PROCEEDINGS OF THE 15TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION (Vol 2)
2012
Portland, Oregon
A Guided Reinvention of the Definitions of Ring, Integral Domain, and Field
Page: 2-380
The struggles of undergraduate students with their first course in abstract algebra are well-documented (Dubinsky, Dautermann, Leron, & Zazkis, 1994; Hazzan & Leron, 1996; Leron & Dubinsky, 1995). The course is often the first encounter with higher mathematics for many students; in particular, they are exposed to algebraic structures which form unifying threads throughout the rest of mathematics (Edwards & Brenton, 1999). Unfortunately, many students struggle with this transition to higher mathematics and fail to understand even the subject’s most basic and fundamental concepts (Dubinsky et al, 1994). As a result, many students who are initially interested in mathematics experience a complete reversal of opinion and become indifferent or disengaged. Leron and Dubinsky (1995) even go so far as to state that “[the] teaching of abstract algebra is a disaster, and this remains true almost independently of the quality of the lectures” (p. 227). To this end, alternative approaches to teaching abstract algebra must be explored.