Exploring the relationship between proof construction and understanding of mathematics: A case study of high school students constructing proof in algebra.

摘要

Proving, the activity of constructing a proof, plays an important role in mathematics. The goal of this case study is to shed light on the possible ways proving helps or hinders individuals' understanding of algebra, where understanding is a person's mental representations and connections between them. The participants for this study are high school students who had completed the course of Geometry and who were taking or had recently taken Algebra II. Their prior exposure to proving and algebra is crucial to the investigation. In task-based interviews the participants were asked to verbalize their thinking as they complete algebra proof tasks. This study hypothesizes that proving promotes understanding and that different types of proofs affect different types of understandings. The significance of this work is it responds to recent calls in the mathematics education community for increased attention to proof and proving in algebra. The study stands to provide algebra teachers with a framework of understanding and the types of understanding affected by proving, important considerations when designing instructional strategies.