The Use of Groups in
Mathematics for Elementary Teachers

1. Why do we use groups?
   We noted in the Syllabus that there is almost a century of research showing that academic achievement, productivity, and self-esteem improve dramatically when students work together in groups. This method emphasizes teamwork, cooperation and support by others, rather than isolation and competition in learning.
   
   
2. How are groups used?
   Groups of three or four will be formed at the consent of students and the instructor. An ideal group has a mix of strengths. Group members must be able to work together efficiently and regularly.
   
   
   • All members of the group must participate fully in all group assignments, so you must find adequate time to prepare for and participate in meetings of your group.
   • Each group member is responsible for the learning of all members of the group, so there must be commitment by each member to the success of all members.
   
   Share serious problems or conflicts within the group with the instructor as soon as possible; ideally, solutions should be worked out by the group itself. In case a subgroup of a given group decides to split, the subgroup leaving the group must notify (in writing) the instructor and the other members of the group. This note must explain the reason for the break up.

   Each group should sit together in class, since there will be times when the group will need to discuss issues or solve problems in class. Often these situations will lead to progress reports for class interaction. The group consensus should be reported; also, all members of the group should report from time to time.
   
   

3. How should groups do their work?
   Each group must develop methods and times for their work, so phone numbers and other relevant information should be exchanged as soon as possible. For work on specific questions and problems, the following suggestions may be helpful.
   
   
   • Do serious individual work in preparation for the group meeting.
   • Begin group work with a general, but focused, discussion of the question or problem.
   • Talk together about what the question or problem really means or requires.
   • Find out who knows what that may help the discussion get started.
   • Get suggestions for a method or approach from each member.
   • Agree on a strategy (brainstorming, assign work on pieces, read the text, etc.).
   • Discuss together and agree on the final answer or solution.
   
   
4. What are some dangers to avoid?
   Some members of your group may be "natural" leaders or talkers, and some members may comprehend certain concepts more quickly than others. You must guard against
   
   
   • domination by one or two members (in discussions, solutions, decision making)
   • silent partners (who are intimidated or embarrassed; all need to understand and contribute)
   • impatience with members who have not "seen it" yet (good students deepen their learning by helping others)

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