Need for a prescriptive taxonomy of interaction for mathematical cognitive tools

Abstract

Cognitive tools encode and display information in different representational forms. Through interaction with these representations, people can make sense of and reason about the information. Mathematical cognitive tools can allow people to interact with mathematical ideas in ways and levels not hitherto possible. These tools can support reasoning and enhance the experience and understanding of mathematics. However, currently, there exists no prescriptive taxonomy of interaction with mathematical representations to guide designers of mathematical cognitive tools. Given different representations, cognitive activities, and users, such a taxonomy can help designers know what interaction techniques to use, when, and to what end. This paper discusses the need for the development of a comprehensive prescriptive taxonomy of interaction with visual representations used in mathematical cognitive tools. Additionally, the paper outlines some inter-related lines of action that can be followed to develop such a taxonomy. © Springer-Verlag 2004.