Insight into Student Conceptions of Proof

Steven Daniel Lauzon, Brigham Young University


The emphasis of undergraduate mathematics content is centered around abstract reasoning and proof, whereas students' pre-college mathematical experiences typically give them limited exposure to these concepts. Not surprisingly, many students struggle to make the transition to undergraduate mathematics in their first course on mathematical proof, known as a bridge course. In the process of this study, eight students of varied backgrounds were interviewed before during and after their bridge course at BYU. By combining the proof scheme frameworks of Harel and Sowder (1998) and Ko and Knuth (2009), I analyzed and categorized students’ initial proof schemes, observed their development throughout the semester, and their proof schemes upon completing the bridge course. It was found that the proof schemes used by the students improved only in avoiding empirical proofs after the initial interviews. Several instances of ritual proof schemes used to generate adequate proofs were found, calling into question the goals of the bridge course. Additionally, it was found that students’ proof understanding, production, and appreciation may not necessarily coincide with one another, calling into question this hypothesis from Harel and Sowder (1998).