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A theory of developing competence with written mathematical symbols

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Abstract

The paper presents a theory of how competence with written mathematical symbols develops. The theory proposes a succession of cognitive processes that cumulate to yield competence: (1) connecting individual symbols with referents; (2) developing symbol manipulation procedures; (3a) elaborating procedures for symbols; (3b) routinizing the procedures for manipulating symbols; and (4) using the symbols and rules as referents for building more abstract symbol systems. Each process must be engaged, and each must be engaged in sequence. Arguments in support of the theory are drawn from the history, philosophy and psychology of mathematics. The theory has implications for the sequencing and the content of instructional activities.

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Authors and Affiliations

  1. College of Education, University of Delaware, 19716, Newark, Delaware, U.S.A.

    James Hiebert

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  1. James Hiebert
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The writing of this paper was supported by a grant from the National Science Foundation (MDR 8651552). However, the opinions are those of the author rather than the Foundation.

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Hiebert, J. A theory of developing competence with written mathematical symbols. Educ Stud Math 19, 333–355 (1988). https://doi.org/10.1007/BF00312451

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