From the Book Shelves

In this issue’s From the Bookshelf, our first book concerns the use of CL in the teaching of undergraduate mathematics. The second book traces the history of the co-operative movement in the UK and later around the world. Books 3 and 4 are both written by Phil Cuseo who offers important insights in CL and its application.

1.          Rogers, E. C., Reynolds, B. E., Davidson, N. A. [Email: Neil_A_DAVIDSON@umail.umd.edu], & Thomas, A. D. (Eds.). (2001). Cooperative learning in undergraduate mathematics: Issues that matter and strategies that work. MAA Notes, volume 55. Mathematical Association of America, 2001. Paperback, 150 pp., $31.50 ($23.95 to MAA members).
ISBN 0-88485-166-0. 

Reviewed by Andrew Perry (andy@perry.net), Assistant Professor of Mathematics at Springfield College in Springfield, MA, USA. (Reprinted by permission from MAA Online - http://www.maa.org/pubs/books/nte55.html.

This book, volume 55 of the MAA (Mathematical Association of America) Notes series, is a magnificent work. Seventeen authors and four editors joined forces to summarize the collective wisdom of nearly 150 mathematics faculty who have participated in the MAA Project CLUME (Cooperative Learning in Undergraduate Mathematics Education) workshops, which began in 1995. [Editor’s note: Project CLUME has been declared a success and ended by MAA.] The authors also draw upon results of the official CLUME survey, which was administered in 1997 and to which 114 mathematics instructors responded.

The main body of the book consists of 100 pages divided into seven chapters. Each chapter deals with a particular topic in the cooperative learning of mathematics and is written by multiple authors. One might expect that this team style would lead to clumsy and disjointed writing. The authors have, however, done a masterful job in coordinating their efforts, being very thorough yet avoiding redundancies. Clearly, these authors are themselves good collaborators. Every chapter was "written and re-written by small groups of authors and then critiqued by the larger group," and it took nearly four years to complete the volume.

The first chapter gives an overview of cooperative learning in mathematics. Why should an instructor use cooperative learning at all? A host of reasons are offered. First, small groups offer a "social support mechanism", and students often feel comfortable asking questions of their peers which they wouldn't ask the instructor. Another reason is that students are more likely to see multiple correct ways of approaching a problem. In a group, students may be able to solve problems which are more complex and thought-provoking than the problems they can solve individually. These reasons and others are analyzed in enough depth to be enlightening without overwhelming the reader in a sea of details. Another particularly interesting feature of this chapter is a series of case studies in large scale implementations of cooperative learning in math by colleges and universities. Although one university found that "the fact that students work together on problems seems to detract from their ability to solve problems individually on tests", most institutions have apparently been very successful in implementing these programs.

Chapter Two is entirely devoted to "practical ways to develop a social climate conducive to cooperative learning in the classroom". For example, how should groups of students be formed: by the students themselves, by random selection, or should the instructor choose the groups? Instructors can choose groups based on math ability (measured perhaps by standardized test scores or previous math grades), or compatible class schedules, or even by personality inventories such as the Meyers-Briggs test. Pros and cons of each method are discussed. In this case, the authors conclude that there is widespread support among math instructors for each of the three major methods of group selection. Occasionally the authors do give specific advice (for example, there is wide consensus that five students in a problem solving group is too many) but in general they are refreshingly nonjudgmental and very slow to impose their own preferences on the reader.

Chapter Three describes many classroom strategies for cooperative learning. For example, the "Groups/Pairs Exchange" method works like so: "Each group or pair of students is asked to investigate a mathematical object. The example is then passed along to a second group or pair who responds in some way to the item received. The response is then returned to the original pair and the results are reviewed. The second group can then pass their work to a third group, which does some further work. If appropriate, they can continue to a fourth group, etc." Sample exercises are provided for each of the most commonly taught college math classes: math for elementary education, statistics, discrete math, precalculus, calculus, linear algebra, and other courses. The many specific examples make this book really practical, and I would think that any instructor wanting to try these strategies could find ideas for several activities which are appropriate for his or her classes.

There is a chapter which provides useful ideas on how an instructor might assess students individually (for grading) when collaborative learning is a component of the course. Two chapters deal with educational theory and how it applies to group learning. There is even a chapter with suggestions for conducting faculty development workshops on this topic. There plenty of helpful examples, anecdotes, and case studies throughout the book.

