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

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.