Collaborative Learning and Groups

The IMP curriculum is designed so that much of the in-class learning takes place as students work together collaboratively in randomly formed groups. This group work is balanced by opportunities for students to work individually.

This section discusses the reasons for the collaborative approach to learning, the process of forming groups, and ways to make collaborative learning work successfully in your classroom.

Why Group Work?

In a traditional mathematics classroom, each student sits at a separate desk and works alone, interacting only with the teacher. Looking at someone else's work is considered cheating. Consequently, many people see mathematics as something to be done in isolation. They believe that if you want to work with people, you do not go into mathematics.

In reality, collaboration is just as necessary in mathematics as it is in other aspects of society. Genuine mathematical work, whether done by mathematicians, plumbers, engineers, or dental hygienists, typically involves collaboration and communication. Indeed, employers identify the ability to work with others as one of the most important skills they look for in job applicants. The IMP curriculum teaches students how to collaborate by having them work together, usually in groups of four.

• Students can learn a great deal by working collaboratively with others. Here are some of the many benefits of group work:
• Students working in groups get to see different approaches to a given problem. Varied approaches to a problem lead to added insight and increased understanding. As students hear each other's approaches, they can ask questions to clarify the ideas.
• Small groups create a safe environment for students to take risks and make mistakes. A student is more likely to ask a question or take a risk in a group of four than in a class of thirty-six.
• When students are in small groups, more of them get to participate in discussions and carry out experiments. A task for four people allows each member to participate, whereas a question or problem thrown out to a whole class will probably get responses from at most a few students.
• In a group, students take the responsibility for each other's work habits and classroom behavior. The students see their groups as somewhat like families, in which it is each member's job to support and keep tabs on the others. This allows the teacher to be more of a facilitator.
• Through the use of randomly assigned groups, students get to work with others outside of their social groups. This promotes appreciation for, or at least an awareness of, people's differences.

How to Form Groups

One way you can create random groups is with playing cards. For example, if you have 32 students in a class, you use the aces through the eights from a standard deck. (If your class size is not a multiple of 4, you might make one or two groups of three or five.)

Shuffle the cards and allow each student to pick one. Students then sit with those who drew the same face value (aces sit together, twos sit together, and so on). Students should record their cards' suits, because the teacher's guide often suggests assigning roles based on the suit. (For example, "Have the heart card student from each group present the group's findings from this investigation.")

It may be helpful to tape onto each desk or table the playing card that corresponds to each group member. Teachers have found this to be helpful in taking attendance and calling on students. One IMP teacher actually hangs the playing cards by a string from the ceiling above each student's head. That way, the teacher can easily see at a glance who has which card and which suit. You should form new groups at the beginning of each unit. The teacher's guide for each unit suggests when to create new groups, but you may change more or less often depending on your own philosophy. Some teachers change more often so that students get a chance to work with every student in the class over the course of the year. Some teachers leave the students in their groups longer to allow them to get really comfortable with their group members.

Why Random Grouping?

Whether you use playing cards or some other tool, it is important that the method you use result in random selection and that students know they are being grouped randomly.

The Interactive Mathematics Program believes that random grouping helps eliminate the labeling and tracking that can occur in a classroom. If you try to "seed" each group with a high-achieving student or plant a less motivated student in each group, the students will figure out what is going on in about two minutes! They will know who the token "smart person" is in their group and whom they will to have to carry along. One of the beauties of the IMP curriculum is that it provides varied activities and opportunities for students. Every student should be able to shine in some area, whether his or her strength is giving presentations, motivating other group members, or sharing unique problem-solving skills.

Facilitating Successful Groups

Once the students are seated in their groups and ready to go, it is up to you to run your class in a way that maximizes the benefits of collaborative learning. You will have to structure your class to ensure that students use their fellow group members.

This is one of the greatest challenges for any teacher; your ability to meet it will increase from unit to unit. Here are some suggestions from experienced IMP teachers:

• Make sure students consult each other before asking you a question. One IMP teacher has the motto "Ask three before you ask me!" posted on her classroom wall.
• If a group is stuck or off task, ask a thought-provoking, open question to get them going. Even better, have the students generate questions to get themselves back on task.
• Instead of brainstorming about a problem as a whole class, have group members brainstorm with each other and post their ideas on sentence strips.
• When discussing homework, have each group prepare a presentation on one part of the assignment.
• Take time periodically to have students do some reflection and discussion about the value of learning to work together.
• To show students how much you value collaborative work, incorporate the group process into students' overall grades. For example, have students assign "group participation" grades to all their group members (including themselves).
• As your students become proficient in working productively as a group and become less dependent on you for guidance, congratulate yourself for creating independent learners who have gained the ability to work effectively in a collaborative setting!