RUME 28
2026
Alexandria, Virginia
A Covariational Lens for Proofwriting in Undergraduate Mathematics
Page: 1440
We examine how undergraduate students navigate proof writing through two complementary “images of activity”: puzzle-piece (“chunky”) assembly and flow (“smooth”) throughlines, and how students transition between them while producing a final, coherent proof write-up. Adapting the chunky/smooth covariational lens (Castillo-Garsow, Johnson, & Moore) from modeling to writing proofs, we examine what episode types arise during student proofwriting, what triggers students’ commitment to and transition between these two images, and how these ideas are visible (or not) in the finished proof. This mixed-method research is conducted using exploratory 40-60 minute think-aloud interviews in which students work two multi-route proof tasks, with a follow-up survey to examine participants’ beliefs about proofwriting and elements of a good proof. Participants are sampled across upper division undergraduate proof-based courses. Results aim to characterize commitment triggers and stalls and to inform instruction that scaffolds productive shifts in proofwriting.