RUME 14 (Volume 1)
2011
Portland, Oregon
BEST PAPER AWARD RECIPIENT: ANALYZING THE TEACHING OF ADVANCED MATHEMATICS COURSES VIA THE ENACTED EXAMPLE SPACE
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In advanced undergraduate mathematics, students are expected to make sense of abstract definitions of mathematical concepts, create conjectures about those concepts, write proofs and exhibit counterexamples of these abstract concepts. In all of these actions, students may draw upon a rich store of examples in order to make meaningful progress. We have drawn on the concept of an example space (Watson & Mason, 2008) for a particular concept. We adapted it and defined the concepts of example neighborhood, methods of example construction, and the functions of examples to create a methodology for studying the teaching of proof-based courses. We demonstrate our method via a case study from an undergraduate abstract algebra course.