This dissertation investigates students' development of the notion of mathematical proof in a Mathematics for Liberal Arts course through the lens of Combinatorial Game Theory. There has been extensive research on the cognitive processes of mathematics majors as they learn about proof; however, much less research has been done on non-mathematics majors, especially in a liberal arts setting. This research aims to contribute toward filling that gap.

Students completed an inquiry-based group activity in which they played and analyzed a partizan combinatorial game called "Stacks" and used a set of three axioms to assign numerical values to positions, making conjectures and developing proofs. After the activity, nine students participated in semi-structured interviews that explored their reasoning in greater depth. These interviews were analyzed using Dubinsky's Action-Process-Object-Schema Theory and Harel and Sowder's Proof Schemes frameworks, which were combined to provide a more in-depth picture of students' cognitive argumentation (proof) structures as they explored the Stacks game.

The study's findings suggest a correspondence between students' cognitive constructions of game strategy and their modes of justification and suggests ways that proof schemes can be used to support the progression of students' abstract reasoning. The study concludes with recommendations for using combinatorial games to teach about mathematical proof in a liberal arts setting, including the development of a preliminary genetic decomposition of winning strategy.