Mathematics instructors who have used group work in their classrooms know that carefully designed assignments and strong individual efforts by students are necessary, but not sufficient, to guarantee a successful activity. Students also need to develop the social skills that support productive mathematical work with peers. To help with this, I give my students a set of guidelines acquainting them with their rights and responsibilities during small group work (see below).

To formulate the guidelines, I first familiarized myself with the characteristics of certain general models of cooperative learning that have been shown to be successful. Second, I studied the video and audio tapes of more than a dozen group sessions in which my precalculus students participated, and noted particular actions that appeared to be critical to the success or failure of the group effort. Typical sessions were about thirty minutes long, and every group handed in a single paper, with each group member receiving the same grade.

Some problem behaviors are easy to correct, such as groups choosing seating arrangements that inhibit interaction, or starting to work before checking that everyone understands the instructions. A more persistent problem, one that is endemic to student conversations about mathematics, is the inappropriate or incorrect use of mathematical language. While difficult to eliminate, its effect on group progress can be minimized if those who are sensitive to the careless use of language make a practice of requesting clarification. A communication problem with more serious consequences is that some students tend to ignore the contributions of less articulate group members, rather than probing for their meaning by asking questions. Most challenging for almost all groups is the process of finding a level and mode of discourse that meets the needs of, and encourages the contributions of all of its members.

Making the ground rules explicit helps to set the stage for effective interaction. The guidelines describe generally the kind of behavior considered appropriate in group work in mathematics, they alert groups to some specific problems that can limit their effectiveness, and they provide a few basic strategies for coping with problems that do arise. As concrete experience shows students the value of the guidelines, the social framework suggested gradually becomes part of the classroom culture. As a result, I have seen my students accomplish more during group work, and the limited class time we have is used more productively.

1. Move into your groups quickly, sit close together, use first names, and get right to work. Do not engage in "off-task" discussion. Make it your responsibility to encourage everyone to participate.
2. Read aloud all instructions and given information. Getting all of the facts into the "record" helps ensure that everyone is aware of the assumptions and the expectations of the assignment.
3. Listen carefully to each other. Try not to interrupt. Respond to, or at least acknowledge, comments made or questions asked by other group members.
4. Do not accept confusion passively. If you do not understand the information that someone is presenting, try to paraphrase what was said, or ask someone to help you paraphrase it.
5. Ask for clarification whenever someone uses a word in a way that you find confusing. The correct use of terminology is an essential part of successful communication in mathematics.
6. Do not split up the work. Everyone should focus their attention on the same problem at the same time. It is much easier to resolve conflicts when group members work together and check for agreement frequently.
7. Make a habit of explaining your reasoning or "thinking out loud", and ask others to do the same. The process of constructing and refining explanations helps everyone to relate the information being presented to what they already know.
8. Monitor your group's progress and be aware of the time constraints. It is important, and appropriate, to ask each other how what you are doing will help your group complete the assignment.
9. If your group gets stuck, review and summarize what you've done so far. This process creates new opportunities for group members to ask questions, and often it will reveal important connections that have been overlooked.
10. Question-asking is the engine that drives mathematical investigations. Re-read the guidelines above and identify as many different ways as you can to generate questions during group work.