392957</id>
	<title>Could be worse...</title>
	<author>Anonymous</author>
	<datestamp>1245439200000</datestamp>
	<modclass>Interestin</modclass>
	<modscore>1</modscore>
	<htmltext>It could be the sad state of science education.  Science is largely taught as memorization of facts, rather than a process for discovery.  We turn out high school graduates who are easily suckered by such frauds as homeopathy and creationism...the latter of which in some places is actually taught as being science rather than its antithesis.</htmltext>
<tokenext>It could be the sad state of science education .
Science is largely taught as memorization of facts , rather than a process for discovery .
We turn out high school graduates who are easily suckered by such frauds as homeopathy and creationism...the latter of which in some places is actually taught as being science rather than its antithesis .</tokentext>
<sentencetext>It could be the sad state of science education.
Science is largely taught as memorization of facts, rather than a process for discovery.
We turn out high school graduates who are easily suckered by such frauds as homeopathy and creationism...the latter of which in some places is actually taught as being science rather than its antithesis.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394689</id>
	<title>Outsider's perspective</title>
	<author>levicivita</author>
	<datestamp>1245402060000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><i> Disclaimer: I am not familiar with the American High School system, since I first came to the US to attend an Ivy League school.  I may sound critical, but please remember, I love being in America, and I am merely pointing out what I came to realize over the years. <br> <br> </i>
I found that, even in an extremely prestigious American college, the mathematics taught in freshman and sophomore courses was at a similar level to what was broadly taught <i> in the public high school system </i> back in Europe where I came from, as early as 9th grade.  I found most my American's colleagues math knowledge to be largely absent, but more importantly, many of them who had not entirely abandoned mathematics were nonetheless not even be aware of <i> what they did not know </i>.  <br> <br>
My impression of why they got to be in this state had to do with the teaching method.  The mathematics textbooks used in 'mainstream' courses even in my $45k/year college (i.e. over 20 students in attendance) are useless because they adopt a teaching style entirely devoid of insight and entirely too focused on mindless calculations.  I suspect similar methods / textbooks are employed in high school.  I found, over time, that I can recognize such a book right away, because they tend to be filled with examples with specific numbers.  It doesn't matter if the topic is linear algebra, calculus, multivariate calculus, differential equations, Fourier analyis, they manage to insert 'exercises' with 'insight-building' arbitrary values, e.g. 'integrate 12.51 x^3 / (2.98 x + 1) from 0.1 to 2.31.'  <br> <br>
There's of course nothing wrong with practicing integration (or other) techniques, and in fact back home we've all had to spend a massive amount of time doing just that.  There's nothing wrong to being able to quickly and correctly do algebra, with large natural numbers or even arbitrary rational numbers - but that is something that is ingrained early on to the point where it doesn't need revisiting.  In fact I would argue I am faster, more accurate, and can perform more complicated algebra, although the last time I was asked to work on it was in 5th grade.  By the time you make it to calculus and beyond there's no need to test whether you can evaluate a function at specific values of its parameters (if you cannot do that, you would have failed a long time ago), so looking at the integral of x^3 / (a x + b) is allowing you to focus on the essence of the problem at hand, and not on mindless algebra.  (Again, the algebra is mindless because you are supposed to know how to do it by the time you're 10, not because you can outsource it to a calculator or India.)  Having examples with actual values is hardly the worst flaw, but it is strongly indicative of the mindset of the author and the teaching method, which I would characterize succinctly as 'lacking insight'.  I would not have been able to understand and learn math had I only been exposed to such methods.
<br> <br>
Math is a combination of art and hard labor, and both components are important.  Good professors are absolutely essential, more important than even good textbooks.  In fact all the good textbooks have already been written, many of them decades and sometimes 100+ years ago, it's just a matter of knowing about them and using them.</htmltext>
<tokenext>Disclaimer : I am not familiar with the American High School system , since I first came to the US to attend an Ivy League school .
I may sound critical , but please remember , I love being in America , and I am merely pointing out what I came to realize over the years .
I found that , even in an extremely prestigious American college , the mathematics taught in freshman and sophomore courses was at a similar level to what was broadly taught in the public high school system back in Europe where I came from , as early as 9th grade .
I found most my American 's colleagues math knowledge to be largely absent , but more importantly , many of them who had not entirely abandoned mathematics were nonetheless not even be aware of what they did not know .
My impression of why they got to be in this state had to do with the teaching method .
The mathematics textbooks used in 'mainstream ' courses even in my $ 45k/year college ( i.e .
over 20 students in attendance ) are useless because they adopt a teaching style entirely devoid of insight and entirely too focused on mindless calculations .
I suspect similar methods / textbooks are employed in high school .
I found , over time , that I can recognize such a book right away , because they tend to be filled with examples with specific numbers .
It does n't matter if the topic is linear algebra , calculus , multivariate calculus , differential equations , Fourier analyis , they manage to insert 'exercises ' with 'insight-building ' arbitrary values , e.g .
'integrate 12.51 x ^ 3 / ( 2.98 x + 1 ) from 0.1 to 2.31 .
' There 's of course nothing wrong with practicing integration ( or other ) techniques , and in fact back home we 've all had to spend a massive amount of time doing just that .
There 's nothing wrong to being able to quickly and correctly do algebra , with large natural numbers or even arbitrary rational numbers - but that is something that is ingrained early on to the point where it does n't need revisiting .
In fact I would argue I am faster , more accurate , and can perform more complicated algebra , although the last time I was asked to work on it was in 5th grade .
By the time you make it to calculus and beyond there 's no need to test whether you can evaluate a function at specific values of its parameters ( if you can not do that , you would have failed a long time ago ) , so looking at the integral of x ^ 3 / ( a x + b ) is allowing you to focus on the essence of the problem at hand , and not on mindless algebra .
( Again , the algebra is mindless because you are supposed to know how to do it by the time you 're 10 , not because you can outsource it to a calculator or India .
) Having examples with actual values is hardly the worst flaw , but it is strongly indicative of the mindset of the author and the teaching method , which I would characterize succinctly as 'lacking insight' .
I would not have been able to understand and learn math had I only been exposed to such methods .
Math is a combination of art and hard labor , and both components are important .
Good professors are absolutely essential , more important than even good textbooks .
In fact all the good textbooks have already been written , many of them decades and sometimes 100 + years ago , it 's just a matter of knowing about them and using them .</tokentext>
<sentencetext> Disclaimer: I am not familiar with the American High School system, since I first came to the US to attend an Ivy League school.
I may sound critical, but please remember, I love being in America, and I am merely pointing out what I came to realize over the years.
I found that, even in an extremely prestigious American college, the mathematics taught in freshman and sophomore courses was at a similar level to what was broadly taught  in the public high school system  back in Europe where I came from, as early as 9th grade.
I found most my American's colleagues math knowledge to be largely absent, but more importantly, many of them who had not entirely abandoned mathematics were nonetheless not even be aware of  what they did not know .
My impression of why they got to be in this state had to do with the teaching method.
The mathematics textbooks used in 'mainstream' courses even in my $45k/year college (i.e.
over 20 students in attendance) are useless because they adopt a teaching style entirely devoid of insight and entirely too focused on mindless calculations.
I suspect similar methods / textbooks are employed in high school.
I found, over time, that I can recognize such a book right away, because they tend to be filled with examples with specific numbers.
It doesn't matter if the topic is linear algebra, calculus, multivariate calculus, differential equations, Fourier analyis, they manage to insert 'exercises' with 'insight-building' arbitrary values, e.g.
'integrate 12.51 x^3 / (2.98 x + 1) from 0.1 to 2.31.
'   
There's of course nothing wrong with practicing integration (or other) techniques, and in fact back home we've all had to spend a massive amount of time doing just that.
There's nothing wrong to being able to quickly and correctly do algebra, with large natural numbers or even arbitrary rational numbers - but that is something that is ingrained early on to the point where it doesn't need revisiting.
In fact I would argue I am faster, more accurate, and can perform more complicated algebra, although the last time I was asked to work on it was in 5th grade.
By the time you make it to calculus and beyond there's no need to test whether you can evaluate a function at specific values of its parameters (if you cannot do that, you would have failed a long time ago), so looking at the integral of x^3 / (a x + b) is allowing you to focus on the essence of the problem at hand, and not on mindless algebra.
(Again, the algebra is mindless because you are supposed to know how to do it by the time you're 10, not because you can outsource it to a calculator or India.
)  Having examples with actual values is hardly the worst flaw, but it is strongly indicative of the mindset of the author and the teaching method, which I would characterize succinctly as 'lacking insight'.
I would not have been able to understand and learn math had I only been exposed to such methods.
Math is a combination of art and hard labor, and both components are important.
Good professors are absolutely essential, more important than even good textbooks.
In fact all the good textbooks have already been written, many of them decades and sometimes 100+ years ago, it's just a matter of knowing about them and using them.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28399733</id>
	<title>Re:The way math is structured is disconnected from</title>
	<author>DrEasy</author>
	<datestamp>1245440340000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>Yeah but the rote learning style only produces robots, not critical thinkers, decision makers and game changers. I agree though that North America is producing neither the former or the latter.</p></htmltext>
<tokenext>Yeah but the rote learning style only produces robots , not critical thinkers , decision makers and game changers .
I agree though that North America is producing neither the former or the latter .</tokentext>
<sentencetext>Yeah but the rote learning style only produces robots, not critical thinkers, decision makers and game changers.
I agree though that North America is producing neither the former or the latter.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393115</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28395385</id>
	<title>Re:Eh.</title>
	<author>Anonymous</author>
	<datestamp>1245404400000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>True.  But kids should probably at least know what an equation is if they are going to be solving them, or know what area of a shape is if they are going to be finding it.</p><p>An equation is a statement that two quantities are the same.  Area of a shape is the amount of space it contains.  Kids don't know these things though.</p></htmltext>
<tokenext>True .
But kids should probably at least know what an equation is if they are going to be solving them , or know what area of a shape is if they are going to be finding it.An equation is a statement that two quantities are the same .
Area of a shape is the amount of space it contains .
Kids do n't know these things though .</tokentext>
<sentencetext>True.
But kids should probably at least know what an equation is if they are going to be solving them, or know what area of a shape is if they are going to be finding it.An equation is a statement that two quantities are the same.
Area of a shape is the amount of space it contains.
Kids don't know these things though.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392961</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28396215</id>
	<title>Re:it's really bad</title>
	<author>Anonymous</author>
	<datestamp>1245408000000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p><div class="quote"><p>Students are not machines.  Some students are going to build rules from examples.  Some are going to want the rules, then apply them to examples.  <b>Some are going to want only to know how to solve the problem then mimic the process on similar problems.  Some are simply going to copy the proof from another student.</b></p> </div><p>The bolded group of students shouldn't be in the same classes as the students mentioned before them. It's clear that the first group of students is interested in the theory of the math while the second group is either not interested at all or only interested in it's applications. Meet your future theorists and engineers.</p></div>
	</htmltext>
<tokenext>Students are not machines .
Some students are going to build rules from examples .
Some are going to want the rules , then apply them to examples .
Some are going to want only to know how to solve the problem then mimic the process on similar problems .
Some are simply going to copy the proof from another student .
The bolded group of students should n't be in the same classes as the students mentioned before them .
It 's clear that the first group of students is interested in the theory of the math while the second group is either not interested at all or only interested in it 's applications .
Meet your future theorists and engineers .</tokentext>
<sentencetext>Students are not machines.
Some students are going to build rules from examples.
Some are going to want the rules, then apply them to examples.
