Math Talk That Matters: Guiding Discourse with the Five Practices

Imagine mathematics classrooms where students are asking questions, sharing their work, and seeking connections across different pieces of their learning. They are not simply copying what the teacher has told them, but instead, they are actively creating mathematics in ways that make the most sense to them. At the same time, they are deepening and improving their mathematical skills by connecting new concepts to their prior knowledge.

Facilitating meaningful mathematical discourse in the classroom is an art that bridges student thinking, teacher guidance, and rich mathematical content. One powerful framework for supporting discourse is outlined in The Five Practices for Orchestrating Productive Mathematics Discussions by Margaret S. Smith and Mary Kay Stein (2018). These five practices (Anticipating, Monitoring. Selecting, Sequencing and Connecting) provide a structured yet flexible approach to turning student responses into opportunities for collective learning and deepened understanding.

Let’s explore how each of the Five Practices can help foster meaningful mathematical discourse in the classroom:

Anticipating involves carefully considering what strategies students are likely to use to approach or solve a challenging mathematical task (both correct and incorrect), how to respond to the work that students are likely to produce and thinking about which student strategies are likely to be most useful in addressing the mathematics goal.


Monitoring students involves paying close attention to students’ mathematical thinking and solution strategies as they work on the task(asking questions to assess and advance students' thinking), moving around the classroom while students work individually or in small group and taking notes on the different strategies that were used and by whom. Sometimes a teacher might use a monitoring chart with a list of anticipated strategies.


The Selecting of students’ responses is guided by the mathematical goal(s) for the lesson and the teacher’s assessment of how each contribution will contribute to that goal.


Sequencing is when teachers make purposeful choices about the sequencing of students’ solutions to maximize the chances of achieving the mathematical goal(s) for the discussion. Rationales for sequencing can vary:

• You might choose to start with strategy used by majority of students and might move to less common strategies. This approach validates work that many students did and makes discussion accessible to them.
• You might start with more concrete strategies (using drawings or concrete materials) and move to more abstract strategies (using symbols and notation). This approach validates less sophisticated approaches and allows for connections among approaches.
• You might start with common misconception(s) first. This approach provides opportunity to clear up common misunderstandings so students can work on developing more successful ways of solving the problem
• You might relate or contrast strategies are presented one right after the other.

The Connecting phase of a lesson is the heart of any mathematics class. It’s where formalization, abstraction, and consolidation of mathematical concepts occur. A well-planned lesson should allocate enough time for this part. During the discussion, the teacher focuses on connecting students' solutions by helping them relate their approaches to those of their peers and to the key mathematical ideas of the lesson. The teacher also encourages students to evaluate the accuracy and efficiency of different methods while recognizing mathematical patterns.

Smith, M. S., & Stein, M. K. (2018). 5 Practices for Orchestrating Productive Mathematics Discussions (2nd ed.). National Council of Teachers of Mathematics.

November 2024 Focus at the Kentucky Mathematics Teacher Leader Professional Learning: Facilitating Meaningful mathematical Discourse

During the November KYMTL professional session, we reviewed the Five Practices by using a mathematics problem to contextualize this learning. Our teacher leaders worked on anticipating strategies, then discussed how these different approaches could be summarized under common themes. We used the popular mathematics task from the Five Practices book, "Leaves and Caterpillars." The problem asks: "A fourth-grade class needs 5 leaves each day to feed its 2 caterpillars. How many leaves would the students need each day for 12 caterpillars?" Teacher leaders created both correct and incorrect solutions, then categorized them based on common mathematical approaches, such as unit rate, scaling up, or scale factor methods. Finally, participants planned for the selection, sequencing, and connecting phases of the lesson using a Google Slides template provided, along with some student work.