Cognitive Science and Mathematics Education

By Alan H. Schoenfeld | Go to book overview

2
Foundations of Cognitive Theory and Research for Mathematics Problem-Solving Instruction*

Edward A. Silver Department of Mathematical Sciences San Diego State University

In recent years, mathematics educators have become more interested in increasing students' ability to use and apply the mathematical knowledge learned in school for solving problems both within and outside of the school setting. The initial emphasis in mathematics was on "problem solving," which included the solution of non-routine problems as well as that of routine textbook exercises. More recently, as the emphasis in problem solving has gained wide acceptance, educators have begun to stress the solution of "real-world" problems, that is, problems with some relevance to the lives of adults or students and with solutions involving the use of some mathematical knowledge.

In the past two decades, the interest of practitioners in problem solving and real-world problems has been supplemented by a considerable amount of research on the learning of mathematics and the use of mathematical knowledge to solve problems. Much of the research has been conducted by cognitive psychologists, who seek to develop and validate theories of human learning and problem solving, and mathematics educators, who seek to understand the nature of the cognitive interaction between students and the mathematical subject matter they study and the problems they solve. This paper summarizes briefly some of the most salient features of the cognitive theory and research and draws from that research a few suggestions for designing mathematics instruction that will

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*
An earlier version of this paper was presented at the annual meeting of the American Educational Research Association, Chicago, IL, April 1985.

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