Innovations in Teaching Abstract Algebra

Abstract of article: This article describes the collaboration of three recent Ph.D.s, each teaching abstract algebra for the first time. The authors describe how they met, how they collaborated and how they addressed various pedagogical issues. In particular, they examine issues that relate to upper-division proof-writing courses. All three of the authors emphasized and encouraged active student participation in their courses. This paper provides a discussion of techniques and examples of assignments used to encourage active learning at the beginning of the course, in the classroom, outside the classroom, and through assessment. Included are notes given to students on the syllabus, some sample exploratory group activities, techniques to encourage conjecture-making and proof-building, methods for refining proof-writing, and various ways of structuring homework.

About the authors: Laurie Burton is an Associate Professor of Mathematics and Mathematics Education at Western Oregon University where she transferred after teaching for four years at Central Washington University. She is trained as a commutative ring theorist and is currently involved in the mathematics education of elementary and middle school teachers. She enjoys designing classes that utilize different educational approaches to enhance active and visual student learning. After attending the California State University at Chico as an undergraduate, she studied at the University of Oregon for her Ph.D., which she received in 1995.

sarah-marie belcastro is an Assistant Professor of Mathematics at the University of Northern Iowa. She specializes in algebraic geometry (surfaces that are hypersurfaces in toric varieties) and the mathematics of paper folding. After attending Haverford College as an undergraduate, she studied at the University of Michigan for her Ph.D., which she received in 1997. In addition to being a mathematician, sarah-marie is also a member of a dance company and thinks about feminist philosophy of science.

Moira McDermott is an Assistant Professor of Mathematics at Gustavus Adolphus College. She specializes in commutative algebra and is particularly interested in characteristic p methods and computational algebra. After attending Bryn Mawr College as an undergraduate, she studied at the University of Michigan for her Ph.D., which she received in 1996. She was a Visiting Assistant Professor at Bowdoin College for two years before joining the faculty of Gustavus.

Links mentioned in article:

• web site on writing in mathematics
• web site for on-line applets for Contemporary Abstract Algebra