Teaching Proof by Mathematical Induction: A Preliminary Report

Abstract: This qualitative exploratory study examined two mathematicians’ approaches to teaching proof by mathematical induction (PMI) to undergraduate pre-service teachers. Data considered in the study included classroom video across three weeks of PMI instruction for each professor, an interview with each instructor, focus group interviews of three students from each professor’s class, and student solutions to common final exam PMI items. We report on the nature of the knowledge for teaching of PMI of the two instructors. Background As part of their preparation, pre-service secondary mathematics teachers take college courses such as discrete mathematics where they learn to make, test, and prove conjectures about mathematical patterns and relationships. In particular, they work with proof by mathematical induction (PMI). Such courses address the call by the National Council of Teachers of Mathematics ’ (2000) Reasoning and Proof Standard that K-12 teachers be prepared to help students create and validate (determine the truth of) logical arguments. Though several studie