Virginia Tech
Relating Understanding of Inverse and Identity to Engagement in Proof in Abstract Algebra
Abstract
dc:description.abstractIn this research, I set out to elucidate the relationships that might exist between students' conceptual understanding upon which they draw in their proof activity. I explore these relationships using data from individual interviews with three students from a junior-level Modern Algebra course. Each phase of analysis was iterative, consisting of iterative coding drawing on grounded theory methodology (Charmaz, 2000, 2006; Glaser and Strauss, 1967). In the first phase, I analyzed the participants' interview responses to model their conceptual understanding by drawing on the form/function framework (Saxe, et al., 1998). I then analyzed the participants proof activity using Aberdein's (2006a, 2006b) extension of Toulmin's (1969) model of argumentation. Finally, I analyzed across participants' proofs to analyze emerging patterns of relationships between the models of participants' understanding of identity and inverse and the participants' proof activity. These analyses contributed to the development of three emerging constructs: form shifts in service of sense-making, re-claiming, and lemma generation. These three constructs provide insight into how conceptual understanding relates to proof activity.
Degree
thesis:*- Name thesis:degree_name
- Ph. D.
- Level thesis:degree_level
- doctoral
- Discipline thesis:degree_discipline
- Mathematics
- Department dc:contributor.department
- Mathematics
- Grantor dc:publisher
- Virginia Tech
- Year dc:date.issued
- 2015
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Plaxco, David Bryant
- Chair dc:contributor.committeechair
-
- Wawro, Megan
- Committee members dc:contributor.committeemember
-
- Johnson, Estrella
- Doolittle, Peter E.
- Wilkins, Jesse L. M.
- Norton, Anderson H. III
Subjects
dc:subject × 4Rights
dc:rights- Statement dc:rights
-
- In Copyright
- Licence dc:rights.uri
Identifiers
dc:identifier.*- Dc Identifier Other
- vt_gsexam:6227
- OAI identifier oai:identifier
- oai:vtechworks.lib.vt.edu:10919/56587