Student: The answer is 17.
Teacher: How did you get that?
Student: I don’t know. I just did it in my head. I got 17.
Examples like the exchange above are all too common in math classrooms. The Common Core State Standards (CCSS) for Mathematics call for students to discuss the math they are learning, and to explain their thinking. This represents an instructional change from traditional math classes, in which the teacher teaches a concept and students practice it individually. Because the idea of “math talk” is relatively new, it can be a challenge for teachers and students. Both groups need guidance, time and practice to get used to it. The benefits of effective math discourse are numerous and varied. The Principles to Actions from the National Council of Teachers of Mathematics identifies math talk as one of the eight Mathematics Teaching Practices: Facilitate Meaningful Mathematical Discourse. The benefits of such discourse include clarifying understandings, constructing convincing arguments, developing the language to express mathematical ideas, and learning to see things from other perspectives. Discourse about meaningful math content is a fundamental way to develop deep conceptual understanding, which is an important aspect of the CCSS (Principles to Actions, p. 30).
Teachers know from experience that when you try to explain something to someone else, you end up understanding it better yourself. Research supports this notion (Maryellen Weimer, Five Reasons Getting Students to Talk is Worth the Effort, Magna, 2012). Talking about a subject helps the brain make connections, making the subject more meaningful. Listening to and evaluating alternate ideas about the subject leads one to compare the new information with what is already known in order to build new knowledge.
Another reason that math talk is vital is that educators are called to prepare students for the demands of their future. The lists of 21st century skills that students should master include abilities such as: collaboration and teamwork, critical thinking, problem solving, creativity and leadership. These skills are enhanced much more through promoting math discussions in the classroom, rather than having students take notes and solve problems on their own. Students need practice in speaking and listening, appropriately disagreeing, and explaining their thinking in order to be successful in work and life.
Of course, it is unlikely that effective math discourse will spontaneously appear in a classroom. Teachers need to understand that learning productive math talk it is a process, and it will take time and effort to make it happen. Many experts recommend that teachers share with students the importance of math talk, so students understand why they are being encouraged to participate in this way. This is helpful for students of all ages.
Another consideration: Classroom climate. Students must feel safe to share their thinking or make a mistake. Teachers can model appropriate dialogue, provide sentence starters, and use thoughtfully considered questions to further discussions. Above all, teachers and students must be patient, knowing that continued practice will make math discourse easier and more beneficial.
Two resources that can help teachers become better at promoting effective math talk are 5 Practices for Orchestrating Productive Mathematics Discussions by Mary Kay Stein and Margaret Schwan Smith and Teaching Students to Communicate Mathematically by Laney Sammons.