COOPERATIVE LEARNING GROUPS

Working in teams is becoming ever more common in the workplace, and there can be many advantages to team efforts for students as well. Practice in communicating about mathematics --- talking about mathematics and formulating difficulties and suggestions in one's own words --- is itself worthwhile. Then too, students can provide each other with immediate help and feedback. Group discussions help students

Weaker students can help the group by asking questions, forcing the group to clarify its thinking. Stronger students can help the group by explaining key concepts to others. In fact, the best way to learn is to teach what you know to someone else. The process of organizing, verbalizing, and elaborating on one's knowledge helps to achieve a deeper level of understanding. Finally, it is not a bad thing to have allies in this enterprise of learning calculus.

You will be assigned to teams of three or four students for the purpose of doing the group homework assignments. There will normally be one group homework assignment a week, and each team will need to meet at least once, and perhaps more often, for each assignment.

You should come up with group solutions to the assigned problems that you all agree on --- continue to discuss a problem until you all agree on its solution. You need to be sure each member of your group understands how to solve each problem and how it relates to the concepts presented in the text and can demonstrate that knowledge in class if called on. Each group will write a single report to be handed in for grading. Everyone is expected to participate by reading the assigned material, attending group meetings, helping each other, asking for help when needed, critically evaluating the group's work, correcting mistakes, encouraging each other, etc.

The following roles should be assigned to specific members of your group. These roles should be rotated after each assignment so that everyone shares the responsibility for each role.

  1. Organizer. The organizer is in charge of setting the time and place of the meeting and getting the group together.
  2. Scribe. The scribe records the group's work by writing out the solution to each problem and an explanation, if appropriate.
  3. Reporter. The reporter explains in writing what the group did and how it did it (e.g., note briefly other unsuccessful strategies tried on some problems). Explain also anything about the way the group worked that was especially helpful to the group's productivity and what needs to be changed.

I expect each group to produce high quality homework papers:

Your paper should include the names and roles of each member of your group and the solutions to the assigned homework problems. The reporter's contribution will usually be one or two paragraphs long, and it won't be graded.

An important feature of cooperative learning is that the help you would normally expect from your instructor or a tutor can often now be provided by other members of your group. Of course, I am also still available in office hours, and we have a Math Center for peer tutoring as well.

Guidelines for Groups

  1. Assign each member of the group a role. (The roles should then be rotated.)
  2. Work on the homework problems together in your group. Do not split up the work --- everyone should focus on the same problem at the same time.
  3. Discuss each problem until a consensus is reached on its solution. Individuals should not accept confusion passively --- ask for clarification from others.
  4. If you get stuck, explain to each other exactly what the question is and what the difficulty is. Oddly enough, a good explanation of this kind is sometimes enough to inspire an answer. Ask for outside help only if everyone in the group agrees that outside help is needed.
  5. Make sure everyone understands the solution. If you can't explain it, you probably don't understand it.
  6. Write a group report --- solutions to the problems plus the reporter's summary.
  7. When the homework paper has been graded, each member of the group should look over the corrections.

Please realize how important the group homework can be. Tackling a difficult problem, puzzling over and explaining to each other the needed ideas, and putting them down in a well-thought out solution can increase both your competence and your confidence with the material. Be sure that everyone in your group understands each solution so that all may benefit from the effort.