Some are going to want only to know how to solve the problem then mimic the process on similar problems.
Some are simply going to copy the proof from another student.
The bolded group of students shouldn't be in the same classes as the students mentioned before them.
It's clear that the first group of students is interested in the theory of the math while the second group is either not interested at all or only interested in it's applications.
Meet your future theorists and engineers.
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393855</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28395329</id>
	<title>Re:The way math is structured is disconnected from</title>
	<author>thethibs</author>
	<datestamp>1245404160000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>Asian students also go to school 250 ten-hour days a year. They not only learn math, they learn the value and satisfaction of hard work.</p></htmltext>
<tokenext>Asian students also go to school 250 ten-hour days a year .
They not only learn math , they learn the value and satisfaction of hard work .</tokentext>
<sentencetext>Asian students also go to school 250 ten-hour days a year.
They not only learn math, they learn the value and satisfaction of hard work.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393115</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28399231</id>
	<title>Mathematics is not about puzzles.</title>
	<author>Animats</author>
	<datestamp>1245432780000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>
The other big problem with the teaching of mathematics is the emphasis on "puzzles".  That's all wrong.  Mathematics is a tool for design and analysis of things you might want to build or understand.  It should be taught that way.  In particular, high school calculus and high school physics should be integrated.  Teach calculus as a way to understand mechanical systems and electrical circuits, and it makes much more sense.
</p><p>
I have (somewhere) a U.S. Navy textbook from WWII which teaches calculus from exactly that standpoint.  During WWII, the Navy needed engineering technicians in a hurry, and they set up a crash training program without much input from the "educational establishment".</p></htmltext>
<tokenext>The other big problem with the teaching of mathematics is the emphasis on " puzzles " .
That 's all wrong .
Mathematics is a tool for design and analysis of things you might want to build or understand .
It should be taught that way .
In particular , high school calculus and high school physics should be integrated .
Teach calculus as a way to understand mechanical systems and electrical circuits , and it makes much more sense .
I have ( somewhere ) a U.S. Navy textbook from WWII which teaches calculus from exactly that standpoint .
During WWII , the Navy needed engineering technicians in a hurry , and they set up a crash training program without much input from the " educational establishment " .</tokentext>
<sentencetext>
The other big problem with the teaching of mathematics is the emphasis on "puzzles".
That's all wrong.
Mathematics is a tool for design and analysis of things you might want to build or understand.
It should be taught that way.
In particular, high school calculus and high school physics should be integrated.
Teach calculus as a way to understand mechanical systems and electrical circuits, and it makes much more sense.
I have (somewhere) a U.S. Navy textbook from WWII which teaches calculus from exactly that standpoint.
During WWII, the Navy needed engineering technicians in a hurry, and they set up a crash training program without much input from the "educational establishment".</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28400183</id>
	<title>I can't count either!</title>
	<author>jonaskoelker</author>
	<datestamp>1245490980000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>fourth!</p></htmltext>
<tokenext>fourth !</tokentext>
<sentencetext>fourth!</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392757</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28397151</id>
	<title>Re:Cue the other subjects</title>
	<author>Anonymous</author>
	<datestamp>1245412800000</datestamp>
	<modclass>Insightful</modclass>
	<modscore>1</modscore>
	<htmltext><p>I decided to have a look at your "proof." In "The Deliberate Dumbing Down of America", the author begins with two commonly held "beliefs" (his word, not mine):</p><p>"1.) If a child can read, write and compute at a reasonably proficient level, he will be able to do just about anything he wishes, enabling him to control his destiny to the extent that God allows (remaining free);<br>2.) Providing such basic educational proficiencies is not and should not be an expensive proposition."</p><p>He then immediately draws the conclusion that since "basic" education is inexpensive:</p><p>"...it becomes obvious that it is only a radical agenda, the purpose of which is to change values and attitudes (brainwash), that is the costly agenda. In other words, brainwashing by our schools and universities is what is bankrupting our nation and our children's minds."</p><p>Yeah, that's certainly the unsupported conclusion I'd draw. It certainly explains why my kid's minds are "bankrupt."</p></htmltext>
<tokenext>I decided to have a look at your " proof .
" In " The Deliberate Dumbing Down of America " , the author begins with two commonly held " beliefs " ( his word , not mine ) : " 1 .
) If a child can read , write and compute at a reasonably proficient level , he will be able to do just about anything he wishes , enabling him to control his destiny to the extent that God allows ( remaining free ) ; 2 .
) Providing such basic educational proficiencies is not and should not be an expensive proposition .
" He then immediately draws the conclusion that since " basic " education is inexpensive : " ...it becomes obvious that it is only a radical agenda , the purpose of which is to change values and attitudes ( brainwash ) , that is the costly agenda .
In other words , brainwashing by our schools and universities is what is bankrupting our nation and our children 's minds .
" Yeah , that 's certainly the unsupported conclusion I 'd draw .
It certainly explains why my kid 's minds are " bankrupt .
"</tokentext>
<sentencetext>I decided to have a look at your "proof.
" In "The Deliberate Dumbing Down of America", the author begins with two commonly held "beliefs" (his word, not mine):"1.
) If a child can read, write and compute at a reasonably proficient level, he will be able to do just about anything he wishes, enabling him to control his destiny to the extent that God allows (remaining free);2.
) Providing such basic educational proficiencies is not and should not be an expensive proposition.
"He then immediately draws the conclusion that since "basic" education is inexpensive:"...it becomes obvious that it is only a radical agenda, the purpose of which is to change values and attitudes (brainwash), that is the costly agenda.
In other words, brainwashing by our schools and universities is what is bankrupting our nation and our children's minds.
"Yeah, that's certainly the unsupported conclusion I'd draw.
It certainly explains why my kid's minds are "bankrupt.
"</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393595</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28399033</id>
	<title>Re:A teachers take</title>
	<author>khallow</author>
	<datestamp>1245430380000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>I don't see a lot of reward in K-12 education for either talent or effort. In my case, I got lucky in that I had enough talent that I didn't need effort. Don't get me wrong. My lack of experience with effort has hindered me in numerous places. But in my view, my K-12 schools were not the place to teach effort solely because the work was for most activities except the few subjects I cared about so dull and pointless. I don't see, for example, that more school work of the sort I was exposed to would be better for me than my doodling in class, my voracious reading, or even my D&amp;D playing. The time might have been spent in fantasizing and entertainment, but it was in my view productively spent.</htmltext>
<tokenext>I do n't see a lot of reward in K-12 education for either talent or effort .
In my case , I got lucky in that I had enough talent that I did n't need effort .
Do n't get me wrong .
My lack of experience with effort has hindered me in numerous places .
But in my view , my K-12 schools were not the place to teach effort solely because the work was for most activities except the few subjects I cared about so dull and pointless .
I do n't see , for example , that more school work of the sort I was exposed to would be better for me than my doodling in class , my voracious reading , or even my D&amp;D playing .
The time might have been spent in fantasizing and entertainment , but it was in my view productively spent .</tokentext>
<sentencetext>I don't see a lot of reward in K-12 education for either talent or effort.
In my case, I got lucky in that I had enough talent that I didn't need effort.
Don't get me wrong.
My lack of experience with effort has hindered me in numerous places.
But in my view, my K-12 schools were not the place to teach effort solely because the work was for most activities except the few subjects I cared about so dull and pointless.
I don't see, for example, that more school work of the sort I was exposed to would be better for me than my doodling in class, my voracious reading, or even my D&amp;D playing.
The time might have been spent in fantasizing and entertainment, but it was in my view productively spent.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394271</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394053</id>
	<title>Its not rocket science...</title>
	<author>DarthVain</author>
	<datestamp>1245443100000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>oh wait...</p></htmltext>
<tokenext>oh wait.. .</tokentext>
<sentencetext>oh wait...</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394245</id>
	<title>Re:Oh give it a rest</title>
	<author>Anonymous</author>
	<datestamp>1245443760000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p><div class="quote"><p> Teaching it to people who don't care and don't want to be there is even harder.</p></div><p>Have you ever spent any time around young children? I mean two, three and four year olds? Children at that age love to learn. They continually experiment and try new things. Human children are born knowing almost nothing. About the only thing a human baby knows is how to suck. A human baby is born to learn. It is what makes us human.</p><p>So what are we doing so wrong in our schools that completely and utterly destroys this passion for learning?</p></div>
	</htmltext>
<tokenext>Teaching it to people who do n't care and do n't want to be there is even harder.Have you ever spent any time around young children ?
I mean two , three and four year olds ?
Children at that age love to learn .
They continually experiment and try new things .
Human children are born knowing almost nothing .
About the only thing a human baby knows is how to suck .
A human baby is born to learn .
It is what makes us human.So what are we doing so wrong in our schools that completely and utterly destroys this passion for learning ?</tokentext>
<sentencetext> Teaching it to people who don't care and don't want to be there is even harder.Have you ever spent any time around young children?
I mean two, three and four year olds?
Children at that age love to learn.
They continually experiment and try new things.
Human children are born knowing almost nothing.
About the only thing a human baby knows is how to suck.
A human baby is born to learn.
It is what makes us human.So what are we doing so wrong in our schools that completely and utterly destroys this passion for learning?
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392993</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28398893</id>
	<title>Re:US School System compared to Europes School Sys</title>
	<author>Dilpo</author>
	<datestamp>1245428640000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>I went to a school about your size, just more recently. My graduating class was somewhere in the mid 700's. There was more than 2 levels of math and science. Granted there was only two with the same name, AP calc 2 and calc 2, or AP calc 1 and calc 1 etc. but not everyone even made it to calc1. By 12th grade students were spread out into any of the following math classes: Algebra 2, Algebra 2 AP, Pre-Calculus, Calc 1, AP Calc 1, Calc 2, or AP Calc2. Thats 7 different "senior" levels of math in a single highschool. If you're goal is just to graduate then Algebra 2 is where you finished. Depending on your academic ability and how far you really wanted to go you could be as much as 7 "levels" ahead of that by the time graduation rolled around. Thats not to say that you'd have to take the other 6 to make it to AP Calc2. The highest "path" you could take would look something like Alg 2AP -&gt; Calc1 AP -&gt; Calc2AP. But in order to do that you'd need to start Alg 1 in 7th grade (Alg1 in middle school was split into two years taking 7th and 8th grade to complete allowing you to go straight into geometry/trig your freshmen year in highschool, again this was optional and a "level" above what most 7th and 8th graders take, as well as 8th graders who took the first part of alg1 in order to breeze through it freshmen year). There was also summer school if you wanted to get ahead although that option wasn't very popular. Most kids I knew also jumped around different levels taking Alg 2 and Calc1 before taking AP Calc2 or say they took AP Calc 1 but not AP Calc2. It was surprisingly close to college where you're just told to take classes in these categories and this is how many years of these classes you had to take and certain classes require other classes to already have been taken or to be taken at the same time. Science and Math crossed paths like that a lot.<br>
<br>
Science was pretty much the same but you could further specialize ending in a physics or chemistry path or a more basic level of both if you wanted and basic levels of each were required before graduation.<br>
<br>
English had less options but still ended up with 4 different levels you could end up taking your senior year, one of those being a "college" level course taught by a professor that drove in from a community college 3 days a week. We didn't have anything called "social studies" past elementary. We had geography, poly sci-ish classes (not called that but the name escapes me and the subject was basically the same), history etc. They each had 3-4 levels you could end up with your senior year as well and again you could sort of 'specialize' in your favorite.<br>
<br>
This is ~5 years ago in a public school in Texas. The district currently has 6 or 7 highschools all about the same size with the same curriculum. I think its 7 now, they keep building more and I dont live in the area anymore and my parents rarely talk to me about it. Also just like to point out that you calling into question someone elses experience, given he did say "most", as atypical is kind of funny seeing as how you only really have on view point to look from as well and it is admittedly ~20 years old if not closer to 30.<br>
<br>
Moral of the story is things change, and public education across the US varies WILDLY in terms of quality and choices available.<br>
Also just remembered that for each of those AP classes there was a "Pre-AP" version. So make that 3 sublevels for each level.</htmltext>
<tokenext>I went to a school about your size , just more recently .
