Math
Introduction
Consider all of the ways that children, families, and educators already “talk math” whether they realize it or not:
- How much longer will it take me to get to school?
- How much money will I need to save?
- What grade do I need to get on the next test?
Whenever a conversation includes concepts such as time, distance, money, size, or shape, math is already a part of it! If you are having conversations like this with your students, you are already starting to engage in math talk.
What Is Math Talk?
Math talk is a term that describes the discussions students and teachers have while engaged in learning math. This often includes the small-group or partner conversations between students as they make sense of and solve problems, and could be as informal as discussions centered on noticeable surroundings, i.e., “What patterns do you notice in our classroom?”
Why Is Math Talk Important?
“The one talking about the math is the one learning it” is the consistent refrain from author, educator, and coach Jennifer Lempp who champions the power of math talk. Rather than relegating math talk to the periphery of lessons, keeping it front and center positively impacts learning. Math talk is a well-researched approach to deepening student engagement, developing social skills, and promoting deep sense-making. In John Hattie’s 2018 research and analysis of influences on student learning, he identifies classroom discussion as having an effect size of 0.82. That means discussion ranks 15th most significant of the 252 learning influences considered in his research.
You get the idea; discussion is a big deal. So, how do we go about creating opportunities and providing structures for math talk? Let’s take a look at how math talks unfold in the classroom.
Math Talk Examples
For math talk examples, let’s examine the different sorts of purposes that classroom discussions can have. The examples are organized with two different scenarios in mind.
Scenario 1: Surfacing multiple student ideas
Classroom Interaction |
Purpose |
---|---|
Classroom Interaction
During a lesson, Ms. Ramirez asks, “Who has an idea about how to solve this problem?” Three student hands fly into the air, the same three that are frequently first to have an idea to share. She pauses momentarily and says, “I see Jacob, Amelie, and Jamila have ideas. Who else has an idea?” |
Purpose
Acknowledge students’ willingness while simultaneously making space for additional ideas to surface. |
Classroom Interaction
She waits a moment longer and a few more hands are raised. “Turn and talk with your elbow partner. What are you thinking here? And if you’re not sure, talk about what might have you confused.” |
Purpose
Redirect discussions into smaller groupings or partners to decrease the pressure to “get the right answer” while also providing opportunities for more voices to get involved in the discussion. |
Classroom Interaction
Students have a couple of minutes to discuss, and Ms. Ramirez circulates listening for common themes, students’ understanding, and areas of possible confusion. |
Purpose
Gather formative assessment information during discussions and give yourself time to decide on the next question for the lesson. |
Classroom Interaction
“I heard some very interesting ideas out there! Jamila, will you start us off with something your partner brought up during your chat?” |
Purpose
Return to a student who was ready to share aloud, and support active listening by asking them to share something they heard. |
Scenario 2: Using math talk to help students see themselves as mathematicians
Classroom Interaction |
Purpose |
---|---|
Classroom Interaction
Mr. Howard noticed that his Algebra 2 students were reluctant to get involved in discussions so he started using warm-ups as a place to get them talking. He posted the statement, “the book is better than the movie,” and asked students to discuss if this was always, sometimes, or never true. |
Purpose
When teaching a new routine, start off with a low-stakes or non-mathematical context to unlock student ideas and provide equitable access into the discussion. The Always, Sometimes, Never routine engages students in sense-making and justifying ideas regardless of context, preparing them for mathematical thinking along those same lines. |
Classroom Interaction
“Take 30 seconds. Form your opinion. Prep your justification! Then you’ll chat with your table groups about it.” |
Purpose
Provide time for students to gather their own ideas prior to discussing with others. |
Classroom Interaction
Students discussed with their partners and then Mr. Howard facilitated a 2-minute whole-class share out. Next, he posted “2x < 3x” on the board and asked again, “Is this always, sometimes, or never true?” |
Purpose
Bridge from the low-stakes or non-mathematical context to a mathematical one using the same routine. |
Classroom Interaction
Students had individual thinking time and then time to discuss with their groups. Mr. Howard circulated to listen to their ideas, noticing that most students said “always.” |
Purpose
Gather formative assessment data during discussions and adjust your approach based on what you hear. |
Classroom Interaction
“Let’s start of with the ‘always true’ crew. Tell me how you know.” “We know that 2 is less than 3, so 2x is less than 3x,” Leigh shared. “Can we think of any instance or any value for x that would make this not true?” Mr. Howard prompts. |
Purpose
Surface initial ideas and extend student thinking from there by asking additional questions. Centering student ideas conveys that you think their ways of thinking are important and worth talking about. |
Getting Started with Math Talk
Having a vision for how you want discussions to go will help make math talk time more focused, meaningful, and productive. As you plan, consider what you will have them talk about, and how you will support their use of academic language. Here are a few math talk strategies for planning high-quality classroom discussions.
