RUME 14 (Volume 4)
2011
Portland, Oregon
EVALUATING MATHEMATICAL QUALITY OF INSTRUCTION IN ADVANCED MATHEMATICS COURSES BY EXAMINING THE ENACTED EXAMPLE SPACE
Page: 71
In advanced undergraduate mathematics, students are expected to make sense of abstract definitions of mathematical concepts, to create conjectures about those concepts, and to write proofs and exhibit counter-examples of these abstract concepts. In all of these actions, students must be able to draw upon a rich store of examples in order to make meaningful progress. We have created a methodology to evaluate what students might learn from a particular course by describing and analyzing the enacted example space (Mason & Watson, 2008) for a particular concept. This method will both give a means to create testable hypotheses about individual student learning as well as provide a way to compare disparate pedagogical treatments of the same content. Here, we describe and assess the enacted example space by studying the teaching of abstract algebra.