This is a very concise handbook of practice supported by research. The book tells its story in eight brief chapters spanning only ninety pages. Forty more pages contain documents and references helpful to anyone using the book. The authors have tried to single out those issues that would assist the practice or the understanding of teaching with groups in our mathematics classrooms.
The book provides a wide variety of practices all from a particular point of view. Cooperative learning offers a wider choice of methodologies than the lecture method. From this scope, the authors advocate a method solidly backed by research. The underlying principles are outlined briefly on page 5.
A significant amount of the work of the course should be done in cooperative groups, A positive esprit de corps exists within groups, Team members share a feeling of mutual responsibility for each other, Group membership is permanent and stable, and Group work is included in the evaluation process.
The chapters go on as follows:
The research on cooperating groups at all ages and in all environments is very compelling. The bibliography here does not reach beyond the classroom to wider settings where groups (such as industrial development or production teams, church committees, volunteer groups, and other assemblages of people) come together to complete a large task. The background is much the same. The groups are small; they work on significant tasks; there is an excitement about the mission of the group; the members share important mutual responsibility; the group must work for an extended period of time; and the whole group is judged (usually by community or organizational standards) for its performance.
The authors discuss the foundations for cooperative learning, but do not address the social process that instructors and students enter when groups are formed. This is the "stuff" of seminars for business leaders who organize their workers into teams. It is equally important to instructors who use cooperative learning. That is, working cooperatively is a socialization process.
Groups have a social dynamic extending through a few phases. Some phases are potentially upsetting. Many of the people I've talked with who "tried groups and found they do not work" quit during a troublesome phase without reaching a more beneficial period. Incidentally, similar socialization processes occur with the lecture method. Except for a few students who come forward, the method is sufficiently depersonalized that the suffering individuals do not identify themselves and quietly disappear or fail for reasons we never discover.
Because they included computer activities in their courses, the authors also discuss laboratory sessions. When students encounter a new technology, suddenly two learning curves are compounded: the mathematics and the technology. Studies show that there are problems associated with the introduction of technology that fall inequitably on different groups (e.g. males and females). Working cooperatively is not a panacea for solving these problems. The authors do not address these issues.
More and more, industry is looking to education to prepare a labor force that will work cooperatively in dynamic teams for extended periods of time. In those teams each person has a pace and a style. Some workers are not terribly productive and will work beside highly efficient people. This is a reality. It happens in the workplace and in the classroom. The authors do intimate that the groups must come to grips with the process of working cooperatively, even if it takes effort, but they do not adequately point out that we must help students to understand that people have varying capacities, that this is all right, and that we can cope. The authors do discuss attitudes and practices that will reduce the probability of difficulties and assist in the resolution of difficulties when they arise.
The information imparted by the authors is strong on practical experience, and therefore quite sound, but lacks the solid background that would come from inclusion of social science research on human beings working in groups and the dynamics of that work. This contrasts with the careful research base they have placed under the learning process.
For those who can look past cheerleading about small group learning, there is an excellent meta-analysis (a technical term referring to an attempt to statistically pull together a large number of studies) of the research on cooperative small groups: David W. Johnson & Roger T. Johnson, Cooperation and Competition: Theory and Research, Interaction Book Company, Edina, MN, 1989. A surprise: this is not in the bibliography. It was from this meta-analysis that I first learned that human beings mastering repetitive small tasks learn better from lecture type instruction followed by individual drill but that complex tasks are better learned in cooperative fashion. I find this relates very well with the way we traditionally teach and what is traditionally learned as opposed to what we might teach and what might be learned in mathematics. I go further than the authors by assigning problems that usually transcend the capabilities of a single student. A group effort is essential. In this way I can assign interesting mathematical problems and not merely exercises. Further, the students encounter deeper mathematics with only a small number of problem settings to remember after the course is over.
The people engaged in reform that I've met are giving 110% to the effort. Most academics I know do give 110% to intellectual effort in some direction. This effort is not always focused on their classroom. I believe this spread of effort is good since there are too many things to be done for all of us to focus just on the classroom. So if reform requires 110% from all instructors then reform is doomed. I don't think this level of involvement is required. I think books like this one begin the process of making reform easier for the rest of us. In a solid way, based upon wide experience and careful research, with brevity sympathetic to busy instructors, this book provides an easy handbook that points to more deep knowledge elsewhere.
---Thomas R. Berger
Thomas R. Berger is Carter Professor of Mathematics and Computer Science at Colby College. He has for many years used cooperative learning techniques in his teaching. His e-mail address is trberger@colby.edu.
A Practical Guide to Cooperative Learning in Collegiate Mathematics
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Last modified: Thu Feb 11 17:48:58 -0500 1999