PROCEEDINGS OF THE 20TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2017
San Diego, California
Students’ conceptions of mappings in abstract algebra
Page: 863
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. Some successful techniques for determining if groups were isomorphic included checking the orders of the groups, looking for invertible maps between groups, and determining the identity element and orders of elements of each group. Successful strategies for approaching the creation of homomorphisms included checking if the groups were isomorphic, seeing if a proposed map would preserve closure, and using strategic trial and error. Stumbling blocks included the inappropriate use of definitions, an inability to interpret definitions, and misunderstanding the distinction between the names and roles of elements in different groups.