Abstract
A theory of expertise has developed over the last few years on the basis of research into expert-novice differences. This research has shown an impressive degree of consistency in a variety of fields of knowledge and is beginning now to have direct implications for the teaching of mathematics and related disciplines. Research data, generated in part by current theories of expertise, call into question many long-held assumptions and procedures. We suggest that some views of mathematics and the way it should be taught owe more to tradition than to our current knowledge of cognitive processes. The purpose of this paper is to outline the theory, describe some of the associated experimental findings, and indicate the consequences of those findings for educational practice in mathematics.
Published Version
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