4 Cognitive Technologies for Mathematics Education

This chapter begins with a sociohistorical perspective on the roles played by cognitive technologies as reorganizers rather than amplifiers of mind. Informed by patterns of the past, perhaps we can better understand the transformational roles of advanced technologies in mathematical thinking and education. Computers are doing far more than making it easier or faster to do what we are already doing. The sociohistorical context may also illuminate promising directions for research and practice on compu-ters in mathematics education and make sense of the drastic reformula-tions in the aims and methods of mathematics education wrought by computers. The chapter then proposes an heuristic taxonomy of seven functions whose incorporation into educational technologies may promote mathe-matical thinking. It distinguishes two types of functions: purpose func-tions, which may affect whether students choose to think mathematically. and process functions. which may support the component mental activi-ties of mathematical thinking. My hope is that the functions falling into these two categories will apply to all cognitive technologies, that they will help students to think mathematically. and that they can be used both retroactively to assess existing software and proactively to guide software development efforts. Definitions and examples of software are provided throughout the chapter to illustrate the functions. The central role that mathematical thinking should play in mathematics education is now receiving more attention, both among educators and i