PROCEEDINGS OF THE 21ST ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2018
San Diego, California
An Initial Exploration of Students’ Reasoning about Combinatorial Proof
Page: 450
Combinatorial proof involves proving relationships among expressions by arguing that the two expressions count sets with the same cardinality. It is an important topic because it is a kind of proof that has not been studied extensively, yet it represents an aspect of combinatorial reasoning that students should develop. In this paper, we report on data from two students who participated in a paired teaching experiment during which they solved tasks involving combinatorial proof. We highlight some productive aspects of their conceptions of combinatorial proof, and we also report on some pedagogical interventions that seemed to help students progress with successful combinatorial proving. We also argue that combinatorial proofs may naturally tend to be semantic rather than syntactic proof constructions (Weber & Alcock, 2004).