When any of the above browsing actions are executed, the new selection is summarized. These summaries are designed to be concise but informative. A typical problem that results when traversing complex structure is the so-called ``lost in space'' problem, where a user gets disoriented with respect to the current selection. We avoid this problem by conveying the following bits of information after each move:
Thus, when moving down the right hand side of Faa de Bruno's formula shown in eq:faa-de-bruno, the listener would hear:
[tabular1838]
Messages like the ones shown above have been found to be sufficient to avoid the lost-in-space problem mentioned earlier.
The nature of an object is conveyed by generic function summarize -methods on this function specify how individual object types are summarized. Below, we show some examples -the following list is not meant to be exhaustive. In cases where insufficient information is available to generate a complete summary of an object instance, the type of that object is spoken.
[tabular1850]
Contextual information (e.g., what the children of math objects are called) is available to AsTeR , -children of an inference are called ``premise'' and ``conclusion''; children of a fraction are called numerator and denominator. Such information was used to advantage in generating meaningful names when applying variable substitution; it is now exploited in giving contextual information about the current selection.
Traversing the structure of mathematical expressions is particularly useful when used in conjunction with the variable-substitution rendering style. In fact, such traversal can be thought of as a dual to variable substitution. If an expression has been rendered once using variable substitution, then future traversals of that expression use the variable names generated in the substitution process when cueing the current selection. This proves to be a very useful memory aid when understanding complex equations like Faa de Bruno's formula shown in eq:faa-de-bruno.
Traversing document structure is also very useful when handling large documents, e.g., entire textbooks. The browser actions described so far enable the listener to move quickly through the document without having to listen to a lot of text. In conjunction with the ability to switch rendering styles, this enables the quick location of portions of interest. For instance, a listener can activate a rule (see fig:read-only-display-math) that renders only the mathematics in a document. Once an equation of interest is encountered, the listener can interrupt the rendering, move the current selection from this point to the enclosing paragraph or sectional unit, and then listen to the relevant portion of the document.