Conditions for proving by mathematical induction to be explanatory

• We focus on the proof method of mathematical induction.
• We examine conditions for proving by induction to be explanatory for provers.
• We studied undergraduate mathematics students working in trios on specially designed problems.
• Students used recursive reasoning to illuminate the truth of statements before using induction to prove them.
• Problem formulation and students’ experience with the use of examples played a major role.

In this paper we consider proving to be the activity in search for a proof, whereby proof is the final product of this activity that meets certain criteria. Although there has been considerable research attention on the functions of proof (e.g., explanation), there has been less explicit attention in the literature on those same functions arising in the proving process. Our aim is to identify conditions for proving by mathematical induction to be explanatory for the prover. To identify such conditions, we analyze videos of undergraduate mathematics students working on specially designed problems. Specifically, we examine the role played by: the problem formulation, students’ experience with the utility of examples in proving, and students’ ability to recognize and apply mathematical induction as an appropriate method in their explorations. We conclude that particular combinations of these aspects make it more likely that proving by induction will be explanatory for the prover.