PROCEEDINGS OF THE 22ND ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2019
Oklahoma City, Oklahoma
Monster-barring as a catalyst for connecting secondary algebra to abstract algebra
Page: 138
This proposal reports on a teaching experiment in which a pair of prospective secondary mathematics teachers leverage their knowledge of secondary algebra in order to develop effective understandings of the concepts of zero-divisors and the zero-product property (ZPP) in abstract algebra. A critical step in the learning trajectory involved the outright rejection of the legitimacy of zero-divisors as counterexamples to the ZPP, an activity known as monster-barring (Lakatos, 1976; Larsen & Zandieh, 2008). This monster-barring activity was then productively repurposed as a meaningful way for the students to distinguish between types of abstract algebraic structures (namely, rings that are integral domains vs. rings that are not). The examples of student activity in this teaching experiment emphasize the importance of identifying, attempting to understand, and leveraging student thinking, even when it initially appears to be counterproductive.