PROCEEDINGS OF THE 15TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION (Vol 1)
2012
Portland, Oregon
Guided Reinvention in Ring Theory: Students Formalize Intuitive Notions of Equation Solving
Page: 1-149
The literature is replete with evidence of student difficulty in abstract algebra. In response, innovative approaches for teaching group theory have been developed, yet no corresponding methods exist for ring theory. In an effort to simultaneously fill this void and build upon Larsen’s (2009) guided reinvention efforts in group theory, I conducted a study to investigate how students might be able to reinvent fundamental notions from introductory ring theory. Rooted in the theory of Realistic Mathematics Education, this paper reports on a teaching experiment conducted in nine sessions (up to 120 minutes each) with two students, neither of whom had prior exposure to abstract algebra. Using the construct of an emergent model, I show how these students formalized their intuitive understandings of linear equation solving and used them to reinvent the definitions of ring, integral domain, and field. In particular, the milestones of the reinvention process are identified and explicated.