What if your best math tool isn’t on the supply list—it’s your students’ voices?

In today’s mathematics classrooms, getting the right answer isn’t enough. Real learning happens when students can explain why an idea works, compare strategies, and listen deeply to others’ thinking.

That’s where quality discourse comes in.

It’s more than talking in class. It’s purposeful, peer-driven, and grounded in reasoning. When students are actively engaged in discourse - asking, challenging, justifying, and revising - they begin to take ownership of mathematical ideas. They stop doing mathematics for the teacher and start doing it with each other.

What Does Quality Mathematics Talk Look Like?

Let’s picture a group of students working on a multiplication problem.

One student says, “I multiplied because that’s what we did yesterday.”

Another responds, “I multiplied because I saw equal groups forming.”

And a third reflects, “I think this would work for any situation where we have equal groups.”

In just a few exchanges, they’ve moved from recall, to reasoning, to generalization. And it all started with student-to-student discourse.

Discourse in Action: Quebec Fuentes' Question-Response Pairs

Quebec Fuentes (2020) identifies eight authentic, student-led interactions that emerge during rich classroom discourse:

1. A asks a clarification question → B answers A’s question
2. A asks B a content question → B answers A’s question
3. A asks B to show work → B shows own work
4. A asks B to explain work → B explains own work
5. A asks B to evaluate own work → B evaluates A’s work
6. A criticizes B’s work → B justifies own work
7. A rejects B’s justification → B reconstructs own work
8. A suggests a strategy to the group → Group tries strategy

These moments may look small but they’re where understanding grows.

How Teachers Guide It: The Four Steps Toward Productive Mathematics Talk

As Chapin et al. (2013) emphasize, teachers play a vital role not by leading every conversation, but by noticing, naming, and nurturing discourse as it happens.

Here are four powerful moves every teacher can make:

1. Clarify – Help students share and sharpen their thinking (e.g., “Can you explain what you were thinking?”)
2. Orient – Help students listen and connect to one another (e.g., “Can someone repeat what she just said in your own words?”)
3. Deepen – Push students to unpack and extend their reasoning (e.g., “Why does that strategy work? Will it always work?”)
4. Engage – Encourage students to challenge and build together (e.g., “Do you agree or disagree and why?”) (Chapin et al., 2013, p. 10)

How They Work Together

Quebec Fuentes gives us a window into what real discourse looks like: spontaneous, peer-driven, and cognitively rich. Chapin et al. show us how to support that discourse without taking it over.

Let’s connect the two with examples:

🔷 When A asks B to explain work, the teacher can deepen the moment by following up: “Why do you think that strategy works?”
🔷 When A rejects B’s justification, the teacher can engage the class: “What do others think? Can we revise the reasoning together?”
🔷 When A suggests a strategy to the group, the teacher might orient everyone: “Whose idea are we building on right now?”

This is how discourse becomes a shared classroom culture - not a technique, but a habit of mind.

Why It All Matters

When classrooms are built on quality discourse:

🔷 Students own the mathematics, not just repeat it.
🔷 Mistakes become learning opportunities, not embarrassments.
🔷 Reasoning, not rushing, becomes the measure of success.

And teachers? We become facilitators of meaning, not just monitors of correctness.

So the next time your students are solving a problem, pause and listen.

You might hear something better than an answer.

You might hear learning in progress.

Because in mathematics … talk really does count.

References

Chapin, S. H., O’Connor, C., & Anderson, N. (2013). Talk moves: A teacher’s guide for using classroom discussions in math (3rd ed.). Math Solutions.

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