My graduating class was somewhere in the mid 700 's .
There was more than 2 levels of math and science .
Granted there was only two with the same name , AP calc 2 and calc 2 , or AP calc 1 and calc 1 etc .
but not everyone even made it to calc1 .
By 12th grade students were spread out into any of the following math classes : Algebra 2 , Algebra 2 AP , Pre-Calculus , Calc 1 , AP Calc 1 , Calc 2 , or AP Calc2 .
Thats 7 different " senior " levels of math in a single highschool .
If you 're goal is just to graduate then Algebra 2 is where you finished .
Depending on your academic ability and how far you really wanted to go you could be as much as 7 " levels " ahead of that by the time graduation rolled around .
Thats not to say that you 'd have to take the other 6 to make it to AP Calc2 .
The highest " path " you could take would look something like Alg 2AP - &gt; Calc1 AP - &gt; Calc2AP .
But in order to do that you 'd need to start Alg 1 in 7th grade ( Alg1 in middle school was split into two years taking 7th and 8th grade to complete allowing you to go straight into geometry/trig your freshmen year in highschool , again this was optional and a " level " above what most 7th and 8th graders take , as well as 8th graders who took the first part of alg1 in order to breeze through it freshmen year ) .
There was also summer school if you wanted to get ahead although that option was n't very popular .
Most kids I knew also jumped around different levels taking Alg 2 and Calc1 before taking AP Calc2 or say they took AP Calc 1 but not AP Calc2 .
It was surprisingly close to college where you 're just told to take classes in these categories and this is how many years of these classes you had to take and certain classes require other classes to already have been taken or to be taken at the same time .
Science and Math crossed paths like that a lot .
Science was pretty much the same but you could further specialize ending in a physics or chemistry path or a more basic level of both if you wanted and basic levels of each were required before graduation .
English had less options but still ended up with 4 different levels you could end up taking your senior year , one of those being a " college " level course taught by a professor that drove in from a community college 3 days a week .
We did n't have anything called " social studies " past elementary .
We had geography , poly sci-ish classes ( not called that but the name escapes me and the subject was basically the same ) , history etc .
They each had 3-4 levels you could end up with your senior year as well and again you could sort of 'specialize ' in your favorite .
This is ~ 5 years ago in a public school in Texas .
The district currently has 6 or 7 highschools all about the same size with the same curriculum .
I think its 7 now , they keep building more and I dont live in the area anymore and my parents rarely talk to me about it .
Also just like to point out that you calling into question someone elses experience , given he did say " most " , as atypical is kind of funny seeing as how you only really have on view point to look from as well and it is admittedly ~ 20 years old if not closer to 30 .
Moral of the story is things change , and public education across the US varies WILDLY in terms of quality and choices available .
Also just remembered that for each of those AP classes there was a " Pre-AP " version .
So make that 3 sublevels for each level .</tokentext>
<sentencetext>I went to a school about your size, just more recently.
My graduating class was somewhere in the mid 700's.
There was more than 2 levels of math and science.
Granted there was only two with the same name, AP calc 2 and calc 2, or AP calc 1 and calc 1 etc.
but not everyone even made it to calc1.
By 12th grade students were spread out into any of the following math classes: Algebra 2, Algebra 2 AP, Pre-Calculus, Calc 1, AP Calc 1, Calc 2, or AP Calc2.
Thats 7 different "senior" levels of math in a single highschool.
If you're goal is just to graduate then Algebra 2 is where you finished.
Depending on your academic ability and how far you really wanted to go you could be as much as 7 "levels" ahead of that by the time graduation rolled around.
Thats not to say that you'd have to take the other 6 to make it to AP Calc2.
The highest "path" you could take would look something like Alg 2AP -&gt; Calc1 AP -&gt; Calc2AP.
But in order to do that you'd need to start Alg 1 in 7th grade (Alg1 in middle school was split into two years taking 7th and 8th grade to complete allowing you to go straight into geometry/trig your freshmen year in highschool, again this was optional and a "level" above what most 7th and 8th graders take, as well as 8th graders who took the first part of alg1 in order to breeze through it freshmen year).
There was also summer school if you wanted to get ahead although that option wasn't very popular.
Most kids I knew also jumped around different levels taking Alg 2 and Calc1 before taking AP Calc2 or say they took AP Calc 1 but not AP Calc2.
It was surprisingly close to college where you're just told to take classes in these categories and this is how many years of these classes you had to take and certain classes require other classes to already have been taken or to be taken at the same time.
Science and Math crossed paths like that a lot.
Science was pretty much the same but you could further specialize ending in a physics or chemistry path or a more basic level of both if you wanted and basic levels of each were required before graduation.
English had less options but still ended up with 4 different levels you could end up taking your senior year, one of those being a "college" level course taught by a professor that drove in from a community college 3 days a week.
We didn't have anything called "social studies" past elementary.
We had geography, poly sci-ish classes (not called that but the name escapes me and the subject was basically the same), history etc.
They each had 3-4 levels you could end up with your senior year as well and again you could sort of 'specialize' in your favorite.
This is ~5 years ago in a public school in Texas.
The district currently has 6 or 7 highschools all about the same size with the same curriculum.
I think its 7 now, they keep building more and I dont live in the area anymore and my parents rarely talk to me about it.
Also just like to point out that you calling into question someone elses experience, given he did say "most", as atypical is kind of funny seeing as how you only really have on view point to look from as well and it is admittedly ~20 years old if not closer to 30.
Moral of the story is things change, and public education across the US varies WILDLY in terms of quality and choices available.
Also just remembered that for each of those AP classes there was a "Pre-AP" version.
So make that 3 sublevels for each level.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393751</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28398249</id>
	<title>Somehow, I overcame...</title>
	<author>wfolta</author>
	<datestamp>1245421500000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>I always knew that I did poorly in classes that required formal proofs, ranging from Geometry to Analysis of Algorithms. I always had problems because I could not tell what was "obvious" and what was not. As an intuitive thinker, I'd either not be "rigorous enough", or, after being told I wasn't rigorous enough, I'd try to compensate and end up trying to prove "obvious" things. (They were somehow defined as "obvious", but I could certainly see lots of nooks and crannies in them that could contain problems.)</p><p>And I still cringe when someone says they "hate theory". I love theory, because it's theory that actually illuminates things. But most people have all kinds of unpleasant experiences with "theory classes" taught by people who do not understand the subject matter. The result is that the teaching is brittle: if you stray away from the teacher's guide in your question, you are herded back onto the straight-n-narrow path with confusing hand-waving and hurled jargon. It makes no sense to you, but the teacher says it with authority and you assume that you're too dumb to understand it, and eventually come to hate "theory classes".</p><p>This starts at early ages with math education. And it might be called "the hard place". Opposite this hard place is the rock of boring, rote repetition.</p><p>Some of us manage to get through this relatively intact. I guess we have a strong attraction to underlying explanations ("theory") and enough school-smarts that we get good grades, encouraging us that perhaps we are smart and what we don't understand is in fact understandable if we apply ourselves.</p><p>The trick is how to balance the ideal math education with the abilities/training of the huge number of teachers required to teach it. (Who have themselves been warped by their own math education.) And to balance the need for rote things (multiplication tables come to mind) with curiosity and enticement to learn.</p></htmltext>
<tokenext>I always knew that I did poorly in classes that required formal proofs , ranging from Geometry to Analysis of Algorithms .
I always had problems because I could not tell what was " obvious " and what was not .
As an intuitive thinker , I 'd either not be " rigorous enough " , or , after being told I was n't rigorous enough , I 'd try to compensate and end up trying to prove " obvious " things .
( They were somehow defined as " obvious " , but I could certainly see lots of nooks and crannies in them that could contain problems .
) And I still cringe when someone says they " hate theory " .
I love theory , because it 's theory that actually illuminates things .
But most people have all kinds of unpleasant experiences with " theory classes " taught by people who do not understand the subject matter .
The result is that the teaching is brittle : if you stray away from the teacher 's guide in your question , you are herded back onto the straight-n-narrow path with confusing hand-waving and hurled jargon .
It makes no sense to you , but the teacher says it with authority and you assume that you 're too dumb to understand it , and eventually come to hate " theory classes " .This starts at early ages with math education .
And it might be called " the hard place " .
Opposite this hard place is the rock of boring , rote repetition.Some of us manage to get through this relatively intact .
I guess we have a strong attraction to underlying explanations ( " theory " ) and enough school-smarts that we get good grades , encouraging us that perhaps we are smart and what we do n't understand is in fact understandable if we apply ourselves.The trick is how to balance the ideal math education with the abilities/training of the huge number of teachers required to teach it .
( Who have themselves been warped by their own math education .
) And to balance the need for rote things ( multiplication tables come to mind ) with curiosity and enticement to learn .</tokentext>
<sentencetext>I always knew that I did poorly in classes that required formal proofs, ranging from Geometry to Analysis of Algorithms.
I always had problems because I could not tell what was "obvious" and what was not.
As an intuitive thinker, I'd either not be "rigorous enough", or, after being told I wasn't rigorous enough, I'd try to compensate and end up trying to prove "obvious" things.
(They were somehow defined as "obvious", but I could certainly see lots of nooks and crannies in them that could contain problems.
)And I still cringe when someone says they "hate theory".
I love theory, because it's theory that actually illuminates things.
But most people have all kinds of unpleasant experiences with "theory classes" taught by people who do not understand the subject matter.
The result is that the teaching is brittle: if you stray away from the teacher's guide in your question, you are herded back onto the straight-n-narrow path with confusing hand-waving and hurled jargon.
It makes no sense to you, but the teacher says it with authority and you assume that you're too dumb to understand it, and eventually come to hate "theory classes".This starts at early ages with math education.
And it might be called "the hard place".
Opposite this hard place is the rock of boring, rote repetition.Some of us manage to get through this relatively intact.
I guess we have a strong attraction to underlying explanations ("theory") and enough school-smarts that we get good grades, encouraging us that perhaps we are smart and what we don't understand is in fact understandable if we apply ourselves.The trick is how to balance the ideal math education with the abilities/training of the huge number of teachers required to teach it.
(Who have themselves been warped by their own math education.
) And to balance the need for rote things (multiplication tables come to mind) with curiosity and enticement to learn.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393751</id>
	<title>Re:US School System compared to Europes School Sys</title>
	<author>Zontar\_Thing\_From\_Ve</author>
	<datestamp>1245442080000</datestamp>
	<modclass>Informativ</modclass>
	<modscore>1</modscore>
	<htmltext><p><div class="quote"><p>You must have attended a very very small school. Most US schools have different courses based on skill level. Your conclusions about the US school system are therefore wrong. They are merely conclusions about very small schools.</p></div><p>Really? "Most US schools" have this?  Maybe <b> your </b> school did, but my high school, which had over 1300 students in grades 10-12, most assuredly did not.  Well, if your definition of "different" means "two", then mine did.  My high school (that's "secondary school" for all you non-North Americans) offered  <b> one </b> advanced level class in chemistry, math, English and Social Studies.  Entry into those classes was restricted to the brighter students (I got in - lucky me).  Then they had normal level classes in all those subjects that everyone else took.  Granted, I graduated in the 1980s, but I don't know what the heck school you went to, but I tend to think that <b> your </b> experience is the atypical one here and not that of the guy who posted.</p></div>
	</htmltext>
<tokenext>You must have attended a very very small school .
