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Seventh grade teacher: "My students have been working together in groups for a while now. They're getting along fine. But I'm finding that a lot of them still don't understand the work. I tell them to |work together and that it is all right to help each other. Sometimes I worry that they are only giving each other the answers. How can I get them to focus on problem solving and not just putting down the right answer?"
Mathematics educators are increasingly placing high priority on developing reasoning and problem-solving skills and have come to recognize the importance of small-group work as a context for developing and communicating mathematical ideas. As explained in the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) for grades 5 to 8 (p.78), "opportunities to explain, conjecture, and defend one's ideas orally and in writing can stimulate deeper understandings of concepts and principles." Curricular frameworks for many states are also increasingly calling for collaborative small-group work to help students persist at, and succeed on, difficult and sophisticated problems (see, e.g., California State Department of Education ). But as the concerned seventh-grade teacher pointed out, copying a fellow student's answers clearly does not help students learn to become independent problem solvers. Simply putting students in small groups will not guarantee that they will interact with each other in ways that are beneficial to learning. What can teachers do to teach students how to help one another learn to solve problems? A good place to start is to look at the research on helping behavior in small groups giving help and receiving help (Webb 1985a, 1985b, 1991). Knowing more about helping behavior gives teachers important information that they can use to enable students to help each other learn without giving answers.
In this article we outline the steps necessary for students to learn how to use one another as resources for doing mathematics. These steps were used in an urban, predominantly minority (Hispanic and African-American) middle school. The activities, explained in the helping behavior activities Handbook (Fariver and Webb 1991), were based on research showing which kinds of helping behaviors in small groups are effective for learning and which ones are not. Although research on cooperative learning has shown that working collaboratively with others can increase achievement (see, e.g., Slavin ), research on helping behaviors in small groups shows that not all behavior is equally effective for leaning. Explaining is more effective for learning than sharing the answer for both the helper and for the student who receives the help (Webb 1985a, 1985b, 1991).
Thorough preparation for working in groups can take as long as one-half the period each day for three weeks. To many this time will seem very long, perhaps too long. To those who already use groups on a regular basis, it will seem normal. Because …