Productive Math Discourse—It’s All About Good Questions

We know from research that the person who talks is the person who learns. In fact, according to John Hattie’s visible learning research, productive discourse—which he defines as a form of instruction in which students are invited to speak about the topic at hand—doubles the rate of learning. In the math classroom, talking about mathematical concepts allows students to demonstrate their understanding, learn from and critique classmates’ ideas, make conjectures and refine strategies, connect to prior knowledge, and most important, own their mathematical learning. But just how do we get students talking about math in a way that promotes deep learning?

A Thoughtful, Strategic Approach

Productive math discourse is about students talking with each other while the teacher guides and informs. Ideally, we should spend two thirds of classroom time engaged in discourse-based instruction. And just like with any instruction, it’s important to plan how best to encourage and sustain rich math talk. It’s both a skill and an art to run an effective discussion, the type of discussion that leads to deep learning.

The book, The 5 Practices for Orchestrating Productive Mathematics Discussion, shares what I believe is some of the best thinking on guiding rich math talk. First, we need to anticipate student responses (Practice #1). I’m a big believer that as teachers we should do the assignments we are asking our students to do as it helps us think more deeply about what students might do while grappling with a particular task. What strategies might they use? Where could they get stuck? What misconceptions may they have? And what questions might you ask to support and guide student thinking.

Spending time on anticipating student responses sets you up to monitor student thinking (Practice #2) because now you know what to look for. What strategies are students using? Where do they get off track? What misconceptions do they demonstrate? And as you move around the classroom and check students’ work, you’ll be able to monitor and question more effectively, because you have a core set of responses you carefully prepared for. The questions you prepared will help students reflect on and discuss different ways of thinking about the task at hand.

Part of discussion is about how best to select (Practice #3) and sequence (Practice #4) the work you want to share. I remember as a teacher asking students to share their thinking and calling on someone who gave the perfect answer—they used the right strategy in the right way. And of course, that shut discussion down because nobody had anything to add. You do want to share that great thinking but not at the beginning of the discussion. So, as you monitor student work, you want to think about (1) what does this work show and why should other students see and discuss and it, (2) how best to organize the work you choose to share, informal to formal, common to unusual, and (3) what questions might you ask to deepen the resulting discussion. I also think it’s important when selecting and sequencing work to share that I let students, especially those who aren’t first to raise their hands, know why I’m sharing their work and when I plan to share it so they have time to prepare as needed.

And finally, you want to connect the work (Practice #5) to specific learning goals because each task you select helps student better understand the underlying mathematical concepts. So, the work you share provides examples of the big ideas you want students to take away from the task. And if the work you share doesn’t illustrate all of the learning goals, as it often doesn’t, you’ll want to have questions prepared that help students to make those connections.

Questions That Encourage Collaboration and Discourse

The art of guiding productive math discourse is all about the questions you ask and when you ask them. And the type of questions you ask is all about your goal for a particular discussion.

Open vs. Closed Questions

Closed questions are great for checking if students are fluent with particular math facts or when you are looking for a single right answer. But they don’t typically lead to robust math talk. For that we need to ask open questions or those that lead to multiple strategies and solution paths. Open questions help students understand that there are different ways to approach a given task or problem. For example, you might give students a computation task they haven’t yet done, but that’s an extension of concepts they’ve already learned, and ask them how they might approach the task. What strategies might they explore? What tools could they use? How might they represent the problem?

Open Questions- (Use when looking for multiple responses.)
• Give ___ examples of …
• Describe ___ situations where you would ….
• How might you…?
• What if…?

Closed Questions- (Use when looking for a single correct answer.)
• What is …?
• Define ….
• Compute ….
• Label …
• Yes/no questions
• Either/or questions

Funneling vs. Focusing Questions

When to use funneling or focusing questions is primarily about whether you are prioritizing your thinking (funneling) or students’ thinking (focusing). If you want students to follow your train of thought, you’re going to ask funneling questions that steer them to a particular idea or strategy. For instance, if a student is stuck (and getting frustrated) with a problem that requires multiplication, you might say, “Have you tried multiplication?” or better yet, “You might consider multiplying, because I see an equal group situation in the problem context.” However, if you want students to clarify their own thinking, you’ll want to lead with focusing questions to help them move forward. So, with that same problem in mind, you might ask, “Which operations have you tried? Which ones are left to consider?”

Funneling Questions- (Use when helping students follow your train of thought.)
• Have you tried…?
• You might want to …
• If I were you, …

Focusing Questions- (Use when helping students to clarify their own thinking.)
• What have you already considered? What else could you consider?
• What have you already tried? What other strategies could you try?
• Of all these ideas, which one do you want to try first?

Recall Questions

Recall questions are often close-ended, and they help students show what they know. Like funneling questions, well-timed recall questions are a great way to help students get back on track if they’ve moved from productive to unproductive struggle. Going back to that same problem that requires multiplication, you might ask, “What are the two values you’re going to multiply?”

Recall Questions- (Use when looking for a single correct answer.)
• What is …?
• Define ….
• Compute ….
• Label …
• Yes/no questions
• Either/or questions

Probing Questions

If you really want to help students to make the connections that lead to deeper learning, ask probing questions. If you are a regular reader of this blog, then you know that the one change I’d like to see all of us all make is that we ask more frequently, “How do you know?” All too often this question leads students to erasing their answer believing that it’s teacher-speak for “Nice try, but that’s wrong.” However, this is just the sort of probing question that leads to students making important connections as they explain and justify their thinking, whether their reasoning if correct or not.

Probing Questions- (Use when you want students to elaborate on their thinking.)
• Tell me more about how you know that.
• What makes you think that?
• Explain the connection between ___ and ___ with more details.

Process Questions

When you want students to reflect on the how behind their reasoning, process questions help them clarify their choices and showcase their solution path. Additionally, process questions, such as “Why did you choose that strategy?” or “What advice would you give to a classmate trying to solve a problem like this?” help other students in the class think more deeply about alternate ways to approach a particular task and may very well lead to an “aha” moment.

Process Questions- (Use when you want students to reflect on their process.)
• Why did you choose that strategy?
• What would you do differently next time?
• What advice would you give someone trying to solve a problem like this?