Most US schools have different courses based on skill level .
Your conclusions about the US school system are therefore wrong .
They are merely conclusions about very small schools.Really ?
" Most US schools " have this ?
Maybe your school did , but my high school , which had over 1300 students in grades 10-12 , most assuredly did not .
Well , if your definition of " different " means " two " , then mine did .
My high school ( that 's " secondary school " for all you non-North Americans ) offered one advanced level class in chemistry , math , English and Social Studies .
Entry into those classes was restricted to the brighter students ( I got in - lucky me ) .
Then they had normal level classes in all those subjects that everyone else took .
Granted , I graduated in the 1980s , but I do n't know what the heck school you went to , but I tend to think that your experience is the atypical one here and not that of the guy who posted .</tokentext>
<sentencetext>You must have attended a very very small school.
Most US schools have different courses based on skill level.
Your conclusions about the US school system are therefore wrong.
They are merely conclusions about very small schools.Really?
"Most US schools" have this?
Maybe  your  school did, but my high school, which had over 1300 students in grades 10-12, most assuredly did not.
Well, if your definition of "different" means "two", then mine did.
My high school (that's "secondary school" for all you non-North Americans) offered   one  advanced level class in chemistry, math, English and Social Studies.
Entry into those classes was restricted to the brighter students (I got in - lucky me).
Then they had normal level classes in all those subjects that everyone else took.
Granted, I graduated in the 1980s, but I don't know what the heck school you went to, but I tend to think that  your  experience is the atypical one here and not that of the guy who posted.
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393241</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393777</id>
	<title>Re:The way math is structured is disconnected from</title>
	<author>LordKazan</author>
	<datestamp>1245442140000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>I can vouch for that.  my home town experimented with a "School of the Arts" system in one elementary school and one middle school - switching those schools 3 years after I was through them.  So my senior year in HS we had these kids as freshmen.  I was the student TA for the Earth Sciences teacher.</p><p>My earth HS's earth sciences teacher was an AWESOME guy (in fact.. all the science teachers were) and were great with demonstrations, etc.  All kinds of things that got most kids involved in sciences they previously considered boring.  I mean our earth sciences teacher yearly took his class out to hunt for marine fossils in a spot where the task wasn't finding one, it was extracting them from the small cliff face without damaging them.</p><p>anyway I'm off topic.</p><p>He had a few students my senior year who were "School of the Arts" graduates.  His tests were simple - 1/3 was "circle the answer", 1/3 was "short answer - one word?" (IE 'What is the name given to molten rock after it is erupted onto the surface'), 1/3 was "Short answer - one sentance".</p><p>Several of these kids refused to do the second 2/3rds of the test.. but their parents yelled at the teacher when he failed them.   I was in grading exams one day when they were yelling at them, I knew who's parents they were.  I extracted their meat-head sons test from the pile, graded it (the 1/3 that was actually done), walked up to them and handed it to them.   Then instructed them to kindly stop treating the best earth sciences teacher I've ever seen like he was an insect under their boots.</p></htmltext>
<tokenext>I can vouch for that .
my home town experimented with a " School of the Arts " system in one elementary school and one middle school - switching those schools 3 years after I was through them .
So my senior year in HS we had these kids as freshmen .
I was the student TA for the Earth Sciences teacher.My earth HS 's earth sciences teacher was an AWESOME guy ( in fact.. all the science teachers were ) and were great with demonstrations , etc .
All kinds of things that got most kids involved in sciences they previously considered boring .
I mean our earth sciences teacher yearly took his class out to hunt for marine fossils in a spot where the task was n't finding one , it was extracting them from the small cliff face without damaging them.anyway I 'm off topic.He had a few students my senior year who were " School of the Arts " graduates .
His tests were simple - 1/3 was " circle the answer " , 1/3 was " short answer - one word ?
" ( IE 'What is the name given to molten rock after it is erupted onto the surface ' ) , 1/3 was " Short answer - one sentance " .Several of these kids refused to do the second 2/3rds of the test.. but their parents yelled at the teacher when he failed them .
I was in grading exams one day when they were yelling at them , I knew who 's parents they were .
I extracted their meat-head sons test from the pile , graded it ( the 1/3 that was actually done ) , walked up to them and handed it to them .
Then instructed them to kindly stop treating the best earth sciences teacher I 've ever seen like he was an insect under their boots .</tokentext>
<sentencetext>I can vouch for that.
my home town experimented with a "School of the Arts" system in one elementary school and one middle school - switching those schools 3 years after I was through them.
So my senior year in HS we had these kids as freshmen.
I was the student TA for the Earth Sciences teacher.My earth HS's earth sciences teacher was an AWESOME guy (in fact.. all the science teachers were) and were great with demonstrations, etc.
All kinds of things that got most kids involved in sciences they previously considered boring.
I mean our earth sciences teacher yearly took his class out to hunt for marine fossils in a spot where the task wasn't finding one, it was extracting them from the small cliff face without damaging them.anyway I'm off topic.He had a few students my senior year who were "School of the Arts" graduates.
His tests were simple - 1/3 was "circle the answer", 1/3 was "short answer - one word?
" (IE 'What is the name given to molten rock after it is erupted onto the surface'), 1/3 was "Short answer - one sentance".Several of these kids refused to do the second 2/3rds of the test.. but their parents yelled at the teacher when he failed them.
I was in grading exams one day when they were yelling at them, I knew who's parents they were.
I extracted their meat-head sons test from the pile, graded it (the 1/3 that was actually done), walked up to them and handed it to them.
Then instructed them to kindly stop treating the best earth sciences teacher I've ever seen like he was an insect under their boots.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393535</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28397529</id>
	<title>here's more info...</title>
	<author>Anonymous</author>
	<datestamp>1245416100000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>Lockhart's paper was referenced March 2008 on the monthly Mathematical Association of America (MAA) online column of Keith Devlin, <a href="http://www.maa.org/devlin/devlin\_03\_08.html" title="maa.org" rel="nofollow">here</a> [maa.org]</p><p>it's a thought-provoking essay, by someone with the credentials to be taken seriously.  Nice to see it finally being slashdotted<nobr> <wbr></nobr>:)</p></htmltext>
<tokenext>Lockhart 's paper was referenced March 2008 on the monthly Mathematical Association of America ( MAA ) online column of Keith Devlin , here [ maa.org ] it 's a thought-provoking essay , by someone with the credentials to be taken seriously .
Nice to see it finally being slashdotted : )</tokentext>
<sentencetext>Lockhart's paper was referenced March 2008 on the monthly Mathematical Association of America (MAA) online column of Keith Devlin, here [maa.org]it's a thought-provoking essay, by someone with the credentials to be taken seriously.
Nice to see it finally being slashdotted :)</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28395227</id>
	<title>Re:I Sympathize With Him But Too Idyllic</title>
	<author>Anonymous</author>
	<datestamp>1245403800000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>If the system was full of people who went through a better system they would be batter at teaching math... an ideal system would  breed ideal teachers of that system<nobr> <wbr></nobr>... The system breeds the system<nobr> <wbr></nobr>.... How to de/re-institutionalize? Maybe that is the question.</p></htmltext>
<tokenext>If the system was full of people who went through a better system they would be batter at teaching math... an ideal system would breed ideal teachers of that system ... The system breeds the system .... How to de/re-institutionalize ?
Maybe that is the question .</tokentext>
<sentencetext>If the system was full of people who went through a better system they would be batter at teaching math... an ideal system would  breed ideal teachers of that system ... The system breeds the system .... How to de/re-institutionalize?
Maybe that is the question.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392903</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394149</id>
	<title>Re:it's really bad</title>
	<author>jandrese</author>
	<datestamp>1245443460000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>Another question to ask:  Since you have graduated college and moved on to the professional field, how many times have you been asked to formally prove your work?  Sure some people do it here and there, but for the majority of students it is not a useful skill.  I know that the people who actually do this look down with disdain at those of us who don't, but I'd wager that in total their numbers are pretty small.</htmltext>
<tokenext>Another question to ask : Since you have graduated college and moved on to the professional field , how many times have you been asked to formally prove your work ?
Sure some people do it here and there , but for the majority of students it is not a useful skill .
I know that the people who actually do this look down with disdain at those of us who do n't , but I 'd wager that in total their numbers are pretty small .</tokentext>
<sentencetext>Another question to ask:  Since you have graduated college and moved on to the professional field, how many times have you been asked to formally prove your work?
Sure some people do it here and there, but for the majority of students it is not a useful skill.
I know that the people who actually do this look down with disdain at those of us who don't, but I'd wager that in total their numbers are pretty small.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393127</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393901</id>
	<title>Excellent article</title>
	<author>module0000</author>
	<datestamp>1245442620000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>I thought the summary was over-the-top, but after the reading the article I agree.  The guy has a "artful" way with words....about <b>math</b>.  I imagine that pretty rare.  I enjoyed reading it. Suppose I never knew how much of a math guy I really was.</p></htmltext>
<tokenext>I thought the summary was over-the-top , but after the reading the article I agree .
The guy has a " artful " way with words....about math .
I imagine that pretty rare .
I enjoyed reading it .
Suppose I never knew how much of a math guy I really was .</tokentext>
<sentencetext>I thought the summary was over-the-top, but after the reading the article I agree.
The guy has a "artful" way with words....about math.
I imagine that pretty rare.
I enjoyed reading it.
Suppose I never knew how much of a math guy I really was.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394211</id>
	<title>Re:I Sympathize With Him But Too Idyllic</title>
	<author>mochan\_s</author>
	<datestamp>1245443700000</datestamp>
	<modclass>Insightful</modclass>
	<modscore>2</modscore>
	<htmltext><blockquote><div><p>Well if you're not asking for teachers needing to be professional published mathematicians, what was that paragraph about?</p></div></blockquote><p>In history, a lot of very prominent mathematicians of their day and age made their living privately teaching high school kids. In modern times, mathematics isn't seen as an important an asset to have to spend that kind of money even if one has it.

</p><p>I don't understand why education is seen the way it is in the US. What does the teacher have to do with the quality of education? Does anyone think their teacher helped them become a good programmer. NO. Why do people think their math teachers will make them good mathematicians?

</p><p>Anyway, I challenge people to name 10 prominent American mathematicians - please non-mathematicians only and let's take Nash as given. Name the last American mathematician to be featured on a postage stamp. Do the same for musician and see how long that takes.

</p><p>My point is that the US doesn't really have a mathematics appreciating society. It reflects in the education as well. And, don't blame the teachers or the administrators for it.</p></div>
	</htmltext>
<tokenext>Well if you 're not asking for teachers needing to be professional published mathematicians , what was that paragraph about ? In history , a lot of very prominent mathematicians of their day and age made their living privately teaching high school kids .
In modern times , mathematics is n't seen as an important an asset to have to spend that kind of money even if one has it .
I do n't understand why education is seen the way it is in the US .
What does the teacher have to do with the quality of education ?
Does anyone think their teacher helped them become a good programmer .
NO. Why do people think their math teachers will make them good mathematicians ?
