For a more extended discussion of the following questions, see Heller and Hollabaugh (1992), Teaching problem solving through cooperative grouping. Part 2: Designing problems and structuring groups, American Journal of Physics, 60: 637-644.
What is the optimal group size?
We have found that groups of three work a little better than pairs or groups of four. With pairs, there is often not enough physics knowledge to solve the problem. In groups of four, one member tends to be left out of the process.
When the class size is not divisible by three, however, we end up with a few pairs or groups of four. In general, we prefer groups of four over pairs.
Should students be allowed to form their own groups? If not, what should be the gender and performance mix of the groups?
We found that mixed-ability groups (based on past performance on problem-solving tests) worked better than homogeneous-ability groups. Therefore, we assign members to groups based on test performance (one from the top third, one from the middle-third, and one from the bottom third of the class).
We also found that groups of two men and one woman did not work well, particularly at the beginning of the course. The men tend to ignore the woman, even if she is the highest ability student in the group. Until instructors get to know their students well, we advise assigning groups of three men, three women, or two women and one man.
How often should groups be changed?
Formal cooperative groups need to stay together long enough to be successful. On the other hand, they should be changed often enough so students realize they can make any group successful -- that their success is not due to being in a "magic" group.
Our students work in cooperative groups for three hours each week (1 hour in discussion section, 2 hours in lab). In the first quarter, we change groups every two to three weeks (i.e., 4 times in 10 weeks). In the second and third quarter, we change groups only twice.
In the beginning of the course, it is important to give students a rationale for assigning them to groups and changing groups often. We tell our students that:
(1) We want them to get to know everyone in the class, so we will change groups often. By the end of the quarter, they will should have worked with almost everyone in their class (section). This helps build a sense of community -- we are all working together to help each other learn physics.
(2) No matter what career they enter, they will have to work cooperatively with many different kinds of people (not just their friends). So they should begin to learn how to work in successfully in groups.
How can problems of dominance by one student and conflict avoidance within a group be addressed?
We use three key elements of cooperative learning groups to alleviate these difficulties:
(1) One Group Product: To promote interdependence in discussion sections, we specify that only one problem solution can be turned in by the groups, and all members must sign the solution.
(2) Roles: Students are taught specific roles (Manager, Checker/Recorder, Skeptic, and Energizer/Summarizer). The roles were selected to correspond to the planning and monitoring strategies individuals must perform independently when solving problems -- the manager who designs plans of action; the skeptic, who questions premises and plans; the recorder, who organizes and writes what has been done so far; and the summarizer, who keeps track of decisions and reasons for different actions. In addition, each person has a responsibility to make sure the group functions effectively. The Manager must ensure that everyone in the group participates and contributes. The Checker/Recorder must ensure that all group members can explicitly explain how the problem was solved. The Energizer/Summarizer must energize the group when motivation is low.
We normally assign groups of three (Manager, Checker/Recorder, and Skeptic): the fourth role of Energizer/Summarizer is used when the size of the class is not divisible by three, so some groups will have four members. In groups of three, the Manager takes on the summarizer role, and all members are asked to energize the group when motivation is low.
The first time students work together, each member is assigned one of these roles. Each subsequent time the group works together, the roles must rotate. The groups stay together long enough so each group member has each role at least once.
(3) Group Processing: Set aside time at the end of a class session to have students discuss how well they worked together and what they could do to work together better next time.
At the beginning of the quarter, we do this every class session. After three to four weeks (i.e., after students have worked in two different groups), we do group processing every two to three weeks, as it seems necessary -- usually the first time new groups are working together.
How can individual accountability (hitch-hiking) be addressed?
We use five techniques to alleviate the "hitch-hiker" problem (one student relying on the other group members to do all the work):
(1) Assign a role to each student, and allow time for group processing (see above).
(2) Make sure the seats are arranged so students are facing each other, "knee-to-knee." This makes it much harder for a student to remain uninvolved with a group.
(3) In both discussion sections and lab, individual students are called on randomly to present their group's results. This person is not usually the Checker/Recorder for the group.
(4) In discussion section, occasionally a group problem counts as a test question. The group test problem is given the day before the rest of the test. If a group member was absent the week before the group test (i.e., did not get to practice with his/her group), then s/he cannot take the group test question. (Note: Towards the end of the first quarter, we let the rest of the group members decide if the absent group member can take the group test problem.)
In lab, each member of the group receives bonus points if all group members earn 80% or better on their individual reports.