Designing Interactive Mathematics

Abstract

The use of interactivity in computer-based mathematics education has been growing explosively in recent years, fueled mainly by the intenet, but also by the production of educational CDs and in-classroom software packages. Unfortunately, the development of design principles for onscreen mathematical interactivity is still in its infancy, and examples of ineffective interaction or completely gratuitous "eye-candy" abound. There is a need for a "grammar of interactivity" as a tool for onscreen communication in much the same sense that the grammar of a language is a necessary tool for verbal communication. Some of the required principles can be adapted from basic principles of HCI or even from webpage design ideas. However, effective mathematical communication also requires a careful examination of the intrinsic mathematical nature of onscreen objects and how users interact with them: how should a curve behave when dragged, for example, or how should an equation transform when the equals sign is clicked? In this talk, I'll try to identify and clarify some of the relevant issues for the design of onscreen mathematical interactivity, and propose some preliminary principles for its grammar.