Innovations in Teaching Abstract Algebra

Abstract of article: In this paper we describe an innovative approach to teaching abstract algebra characterized by collaborative learning and special computer activities. This approach eschews the lecture method, advocates a constructivist approach to learning, embraces cooperative learning, and makes computers and a mathematical programming language, ISETL, an integral part of the learning process. In the computer laboratory, teams of students use ISETL to construct and internalize mathematical ideas. In the classroom, activities focus on conjectures and shared explorations. In addition to pedagogical considerations, we discuss practical issues related to adoption of these innovative methods.

About the author: Robert Smith is a Professor of Mathematics and Statistics at Miami University and the Director of the Junior Scholars Program, a pre-college program for high school students. He received a B.S. from Morgan State College in 1963 and graduate degrees from Pennsylvania State University in 1967 and 1969. While he has been at Miami since 1969, his career has been punctuated with visiting positions in the U.S. and Australia. Since 1987, he has been involved in numerous innovative computer-based teaching projects. Perhaps the most fascinating of these is teaching abstract algebra using ISETL (a mathematical programming language) and cooperative learning.

Software used: ISETL

Files to download: (These are all pdf files. Go to www.adobe.com to download Acrobat Reader to read these if your browser does not automatically open a file.)

• 421 Course Requirements and Operating Procedure
• Course Philosophy for Learning Abstract Algebra with ISETL
• Math 421, Section A Information Form
• Learning Abstract Algebra with ISETL