Overview of Interactive Mathematical Texts

Mathwright32 documents are intuitive and object-oriented. Using the metaphor that relates a "screen" to a "page", the author creates paginated interactive mathematical texts as hypertext documents. The "pages" of these documents are decorated with text, gadgets, and mathematical display objects. Navigation from one page to another may be controlled by buttons or by run-time conditions (such as reader response to questions). Pages are easily copied and inserted from other texts, and they retain all of their functionality. When these documents are embedded in HTML documents (web pages) they become a part of the latter, distinguishable only by their interactive content. The combination is what we call a Mathwright Microworld in the case of a single web page, or a Mathwright Interactive Web Book in the case of a multiple page HTML document. These are read in the browser on the web with the (free) MathwrightWeb ActiveX Control. You may read them over the Internet or local network, or off line from a CD or your local hard drive. The Mathwright Document itself may also be read off line, outside of the browser, by the (free) Mathwright32 Reader program. Mathwright32 Documents tend to be faster than Microworlds.

By "object-oriented" we mean that a document is built on a hierarchy of Abstract Java Object Classes (such as the Document class, the Page class, the 3D Graphics class, the Mathematical Function class, and so on). However, no knowledge of Java itself is required! The author builds her document from the top down, creating actual objects from each class where they are needed and when they are needed, using the intuitive Mathwright32 idiom. Each object in a class has its individual and distinctive attributes, but all objects in a class share the same generic properties: they process the same messages from other objects through the Mathscript Language, and stand in the same relationship with objects above or below them in the hierarchy. For example, 2D Graphics windows may be given their own background colors, pen colors, and pen widths, but each will graph functions of a single variable. At a deeper level of individual attributes, one such window may display graphs in Cartesian coordinates, another may display them (automatically) in polar coordinates.

The advantage of this architecture is that it guarantees a certain uniformity and consistency of behavior and appearance of all Mathwright32 documents. This object idiom is also intuitive and visual. Thus, authors invariably find it easy to build their documents in simple steps: screen by screen, object by object, and script by script, so that the testing and refinement cycle is relatively painless. For example, authors quickly learn to insert pages of existing documents into their own books, then to modify them for the functionality they desire. And this means that it is easier for authors to customize the documents for their students, taking into account the students' learning styles and abilities, and especially considering the "contexts" in which the students will undertake their mathematical investigations. In fact, authors often approach the creation of documents in a playful, experimental way.

All computer based learning environments are in the business of creating successful illusions. To the extent that Interactive Mathematical Texts (with their dynamic simulations, and their representations of abstract mathematical objects and their relations and transformations) succeed, they support visualization and they help the reader form more stable and balanced mathematical concepts. To provide this heuristic support, it is necessary that the computer environment and its language recede into the background. These environments must, therefore, be created by teachers, not by programmers. For this reason, we chose to develop an architecture and a language that minimizes the distance that a teacher must traverse to pass from a design idea to a dynamic interaction, and that equally encourages students to ask their own questions, even perhaps questions the teacher/author hadn't anticipated.