Secondary School Teachers’ Conceptions of Mathematical Proofs and Their Role in the Learning of Mathematics

Abstract

Mathematical proofs are a part of mathematics that involves thinking and reasoning, rather than computation. The conceptions of Ontario high school mathematics teachers, of what they consider to be mathematical proofs and the role proofs have in their teaching practice, were examined through the use of individual interviews (60 minutes per participant) and a focus group discussion (one 90 minute session). The transcripts were each analyzed through emergent coding before themes were formed from comparing codes across transcripts. The interpretive lens included looking at teacher beliefs on the nature of mathematics, roles of proofs, and mathematical authority. The participants distinguished their university experiences with mathematical proofs from their high school teaching experiences. They saw proofs through the Mathematical Process Expectation, Reasoning and Proving, and they also used proof-related words when describing how they would enact Reasoning and Proving. The participants valued the development of argumentation and sense-making, based on logic and reasoning, as an enduring life-skill, and outcome of school mathematics. The perspectives of the participants provided insight on how teachers inform their teaching practice with the Ontario Mathematics Curriculum. It also revealed some thoughts, desires, values, and struggles teachers may face when teaching mathematics.