Comparing Student Proofs to Explore a Structural Property in Abstract Algebra. Issue 1 (2nd January 2022)

• Record Type: Journal Article
• Authors: Melhuish, K.; Lew, K.; Hicks, M.
• Is Part Of: PRIMUS. Volume 32:Issue 1(2022)
• Page Start: 57
• Page End: 73
• Publication Date: 2022-01-02
• Subjects: Best practices in instruction -- abstract algebra -- proof presentations; Mathematics -- Study and teaching (Higher) -- Periodicals; 510.711
• DOI: 10.1080/10511970.2020.1827325
• Languages: English
• ISSNs: 1051-1970

Abstract

ABSTRACT: Connecting and comparing across student strategies has been shown to be productive for students in elementary and secondary classrooms. We have recently been working on a project converting such practices from the K–12 level to the undergraduate classroom. In this paper, we share a particular instantiation of this practice in an abstract algebra setting. Students compare across two common proof approaches to showing that the Abelian property is preserved by isomorphism. We share a complete sample lesson where students make sense of the theorem and the two proof approaches, then leverage the differences between them in order to modify both proofs and mathematical statements. We conclude with the students' reflections on the activities, and share our learnings from adapting best practices from K–12 to this new setting.