PROCEEDINGS OF THE 20TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2017
San Diego, California
Students’ conceptions of mappings in abstract algebra
Page: 259
In an effort to understand ways students approach constructing homomorphisms and isomorphisms between groups, six undergraduate math and engineering students in a lecture- based introductory abstract algebra course were interviewed. These students experienced varied success in creating isomorphisms and homomorphisms, which allowed both successful techniques for map creation and stumbling blocks to map creation to emerge from the data. Additionally, a genetic decomposition for homomorphism is outlined and students’ mental constructions of both homomorphism and isomorphism are discussed. Finally, students’ conceptual metaphors for homomorphic and isomorphic mappings are examined. Combining these three analyses paints a picture of the interaction between students’ knowledge of properties of groups and mappings and their flexibility in creating mental images while interpreting those properties.