Definitions of Terms

A Mathwright Microworld is a single-page HTML document that presents interactive mathematics in a "portal" using the MathwrightWeb ActiveX Control. Readers may download this free Control once (roughly 2.4 M) from the web site displaying the Microworld and then may view any Mathwright Microworld in their ActiveX-enabled browser. The portal becomes part of the web page and is indistinguishable from the rest of the page, except that it displays 2- or 3-dimensional graphics objects (the latter using OpenGL), Access Data Tables, MathEdit Objects that display input and output mathematical formulas in intuitive, human readable form, Command Lines, TextFields, Buttons, Slider Bars, and other scripted gadgets. The portal is part of the Microworld, but it is not the Microworld. Our new Interactive Web Books are, by contrast, multipage HTML documents, with the web pages connected by ordinary hyperlinks. The individual pages may have portals taken from a single MathwrightWeb document.

We make this distinction between the HTML document and the underlying MathwrightWeb document in order to clarify the process of authorship. Mathwright is designed to encourage teachers to write interactive mathematical documents for their students. While most teachers are familiar with web page design using an HTML editor, few have the time or inclination to program the interactions (sprite animations, 3D simulations, differential equations, and so on) that can bring these books to life for their students. "Bringing the book to life" means making it capable of answering student "what if?" questions, by showing students the answers to their own questions (posed at their level of understanding), as well as providing simulations, explanations and examples.

For this to be possible, it is helpful if the author can make a conceptual separation (before beginning to write the web document) between the screen/page design and the dynamic behavior. HTML is superbly competent to support the organization and presentation of information on the screen. But it provides little support for the mathematics. On the other hand, the MathwrightWeb control is a fully capable object-oriented computer algebra system that knows how to present the results of its calculations in its variety of display objects.

Being object-oriented means that, unlike most other computer algebra systems, Mathwright enables teachers who are not programmers to translate their ideas quickly into working code. While there is no "royal road" to creating powerful interactions, authors find that our "scripting" approach takes much of the tedium out of programming. Our approach is like the approach of Logo. Authors create their scripts from the top down, testing and experimenting with them at each step of the way. Mathwright is also extremely flexible and is designed to allow the author or reader to create new mathematical objects on the fly. Many Mathwright Microworlds, such as Spherical Logo or Cardano, allow authors to design intuitive command languages that enable the reader to ask questions in 3D Riemannian Geometry or in Abstract Algebra.

Thus, authors find all the tools needed to support the mathematical explorations in single MathwrightWeb documents that they create, and they can simultaneously design the HTML pages of theri stories with confidence that, when they place the portals on their web pages, the underlying language support will be there. Often, display objects used in one portal can be reused (without having to be redesigned) in another portal of an Interactive Web Book.