DUALITY, AMBIGUITY, AND FLEXIBILITY - A PROCEPTUAL VIEW OF SIMPLE ARITHMETIC
UNSPECIFIED. (1994) DUALITY, AMBIGUITY, AND FLEXIBILITY - A PROCEPTUAL VIEW OF SIMPLE ARITHMETIC. JOURNAL FOR RESEARCH IN MATHEMATICS EDUCATION, 25 (2). pp. 116-140. ISSN 0021-8251Full text not available from this repository.
In this paper we consider the duality between process and concept in mathematics, in particular, using the same symbolism to represent both a process (such as the addition of two numbers 3 + 2) and the product of that process (the sum 3 + 2). The ambiguity of notation allows the successful thinker the flexibility in thought to move between the process to carry out a mathematical task and the concept to be mentally manipulated as part of a wider mental schema. Symbolism that inherently represents the amalgam of process/concept ambiguity we call a ''procept.'' We hypothesize that the successful mathematical thinker uses a mental structure that is manifest in the ability to think proceptually. We give empirical evidence from simple arithmetic to support the hypothesis that there is a qualitatively different kind of mathematical thought displayed by the more able thinker compared to that of the less able one. The less able are doing a more difficult form of mathematics, which eventually causes a divergence in performance between them and their more successful peers.
|Item Type:||Journal Article|
|Journal or Publication Title:||JOURNAL FOR RESEARCH IN MATHEMATICS EDUCATION|
|Publisher:||NATL COUNC TEACH MATH|
|Number of Pages:||25|
|Page Range:||pp. 116-140|
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