"The one doing the talking is doing the learning."
— Scott Collins, Lemont HS
It's the reminder most of us have muttered to ourselves at some point, usually while standing at the front of the room realizing we've been the only person making any sound for the last six minutes. It also happens to be a fair one-sentence summary of about forty years of research on math instruction.
Every routine ends in a class discussion, and it's tempting to treat that discussion as the cool-down: the part where you tie a bow on what already happened. It's the opposite. The worksheet, the partner work, the gallery walk are the setup. The discussion is where the learning gets finalized. If that's true, it's worth being deliberate about what happens in that last stretch.
This is a guide to that stretch: what it looks like to move the talking from the front of the room to the students, why that move matters, and the small, repeatable things that make it possible.
The move that helps most is the one that's easiest to skip
In 1979, Tom Good and Doug Grouws ran a study with fourth-grade teachers in Missouri (Good & Grouws, 1979). They found the teachers whose students gained the most, watched their classrooms, and tried to name what those teachers did differently. The answer was a stretch of the lesson they called "development" — the part where the teacher worked on meaning. Not procedures, not practice, not review. Meaning. It was also the part teachers had the most trouble protecting, because when the period runs short, it's the easiest thing to cut.
Fourteen years later, Jim Hiebert and Diana Wearne followed second-grade classrooms learning place value for twelve weeks (Hiebert & Wearne, 1993). Some ran traditional lessons; some had broken from the textbook and were running discussion-heavy ones. The discussion-heavy rooms covered fewer problems per lesson and spent more time on each. They asked more about how students were thinking, not just whether the answer was right. Student responses were longer. By the end, those students had learned more.
Hiebert and Wearne published transcripts, and two of them are worth putting side by side.
Classroom A (traditional):
Teacher: Look at Row A. See where it says 580 take away 234? What are you going to ask yourself? Student: Can I take 4 from 0? Teacher: Can you? Student: No. Teacher: What do you do? Student: Go to the tens, cross out the 8 and put 7. Teacher: Cross out the 8 and put 7. Good. What are you going to do with the 10 you took away?
Classroom D (discussion-focused):
Teacher: Jane, can you tell us how you did this? I didn't see any blocks on your desk, so I want to see how you did it. Student: I counted in my head. Teacher: Where did you start? Student: I put 145 down and then I counted 135. Teacher: How did you count 135? Student: I put a hundred with the 135 to make 200. Teacher: So you combined the 100 here with the 100 here and got 200. Then what? Student: I put the 4 and the 3 together. Teacher: Why did you put the 4 and the 3 together? Student: Because they're the ones. Teacher: So you're combining the 4 and the 3 for a specific reason. Can you say more about that?
The difference isn't subtle. In the first, the teacher walks the student through a procedure and the student fills in the next step. In the second, the teacher asks the student to show her thinking, then pauses on "you're combining the 4 and the 3 for a specific reason" to let a small misstatement become something the student rethinks rather than something the teacher corrects. That pause is the whole game.
Two kinds of questions, and only one starts a discussion
Good and Grouws named the two kinds of questions teachers ask: product questions and process questions.
A product question asks for an answer. What's 580 minus 234? Is this line a good fit? Which statement is correct?
A process question asks for thinking. How did you get there? What made you decide that? Why did you put the 4 and the 3 together?
Both have a place. You need product questions to check whether students can do the math. But product questions don't generate discussion. They generate a one-word answer, then silence, then the teacher filling the silence. Process questions move the talking to the students. They're harder to ask, because they require you to genuinely not know what the student will say. The moment you already have the answer you want to hear in your head, you start steering the student toward it, and the student stops thinking and starts guessing what you want.
The routines are built to make process questions easy to ask. Learn from Mistakes hands you student work to point at: what was this person trying to do? Decide & Defend gives you four arguments to compare: which is most convincing, and why? Graph Sort gives you a pile of groupings: what did these have in common? The activity creates something specific to ask a process question about.
What you're actually doing when you're not explaining
Mary Kay Stein and Peg Smith wrote a book called 5 Practices for Orchestrating Productive Mathematics Discussions (Smith & Stein, 2018). It's essentially a manual for the part of a routine where students are talking, and it's worth owning. The five practices are:
- Anticipate. Before class, work the problem yourself and predict how students will approach it. What strategies will come up? What confusions?