Anyway , I challenge people to name 10 prominent American mathematicians - please non-mathematicians only and let 's take Nash as given .
Name the last American mathematician to be featured on a postage stamp .
Do the same for musician and see how long that takes .
My point is that the US does n't really have a mathematics appreciating society .
It reflects in the education as well .
And , do n't blame the teachers or the administrators for it .</tokentext>
<sentencetext>Well if you're not asking for teachers needing to be professional published mathematicians, what was that paragraph about?In history, a lot of very prominent mathematicians of their day and age made their living privately teaching high school kids.
In modern times, mathematics isn't seen as an important an asset to have to spend that kind of money even if one has it.
I don't understand why education is seen the way it is in the US.
What does the teacher have to do with the quality of education?
Does anyone think their teacher helped them become a good programmer.
NO. Why do people think their math teachers will make them good mathematicians?
Anyway, I challenge people to name 10 prominent American mathematicians - please non-mathematicians only and let's take Nash as given.
Name the last American mathematician to be featured on a postage stamp.
Do the same for musician and see how long that takes.
My point is that the US doesn't really have a mathematics appreciating society.
It reflects in the education as well.
And, don't blame the teachers or the administrators for it.
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392903</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28396043</id>
	<title>Re:it's really bad</title>
	<author>Anonymous</author>
	<datestamp>1245407220000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p><div class="quote"><p>For instance, if you had 10 x 20 as a problem, many of us remember the trick we were taught when multiplying numbers with zeroes at the end: set aside the zeroes, multiply the remaining integers, and then append all of the zeroes to the end. (So 10 x 20 would be 1 x 2 = 2, and then append the two zeroes at the end for 200.)</p></div><p>That's not a "trick". That's math.</p><p>10x20<br>10x1x10x2<br>100x1x2<br>100x2<br>200</p></div>
	</htmltext>
<tokenext>For instance , if you had 10 x 20 as a problem , many of us remember the trick we were taught when multiplying numbers with zeroes at the end : set aside the zeroes , multiply the remaining integers , and then append all of the zeroes to the end .
( So 10 x 20 would be 1 x 2 = 2 , and then append the two zeroes at the end for 200 .
) That 's not a " trick " .
That 's math.10x2010x1x10x2100x1x2100x2200</tokentext>
<sentencetext>For instance, if you had 10 x 20 as a problem, many of us remember the trick we were taught when multiplying numbers with zeroes at the end: set aside the zeroes, multiply the remaining integers, and then append all of the zeroes to the end.
(So 10 x 20 would be 1 x 2 = 2, and then append the two zeroes at the end for 200.
)That's not a "trick".
That's math.10x2010x1x10x2100x1x2100x2200
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393543</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28408615</id>
	<title>Re:I Sympathize With Him But Too Idyllic</title>
	<author>Anonymous</author>
	<datestamp>1245616080000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>Yes, this.  I wish I had points to mod you up.<br>
&nbsp; </p><p>One big problem (though not the only one) is that math lacks MEANING to a lot of students.  The solution isn't to simply insist that it has inherent beauty and dammit why can't you see that!  The solution is to look at all the students on a case by case basis and ask yourself how you can make math meaningful to them (not to yourself).  I hear all the time from people that they think math is "mental masturbation", it may be partly sour grapes but I think it may also be because people like Lockhart want it to be like masturbation: inherently pleasurable but not really achieving anything practical.  Chances are he might generate a lot of interest and enthusiasm in the students with a similar bent but some of the students with more practical personality types will forever be turned off by the discipline, which is a shame because it's a rich and diverse subject that could really benefit from all types of personalities (if not in the actual theoretical development and research, then in the applications).<br>
&nbsp; </p><p>I say this as someone who used build polyhedra from cardboard as well as trig proofs that weren't assigned because they were fun (and I also love philosophy and pretty much anything theoretical or conceptual), so if even I think Lockhart is a little extreme in his recommendations, then I'd be really scared to know what more practical and down to earth people would think.<br>
&nbsp; </p><p>I do agree with Lockhart on many points, though.  In particular, I think he's right about the standardized curriculum being too rigid.  I'm not sure I would endorse integrated math 100\% (I believe that's where you don't have Algebra, Geom., Trig., Calculus, but instead have Math 1, Math 2, Math 3, and so on) but the current system is very limiting and I fear comprehensiveness (read: being able to satisfy all the items on a really long checklist) may be detracting from the quality of education you could get with a more relaxed and free-form approach.<br>
&nbsp; </p><p>There are also broader issues such as the problems of society and culture as a whole that impact the students before the first class even starts.  The combined recommendations of Lockhart and myself would not fix the real underlying problems.  This may seem strange but the best thing might actually be more movies like Pi and Good Will Hunting.  If you can make it seem cool and worthwhile OUTSIDE of the classroom, it will be that much easier to teach inside the classroom.  There are lots of possibilities with xkcd, Google, YouTube, Wikipedia, and now Mathematica.  I sort of agree with the other poster who thought Wikipedia was a little jargon-laden, but look at it this way, it's better than nothing and certainly more than I had access to when I was in school.  I had Microsoft Encarta and thought I had it good.  God, that makes me feel old<nobr> <wbr></nobr>:(</p></htmltext>
<tokenext>Yes , this .
I wish I had points to mod you up .
  One big problem ( though not the only one ) is that math lacks MEANING to a lot of students .
The solution is n't to simply insist that it has inherent beauty and dammit why ca n't you see that !
The solution is to look at all the students on a case by case basis and ask yourself how you can make math meaningful to them ( not to yourself ) .
I hear all the time from people that they think math is " mental masturbation " , it may be partly sour grapes but I think it may also be because people like Lockhart want it to be like masturbation : inherently pleasurable but not really achieving anything practical .
Chances are he might generate a lot of interest and enthusiasm in the students with a similar bent but some of the students with more practical personality types will forever be turned off by the discipline , which is a shame because it 's a rich and diverse subject that could really benefit from all types of personalities ( if not in the actual theoretical development and research , then in the applications ) .
  I say this as someone who used build polyhedra from cardboard as well as trig proofs that were n't assigned because they were fun ( and I also love philosophy and pretty much anything theoretical or conceptual ) , so if even I think Lockhart is a little extreme in his recommendations , then I 'd be really scared to know what more practical and down to earth people would think .
  I do agree with Lockhart on many points , though .
In particular , I think he 's right about the standardized curriculum being too rigid .
I 'm not sure I would endorse integrated math 100 \ % ( I believe that 's where you do n't have Algebra , Geom. , Trig. , Calculus , but instead have Math 1 , Math 2 , Math 3 , and so on ) but the current system is very limiting and I fear comprehensiveness ( read : being able to satisfy all the items on a really long checklist ) may be detracting from the quality of education you could get with a more relaxed and free-form approach .
  There are also broader issues such as the problems of society and culture as a whole that impact the students before the first class even starts .
The combined recommendations of Lockhart and myself would not fix the real underlying problems .
This may seem strange but the best thing might actually be more movies like Pi and Good Will Hunting .
If you can make it seem cool and worthwhile OUTSIDE of the classroom , it will be that much easier to teach inside the classroom .
There are lots of possibilities with xkcd , Google , YouTube , Wikipedia , and now Mathematica .
I sort of agree with the other poster who thought Wikipedia was a little jargon-laden , but look at it this way , it 's better than nothing and certainly more than I had access to when I was in school .
I had Microsoft Encarta and thought I had it good .
God , that makes me feel old : (</tokentext>
<sentencetext>Yes, this.
I wish I had points to mod you up.
  One big problem (though not the only one) is that math lacks MEANING to a lot of students.
The solution isn't to simply insist that it has inherent beauty and dammit why can't you see that!
The solution is to look at all the students on a case by case basis and ask yourself how you can make math meaningful to them (not to yourself).
I hear all the time from people that they think math is "mental masturbation", it may be partly sour grapes but I think it may also be because people like Lockhart want it to be like masturbation: inherently pleasurable but not really achieving anything practical.
Chances are he might generate a lot of interest and enthusiasm in the students with a similar bent but some of the students with more practical personality types will forever be turned off by the discipline, which is a shame because it's a rich and diverse subject that could really benefit from all types of personalities (if not in the actual theoretical development and research, then in the applications).
  I say this as someone who used build polyhedra from cardboard as well as trig proofs that weren't assigned because they were fun (and I also love philosophy and pretty much anything theoretical or conceptual), so if even I think Lockhart is a little extreme in his recommendations, then I'd be really scared to know what more practical and down to earth people would think.
  I do agree with Lockhart on many points, though.
In particular, I think he's right about the standardized curriculum being too rigid.
I'm not sure I would endorse integrated math 100\% (I believe that's where you don't have Algebra, Geom., Trig., Calculus, but instead have Math 1, Math 2, Math 3, and so on) but the current system is very limiting and I fear comprehensiveness (read: being able to satisfy all the items on a really long checklist) may be detracting from the quality of education you could get with a more relaxed and free-form approach.
  There are also broader issues such as the problems of society and culture as a whole that impact the students before the first class even starts.
The combined recommendations of Lockhart and myself would not fix the real underlying problems.
This may seem strange but the best thing might actually be more movies like Pi and Good Will Hunting.
If you can make it seem cool and worthwhile OUTSIDE of the classroom, it will be that much easier to teach inside the classroom.
There are lots of possibilities with xkcd, Google, YouTube, Wikipedia, and now Mathematica.
I sort of agree with the other poster who thought Wikipedia was a little jargon-laden, but look at it this way, it's better than nothing and certainly more than I had access to when I was in school.
I had Microsoft Encarta and thought I had it good.
God, that makes me feel old :(</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393903</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392771</id>
	<title>Zeroth Post.</title>
	<author>mosel-saar-ruwer</author>
	<datestamp>1245438420000</datestamp>
	<modclass>Offtopic</modclass>
	<modscore>0</modscore>
	<htmltext><br>
Pwned.</htmltext>
<tokenext>Pwned .</tokentext>
<sentencetext>
Pwned.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393599</id>
	<title>Re:Cue the other subjects</title>
	<author>Anonymous</author>
	<datestamp>1245441480000</datestamp>
	<modclass>Interestin</modclass>
	<modscore>1</modscore>
	<htmltext><p>If education is an investment in the future, that would imply that I'm going to get a payoff for my financial contributions.<br>When we couch the discussion in those terms, would you say that it's a "good investment" to spend 3x as much on kids with<br>brain damage brought on by Fetal Alcohol Syndrome than on kids that don't have brain damage?</p><p>Really, when you start talking about education as an investment in the future, that opens the door to discussions about how to<br>maximize the return on the investment.  Maybe I spend shitloads on kids that show promise, a little bit on average kids, and jack shit<br>on 3rd graders that can't tie their shoes.  How do you think the social justice set would take that?</p></htmltext>
<tokenext>If education is an investment in the future , that would imply that I 'm going to get a payoff for my financial contributions.When we couch the discussion in those terms , would you say that it 's a " good investment " to spend 3x as much on kids withbrain damage brought on by Fetal Alcohol Syndrome than on kids that do n't have brain damage ? Really , when you start talking about education as an investment in the future , that opens the door to discussions about how tomaximize the return on the investment .
Maybe I spend shitloads on kids that show promise , a little bit on average kids , and jack shiton 3rd graders that ca n't tie their shoes .
How do you think the social justice set would take that ?</tokentext>
<sentencetext>If education is an investment in the future, that would imply that I'm going to get a payoff for my financial contributions.When we couch the discussion in those terms, would you say that it's a "good investment" to spend 3x as much on kids withbrain damage brought on by Fetal Alcohol Syndrome than on kids that don't have brain damage?Really, when you start talking about education as an investment in the future, that opens the door to discussions about how tomaximize the return on the investment.