An appendix lists the responses to the 1997 CLUME survey numerically tabulated, along with summaries of respondents' additional are comments. Finally, a substantial bibliography is provided. It is conveniently arranged into a section on further reading for instructors, and a section on textbooks and course materials that work well in a cooperative classroom.

Overall, this book is a fantastic resource for any college mathematics instructor who uses cooperative learning or is interested in incorporating it into his or her classroom. It's packed with practical, usable information, and very comprehensive. I highly recommend it.

[Editor’s Note: In the 1990s, the publisher of the above book, the Mathematics Association of America (MAA), sponsored Project CLUME (Cooperative Learning in University Mathematics Education). CLUME’s goal was to encourage greater use of CL in the teaching of tertiary mathematics. MAA feels that CLUME has achieved its goal and has diverted resources to other matters. The CLUME website, though, is still up, but no longer updated, at www.uwplatt.edu/~clume.

2.         Birchall, J. (1994). Co-op: The people’s business. Manchester: Manchester University Press.

IASCE’s 2002 conference was jointly sponsored by the Co-operative College of the UK (http://www.co-op.ac.uk). The Co-operative College is just one part of the International Co-operative Alliance (ICA) (http://www.coop.org/ica) which encompasses more than 700 million members in countries all over the world. However, education is but a small part of what ICA does. Its principal focus is economic, as its members co-operate for their mutual benefit in such areas as agriculture, banking, credit, energy, housing, insurance, and purchasing of groceries.

This book traces the history of the Co-operative Movement from its beginnings in early 1800s, during the dark days of the industrial revolution. Despite the failure of initial attempts,  “co-operators” continued to experiment until the 1840s when on-going success was achieved in Rochdale (near Manchester). Among the principles of the people known as the Rochdale Pioneers was the promotion of education. Toward this end, a levy for education was imposed on the surpluses of co-operative ventures. This was used to establish a wide range of educational activities for co-op members and their families. It included classes and activities for children as well as pioneering adult education programmes to help ensure that members were equipped to play a full part in their Societies. Early Co-operative education programmes also had a strong cultural element - with support for drama and choral work and, later, wide use of film.

The present book provides insight into an area of co-operation which may or may not be relevant to people working for co-operation in education. The author, Johnston Birchall, makes extensive use of photographs and other illustrations to accompany his narration of the Co-operative Movement’s changes through to the mid-1990s. The book describes the great variation in the forms that economic co-operation has taken in various times and places, and how principles have varied as well. A companion volume is Birchall (1997).

References

Birchall, J. (1997). The international co-operative movement. Manchester, UK: Manchester University Press.

3. & 4. Here are two new books by Joe Cuseo of Marymount College (USA) [Email: cuseog@aol.com]

who has done a lot of good work on cooperative learning, especially at the tertiary level. Below is information on the books from the website of the publisher, New Forums Press.

http://www.newforums.com/store/list.asp?numberpage=10&images=&display=&category=23

Cuseo, J. (2002). Igniting student involvement, peer interaction, and teamwork: A taxonomy of specific cooperative learning structures and collaborative learning strategies. Stillwater, OK: New Forums Press.
 
The student-centered pedagogical practices of cooperative learning, collaborative learning, and team learning can be united and defined inclusively as two or more learners who work interdependently toward a common goal, on a common task, that culminates with a consensual decision or creation of a common product. The purpose of this monograph is to provide a description and rationale for a taxonomy designed to delineate and categorize itself is included as a separate unit, with the intention that it may serve as a stand-alone "user's manual" or "procedural index file" containing specific, step-by-step practices that can be accessed conveniently and implemented expeditiously.

Cuseo, J. (2002). Organizing to collaborate. Stillwater, OK: New Forums Press.

This book focuses on the terms "collaborative learning," "cooperative learning," and "learning community" which have been bandied about in American higher education with great frequency and enthusiasm. One primary purpose of this monograph is to provide a more precise delineation of post secondary practices that are subsumed or assumed to be embraced by the umbrella terms, collaborative learning, cooperative learning, and learning community, and organize these practices into a coherent classification system or taxonomy. Other major objectives of the taxonomy are to: (a) create a common language for improving the clarity of communication and discourse about diverse forms of collaboration in higher education; (b) articulate a strong, research based rationale for greater use of collaboration practices in post secondary education, (c) provide a panoramic overview of, and a convenient catalogue for, the wide range of collaborative initiatives that have been implemented at colleges and universities; and (d) serve as a stimulus for triggering wider use of collaborative practices in higher education.