Theories of Mathematical Learning

By International Congress on Mathematical Education; Leslie P. Steffe et al. | Go to book overview

23
A Joint Perspective on the Idea of Representation in Learning and Doing Mathematics1

Gerald A. Goldin Rutgers University

James J. Kaput University of Massachusetts/Dartmouth

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.

In approaching the issue of representation, we recognize the complexity and magnitude of the challenge. On the one hand, there is a long history of attempts to make sense of the many forms taken by representational activity, attempts that have achieved various degrees of success; on the other hand, some mathematics education researchers reject the construct of representation entirely (e.g., Marton and Neuman, chapter 19, this volume). Nonetheless, we feel that the sharpening of certain notions related to representation, and development of a way to discuss them more systematically and precisely, can greatly benefit the field of mathematics education--and can clarify some of the points of disagreement among researchers.

We also recognize that making a commitment to particular ways of theorizing

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1
This chapter was substantially written during 1991-1992, with final revisions in 1994. The authors' current work extends many of the ideas introduced here and will appear in subsequent publications.

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