Using communication in the classroom shapes the way students learn mathematics. It supports a social learning environment for children, creating a community of encouragement, respect and the exchange of ideas. According to the National Council of Teachers of Mathematics Standards and two recent National Research Council reports (Adding it Up: Helping Children Learn Mathematics and How Students Learn: Mathematics in the Classroom), developing mathematical language deepens a child’s understanding of mathematical concepts.
Teachers can create an environment of communication by developing specific structures within which students can carry on constructive discussions about how they solved problems by explaining their solutions, answering questions from others in the group and justifying their answers. One very effective strategy, or “talk move”, is revoicing. As students work independently to solve a problem, the teacher notes several different strategies students are using to solve that problem. She then chooses two or three different strategies to highlight—one strategy that is commonly used to solve the problem, and two that are somewhat different. For example, take the following problem: “Mark counted 9 paper clips in his bucket. Corey counted five in hers. How many paper clips did they have in all?”
First, the teacher asks a student (this student represents a strategy that was widely used) to come to the front of the group and write the problem and the answer he came up with on the whiteboard. The teacher then asks the student to describe how he came up with that answer. Student #1 chose to solve the problem this way: “The number problem is 9 + 5 = ____. I know that 10 is one more than 9, so I said, 10 + 5 is equal to 15. Then I had to subtract because the number was 9 in the problem, not 10. I took one away from 15 and knew the answer was 14.” The teacher asks the group if they have any questions for student #1, or if they agree or disagree.
Next, the teacher will ask another student to come to the front of the group and restate student #1’s reasoning. “Can you repeat what he said?” (if the student forgets some of the reasoning steps, the teacher will ask student #1 to repeat his reasoning). The student will, again, try to revoice students #1’s reasoning. Finally, the teacher will ask student #1, “Is that what you said?” The first student will acknowledge that it was, and the teacher will thank the student and call on someone else in the group to come forward to explain the reasoning again. The teacher can call on two or three students to revoice. Student #1 remains in the front of the group as others revoice his strategy for solving the problem.
The teacher repeats these steps by calling on a student who solved the same problem using a different strategy. This “talk move” should be modeled sufficiently so that students are comfortable with the procedures. As students become familiar with the revoicing steps, they will become more comfortable speaking in front of the group.
Communication about mathematical thinking highlights various approaches to solving the same problem, helping everyone in the classroom understand a concept or method. As children describe their methods to others, they clarify their own thinking, and learn to explain and justify their reasoning.