Hear that? Math class doesn't sound like it used to—at least it shouldn't.
You could hear a pin drop in my childhood math classes. We sat in rows, worked on our own, listened to the teacher at the center of the classroom, and spoke only when spoken to. Today, there is a growing understanding that academic discourse and peer-to-peer collaboration help all students make learning gains in mathematics. Students can exchange ideas in whole groups, small groups, and pairs. The common-sense idea that fostering math discussions would improve math language acquisition and learning is also validated by research. In Visible Learning for Mathematics (2016), John Hattie finds student-to-student and student-to-teacher dialogue positively influences student achievement.
Provide Structures That Promote Discussion
Teachers should plan groups thoughtfully to ensure that discussions elicit evidence of understanding from all students. There should be an emphasis on structuring academically diverse groups, which Hattie's research shows is far more effective than grouping kids by ability. Common to English language arts and social studies classrooms, discussion aids that set a clear structure for conversations (such as Save the Last Word for Me, Whip Around, or Concentric Circles) give teachers strategies for engaging all students in discussions because all students must participate and be active listeners (Harvard Graduate School of Education, 2017). Teachers need to build students' capacity to attentively listen and provide useful feedback through demonstration, or by using tools like Talk Cue Cards, Talking Points, or Ground Rules for Exploratory Talk offered by the University of Cambridge in the Thinking Together project (2018).
For teachers interested in incorporating technology, using a platform like the Desmos Activity Builder and its Polygraphs activities requires every student to be actively involved in developing mathematical language through electronic communication with classmates. Although these tools and strategies work well for specific discussions, implementing an overall classroom structure that fosters ongoing dialogue is also a good idea. The technique Talk Moves, in which teachers use prompts to ensure that all students speak, listen, and respond to one another, helps move conversations in all class settings (Chapin, O'Conner, and Anderson, 2013).
The Talk Moves technique revolutionized my classroom by establishing an expectation for what communication looks like in math class. To begin, I focused on implementing one prompt at a time so that I didn't overwhelm my students. At first, my students were a bit awkward responding to me when I asked, "Caroline, would you repeat or rephrase what Abel just said?" or "Lindsey, would you add on to what Brad just said?" But as we practiced revoicing together, students needed less prompting from me.
Support the Three Different Types of Talk
Research has identified three categories of talk in classrooms: disputational talk, cumulative talk, and exploratory talk (Mercer, 1995). Disputational talk usually centers on a dispute or has a competitive nature in which students go back and forth on decisions. To keep this type of talk productive, I find it helpful to require students to use sentence frames—a sentence or question with words removed. One of my favorite sentence frames for this is, "I disagree with your [answer/process/strategy] because …"
Cumulative talk is characterized by students simply agreeing with each other. As a deterrent for blindly agreeing with others, I occasionally plant some "wrong answers" within groups by discreetly asking a student to make mistakes on purpose to see if there is any pushback from the other students. I also find it effective to require groups to provide multiple solution strategies or have a group member explain another's work to me.
The most effective type of discussion is exploratory talk (Mercer, 1995). This involves sharing knowledge, providing reasoning, challenging others' reasoning, providing alternate hypotheses, and joint consideration of all ideas. A study of elementary-age students found that the way language is used during exploratory talk within groups positively affects the way students solve problems independently (Dawes, Littleton, Mercer, Wegerif, and Warwick, n.d.).
Measure Participation and Assign Roles
Teachers sometimes believe that it is hard to assess each student's contribution and progress when doing group work. Using clearly defined group roles can ensure that you get active contributions from everyone. One note of caution: Using group roles usually results in a single student being appointed to record the group's cumulative findings. I think it's better to have each student in the group individually record the group's data and formulate written responses. Then, I like to have the group negotiate a collective response to present as their final product to ensure that all students are really learning the material. This individualized thinking can then be recorded in a group chart with each student assigned a specific colored marker. This approach gives all students ownership and evidence of their learning.
Balance Group and Individual Work
Students shouldn't work in groups all the time. Students must also be self-reliant to ensure that they develop individual mental stamina, which the Standards for Mathematical Practice refer to as perseverance, to do complex math. As teachers use more challenging curricular materials, students need time to think deeply before they engage in group discussions. Some teachers find it helpful to pose a few reflective questions or sentence frames for students to consider on their own before calling for small-group discussions.
Worth the Effort
Teachers have to work to build a supportive and highly communicative culture for students. I know this can sound daunting on top of all the other requirements we face every day as math teachers. But fostering true student collaboration by creating an open and safe classroom in which lively math discussions are the norm is worth the investment of time and energy and will reap immense benefits for teachers and students alike.
