Mathematics Professional Series Cooperative Learning — Pre-Algebra   What Is Cooperative Learning? Cooperative Learning IS . . . Group members understanding that they are part of a team and all members of the team are working toward a common goal. Group members understanding that the successes or failures of the group will be shared by all members. Therefore, each member must contribute as much as he or she can to the group goal. All students learning to talk and discuss problems with each other in order to accomplish the group goal. Group success being dependent on, and being a direct effect of, the individual work of each member of the group. A process that capitalizes on the presence of student peers, encourages interaction among students, and establishes positive relationships among team members. A process that requires the guidance of a teacher who can help students develop the cooperative learning skills they need, understand group dynamics, and learn mathematics by working in groups. Students asking for help only after each one in the group has considered the question. Helping students to be individually accountable for their learning. This is discussed in detail by Spencer Kagan in his book Cooperative Learning. Cooperative Learning IS NOT . . . Separating students into small groups to work on a problem or a group of problems without direction or individual responsibility. Students sitting together in groups and working on problems individually without conversation or interaction regarding the method or process being used for problem solving. Students sitting together in groups and letting one student do all of the work while the others watch or listen. Learning to Work Together Checking homework daily is an excellent and efficient method to help teams learn to work together. It can be done in this way. The teacher displays correct answers on the overhead projector. Students in cooperative groups check their homework and discuss any differences with their team members. Many will find answers to their questions from members of their team. Each team must agree upon the problems that they cannot solve. The teacher then asks each team to indicate which problems they would like discussed. The teacher then guides students through a solution of those problems. This method will reduce the number of problems addressed by the teacher and thus allow for better use of class time. Students will have more peer pressure to complete homework fully and on time. Teachers may choose to have students keep their own weekly homework records by team, individually, or both. The teacher may choose to select a problem or two for discussion based on information gathered by circulating around the room while students are checking and talking about their homework. Calling on a random person in a random group can add responsibility to this method. Structures to Deliver Instruction to Students There are a variety of structures that can be used to deliver instruction to students via cooperative learning. One structure is called Brainstorming. It is a way to get students to open doors to creativity and allows for collecting many possible answers to a problem. The team throws out as many ideas as possible while a recorder records each idea on a piece of paper. Roles are assigned to each team member and group discussion follows. The 4 S's of Brainstorming suggested by Spencer Kagan—speed, suspend judgement, silly, synergy—should be used as guidelines for the structure Brainstorming. Speed — fast work under time pressure to create as many ideas as possible. Suspend Judgement — do not evaluate or judge. All ideas count. Silly — all ideas should be relevant and are always included. They may sound silly but could turn out to be of value. Synergy — build on the ideas of others. The following example problems could be used to practice using the structure Brainstorming in a pre-algebra classroom. Pre-Algebra Examples Brainstorm as many ways as possible to represent the number 12. Brainstorm reasons for measuring perimeter. Brainstorm when you should use estimation in solving a problem. Brainstorm ways to collect data when conducting a survey. Brainstorm ways to analyze data after it has been collected. More Information For more information on cooperative learning, see "Cooperative Learning in the Mathematics Classroom", part of the Glencoe Professional Mathematics Series.