Tuesday / April 23

Practicing Techniques that Teach Students to Engage in Math Talk 

If 2020 taught us anything, it was that everything can change, and change quickly! Who would have thought that school buildings could be closed for a prolonged period of time? And teachers would pivot to teaching online within a few days? Who would have thought that students would engage in learning through video cameras and that their phones would not be taken away, but rather serve as a key learning tool?  Now a year later, we are trying to make sense of it all and decide how best to move forward. As you return to your classroom with your elementary students, what changes do you plan to keep? And what further changes do you hope to implement?  

For your elementary students, a key change to support learning is strengthening mathematics discourse. As we reconnect with students, we can expect wide variations in  where they are in their mathematics learning. More than ever, we need to listen to our students and understand their mathematical reasoning. We need to ask questions that probe their thinking, support them as they connect mathematical ideas, and build from where they are without losing sight of our learning goals. Purposeful, intentional, and most importantly–planned–mathematical discourse can do all this. 

How will you reconnect with students and plan and prepare for mathematical conversations with them , either during summer recovery programs or in the next academic year? To get started, it will be important to set up norms, consider teaching moves you can use, and implement successful practices for orchestrating discourse.  It is also key to implement techniques that not only engage students, but explicitly teach them how to participate effectively in math talk . Even the best discourse-promoting tasks do not self-actualize. Students must know what they are expected to do for such tasks to become powerful learning tools. 

For many years, our team has looked at techniques that have been successful in implementing productive discourse in elementary literacy lessons and considered what they would look like in mathematics teaching. Our work resulted in a series of techniques that can help you successfully organize your work with your students (Sztajn, Heck, Malzahn, 2021).  We even learned last year that teachers who successfully used these techniques in face-to-face instruction were also able to quickly adapt them to other learning situations as they unfolded. As one teacher told us, “my classroom went mute when we switched to online instruction, but I used the techniques I knew to get my students to participate.” 

Studying some of these techniques so you are ready to implement them can help you get reconnected with your students.  Each of them includes a series of steps that you and students can practice to become proficient. These discourse techniques are designed to support teachers and students learning to work together around four important dimensions of discourse: listening, questioning, explaining, and using several modes of communication in the classroom. Here are three you can try right now: 

  • Math Bet Lines. This technique helps students listen and attend carefully to story problems. As the teacher presents a problem one statement at a time, students predict what comes next. Students need to carefully listen to what is happening in the story and make sense of what math problem they might be trying to solve. Listening carefully to each student’s “bet,” the teacher is also working on making sense of students’ thinking and the aspects of the problem (contextual or mathematical) students are considering.  

Fourth grade teacher Ms. Tate Salinas reflected on how listening to her students’ predictions through Math Bet Lines helped her reorganize a lesson plan because there were more questions than she had anticipated regarding what was going on in the problem. “I was glad to hear students articulate their thoughts and ideas. And they successfully listened to others and respectfully agreed or disagreed with their peers. It was the Launch [of the problem] that made me realize that perhaps my planned lesson was still too ambitious for my students at this point” (Sztajn, Heck, Malzahn, 2021, p. 92). 

  • Talk Triangle. This is another proven technique that provides a structure for students to ask questions and share their thinking. It involves assigning roles to students during problem solving, such as the talker/problem doer; the questioner; and the listener/explainer. Using the Talk Triangle when solving a problem, the taker shares how they are working on the problem and what they are thinking. The questioner is probing the talker to draw out more information in order to  make sense of what they are doing. Scaffolding the questioner with question-starters is one way to get the conversation going.  Finally, the listener is paying attention to what is going on so they can explain or restate both what the talker is doing and what the questioner is asking.  

In her third grade classroom, Ms. Szabo used the Talk Triangle to help students solve multi-steps problems. She later reflected on the strength of the conversations in the triads, and on how students were not only questioning and explaining, but also listening to each other. Ms. Szabo’s students were not able to complete all the problems she had assigned to them for the lesson, and she concluded: “I thought that was OK because I always think that quality supersedes quantity, and we had some very good mathematical discussions in this lesson about how to set up and solve two-step story problems” (Sztajn, Heck, Malzahn, 2021, p. 129). 

  • Math Four Square. This is a great technique for supporting multiple modes of communication. The teacher gives students  a graphic organizer that asks them to represent their ideas with pictures, numbers and words. This organizer accommodates students’ communication preferences, brings forth different representations, and fosters connections among these representations.  

Also reflecting on a lesson for her first grade students in which she used the Math Four Square, Ms. Sonder noted that this technique gave her “a great way to see how they (the students) were making sense of and representing the story problem” (Sztajn, Heck, Malzahn, 2021, p. 117). 

As remote students return to classrooms, understand that many will be eager to talk while others may be hesitant to engage in conversations if that was not part of their daily distance learning . We want to  give every student a voice and guide the discourse in particular ways to support learning, especially in math. Having a variety of techniques that provide structure for students to participate in all dimensions of discourse can foster conversations that help all students get re-engaged, as well  help you learn about your students mathematical understanding. 

Written by

Paola Sztajn is a professor of mathematics education at North Carolina State University and is a principal investigator in Project AIM (All Included in Mathematics). Daniel Heck is vice president of Horizon Research, Inc. in Chapel Hill, North Carolina, and is a principal investigator in Project AIM. They are co-authors with Kristen Malzahn of Activating Math Talk: 11 Purposeful Techniques for Your Elementary Students. 

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