PROCEEDINGS OF THE 15TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION (Vol 2)
2012
Portland, Oregon
Assessing Proof Schemes: An Interesting “Proof” By Mathematical Induction
Page: 2-463
Students face an array of difficulties when they learn to understand and write proofs by mathematical induction (MI). This paper describes the responses of students in an inquiry-based (IBL) number theory course when presented with a false proof by MI asserting that all humans are the same height. The proof schemes of Harel, Sowder and others provided a lens through which to analyze student responses. Some were consistent with the misconceptions already in the literature on MI, while others may be especially revealing of IBL students’ ways of understanding mathematical proof in general and MI in particular.