PROCEEDINGS OF THE 23RD ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2020
Boston, Massachusetts
Student mathematical activity during analogical reasoning in abstract algebra
Page: 1010
This paper examines the mathematical activity of two students as they engage in reasoning about topics in ring theory by analogy with topics in group theory. Analogies are represented by mappings between a source and target domain (Gentner, 1983). Participants were given task-based interviews, each focused upon a particular structure from ring theory: rings, subrings, ring homomorphisms, and quotient rings. Techniques from grounded theory were utilized to analyze the interview transcripts with the goal of interpreting and describing the mathematical activity of the students. Preliminary results indicate that there are three main categories of activity: foregrounding the source or target domain, focusing on similarities or differences, and which mapped aspects of the domains are the focus of the reasoning. “Pathways” are identified as a way to capture the dynamic nature of students’ reasoning by analogy in abstract algebra.