1. Conditions for proving by mathematical induction to be explanatory
- Author
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Anne Watson, James T. Sandefur, and Gabriel J. Stylianides
- Subjects
Process (engineering) ,Applied Mathematics ,05 social sciences ,Final product ,050301 education ,06 humanities and the arts ,Gas meter prover ,0603 philosophy, ethics and religion ,Education ,Mathematics (miscellaneous) ,060302 philosophy ,Mathematical induction ,Calculus ,0503 education ,Algorithm ,Mathematics - Abstract
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.
- Published
- 2016