# Cognitive Science and Mathematics Education

# Cognitive Science and Mathematics Education

## Synopsis

## Excerpt

This is an unusual book, produced by an unusual collection of people. Its contributors include professional mathematicians, classroom teachers, mathematics educators, and cognitive scientists--members of groups rarely found in the same room, much less in active collaboration on a substantial project. What brought these people together was a common interest in mathematics instruction and the hope that their combined efforts might help improve it.

Two main observations motivated these efforts. The first is that an emerging discipline called cognitive science is making significant strides in helping to understand "the way the mind works"--and in particular, to understand the nature of thinking and learning processes. Work in cognitive science would, we hoped, be of interest and use to people involved in mathematics education. The second observation is that neither cognitive science nor any of the other disciplines mentioned in the previous paragraph can provide all the ingredients necessary for successful mathematics instruction.

What are some of those ingredients? You need a deep understanding of the subject matter, for without it you may not be teaching "the right stuff." That's one reason for involving mathematicians. You need an equally deep sense of classroom reality to know what's feasible and what's pie in the sky. Classroom teachers live that reality, and mathematics educators study it; both are essential. Finally, you need an understanding of learning and thinking processes. That's where the cognitive scientists come in.

The picture, then, looks something like Fig. P.1. If contributions from all four groups are necessary, then progress in understanding mathematics teaching and learning is most likely to take place at the intersection of the . . .