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DUALITY, AMBIGUITY, AND FLEXIBILITY - A PROCEPTUAL VIEW OF SIMPLE ARITHMETIC
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UNSPECIFIED (1994) DUALITY, AMBIGUITY, AND FLEXIBILITY - A PROCEPTUAL VIEW OF SIMPLE ARITHMETIC. JOURNAL FOR RESEARCH IN MATHEMATICS EDUCATION, 25 (2). pp. 116-140.
Research output not available from this repository, contact author.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 | ||||
| Official Date: | March 1994 | ||||
| Dates: |
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| Volume: | 25 | ||||
| Number: | 2 | ||||
| Number of Pages: | 25 | ||||
| Page Range: | pp. 116-140 | ||||
| Publication Status: | Published |
Data sourced from Thomson Reuters' Web of Knowledge
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