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Readings in Cooperative Learning for Undergraduate Mathematics

Ed Dubinsky, David Mathews and Barbara E. Reynolds, editors
Mathematical Association of America
Publication Date: 
Number of Pages: 
MAA Notes 37
[Reviewed by
Agnes Tuska
, on

In 1995, the Mathematical Association of America formed Project CLUME (Cooperative Learning in Undergraduate Mathematics Education) to disseminate ideas about cooperative learning among collegiate mathematics faculty. Project CLUME activities include conducting residential summer workshops, and running courses via the World Wide Web. The 17 papers in the Readings in Cooperative Learning for Undergraduate Mathematics anthology were field-tested and selected for inclusion based on their effectiveness in such faculty development courses.

The papers are organized into three parts. Part 1 covers constructivism and the teacher's role in the classroom. Part 2 discusses the effectiveness of cooperative learning, supported by educational research. Finally, the focus of Part 3 is on implementation issues.

The papers were originally published in the 1980's and 1990's. Each paper is preceded by short comments and discussion questions posed by the editors. Many of the questions seem to have the sole purpose of checking whether a person really read through the paper. However, there are a few questions which I believe could (and most probably did) generate excellent discussions among readers.

While most papers have long reference lists of their own, the book concludes with a valuable annotated bibliography of science, mathematics, engineering and technology resources in higher education.

Although the need for the incorporation of learning groups into college level classes was clearly argued for in some of the articles, such as Finkel and Monk's "Teachers and Learning Groups: Dissolution of the Atlas Complex" (published in 1983, included in Part 1), there appears to be insufficient research in this area. Most of the studies discussed in Part 2 as research findings are based on research at elementary or high school level, and/or in subject areas other than mathematics. How well would those results and conclusions transfer to undergraduate mathematics, and how valid is it to emphasize in the book title that it is on undergraduate mathematics if more than half of the papers discuss something else? The reader should decide. However, since I, like many other college mathematics faculty, deal with the pre-service education of teachers, learning the facts about precollege teaching results is also very useful for me.

If the reader has only limited time, and is interested only in getting an idea about what, why, and how could he or she do differently and better in an undergraduate mathematics classroom, I recommend reading the above mentioned paper of Finkel and Monk together with Neil Davidson's article on the small-group discovery method in secondary- and college-level mathematics. The latter, after discussing effective classroom practices, procedures, and interactions derived from educational philosophy and social psychology, also spends time on sharing unforeseen misconceptions, difficulties, and surprises regarding cooperative learning.

Overall, I give 1.2 times the square root of 2 minus epsilon thumbs up to this book.

Agnes Tuska ( agnes@math.math.CSUFresno.EDU) is an assistant professor at California State University, Fresno. Her main professional interests are secondary teacher education and the history of mathematics.

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