A Joint Perspective on the Idea of Representation in Learning and Doing Mathematics

Abstract

For some time each of us in his own way has been developing the concept of representation in the psychology of mathematical learning and problem solving (Goldin, 1982, 1983, 1987, 1988a, 1988b, 1990, 1992a, 1992b; Goldin & Herscovics, 1991a, 1991b; Kaput, 1979, 1983, 1985, 1987, 1989, 1991, 1992, 1993). In this chapter we explore the compatibility of our ideas, and begin to develop a joint perspective-one that we hope can lay a foundation for future theoretical work in mathematics education based on representations and symbol systems. We believe that the constructs offered here provide a sound basis for further development.

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