For our second colloquium talk, we will have Dr. Keith Weber from Rutgers University.
Proof Comprehension in Advanced Mathematics
Thursday, October 17th; 3:00-4:00 PM, Aderhold _____
In advanced mathematics courses, students spend a substantial amount of time reading propositions and their proofs. Yet research suggests that students often learn little from reading these proofs. In this presentation, I address four questions about students’ reading of mathematical proof: (1) Why do students have so much difficulty understanding a proof? (2) What does it mean to understand a proof and how can this understanding be assessed? (3) What strategies should students use when reading a proof to facilitate comprehension? (4) What beliefs do students hold about their responsibilities in proof reading? These questions are addressed using qualitative and quantitative data. Initially task-based interviews with students and interviews with mathematicians were used to generate hypotheses about what students should do, but do not do, when reading a proof. A survey was then used to demonstrate statistically reliable differences in mathematics majors’ approaches to proof reading and the approaches that mathematicians would like them to take.