Three Essential Strategies for Supporting Mathematical Thinking and Discourse during Distance Learning

By: , | 09/25/2020
Categories: Distance Learning, Instruction

In the classroom, teachers work very hard to design and deliver learning experiences that support all students’ mathematical thinking. We want to make sure that those supports aren't lost in a remote setting when students and teachers don’t have face-to-face interactions. In the worst-case scenario, remote instruction can be reduced to a one-way dissemination of information: The teacher delivers information, and students passively take it in. So, the question becomes: How can you apply the multimodal processing supports you have in place in the classroom to distance learning?

Fortunately, many proven instruction strategies that work in the classroom can be adapted to work during distance learning. Mathematical instructional strategies—including Individual Think Time, Turn and Talks, and the 4 Rs (Repeat, Rephrase, Reword, and Record)—that support and engage all students in mathematical thinking and discourse in the classroom can be adapted for and applied in a remote setting.

Individual Think Time

Individual Think Time (ITT) gives students an opportunity to think about a math concept and work privately on a problem before discussing their thinking with a partner, a small group, or the whole class. ITT allows students time to make sense of what’s in front of them and gives them space to begin to gather their thoughts and questions. It also helps avoid the all-too-common pitfall of one student dominating partner work because their classmate has not yet fully processed the task at hand. ITT significantly increases both the quantity and quality of students’ mathematical thinking and communication.

Before implementing ITT, take care to name it, provide a time estimate, and give students a question or prompt to guide their thinking. For example, you might say, “Take one to two minutes of private think time to determine the important quantities in this problem” or “Before picking up your pencil, take 30 seconds to quietly consider what you notice about this representation.”

Integrating ITT into Remote Learning

  • If you are creating materials to send home, include consistent and regular written reminders “to pause and think before jumping to problem solving” on student pages.
  • If you are creating prerecorded lessons for your students:
    • Add deliberate pauses to the recording to allow time for students to think.
    • Add explicit prompts for ITT that ask students to pause the video themselves.
    • Divide video lessons into chunks. Have videos end with an ITT prompt. Ask students to start a new video clip after they have had time to think.
  • If you are facilitating interactive online synchronous learning, simply pause and prompt students to take ITT as they would in the classroom.

Learn more from Ready Classroom Mathematics authors, Grace Kelemanik and Amy Lucenta.

Download their whitepaper, Integrating Effective Teaching Practices Teacher Moves That Engage Students in Discourse and Mathematical Thinking.


Turn and Talks

Turn and Talks provide students with opportunities to share their mathematical thinking or ideas with a partner. They create space for each and every student to speak, think, and develop language. Ideally, Turn and Talks also give teachers opportunities to listen in and get a sense of the range of student ideas.

When implementing Turn and Talks, start by setting norms and communicating the importance of talking through mathematical ideas with a partner. Ensure that each student knows who their partner is—in a remote setting, that “partner” may be a peer, a family member, a stuffed animal, or even the student themself. When you ask students to turn and talk, ensure that the idea they have been asked to ponder is worth talking about, then frame a clear prompt and provide a sentence frame for students to get started.

In the Classroom Example:

“Will Olivia’s strategy always work? Turn and talk to your partner and decide if you think it will. Justify your decision. Start by saying, ‘I agree/disagree with Olivia’s strategy because . . .’”

Integrating Turn and Talks into Remote Learning

  • If you are creating materials to send home, make sure they include prompts for students to process and share their thinking with a family member or through self-talk. Include sentence starters or frames that they can use while turning and talking.
  • If you are creating prerecorded lessons for your students, add turn and talk and pauses: Ask students to talk through their ideas with a family member, stuffed animal, pet, or themselves.
  • If you are facilitating interactive online synchronous learning, simply pose a Turn and Talk and pause for students to talk out loud either to themselves or to someone or something at home. If the software you’re using allows, you can send students to virtual breakout rooms for small chat groups.

The 4 Rs (Repeat, Rephrase, Reword, Record)

The 4 Rs help students process and refine mathematical ideas and language and (ideally) get them listening to one another. The 4 Rs also give students multiple passes at the idea and language in order to develop understanding and precision in both areas.

When implementing the 4 Rs, first decide which R to use. If it’s possible that not everyone heard a response, then have one or two students repeat what was said. If the math idea is important and students need time to process it, then have students rephrase the idea using different words. If there is specific language students can use to express this idea more precisely, then prompt students to reword the idea using the more precise language. If there are important ideas, words, or images being shared that students would benefit from seeing and referencing, then record the ideas to help students process or remember key concepts and participate in the conversation.

Once you’ve chosen which R to use, prompt students to repeat, rephrase, or reword and ensure that they stick to the original idea in doing so. Record important language and ideas where all can see. You might say, for example, “Let’s process what Nadia just said. Who can rephrase her idea?” or “I’d like you all to process what Nadia just said. So, I’m turning the mics off, and I want you each to rephrase her idea in your own words” or  “Who can reword what Connor just said using precise mathematical language?”

Integrating the 4 Rs into Remote Learning

  • If you are creating materials to send home, include rephrase/reword prompts in them. Ask students to refine ideas and/or ask family members to have students rephrase/reword.
  • If you are prerecording lessons for your students, add regular prompts and pauses to the videos. Ask your students to repeat/rephrase/reword what they just heard to a family member, stuffed animal, pet, or themselves.
  • If you are facilitating interactive online synchronous learning through videoconferencing software (i.e., Zoom™), prompt students to perform an R and pause for all students to talk at home with their mics off, or prompt an R and turn on one mic for one student to respond. While students respond, record their language on a shared screen.

As you continue on your journey of facilitating discourse at a distance, try to leverage routines that students already know. Remember that hand signals and emojis can provide feedback that you may typically gather by scanning the room. Just like when they are in front of you in a classroom, students need time to think and talk. Don’t forget to support learning through engaging multiple modalities—visuals, annotation, etc.

If you initially struggle to make these strategies part of your distance-learning instruction, forgive yourself. We didn’t learn about remote teaching in teacher preparation programs, but with regular attention, just like in your classroom, you can make math discourse a routine part of your remote instruction!


Kelemanik, G., Lucenta, A., & Janssen, Creighton, S. (2016). Routines for reasoning: Fostering the mathematical practices in all students. Heinemann: Portsmouth, NH.

Interested in learning more? Watch a recording of Teacher Moves That Engage Students in Mathematical Practices, Grace and Amy’s webinar about mathematical discourse and distance learning.

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