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Purposeful Discussion in the Math Classroom

Amanda Haecker – 3rd grade teacher

When I reflect on what is most important to me as an educator, I land time and again on student voice and belonging. Each year, I work hard to build a safe, purposeful learning community where students understand that their voice and ideas are valued, and their classroom is a safe space to learn and grow. I believe that students need to see that their community is a safe place to express their ideas, to grapple with something when they feel unsure, and to take risks and make mistakes in front of others. At the start of each school year, a great deal of intentional work goes into building community norms and practices that support this.

This work is especially vital in the math classroom. My goal each year for students is to develop a positive relationship with math and to understand that math is for everyone. I strive to support students in seeing the ways that math can be fascinating, playful, and even beautiful. Building routines for purposeful discussion and sense-making with one another is one of the ways I strive to make math learning accessible for all. Discussion routines that allow students to talk through new ideas with one another, uncover patterns or compare and connect strategies help students strengthen and deepen their mathematical ideas. Listening to a variety of perspectives dispels the myth that in math there is only one right answer or approach.

Students benefit from being explicitly taught what a productive discussion looks like. We can guide students how to put words to their thinking through modeling, sentence starters and targeted questions. It’s important that students engage in accountable talk, meaning they are listening to and responding to one another’s ideas. Orienting students to one another and using talk structures such as, “Adding on to _____’s idea ...,” “I agree with _____ because ...,” and “I respectfully disagree with _____ because ...” supports students in engaging in a discussion together, rather than just directing their comments toward the teacher. Students are guided to show one another that they are listening by turning their bodies to the speaker, making eye contact or using “I agree” hand signal to indicate their connection.

Comparing and Connecting Strategies

A natural place to start building discussion routines in the math classroom is through strategy shares. After solving a problem, I often invite my students to share their approaches with the group. Sharing, discussing, and documenting the variety of approaches students take when solving a problem helps to make students’ thinking visible. The question “Who thought about it in a different way?” normalizes the natural variation in approach. Students get the chance to describe their approach using phrases like, “How I thought about it was ...” As more strategies get added, students are guided to compare and connect across strategies by thinking about what aspects are similar or different. They investigate and name the mathematical relationships amongst these strategies. For example, each person made the problem more manageable by breaking the numbers down into friendlier parts. This can support students in thinking flexibly. Students might then be guided to try a classmate’s strategy as we say, “Let’s all try out ______’s way.” As we seek to promote equity and belonging in the classroom, it is a powerful moment for many children to be recognized in this way.

Investigating Patterns

Children are natural pattern detectives, and mathematics is full of patterns. Opportunities to examine and identify patterns support students to think more deeply about why our number system behaves as it does. Our mathematical calendar is a springboard for this type of discussion. Open-ended questions like, “What do you notice,” or “What does this make you think,” launch the discussion and allow students to engage from a variety of entry points. Students might share observations about color or shape patterns. Others might share the fractions that they see or begin to make connections about equivalencies. They might share predictions about what they think might appear next, grounded in reasoning about what is already visible. As they share, students practice tuning into each other’s ideas and building off of one another’s thoughts.

When studying multiplication, we might do a choral count as a class and document the multiples of a number within a particular range. After choral counting the multiples of 3, 6, and 9 one week, my class examined the charts side-by-side with the same type of opening question: “What do you notice?” Students shared their observations about patterns and connections within the three charts, pointing out where and how numbers repeated, patterns within the digits, or patterns of even and odd. These discussions allow us to think about the next question of “Why?” “Why are these patterns occurring?” and support students in constructing conjectures about relationships within our number system.

Justifying Ideas Using Mathematical Reasoning

Finally, discussion structures can support students in learning to justify their ideas. An important mathematical goal for students as they strengthen their skills is to begin asking themselves, “Does this make sense?” and furthermore, “Why does this make sense?” As students lean into the “Why?” questions in math, they are learning to articulate important mathematical ideas. Giving students opportunities to make sense of mathematics together and to construct generalizations about what they are observing, rather than just teaching students a “rule,” deepens their conceptual understanding and bolsters their number sense.

Estimation routines offer students a good entry point to practice justifying their thinking. Throughout the year, my students practice estimating quantity, distance, time, or by using rounding and estimation to check their work asking, “Is this answer reasonable?” Our estimation routines support students to focus in on the most reasonable idea by first thinking about of a too-low and too-high estimate. Students then discuss their predictions with one another, using phrases like: “I think this choice is best because ...” or “This is the most reasonable to me because ...” Learning to visually analyze a problem and to reason aloud about a mathematical decision are important mathematical practices.

Giving space for students to make sense of mathematics together, in the same way we might make sense of a text in a literature discussion, has changed my students’ relationships with math. Through these discussions, students learn that it is ok to take a risk and to be wrong and that it is ok to have a different perspective or method than their peers. Open-ended discussions provide multiple entry points to elevate student voice and to make the math classroom an equitable space for all.


 

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