Maybe I spend shitloads on kids that show promise, a little bit on average kids, and jack shiton 3rd graders that can't tie their shoes.
How do you think the social justice set would take that?</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393083</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28396869</id>
	<title>I teach Maths and English</title>
	<author>boggis</author>
	<datestamp>1245411180000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>I teach secondary maths and English is Australia. In English it's common to try to give students an appreciation of the beauty of what you're teaching. I tell them when poetry makes the hairs on the back of my neck stand on end and which novels still make me cry the third time I read them. Sometimes this gets across to students and they become curious enough to be engaged. I certainly try to get them writing stuff that they are emotionally engaged with. <p>

I have some of the same attitudes to some mathematics. But there are two strong forces against me. </p><p>

First, the curriculum is crammed with gumpf. There is a small set of mathematical knowledge that I think is important for citizens of a developed democracy to know, stuff around finance and statistical reasoning mostly. But I could probably cover this in one semester in Year 10. And there is a small amount of foundational number knowledge that makes it possible to teach much of the rest of mathematics - times tables, an understanding of place value. Again if this were done carefully it could be done in about a semester - I'd prefer if it were done in primary school. But I have to spend an awful lot of my time teaching other stuff that is not in any sense necessary or useful, coordinate geometry, trigonometry, calculus, volumes of complex shapes, multi-variable algebra etc etc etc. Any one of these would be fun to go into in some depth but the necessity of covering them all means that none of them are covered properly and the connections between different areas of mathematics are totally obscured. </p><p>

Secondly, my students all come to me with a history of mathematics classes. Mostly, this history teaches them that there is a right answer and they are too stupid to find it. They wait to be told, they attempt to memorise formulae and they lack curiosity about how things work. I make attempts to reverse this but when the rubber hits the road and I need to cover content quickly, I reinforce it despite my best intentions.</p><p>

If someone wants to found a charter school where I can use Godel Escher Bach as my only maths textbook just tell me  where - I'll catch the next plane. </p></htmltext>
<tokenext>I teach secondary maths and English is Australia .
In English it 's common to try to give students an appreciation of the beauty of what you 're teaching .
I tell them when poetry makes the hairs on the back of my neck stand on end and which novels still make me cry the third time I read them .
Sometimes this gets across to students and they become curious enough to be engaged .
I certainly try to get them writing stuff that they are emotionally engaged with .
I have some of the same attitudes to some mathematics .
But there are two strong forces against me .
First , the curriculum is crammed with gumpf .
There is a small set of mathematical knowledge that I think is important for citizens of a developed democracy to know , stuff around finance and statistical reasoning mostly .
But I could probably cover this in one semester in Year 10 .
And there is a small amount of foundational number knowledge that makes it possible to teach much of the rest of mathematics - times tables , an understanding of place value .
Again if this were done carefully it could be done in about a semester - I 'd prefer if it were done in primary school .
But I have to spend an awful lot of my time teaching other stuff that is not in any sense necessary or useful , coordinate geometry , trigonometry , calculus , volumes of complex shapes , multi-variable algebra etc etc etc .
Any one of these would be fun to go into in some depth but the necessity of covering them all means that none of them are covered properly and the connections between different areas of mathematics are totally obscured .
Secondly , my students all come to me with a history of mathematics classes .
Mostly , this history teaches them that there is a right answer and they are too stupid to find it .
They wait to be told , they attempt to memorise formulae and they lack curiosity about how things work .
I make attempts to reverse this but when the rubber hits the road and I need to cover content quickly , I reinforce it despite my best intentions .
If someone wants to found a charter school where I can use Godel Escher Bach as my only maths textbook just tell me where - I 'll catch the next plane .</tokentext>
<sentencetext>I teach secondary maths and English is Australia.
In English it's common to try to give students an appreciation of the beauty of what you're teaching.
I tell them when poetry makes the hairs on the back of my neck stand on end and which novels still make me cry the third time I read them.
Sometimes this gets across to students and they become curious enough to be engaged.
I certainly try to get them writing stuff that they are emotionally engaged with.
I have some of the same attitudes to some mathematics.
But there are two strong forces against me.
First, the curriculum is crammed with gumpf.
There is a small set of mathematical knowledge that I think is important for citizens of a developed democracy to know, stuff around finance and statistical reasoning mostly.
But I could probably cover this in one semester in Year 10.
And there is a small amount of foundational number knowledge that makes it possible to teach much of the rest of mathematics - times tables, an understanding of place value.
Again if this were done carefully it could be done in about a semester - I'd prefer if it were done in primary school.
But I have to spend an awful lot of my time teaching other stuff that is not in any sense necessary or useful, coordinate geometry, trigonometry, calculus, volumes of complex shapes, multi-variable algebra etc etc etc.
Any one of these would be fun to go into in some depth but the necessity of covering them all means that none of them are covered properly and the connections between different areas of mathematics are totally obscured.
Secondly, my students all come to me with a history of mathematics classes.
Mostly, this history teaches them that there is a right answer and they are too stupid to find it.
They wait to be told, they attempt to memorise formulae and they lack curiosity about how things work.
I make attempts to reverse this but when the rubber hits the road and I need to cover content quickly, I reinforce it despite my best intentions.
If someone wants to found a charter school where I can use Godel Escher Bach as my only maths textbook just tell me  where - I'll catch the next plane. </sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393549</id>
	<title>I don't understand</title>
	<author>Anonymous</author>
	<datestamp>1245441300000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>This will sound rich coming from an Anonymous Coward, but an expert on exactly what is wrong is a fortiori an expert on what is right.  So I hope the author publishes a teaching manual with his ideas.  No doubt, it'll bring a revolution in math teaching.</p></htmltext>
<tokenext>This will sound rich coming from an Anonymous Coward , but an expert on exactly what is wrong is a fortiori an expert on what is right .
So I hope the author publishes a teaching manual with his ideas .
No doubt , it 'll bring a revolution in math teaching .</tokentext>
<sentencetext>This will sound rich coming from an Anonymous Coward, but an expert on exactly what is wrong is a fortiori an expert on what is right.
So I hope the author publishes a teaching manual with his ideas.
No doubt, it'll bring a revolution in math teaching.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392903</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394591</id>
	<title>A false hope.</title>
	<author>Anonymous</author>
	<datestamp>1245444900000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>While there may be great modern artists, there is no rigor in modern art and great art is no longer appreciated.  Wishing mathematics could enrich society is nice but misguided.  There are reasons our education is the way it is, and although lamentable, it cannot be fundamentally changed without culture experiencing a true rebirth.  Not likely.</p></htmltext>
<tokenext>While there may be great modern artists , there is no rigor in modern art and great art is no longer appreciated .
Wishing mathematics could enrich society is nice but misguided .
There are reasons our education is the way it is , and although lamentable , it can not be fundamentally changed without culture experiencing a true rebirth .
Not likely .</tokentext>
<sentencetext>While there may be great modern artists, there is no rigor in modern art and great art is no longer appreciated.
Wishing mathematics could enrich society is nice but misguided.
There are reasons our education is the way it is, and although lamentable, it cannot be fundamentally changed without culture experiencing a true rebirth.
Not likely.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393023</id>
	<title>An allegedly true story from a professor</title>
	<author>thirty-seven</author>
	<datestamp>1245439440000</datestamp>
	<modclass>Interestin</modclass>
	<modscore>4</modscore>
	<htmltext><p>While I was in university, a computer science professor in the faculty of mathematics told me (and the rest of the class) a cute and funny story about what happens "when the children of math professors get together".  He and a colleague, who each had a young daughter at that time, were walking together in a park with their daughters.  The children were old enough to have picked up some math-related words and phrases from their fathers, but young enough to have no idea what they really meant - six or seven years old, maybe?  The daughters went off to play and their fathers overheard them arguing about who had seen the most flowers in the park.</p><p>My professor's daughter said, "I saw five flowers!"</p><p>"And I saw... six!", the other girl replied.</p><p>Not to be outdone, my professor's daughter said, "I saw a million flowers."</p><p>"Oh yeah?  I saw infinity flowers."</p><p>This, according to my professor, caused his daughter to pause - she had never heard of "infinity" before.  How could she top "infinity flowers", especially since she didn't know what it meant?</p><p>But after thinking for a few seconds, she said, "Well, I saw <i>all</i> the flowers."</p></htmltext>
<tokenext>While I was in university , a computer science professor in the faculty of mathematics told me ( and the rest of the class ) a cute and funny story about what happens " when the children of math professors get together " .
He and a colleague , who each had a young daughter at that time , were walking together in a park with their daughters .
The children were old enough to have picked up some math-related words and phrases from their fathers , but young enough to have no idea what they really meant - six or seven years old , maybe ?
The daughters went off to play and their fathers overheard them arguing about who had seen the most flowers in the park.My professor 's daughter said , " I saw five flowers !
" " And I saw.. .
six ! " , the other girl replied.Not to be outdone , my professor 's daughter said , " I saw a million flowers .
" " Oh yeah ?
I saw infinity flowers .
" This , according to my professor , caused his daughter to pause - she had never heard of " infinity " before .
How could she top " infinity flowers " , especially since she did n't know what it meant ? But after thinking for a few seconds , she said , " Well , I saw all the flowers .
"</tokentext>
<sentencetext>While I was in university, a computer science professor in the faculty of mathematics told me (and the rest of the class) a cute and funny story about what happens "when the children of math professors get together".
He and a colleague, who each had a young daughter at that time, were walking together in a park with their daughters.
The children were old enough to have picked up some math-related words and phrases from their fathers, but young enough to have no idea what they really meant - six or seven years old, maybe?
The daughters went off to play and their fathers overheard them arguing about who had seen the most flowers in the park.My professor's daughter said, "I saw five flowers!
""And I saw...
six!", the other girl replied.Not to be outdone, my professor's daughter said, "I saw a million flowers.
""Oh yeah?
I saw infinity flowers.
"This, according to my professor, caused his daughter to pause - she had never heard of "infinity" before.
How could she top "infinity flowers", especially since she didn't know what it meant?But after thinking for a few seconds, she said, "Well, I saw all the flowers.
"</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392757</id>
	<title>Can't count</title>
	<author>Anonymous</author>
	<datestamp>1245438360000</datestamp>
	<modclass>Funny</modclass>
	<modscore>5</modscore>
	<htmltext><p>second!</p></htmltext>
<tokenext>second !</tokentext>
<sentencetext>second!</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28396489</id>
	<title>And your conclusions are just false.</title>
	<author>basicio</author>
	<datestamp>1245409380000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>Even small schools almost always have different math courses based on skill level (I went to a tiny high school, and we certainly did). You misunderstand the issue.</p><p>Unless you have classes with only 2-3 students of equal ability you're going to have this problem. Even in advanced classes there are some people who learn things faster than others, and the people who learn faster are almost always forced to sit through lectures and do work that is for them pointless.</p><p>The prevailing attitude in US education is that people who learn slowly are most helped by being in the same classes as those who learn quickly. This isn't wrong, but it does mean that those who learn quickly are slowed down to help others keep up.</p><p>This isn't a problem unique to math education though--it's an issue for almost everything. Unsurprisingly, things like art classes and music classes are least susceptible to this problem. The people who excel can do so, and the people who don't are still able to learn from those who do.</p></htmltext>
<tokenext>Even small schools almost always have different math courses based on skill level ( I went to a tiny high school , and we certainly did ) .
