PROCEEDINGS OF THE 17TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2014
Denver, Colorado
The Selection and Use of Examples by Algebraists: An Exploratory Study
Page: 503
This paper reports on an exploratory study of 10 algebraists designed to investigate the reasoning behind their selection of examples for their own teaching and research. Variation theory provided a lens with which to analyze the algebraists’ goals for their collections of examples and to speculate about the resulting pedagogical implications. Though findings from this exploratory study should be regarded only as preliminary and in need of further justification, our results provide some initial evidence that mathematicians use a relatively small number of very well- chosen classes of examples in both their teaching and their research (suggesting that this might be a useful pedagogical strategy for students as well). We also report on the examples of groups and rings that the algebraists deemed to be the most important for students of introductory abstract algebra.