PROCEEDINGS OF THE 22ND ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2019
Oklahoma City, Oklahoma
Multiple representation systems in binomial identities: An exploration of proofs that explain and proofs that only convince
Page: 774
In the mathematics education literature on proof, there is a longstanding conversation about proofs that only convince versus proofs that explain. In this theoretical report, we aim to extend both of those ideas by exploring proofs in the domain of combinatorics. As an example of an affordance of the combinatorial setting, we explore proofs of binomial identities, which offer novel insights into current distinctions and ideas in the literature about the nature of proof. We demonstrate examples of proofs that can be explanatory or convincing (or both), depending on how a person understands the claim being made (which we refer to as their preferred semantic representation system). We conclude with points of discussion and potential implications.