You misunderstand the issue.Unless you have classes with only 2-3 students of equal ability you 're going to have this problem .
Even in advanced classes there are some people who learn things faster than others , and the people who learn faster are almost always forced to sit through lectures and do work that is for them pointless.The prevailing attitude in US education is that people who learn slowly are most helped by being in the same classes as those who learn quickly .
This is n't wrong , but it does mean that those who learn quickly are slowed down to help others keep up.This is n't a problem unique to math education though--it 's an issue for almost everything .
Unsurprisingly , things like art classes and music classes are least susceptible to this problem .
The people who excel can do so , and the people who do n't are still able to learn from those who do .</tokentext>
<sentencetext>Even small schools almost always have different math courses based on skill level (I went to a tiny high school, and we certainly did).
You misunderstand the issue.Unless you have classes with only 2-3 students of equal ability you're going to have this problem.
Even in advanced classes there are some people who learn things faster than others, and the people who learn faster are almost always forced to sit through lectures and do work that is for them pointless.The prevailing attitude in US education is that people who learn slowly are most helped by being in the same classes as those who learn quickly.
This isn't wrong, but it does mean that those who learn quickly are slowed down to help others keep up.This isn't a problem unique to math education though--it's an issue for almost everything.
Unsurprisingly, things like art classes and music classes are least susceptible to this problem.
The people who excel can do so, and the people who don't are still able to learn from those who do.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393241</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28404983</id>
	<title>Re:Cue the other subjects</title>
	<author>Anonymous</author>
	<datestamp>1245497820000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p><div class="quote"><p>A lot of the rest, IMO, can be traced to schools not teaching children how to think critically, just to memorize stuff.</p><p>And that sucks.</p></div><p>Governments, Corporations, and Religions don't necessarily want us to be able to think critically (and it can be argued that they'd prefer us to "think" uncritically), so it's not surprising that none of that enters into most schools.  But yeah, I agree with what you said.</p></div>
	</htmltext>
<tokenext>A lot of the rest , IMO , can be traced to schools not teaching children how to think critically , just to memorize stuff.And that sucks.Governments , Corporations , and Religions do n't necessarily want us to be able to think critically ( and it can be argued that they 'd prefer us to " think " uncritically ) , so it 's not surprising that none of that enters into most schools .
But yeah , I agree with what you said .</tokentext>
<sentencetext>A lot of the rest, IMO, can be traced to schools not teaching children how to think critically, just to memorize stuff.And that sucks.Governments, Corporations, and Religions don't necessarily want us to be able to think critically (and it can be argued that they'd prefer us to "think" uncritically), so it's not surprising that none of that enters into most schools.
But yeah, I agree with what you said.
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393137</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394975</id>
	<title>Re:I Sympathize With Him But Too Idyllic</title>
	<author>avandesande</author>
	<datestamp>1245402960000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>Our HS music teacher was a goof ball but you could tell that he loved music.<br>I don't think it is that rare.</p></htmltext>
<tokenext>Our HS music teacher was a goof ball but you could tell that he loved music.I do n't think it is that rare .</tokentext>
<sentencetext>Our HS music teacher was a goof ball but you could tell that he loved music.I don't think it is that rare.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392903</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394329</id>
	<title>Re:it's really bad</title>
	<author>Anonymous</author>
	<datestamp>1245444060000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>Well, should they be taught binary (classical) logic as the logic that describes reality and then be punished when they ask: and why implication is true whenever antecedent is false?</p><p>Even the founder of this way of thinking, Aristotle, had a problem with that and created first modal logic. Are we going to force 80\% of people that don't get it, to believe they are wrong and punish them that their brain doesn't work as the brain of a mathematician prototype?</p><p>And anyway, I find Hilbert Proof System disgusting, I rather use Smullyan's semantic tableaux whenever possible. Should we teach kids this?</p></htmltext>
<tokenext>Well , should they be taught binary ( classical ) logic as the logic that describes reality and then be punished when they ask : and why implication is true whenever antecedent is false ? Even the founder of this way of thinking , Aristotle , had a problem with that and created first modal logic .
Are we going to force 80 \ % of people that do n't get it , to believe they are wrong and punish them that their brain does n't work as the brain of a mathematician prototype ? And anyway , I find Hilbert Proof System disgusting , I rather use Smullyan 's semantic tableaux whenever possible .
Should we teach kids this ?</tokentext>
<sentencetext>Well, should they be taught binary (classical) logic as the logic that describes reality and then be punished when they ask: and why implication is true whenever antecedent is false?Even the founder of this way of thinking, Aristotle, had a problem with that and created first modal logic.
Are we going to force 80\% of people that don't get it, to believe they are wrong and punish them that their brain doesn't work as the brain of a mathematician prototype?And anyway, I find Hilbert Proof System disgusting, I rather use Smullyan's semantic tableaux whenever possible.
Should we teach kids this?</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392911</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28405579</id>
	<title>Re:Housecats</title>
	<author>ChaosDiscord</author>
	<datestamp>1245501360000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>Nope, he's directly addressing both of your goals.  He claims that the current system fails at both.  Rote memorization and robotic application of cryptic rules doesn't stick with people.  So we'll give someone 12 years of math education, but after a few years in the real world they'll only remember maybe the first 5.  So what was the point of all that time?  Secondly, because math is presented so poorly, many people who might love math are turned off.  Worse, some people who enjoy and are good at rote memorization and robotic application might erroneously think they want to be math majors, only to discover that upper level math is a very different beast.  As he notes, it's like teaching students musical notation without actually listening to music as a way to discover who might have a love of music.  He believes that his proposal may cover less material, but students will actually understand it better and will retain it and will be better able to learn whatever else they need to know.  And because they're learning "real" math, the people with a predisposition to loving math have a better chance to discover it.</htmltext>
<tokenext>Nope , he 's directly addressing both of your goals .
He claims that the current system fails at both .
Rote memorization and robotic application of cryptic rules does n't stick with people .
So we 'll give someone 12 years of math education , but after a few years in the real world they 'll only remember maybe the first 5 .
So what was the point of all that time ?
Secondly , because math is presented so poorly , many people who might love math are turned off .
Worse , some people who enjoy and are good at rote memorization and robotic application might erroneously think they want to be math majors , only to discover that upper level math is a very different beast .
As he notes , it 's like teaching students musical notation without actually listening to music as a way to discover who might have a love of music .
He believes that his proposal may cover less material , but students will actually understand it better and will retain it and will be better able to learn whatever else they need to know .
And because they 're learning " real " math , the people with a predisposition to loving math have a better chance to discover it .</tokentext>
<sentencetext>Nope, he's directly addressing both of your goals.
He claims that the current system fails at both.
Rote memorization and robotic application of cryptic rules doesn't stick with people.
So we'll give someone 12 years of math education, but after a few years in the real world they'll only remember maybe the first 5.
So what was the point of all that time?
Secondly, because math is presented so poorly, many people who might love math are turned off.
Worse, some people who enjoy and are good at rote memorization and robotic application might erroneously think they want to be math majors, only to discover that upper level math is a very different beast.
As he notes, it's like teaching students musical notation without actually listening to music as a way to discover who might have a love of music.
He believes that his proposal may cover less material, but students will actually understand it better and will retain it and will be better able to learn whatever else they need to know.
And because they're learning "real" math, the people with a predisposition to loving math have a better chance to discover it.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394309</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28395243</id>
	<title>Re:US School System compared to Europes School Sys</title>
	<author>Anonymous</author>
	<datestamp>1245403860000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>Let's not argue about anecdotes!</p><p>The Simpsons had the best summary of education ever: "Let me get this straight: I'm behind the rest of the class, and I'm going to catch up by going slower?"</p><p>If students aren't grokking concepts as quickly as other students, the students who learn slower need to spend more time on the concepts in order to compensate. Putting them in a separate class of equal length doesn't accomplish anything. They need a unique -tract- of classes that spends more time on concepts, and they need to remain in that tract until they can learn at the same speed as the other students.</p><p>More time is really the only way to help struggling students catch up. Logistically, this is a nightmare for even large schools. It's difficult enough to schedule students, teachers, and classrooms into basic timeblocks. Trying to add more classes of different lengths that progress at different speeds is borderline impossible.</p><p>I believe that the best, most feasible solutions are online courses and self-guided curriculum:</p><p>
&nbsp; - Individual schools don't have enough teachers to have nine different Pre-Calculus courses, going at different speeds, each offered several times throughout the day, nor would they have enough students to fill all those sections...but if you connect schools with online learning, then you can share teachers and students among many schools.</p><p>
&nbsp; - Self-guided curriculum allows individual students to schedule their time as necessary. If two students are both taking English I and Algebra I, one could spend 2 hours a day on English and 1 on Algebra, and the other spend 2 hours a day on Algebra, and 1 hour on English, and they'd both complete the year at roughly the same level in each.</p><p>Both of these ideas as 100\% possible right now, but each has an obstacle caused by cultural inertia:<br>
&nbsp; - Schools and districts very rarely work together. Yes, we can all find a thousand examples of when they work together, but these are less than a drop in the bucket compared with the shear number of classes and projects going on every school day.<br>
&nbsp; - The education industry simply doesn't change at such a core level, mostly because training for educators is pathetic. Educational schools are largely guided by conservative former educators who perpetuate the status quo. School- and district-run professional development suffers from the same problems facing classes for students: all the teachers are at different levels of aptitude, so the classes sink to the lowest common denominator and most people don't learn anything new.</p><p>So, add another layer to the top of the two ideas above: before they can be implemented, schools need to develop individualized professional development for teachers. Then teachers will be equipped to grow and change, and then students will finally get an education in a style that is different from and improved over education from the first half of the last century.</p></htmltext>
<tokenext>Let 's not argue about anecdotes ! The Simpsons had the best summary of education ever : " Let me get this straight : I 'm behind the rest of the class , and I 'm going to catch up by going slower ?
" If students are n't grokking concepts as quickly as other students , the students who learn slower need to spend more time on the concepts in order to compensate .
Putting them in a separate class of equal length does n't accomplish anything .
They need a unique -tract- of classes that spends more time on concepts , and they need to remain in that tract until they can learn at the same speed as the other students.More time is really the only way to help struggling students catch up .
Logistically , this is a nightmare for even large schools .
It 's difficult enough to schedule students , teachers , and classrooms into basic timeblocks .
Trying to add more classes of different lengths that progress at different speeds is borderline impossible.I believe that the best , most feasible solutions are online courses and self-guided curriculum :   - Individual schools do n't have enough teachers to have nine different Pre-Calculus courses , going at different speeds , each offered several times throughout the day , nor would they have enough students to fill all those sections...but if you connect schools with online learning , then you can share teachers and students among many schools .
  - Self-guided curriculum allows individual students to schedule their time as necessary .
If two students are both taking English I and Algebra I , one could spend 2 hours a day on English and 1 on Algebra , and the other spend 2 hours a day on Algebra , and 1 hour on English , and they 'd both complete the year at roughly the same level in each.Both of these ideas as 100 \ % possible right now , but each has an obstacle caused by cultural inertia :   - Schools and districts very rarely work together .
Yes , we can all find a thousand examples of when they work together , but these are less than a drop in the bucket compared with the shear number of classes and projects going on every school day .
  - The education industry simply does n't change at such a core level , mostly because training for educators is pathetic .
Educational schools are largely guided by conservative former educators who perpetuate the status quo .
