It has been so interesting to read everyone's commentary on Cooperative Learning and I have been eager to join in the discussion. I just finished teaching an on-line forum on Cooperative Learning with 12 teachers interested in improving their skills in using this technique with their classes. The question that seemed to cause them most disequilibrium was: What is the difference, if any, between groupwork and cooperative learning? I personally see a significant difference between the two. I consider groupwork to be a joint effort on the part of students to carry out a prescribed task toward a well-defined goal usually prescribed by the teacher. Do this, then this, and so on until you come out with this learning. Strategies that involve the efficient use of time, effort, assigned jobs for different members of the group come into play in a group directed effort. Often the person who has a specific ability is encouraged to use that ability in the interest of the group's efficiency. One of the problems that I see in groupwork is that the work is often unevenly distributed and the person in charge of materials, or notetaking is often left out of the thinking processes involved. Often one of the group members is determined to be the math brain and others defer to him/her. The emphasis in groupwork is on the required outcome: the homework is checked, the answers shared, an answer is arrived at, the project is finished or some such outcome.
When I think of cooperative learning, I think of a much more integrated interaction between the students, where each and every student in the group is trying to build a mathematical understanding while hearing and thoughtfully considering the other students' thinking in the group. The goal of the group is for each memberto build understanding. Someone in this discussion mentioned that a failing of cooperative learning occurs when someone in the group takes on the *traditional* role of teacher and tells the others what to do or what the answer is. (If this happens, it isn't much better than the teacher standing in front of the class and saying: This is the way it is. Pay attention and at the end of the week I'll see if you can repeat what I told you.) The end result of a rich cooperative learning experience may well result in divergent responses to a stimulus, intense argument over situations, processes, definitions --all of which can invite the teacher to engage with the students with a probing question, a counter example, a purposeful anecdote... The sharing process at the end is not so much the result of a majority rule determining the *correct* process but as a joint consideration of what the groups discussed, where were the sticking points, what still doesn't hang together logically and so on. From this kind of discussion at the end, with the teacher not coming off as the authority with THE answer or THE process, each student goes away in an empowered position, aware that s/he can build mathematical understanding for him/herself, verified by the strength of his/her own logical thinking.
I personally find cooperative learning useful for maximizing each person's time for thinking out loud and being heard, I have also seen teachers use a *lecture* or front of room format to engage students in an empowering manner, considering each student's ideas and contributions of thinking and engaging other students to respond to each person's offering, building on the students' conceptions of a mathematical stimulus until everyone has had the opportunity to be heard and considered. It's not impossible to stand in front of the room and still allow students to build their own mathematical understandings.
This is the major point. In order to understand mathematics, the student has to construct the meaning for him/herself. No amount of memorization of fact or process alone will produce a mathematician (IMHO). This is much more work for the student. S/he can't hide in the back of the room, can't cram for the term exam, can't rely on blindly memorizing formulas, can't copy the homework, can't get out of the real work of thinking. So whatever method is used, this must be the underpinning of the pedagogy. Whether the teacher prefers lecture, groupwork or cooperative learning as a modus operandi doesn't matter as much as whether the teacher sees the need to establish an environment in which each student has the maximal opportunity to build his/her own mathematical understanding. Every student must come away from school with the ability and confidence to construct his or her own mathematical understanding.
Just one more thought (I've gone on way too long) Everytime I allow students to work together to sort out a mathematical situation, I learn something new. Another way of looking at a familiar old friend of a problem, a new question to set me off in another direction, a new connection to be made or a new insight into the way we think and learn. This has happened to me whether I am teaching second graders or high school students or math teachers. It's a big part of the fun of teaching.
Thanks for starting this discussion, Ted.
Lucille L. Peterson Math Leadership Program Bank Street Graduate School of Education Tel: 212-875-4665 610 West 112th Street Fax: 212-875-4753 New York, NY 10025 E-mail: firstname.lastname@example.org