Undergraduate mathematics students’ at-home exploration of a prove-or-disprove task

A common genre of task in proof-centered mathematics courses involves prompting students to evaluate the veracity of a mathematical claim by either proving the claim, or providing a proof that the claim is false (disproving the claim). The way in which students interact with these prove-or-disprove tasks is not well understood. We examine students’ at-home work as a way of learning about their processes of generating disproofs of claims. In particular, we study the interactions between example/counterexample generation activities, attempts to prove the (false) claim, and attempts to prove related results.