Cognitive Science and Mathematics Education

By Alan H. Schoenfeld | Go to book overview

4
Cognitive Technologies for Mathematics Education

Roy D. Pea Educational Communication and Technology New York University

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 computers in mathematics education and make sense of the drastic reformulations 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 mathematical thinking. It distinguishes two types of functions: purpose functions, which may affect whether students choose to think mathematically, and process functions, which may support the component mental activities 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 in the research community (e.g. Schoenfeld, 1985a; Silver, 1985). As Schoenfeld says, "You understand how to think mathematically when you are resourceful, flexible, and efficient in your ability to deal with new

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