Grading is inherently subjective. Professors are required to pass judgement on students' work. In judging, it is necessary to encorporate fairness.
While it is advisable to present a histogram of scores which includes the corresponding letter grades for score ranges, allow the boundaries between grade categories to be ambiguous on your graph. This discourages students from fighting for an extra point to move up a grade category.
Reporting grades in a linear list by student ID is the wrong way to present the data. One wants to indicate what a score corresponds to along an excellent to poor ranking.
In addition to reporting the average score for the entire exam, report the average score for each problem on the exam. This indicates which problems were the hard problems and which were straightforward. This helps the student evaluate their performance and also lets the professor spot topics that he or she may have taught poorly.
This information can also be used to spot students who have had a flash of "brilliance" on the exam. One may want to reward these students with extra discretionary points.
If an exam has an abnormally low median students may face morale problems from getting low scores even though comparatively their performance is fine. It is best to avoid this situation. One way to do this is to first look through the exams and figure out for each problem whether the students tended to find it difficult or easy. Grade the easiest problems first and then progress on to the harder problems. If it appears that the median is going to be too low, give more partial credit for the harder problems.
Another option that Dexter Kozen suggests is to not assign any grades until all of the problems have been graded. Instead, keep notes on what errors have been made and assign scores on a second pass, giving partial credit to the degree that problem seems to merit. This method tries to ensure that assignments are graded consistently between students.
To avoid low medians when writing an exam, make about 50% of the problems so straightforward that most students will be able to do them. Because half of the test is on material that all students should be required to know in order to pass the class, this also provides a justification for failing students with a grade below a certain level.
Instead of using multiple choice (or true/false) questions, rewrite the questions so that the students can give written answers. Besides admitting that there may be multiple answers to any given question and that different students may interpret the same question differently, this also allows the professor to grade the question even if it turns out there was a flaw in it.
Though students spend most of their time in a course doing homework, that does not necessarily mean that most of the points in their grade should come from the homework. By having the homework questions count for a lower percentage of the students' final grades, one can achieve a lower incidence of cheating in the class.
When grading homeworks, use a coarse grained grading scheme. Instead of grading a problem on a scale of 0 to 10, grade it on a scale of 0 to 3, where each score is assigned the following meanings:
Better yet, one can use a binary grading scheme where questions receive 0 points for no attempt and 1 point for any attempt. In this case, the grade is being used as an incentive for students to at least try the problem.
With either of these schemes, one should then tightly couple the exam questions with the homework questions. In effect, the points that students are not getting on their homework are being given back to them on the exam. The time that students have spent doing homework now "pays off".
Do not spend too much time grading any one student's solution to a problem. If a student gives a solution that is convoluted, grade hard and then note on the paper that they can come see you to explain their solution. This puts the burden of figuring out a complex solution on the student and makes for more efficient use of the professor's time.
Key principle: Subjective + Fair = Objective
Given a set of homeworks, prelims, projects and a final exam, how should the students' scores on each one factor into their final grades?
Step one is to assign each graded object a percentage of the final grade. As discussed before, it is recommended to make homeworks a small percentage of the final grade as this helps to ensure academic integrity. This is the "subjective" part of the equation; percentages cannot totally measure a student's performance.
Step two is to adjust these grades so that they are "fair". This requires looking at each student's grades individually and evaluating their performance. If a student has done exceptionally well on one exam, one might reward that by raising their grade a half mark. One can also take improvement on the part of the student into account.
Adjusting grades for fairness is improved if a student's scores on each problem of each homework and exam are recorded along the way. This means that one can check if a student who got a problem wrong on the homework learned and got it correct on the exam or not. The grading process is more fine tuned. In a large class where this might not be possible, students who are in trouble can be asked to bring their past exams and/or homeworks to the final so that this evaluation can be done on the subset of students who are in risk of failing.
Note that by letting these "fairness" criteria factor into final grades, a student with a lower numerical grade might get a higher mark than another student with a slightly higher numerical mark.
As with reporting exam grades, reporting course grades should not be done by a list posted by student ID or some other identifier because it promotes competition between students to no end. If a histogram is used, sharp cutoffs between grades must be avoided as discussed above. However, because the "fairness" factor can result in shifts in grades that the professor might not wish to explain, or which could not be shown on a histogram (such as grade ordering not matching score ordering of students), a histogram of the scores might not be acceptable.
Solution: Creative Underreporting
When reporting grades, show the histogram generated from the flat scores in Step One of computing the final grades. Comment at the bottom of the histogram that individual grades may be shifted up under the course's previously described criteria (e.g., improvement over time). Do not show students the histogram that results from adding in the "fairness" factor.
One might also chose not to publically report the course grades. While this is probably okay, it does not give the students any context in which to evaluate themselves. Also, if the students have received grade distribution information during the rest of the class (and this is a vital method of feedback), withholding this information at the end of the class may make the grading system seem inconsistent.
The announced meaning of letter grades:
is not the same as the meaning that admissions offices or employers assume that letter grades have in undergraduate classes, namely:
The higher the level of a course, the more of an upwards shift the grading curve has. In a typical grad course, the meaning of letter grades might be taken as:
The way that one's grades will be interpreted by others must, to some extent, be taken into account when assigning grades. However, there is always variation in the meaning of grades across professors, departments, and time. This makes grading with incredible precision a somewhat useless pursuit; the "subjective + fair" model might give the best results given the overall grading environment.
Ideally, the quality of a student's transcript is a function both of their GPA and of their course choices. However, some employers or interviewers have GPA cutoffs so GPAs cannot be ignored. Grade inflation both aggravates this problem and makes it difficult to tell what a given grade means. To solve this, some schools report the average grade for a class along with the student's grade in the class on transcripts.
The S/U option has advantages and disadvantages for students. On the positive side, a student may be more likely to take a class which would be a stretch for them rather than avoiding the class to preserve their GPA. However, grades act as an incentive for students to do course work. Taking a class S/U lessens these pressures and the student may not learn as much as he or she could.
Allowing team work on homeworks or projects can increase overall academic integrity in a class. However, the issue then arises of how to fairly grade team projects. How do you separate the grades of individuals on the same team? Do you?
When assigning letter grades, how should +'s and -'s be used? One can split all of the B students so that 1/3 receive a B+, 1/3 receive a B and 1/3 receive a B-. But it might be better to assign mostly B's and use +'s and -'s sparingly, mostly to indicate the effects of the "fairness" factor.
The previous condemnation of multiple choice questions on exams also holds for multiple choice questions on course evaluations. The statistics generated are most likely meaningless. With university-wide forms, the questions asked are sometimes irrelevant for the class. If possible, try to get a written evaluation of the class.
There may be internal criteria for "good standing" at the university or required grade levels for financial support. These grade levels are often inconsistent with the "C is satisfactory" interpretation of grades. As professors respond to these pressures they contribute to grade inflation. However, these high required levels are reasonable to some extent. By requiring a "B-" average, a student is not penalized for a single poor performance but rather for overall poor performance. Also, by having a slightly high grade criterion for "good standing" a university is able to detect potential problems while the the student can still be helped.