How can teachers design more meaningful math discussions, where every student is heard even in online or hybrid classrooms? 

In a conversation with the National Council for Teachers of Mathematics (NCTM), Dr. Sarah Quebec Fuentes and Dr. Theresa Wills offered thoughtful guidance on how the 5 Practices framework (Smith & Stein, 2018) supports rich, equitable small-group math learning.

“The 5 Practices are this amazing structure built by Smith and Stein,” Theresa explained, “all about anticipating student moves, monitoring them, selecting and sequencing purposeful representations, and connecting them to each other and our math goal.”

Theresa described how adapting the 5 Practices to an online environment takes new thinking. Teachers must anticipate not only students’ strategies, but also the digital tools, virtual manipulatives, and even home resources (like Cheerios or spaghetti!) students might use. But, she also found a surprising benefit:

“Instead of walking around the classroom,” Theresa shared, “I’m able to move between breakout rooms, listen in, and at the same time look at the slides of other groups. That gives me more flexibility in overseeing more of my class.”

Sarah emphasized the importance of establishing and sustaining group norms for effective discussion:

“Often students don’t know what the expectations are for small-group work,” Sarah noted. “It’s our job as teachers to establish those norms, and that takes time and commitment.”

She recommended a mix of explicit strategies (like co-creating group norms with students and posting discussion starters) and implicit strategies (such as consistently using talk moves like asking students to explain their thinking rather than simply giving them the answer). These repeated moves, she stressed, build a culture of student-to-student accountability over time.

Both experts made a strong case for rich mathematical tasks in supporting student-centered learning.

“Rich tasks open up the type of communication that students will have,” Sarah said. “If our goal is for students to evaluate and compare strategies, we need to incorporate high-level tasks.”

Theresa agreed, pointing to NCTM’s (2018) Eight Effective Teaching Practices:

“They build on conceptual understanding, productive struggle, meaningful discourse and rich tasks address all of those,” she explained.

They also addressed common challenges teachers might face, including students who hesitate to use their microphones or who disengage in breakout rooms. Theresa suggested lowering the stakes with familiar tasks while building new discussion skills, using chat boxes, screenshots, and partner-share strategies:

“Microphone isn’t the only way to hear student voice,” she noted. “Chat boxes, images, videos all help students feel safe to share.”

Finally, both experts offered a note of encouragement.

“Change takes time,” Sarah reminded us. “When you hear a group having an incredible math conversation, you realize your work paid off.”

Theresa added:

“Give yourself the same grace you give your students. When they see you calmly working through challenges, they’ll be more willing to do the same.”

If you would like to hear Sarah and Theresa’s full discussion including their detailed tips, examples, and ideas to immediately apply in your own classroom, watch the video here:

👉 NCTM—Sarah Q. Fuentes and Theresa Wills Discuss 5 Practices

References

National Council of Teachers of Mathematics [NCTM]. (2014). Principles to actions: Ensuring mathematical success for all. NCTM.

Quebec Fuentes, S. (2020). S3D: Fostering and improving small-group, student-to-student discourse. NCTM.

Smith, M., & Stein, M. K. (2018). 5 practices for orchestrating productive mathematics discussions (2nd ed.). NCTM.

Wills, T. (2020). Teaching math at a distance, grades K-12: A practical guide to rich remote instruction. Corwin and NCTM.