PROCEEDINGS OF THE 23RD ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2020
Boston, Massachusetts
Folding back in the Arzel`a-Ascoli theorem
Page: 475
While learning is often characterized as a process of abstractions from robust understandings, students’ reasoning in advanced contexts can be a more dynamic process of reflection across multiple layers of complex cognitive structures. To explore the ways that real analysis students’ understandings of abstract mathematical concepts evolve in the context of multi-faceted proofs, we observed students’ attempts to prove the Arzel`a-Ascoli Theorem. We describe the understandings from which students built to engage in more complex reasoning and demonstrate their folding back (Pirie & Kieren, 1994) to facilitate the co-evolution of their foundational and advanced understandings.