- Build a Safe Math Talk Community: Sharing ideas can be risky. Establish and maintain an environment in which each students’ ideas and contributions are valued. Invite students to co-create norms for discussions by facilitating an opportunity for them to think about a time when their ideas were heard and they felt important, and a time when that was not the case. Use the commonalities in students’ experiences as a baseline for your discussion norms.
- Start Small: When you’re first establishing norms and routines for productive discussions, start with a low-stakes discussion prompt that provides an entry point for every student. This might include something like a Which One Doesn’t Belong or a Notice and Wonder prompt. Choose something open-ended, with multiple “right” answers and ways to think about the problem. Plan to give students individual thinking time before sharing their ideas with a partner or small group.
- Provide Language Scaffolds: Whatever prompt you start with, be sure to provide sentence starters or sentence frames so students have a framework for sharing their ideas. For a Notice and Wonder prompt, sentence frames could include “I notice _____, and I wonder _____” or “I noticed the same thing as _____, but I wondered _____.” Be sure your sentence frames are posted so students can reference them during their discussions.
- Be Clear about Your Why: When you’re planning your lesson, ask yourself Why am I having students talk at this point? Is it so you can circulate and hear how they’re thinking about the mathematics? Is it to provide an opportunity for them to digest what they’re learning? Is it to foster your math learner community? Students may disengage from discussions that are disingenuous. Consider transparently sharing with students the purpose of the discussion to help them know what you’re trying to achieve. For example, when using a Which One Doesn’t Belong discussion for a warm-up, you might say, Let’s kick off class today by looking for some patterns. How you think is important! Let’s get all your important ways of thinking out in the open so we can learn from one another.
3 Tips for Keeping Discussions On-Track
We’ve all experienced or taught lessons that did not go as planned. Opening up time in the lesson for students to discuss may feel nerve-wracking if you’re not sure how it will go, or how to get students re-engaged if their discussions digress. Here are a few ideas to help overcome common challenges with facilitating high-value discussions:
- Choose discussion opportunities that are authentically open-ended. Give students something interesting to talk about. Many routine math problems can be transformed into discussions by choosing a format such as Which One Doesn’t Belong or Always, Sometimes, Never (see above). One quick way to create an open-ended task is to post the answer and ask students, “Here’s the answer. What might the question be?”
- Engage students in choosing the discussion prompt. After introducing the routine of something like Which One Doesn’t Belong, ask students to curate a set of 3–5 items that you will incorporate in the next WODB.
- Shift to writing to create equity and incorporate various student perspectives. When you’re trying to achieve a balanced discussion, during which multiple and varied student voices are heard, try having students jot down their initial ideas in writing, then pass their papers or thoughts to a partner who then will read and respond. This equalizes the “talk time” and provides time and space for all students to engage in the discussion. This approach also works well when having small groups discuss verbally, then write down their key ideas to pass to another group.
Remember that success tends to foster success. Start with small increments of time during which student discussions are focused and on-topic and wrap it up before discussions get off track. Over time, the length of discussions will naturally extend as students have developed the muscle memory, and desire to engage in, the discussion opportunities you have created.
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Find ideas and opportunities for math talk with HMH Into Math and Into AGA. These math programs inspire students to see the value and purpose of math in their daily lives through rewarding, real-life activities and lessons.
For more strategies to make math talk more intentional in the classroom, watch the webinar "Make Math Talk More Productive with Questioning Strategies" with Cynthia Goodman.
Get our FREE guide "Optimizing the Math Classroom: 6 Best Practices."
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