A Modified Discovery Approach to Teaching and Learning Abstract Algebra
A Modified Discovery Approach to Teaching and Learning Abstract Algebra
Steve Benson with Brad Findell
Abstract of article: In this article, we describe an abstract algebra class taught at the University of New Hampshire. Rather than the traditional lecture/discussion model, the course was taught using a modified discovery approach in which students worked in cooperative groups. Activities were designed to encourage students to think through, debate, and come to a consensus about the essential concepts and methods of group theory. With this approach, the instructor was able to observe students working in class, ascertain their understanding, and plan subsequent lessons based on these observations. In addition to a general overview of the course, specific significant events are described and some suggestions for future implementations are provided.
About the authors: Steve Benson received his Ph.D. in 1988 from the University of Illinois, working under the direction of Leon McCulloh in algebraic number theory. Having held faculty positions at St. Olaf College, Santa Clara University, University of New Hampshire, and University of Wisconsin -- Oshkosh, he is currently a Senior Research Associate at Education Development Center, in Newton, Massachusetts and a Co-Director of the Master of Science for Teachers program at the University of New Hampshire.
Brad Findell earned an M.A. in mathematics from Boston University in 1990 and recently completed his Ph.D. in mathematics education at the University of New Hampshire under the direction of Joan Ferrini-Mundy and Karen Graham. He is now in the Mathematics Education Department at the University of Georgia. From 1997 to 2001, he was at the National Research Council in Washington, DC, working for the Mathematical Sciences Education Board (MSEB) and on various projects in mathematics education. He served as editor of High School Mathematics at Work (MSEB, 1998), and is coeditor, with Jeremy Kilpatrick and Jane Swafford, of Adding It Up: Helping Children Learn Mathematics (2001), both published by the National Academy Press.
Software used: Mathematica and AbstractAlgebra
Files to download: Accompanying this article, we have sample problem sets, quizzes, and exams, as mentioned in the article. These are available in Latex format or pdf format. These can be found below.