Comparing Student Proofs to Explore a Structural Property in Abstract Algebra
Saved in:
| Title: | Comparing Student Proofs to Explore a Structural Property in Abstract Algebra |
|---|---|
| Language: | English |
| Authors: | Melhuish, K. (ORCID |
| Source: | PRIMUS. 2022 32(1):57-73. |
| Availability: | Taylor & Francis. Available from: Taylor & Francis, Ltd. 530 Walnut Street Suite 850, Philadelphia, PA 19106. Tel: 800-354-1420; Tel: 215-625-8900; Fax: 215-207-0050; Web site: http://www.tandf.co.uk/journals |
| Peer Reviewed: | Y |
| Page Count: | 17 |
| Publication Date: | 2022 |
| Sponsoring Agency: | National Science Foundation (NSF) |
| Contract Number: | IUSE1836559 |
| Document Type: | Journal Articles Reports - Descriptive |
| Education Level: | Elementary Secondary Education Higher Education Postsecondary Education |
| Descriptors: | Mathematics Instruction, Teaching Methods, Best Practices, Algebra, Mathematical Logic, Validity, Elementary Secondary Education, Higher Education, Metacognition |
| DOI: | 10.1080/10511970.2020.1827325 |
| ISSN: | 1051-1970 |
| 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. |
| Abstractor: | As Provided |
| Entry Date: | 2022 |
| Accession Number: | EJ1322221 |
| Database: | ERIC |
| 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. |
|---|---|
| ISSN: | 1051-1970 |
| DOI: | 10.1080/10511970.2020.1827325 |
