three exams during the semester and a final. Usually I arrange matters so that the students have as much time as they need for the exams which are closed-book. The first exam is taken in their groups and every member of the group gets the same grade. The second exam is taken individually, but each student receives two grades. The first is the score of her or his exam and the second is the average of the scores of the members of the student's group. The third exam and the final are taken individually and the students get only their individual score.

I and others have been using this approach for over a decade and we have published papers with data indicating its effectiveness. Of course CL is not the only pedagogical strategy we are using. Our approach uses research and epistemological analyses of concepts, having students implement mathematical concepts on the computer and the minimization of lecturing in favor of small-group problem solving. As an almost moral stand, because we believe that all of these factors contribute to student learning and we want every course to be a good as it possibly can, we have never conducted experiments that try to isolate factors and determine their individual effectiveness. Therefore, we cannot assert that CL alone helps students learn. What the data does suggest is that CL, together with these other factors appears to be very effective in
helping students learn collegiate level mathematics concepts.

Ed Dubinsky edd@zeus.cs.gsu.edu received his Ph.D. in mathematics from the University of Michigan in 1962. For the next 25 years he did theoretical research in mathematics. Since 1985 he has done research and curriculum development in post-secondary education. He has taught at nine universities in six countries on three continents. He is presently retired, dividing his time between Pyrites, NY, and Cincinnati, OH.

Multi-ethnic Groups in Cooperative Learning:
Initial Observations in the Malaysian Context
Shameem Rafik-Galea
English Language Department
Faculty of Modern Languages and Communication
Universiti Putra Malaysia
shameem@fbm.upm.edu.my

Cooperative learning is a good means of enhancing learning by fostering greater interaction, helping resolve learning conflicts, and promoting tolerance among students particularly in multi-ethnic contexts. For the last three and a half years, I have used the cooperative/collaborative-learning concept in my undergraduate Critical Reading and Thinking course at a university in Kuala Lumpur, Malaysia. Malaysia's three largest ethnic groups are Malays, Chinese, and Indians.

During this time, I have noticed that students who voluntarily belonged to culturally mixed group seem to learn more effectively and to develop assignments that show better logic and reasoning.

It appears that multi-ethnic groupings are beneficial for the development of learning, because the learners bring with them their own cultural values to their groups and share these values with their group mates. For example, in a project on "Capital Punishment," the multi-ethnic groups were able to discuss how each of their cultures and religions view capital punishment. They were also able to discuss the pros and cons in relation to their own cultural attitudes, relate them to their own reasoning, and decide on a common understanding that could be accepted by all the group members. However, groups composed of members who belonged to the same ethnic group were not able to enrich their learning experience in the same manner.