- Monitor. While students work, walk the room and notice what they're actually doing. Not to help — to learn.
- Select. Pick two or three pieces of student work to put in front of the class. Not the best ones. The ones that surface the ideas you want discussed.
- Sequence. Decide what order to share them in. Often you start with something accessible and build toward something more sophisticated.
- Connect. Make the relationships between the pieces explicit. Notice that what Jamal did at the start is the same thing Ava did at the end; they just got there in a different order.
The five practices answer a question most teachers have asked themselves: if I'm not the one explaining, what am I actually doing? You're doing all of that. The work of running a thinking-centered discussion is mostly invisible from the outside, which is part of why it's hard to learn. You're listening for specific things. You're holding three student approaches in your head and deciding which to call on first. You're letting a small error sit in the air two extra seconds to see if anyone catches it. None of that looks like teaching the way most of us were taught to picture it. All of it is teaching.
The practice that gets cut most is the last one. Connecting — saying out loud how one student's idea relates to another's — is where separate pieces of student thinking become one idea the class shares. When time is short, it's the first thing to go, and it's the thing most worth protecting.
What the five practices look like inside a routine
Before class — anticipate. Look at the worksheet, gallery, or slides before students arrive. Solve a few problems yourself. Jot down what mistakes and strategies you expect. If you've run the routine before, note what came up last time.
During the activity — monitor. Students work alone, then with a partner, then walk the gallery. Your job isn't to help individuals. It's to walk the room and notice. Carry a sticky note. Write down two or three things to come back to.
Before the discussion — select and sequence. You don't have to cover everything that came up. Pick two or three things: a mistake that surfaces a common confusion, a strategy nobody else used, two arguments that look alike but reach different conclusions. Decide the order.
During the discussion — connect. This is where the talking shifts to students and where the process questions live. Why did you start there? What were you noticing? Is this the same as what Ava said, or different? The connecting part is the part most often lost to the clock. Don't lose it. It's where the routine pays off.
A field guide to process questions
A few worth keeping in your back pocket. Most work in any routine.
- How did you decide that?
- Where did you start?
- What were you trying to do here?
- What made you change your mind?
- Is that the same as what they did, or different?
- What would convince you you were wrong?
- What's the part you're least sure about?
- Can you say more about that?
And a few worth noticing when you want a real discussion. They aren't bad questions, but they tend to close conversation rather than open it.
- Is that right?
- Does everyone agree?
- What's the answer?
- Did you get it?
The point isn't to ban the second list. It's to notice that when you ask one of them, the room usually goes quiet, the silence makes you nervous, you fill it, and the talking is back at the front of the room.
The first time might be bumpy
If you haven't run discussions like this, the first one will probably feel rough. Students used to product questions won't suddenly hand you long, thoughtful answers when you start asking process questions. Some go quiet. Some give back the answer they think you wanted. Some say "I don't know" because they aren't sure what kind of answer counts.
That's normal, and it isn't a sign the routine isn't working. It's a sign students are learning a new kind of classroom behavior, which takes time the same way a new procedure does. By the third or fourth run, something shifts. Students start expecting how did you get there, so they come ready to explain. They listen to each other, because they might be asked whether they agree. The discussions get longer. The talking moves to the students. That's the routine working, and it's where the meaning gets made.
References
Good, T. L., & Grouws, D. A. (1979). The Missouri Mathematics Effectiveness Project: An experimental study in fourth-grade classrooms. Journal of Educational Psychology, 71(3), 355–362.
Hiebert, J., & Grouws, D. A. (2007). The effects of classroom mathematics teaching on students' learning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 371–404). Information Age Publishing.
Hiebert, J., & Wearne, D. (1993). Instructional tasks, classroom discourse, and students' learning in second-grade arithmetic. American Educational Research Journal, 30(2), 393–425.
Smith, M. S., & Stein, M. K. (2018). 5 practices for orchestrating productive mathematics discussions (2nd ed.). National Council of Teachers of Mathematics.