Learning from Their Mistakes: Using Students' Incorrect Proofs as a Pedagogical Tool

Abstract

We describe a system whereby students in a proof-based mathematics course review and critique the proofs written by their peers. This peer review system—which is roughly modeled on the way peer reviews are used in teaching college composition—requires students to read mathematics more actively than they might if only reading proofs that are known to be correct. In this way, the potential for mistakes in the students' work is used as a pedagogical tool that can benefit the entire class.

Keywords:

• Peer feedback
• active reading of proofs
• critical reading of proofs
• incorrect proofs

ACKNOWLEDGMENTS

The authors would like to thank the reviewers of this article for their very careful reading and thoughtful comments. The resulting article has benefited greatly from their efforts.