UNSPECIFIED (1994) DUALITY, AMBIGUITY, AND FLEXIBILITY - A PROCEPTUAL VIEW OF SIMPLE ARITHMETIC. JOURNAL FOR RESEARCH IN MATHEMATICS EDUCATION, 25 (2). pp. 116-140. ISSN 0021-8251

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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.

Item Type:	Journal Article
Subjects:	L Education
Journal or Publication Title:	JOURNAL FOR RESEARCH IN MATHEMATICS EDUCATION
Publisher:	NATL COUNC TEACH MATH
ISSN:	0021-8251
Date:	March 1994
Volume:	25
Number:	2
Number of Pages:	25
Page Range:	pp. 116-140
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/20762

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