School- and district-run professional development suffers from the same problems facing classes for students : all the teachers are at different levels of aptitude , so the classes sink to the lowest common denominator and most people do n't learn anything new.So , add another layer to the top of the two ideas above : before they can be implemented , schools need to develop individualized professional development for teachers .
Then teachers will be equipped to grow and change , and then students will finally get an education in a style that is different from and improved over education from the first half of the last century .</tokentext>
<sentencetext>Let's not argue about anecdotes!The Simpsons had the best summary of education ever: "Let me get this straight: I'm behind the rest of the class, and I'm going to catch up by going slower?
"If students aren't grokking concepts as quickly as other students, the students who learn slower need to spend more time on the concepts in order to compensate.
Putting them in a separate class of equal length doesn't accomplish anything.
They need a unique -tract- of classes that spends more time on concepts, and they need to remain in that tract until they can learn at the same speed as the other students.More time is really the only way to help struggling students catch up.
Logistically, this is a nightmare for even large schools.
It's difficult enough to schedule students, teachers, and classrooms into basic timeblocks.
Trying to add more classes of different lengths that progress at different speeds is borderline impossible.I believe that the best, most feasible solutions are online courses and self-guided curriculum:
  - Individual schools don't have enough teachers to have nine different Pre-Calculus courses, going at different speeds, each offered several times throughout the day, nor would they have enough students to fill all those sections...but if you connect schools with online learning, then you can share teachers and students among many schools.
  - Self-guided curriculum allows individual students to schedule their time as necessary.
If two students are both taking English I and Algebra I, one could spend 2 hours a day on English and 1 on Algebra, and the other spend 2 hours a day on Algebra, and 1 hour on English, and they'd both complete the year at roughly the same level in each.Both of these ideas as 100\% possible right now, but each has an obstacle caused by cultural inertia:
  - Schools and districts very rarely work together.
Yes, we can all find a thousand examples of when they work together, but these are less than a drop in the bucket compared with the shear number of classes and projects going on every school day.
  - The education industry simply doesn't change at such a core level, mostly because training for educators is pathetic.
Educational schools are largely guided by conservative former educators who perpetuate the status quo.
School- and district-run professional development suffers from the same problems facing classes for students: all the teachers are at different levels of aptitude, so the classes sink to the lowest common denominator and most people don't learn anything new.So, add another layer to the top of the two ideas above: before they can be implemented, schools need to develop individualized professional development for teachers.
Then teachers will be equipped to grow and change, and then students will finally get an education in a style that is different from and improved over education from the first half of the last century.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393241</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28399973</id>
	<title>Re:tl;dr</title>
	<author>oh2</author>
	<datestamp>1245530460000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>Well,I am one of those statistical anomalies. I am a man and I  teach kids 6-12 years old and I find that a lot more rewarding than when I taught in a high school. As for "women are generally more interested in teaching and being around small children than men", thats not true. Men like kids just as much as women, but its not considered macho enough by many to work with kids. Theres appearances to maintain, yes?</htmltext>
<tokenext>Well,I am one of those statistical anomalies .
I am a man and I teach kids 6-12 years old and I find that a lot more rewarding than when I taught in a high school .
As for " women are generally more interested in teaching and being around small children than men " , thats not true .
Men like kids just as much as women , but its not considered macho enough by many to work with kids .
Theres appearances to maintain , yes ?</tokentext>
<sentencetext>Well,I am one of those statistical anomalies.
I am a man and I  teach kids 6-12 years old and I find that a lot more rewarding than when I taught in a high school.
As for "women are generally more interested in teaching and being around small children than men", thats not true.
Men like kids just as much as women, but its not considered macho enough by many to work with kids.
Theres appearances to maintain, yes?</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394487</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28402583</id>
	<title>He's consfusing different meaning of "art"</title>
	<author>ET3D</author>
	<datestamp>1245520080000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>Math may be an art, in the same sense that programming is art, but it's not an art form. I like Wikipedia's definition of art: "Art is the process or product of deliberately arranging elements in a way that appeals to the senses or emotions." In this sense, programming is not an art, but computer games are. Yes, the work 'art' has other meanings, some of which apply to math and programming, but it's not the same meaning applied to music or painting.</p><p>That's why to me this article doesn't make sense or propose a real solution. Math is no different than history or science, or, for that matter, literature. They are all taught mainly as a collection of facts, with just glimpses of the way these are arrived at. Putting math on a different pedestal IMO makes it more difficult to reach a better solution to teaching it, rather than seeing where the problems of teaching lie.</p><p>Frankly, everything that's taught in school is boring. You need a good teacher who really likes the subject to make it feel interesting. Even if he or she teaches the exact same material, it'd feel more interesting. That's in my experience, at least.</p></htmltext>
<tokenext>Math may be an art , in the same sense that programming is art , but it 's not an art form .
I like Wikipedia 's definition of art : " Art is the process or product of deliberately arranging elements in a way that appeals to the senses or emotions .
" In this sense , programming is not an art , but computer games are .
Yes , the work 'art ' has other meanings , some of which apply to math and programming , but it 's not the same meaning applied to music or painting.That 's why to me this article does n't make sense or propose a real solution .
Math is no different than history or science , or , for that matter , literature .
They are all taught mainly as a collection of facts , with just glimpses of the way these are arrived at .
Putting math on a different pedestal IMO makes it more difficult to reach a better solution to teaching it , rather than seeing where the problems of teaching lie.Frankly , everything that 's taught in school is boring .
You need a good teacher who really likes the subject to make it feel interesting .
Even if he or she teaches the exact same material , it 'd feel more interesting .
That 's in my experience , at least .</tokentext>
<sentencetext>Math may be an art, in the same sense that programming is art, but it's not an art form.
I like Wikipedia's definition of art: "Art is the process or product of deliberately arranging elements in a way that appeals to the senses or emotions.
" In this sense, programming is not an art, but computer games are.
Yes, the work 'art' has other meanings, some of which apply to math and programming, but it's not the same meaning applied to music or painting.That's why to me this article doesn't make sense or propose a real solution.
Math is no different than history or science, or, for that matter, literature.
They are all taught mainly as a collection of facts, with just glimpses of the way these are arrived at.
Putting math on a different pedestal IMO makes it more difficult to reach a better solution to teaching it, rather than seeing where the problems of teaching lie.Frankly, everything that's taught in school is boring.
You need a good teacher who really likes the subject to make it feel interesting.
Even if he or she teaches the exact same material, it'd feel more interesting.
That's in my experience, at least.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393255</id>
	<title>bfrist ps0t</title>
	<author>Anonymous</author>
	<datestamp>1245440280000</datestamp>
	<modclass>Offtopic</modclass>
	<modscore>-1</modscore>
	<htmltext>ggeting together to I type this. I won't bore you dead. It is a dead But I'd rather hear I DON'T WANT TO</htmltext>
<tokenext>ggeting together to I type this .
I wo n't bore you dead .
It is a dead But I 'd rather hear I DO N'T WANT TO</tokentext>
<sentencetext>ggeting together to I type this.
I won't bore you dead.
It is a dead But I'd rather hear I DON'T WANT TO</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393377</id>
	<title>Re:Cue the other subjects</title>
	<author>Anonymous</author>
	<datestamp>1245440640000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>Fail.</p></htmltext>
<tokenext>Fail .</tokentext>
<sentencetext>Fail.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28393123</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394941</id>
	<title>Speaking of hot mathematicians</title>
	<author>geekoid</author>
	<datestamp>1245402840000</datestamp>
	<modclass>Informativ</modclass>
	<modscore>4</modscore>
	<htmltext><p><a href="http://www.danicamckellar.com/" title="danicamckellar.com">http://www.danicamckellar.com/</a> [danicamckellar.com]</p><p>I can't believe Summer Glau is the chick geeks are hot after. Danica is Hot, has her name on a physic theorem, mathematician, and has written math books for girls.<br>Her acting career is full of geek as well.</p><p>Not to say either one of them is a geek, just that I scratch my head over why geeks prefer Summer.</p></htmltext>
<tokenext>http : //www.danicamckellar.com/ [ danicamckellar.com ] I ca n't believe Summer Glau is the chick geeks are hot after .
Danica is Hot , has her name on a physic theorem , mathematician , and has written math books for girls.Her acting career is full of geek as well.Not to say either one of them is a geek , just that I scratch my head over why geeks prefer Summer .</tokentext>
<sentencetext>http://www.danicamckellar.com/ [danicamckellar.com]I can't believe Summer Glau is the chick geeks are hot after.
Danica is Hot, has her name on a physic theorem, mathematician, and has written math books for girls.Her acting career is full of geek as well.Not to say either one of them is a geek, just that I scratch my head over why geeks prefer Summer.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28392961</id>
	<title>Eh.</title>
	<author>Anonymous</author>
	<datestamp>1245439200000</datestamp>
	<modclass>Interestin</modclass>
	<modscore>4</modscore>
	<htmltext>Found it here: <a href="http://plato.asu.edu/LockhartsLament.pdf" title="asu.edu">http://plato.asu.edu/LockhartsLament.pdf</a> [asu.edu] <br> <br>The whole idea behind his essay is that he liked playing with numbers and shapes as if it's an art, but he doesn't seem to realize most people don't share this love for math, like pretty much 90\% of any student population. This is me speaking as a just-graduated senior: the things he suggests is beyond the ability of most math students in high school.</htmltext>
<tokenext>Found it here : http : //plato.asu.edu/LockhartsLament.pdf [ asu.edu ] The whole idea behind his essay is that he liked playing with numbers and shapes as if it 's an art , but he does n't seem to realize most people do n't share this love for math , like pretty much 90 \ % of any student population .
This is me speaking as a just-graduated senior : the things he suggests is beyond the ability of most math students in high school .</tokentext>
<sentencetext>Found it here: http://plato.asu.edu/LockhartsLament.pdf [asu.edu]  The whole idea behind his essay is that he liked playing with numbers and shapes as if it's an art, but he doesn't seem to realize most people don't share this love for math, like pretty much 90\% of any student population.
This is me speaking as a just-graduated senior: the things he suggests is beyond the ability of most math students in high school.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28425973</id>
	<title>This is now a book</title>
	<author>lee1</author>
	<datestamp>1245698640000</datestamp>
	<modclass>Informativ</modclass>
	<modscore>2</modscore>
	<htmltext>I didn't see in the comments, and the story submitter doesn't mention, that this essay, which is from 2002, has blossomed recently (April, 2009) into a <a href="https://www.amazon.com/gp/offer-listing/1934137170?tag=leephillipsor-20&amp;camp=0&amp;creative=0&amp;linkCode=am1&amp;creativeASIN=1934137170&amp;adid=1X0C4V847FMWFXSY1JYC" title="amazon.com">book</a> [amazon.com].</htmltext>
<tokenext>I did n't see in the comments , and the story submitter does n't mention , that this essay , which is from 2002 , has blossomed recently ( April , 2009 ) into a book [ amazon.com ] .</tokentext>
<sentencetext>I didn't see in the comments, and the story submitter doesn't mention, that this essay, which is from 2002, has blossomed recently (April, 2009) into a book [amazon.com].</sentencetext>
</comment>
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	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment09_06_19_1520218.28394541</id>
	<title>Proofs</title>
	<author>Anonymous</author>
	<datestamp>1245444780000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>TFA doesn't make any sense unless you start with a spherical educational system...</p></htmltext>
<tokenext>TFA does n't make any sense unless you start with a spherical educational system.. .</tokentext>
<sentencetext>TFA doesn't make any sense unless you start with a spherical educational system...</sentencetext>
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