Duality, Ambiguity, and Flexibility: A "Proceptual" View of Simple Arithmetic
- 1 March 1994
- journal article
- research article
- Published by National Council of Teachers of Mathematics in Journal for Research in Mathematics Education
- Vol. 25 (2), 116-140
- https://doi.org/10.2307/749505
Abstract
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.This publication has 10 references indexed in Scilit:
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