Relating Understanding of Inverse and Identity to Engagement in Proof in Abstract Algebra

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dc.contributor.authorPlaxco, David Bryanten
dc.contributor.committeechairWawro, Meganen
dc.contributor.committeememberJohnson, Estrellaen
dc.contributor.committeememberDoolittle, Peter E.en
dc.contributor.committeememberWilkins, Jesse L. M.en
dc.contributor.committeememberNorton, Anderson H. IIIen
dc.contributor.departmentMathematicsen
dc.date.accessioned2015-09-18T20:06:35Zen
dc.date.available2015-09-18T20:06:35Zen
dc.date.issued2015-09-05en
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.en
dc.description.degreePh. D.en
dc.format.mediumETDen
dc.identifier.othervt_gsexam:6227en
dc.identifier.urihttp://hdl.handle.net/10919/56587en
dc.publisherVirginia Techen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectMathematical Proofen
dc.subjectConceptual Understandingen
dc.subjectAbstract Algebraen
dc.subjectUndergraduate Mathematics Educationen
dc.titleRelating Understanding of Inverse and Identity to Engagement in Proof in Abstract Algebraen
dc.typeDissertationen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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