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Prospective Teachers’ Conceptions of Proof Comprehension: Revisiting a Proof of the Pythagorean Theorem

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Abstract

A significant body of research literature in mathematics education attends to mathematical proofs. However, scant research attends to proof comprehension, which is the focus of this study. We examine perspective secondary teachers’ conceptions of what constitutes comprehension of a given proof and their ideas of how students’ comprehension can be evaluated. These are explored using a relatively novel approach, scripted dialogues. The analysis utilizes and expands the proof comprehension framework of Mejia-Ramos, Fuller, Weber, Rhoads & Samkoff (Educational Studies in Mathematics, 79, 3–18, 2012). We suggest that this expansion is applicable to other studies on proof comprehension.

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Notes

  1. Use of the word “surface” to describe these modes of assessing proof comprehension metaphorically views proof as a building up of results, based on mathematical concepts and definitions. Thus, the word surface should not be interpreted to mean not essential to understanding a particular proof as with the phrase “he only has a surface understanding of the course.” Rather, the word should be viewed as consistent with the idiom “scratched the surface.” Thus, it indicates prerequisite base level knowledge and does not imply anything about what other levels exist.

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Zazkis, D., Zazkis, R. Prospective Teachers’ Conceptions of Proof Comprehension: Revisiting a Proof of the Pythagorean Theorem. Int J of Sci and Math Educ 14, 777–803 (2016). https://doi.org/10.1007/s10763-014-9595-0

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  • DOI: https://doi.org/10.1007/s10763-014-9595-0

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