Posing Purposeful Questions with Dr. DeAnn Huinker

Educational theorist Charles Degarmo once said, "To question well is to teach well. In the skillful use of the question more than anything else lies the fine art of teaching." Today, Dr. DeAnn Huinker, author of Taking Action: Implementing Effective Mathematics Teaching Practices in Grades K-5, talks about the art and the science of questioning and ways that teachers can maximize the impact of their questions on student learning.

Mike Wallus: Educational theorist Charles De Garmo once said, 'To question well is to teach well. In the skillful use of the question, more than anything else, lies the fine art of teaching.' Our guest today, DeAnn Huinker, is one of the co-authors of 'Taking Action: Implementing Effective Mathematics Teaching Practices in Grades K–5.' We'll talk with DeAnn about the art and the science of questioning and the ways that teachers can maximize the impact of their questions on student learning. DeAnn, welcome to the podcast. It's great to have you.

DeAnn Huinker: I'm happy to be here, Mike. I'm looking forward to our conversation today.

Mike: So, I'd like to start by noting that NCTM (National Council of Teachers of Mathematics) has identified posing purposeful questions as a high-leverage practice in 'Principles to Actions,' and then again in 2017 with the publication of 'Taking Action.' And I'm wondering if you can make the case for why educators should see purposeful questions as a critical part of this practice.

DeAnn: Yeah, certainly. Let's just jump right in here. As we think about purposeful questions and why we as teachers need to be more intentional and strategic in the questions we use … I was honored to be a member of the writing team for 'Principals to Actions.' And in writing that document, we were really tasked with identifying a set of high-leverage teaching practices for mathematics. We reviewed the research from the previous 25 years (chuckles), and it was really clear: There's been a lot of research on teacher questioning. And what are the characteristics of effective questioning. So, as I think about making this case for purposeful questions, a couple things come to mind. First of all, researchers have estimated that teachers ask up to 400 questions each day in the classroom. I mean, that's more than one question every minute for the entire school day.

Mike: That's incredible (sniffs).

DeAnn: (chuckles) I know. That's a lot of questions. Also, if we think about it, it's not just how many questions we ask, but what questions. Because that depth of student learning is really dependent on the questions we ask them because our questions prompt them to consider and engage with the specific mathematical ideas that we're helping them to learn. The other thing I'd like to add to this, is that our questions also set the tone for what it means to learn and do mathematics.

Mike: Hmm.

DeAnn: Are we asking questions about getting answers or are we asking questions that let students know we value and respect their inquiries into mathematical ideas into problem solving, and that we really are about helping them make sense of mathematics? I think it's essential that we critically examine the types of questions we ask and how we can use them to best serve our students.

Mike: That's a really interesting way to think about it. That the questions we ask are really signaling to kids, 'What is mathematics?' In some ways we're informing their definition of mathematics via the questions that we ask.

DeAnn: Yeah, I absolutely agree with you.

Mike: Well, I think one of the most eye-opening things for me to think about lately has been just learning more about the different categories of questions and the different purposes that they can serve. So, I'm wondering if you can briefly sketch out some of the types of questions teachers could put to use in their classrooms.

DeAnn: So, in 'Principals to Actions,' we really looked at a lot of different frameworks that people have established over the years for questioning. And we kind of boiled it down to four specific types that are particularly important for mathematics teaching. One is to gather information. For example, can students remember the names for different types of triangles? Another is to probe student thinking. This is when we want them to further explain, elaborate or clarify their thinking. Uh, third type—which is my favorite category—are questions that make the mathematics visible. In other words, these are questions that prompt students to consider and explicitly discuss the underlying math concepts. Or that we want them to make connections among math ideas and relationships. Let me give you an example. If I were going to ask students to explain how to represent 3 × 5 with an array, they would have to consider more deeply the meaning of each of those numbers and that expression, and how that would connect to the representation. So, we're really getting at the mathematics there, not perhaps the problem or tasks that cause them to think about 3 × 5.

Mike: I see. I see.

DeAnn: Fourth category [is] questions that encourage students to reflect and justify. And I think of these as the why questions. Why does it work to solve 4 × 6 by adding 12 + 12? So, those are the four categories that we identified in 'Principles to Actions.' But since that time, in the 'Taking Action' book at the elementary level, my co-author and I decided to add a fifth category, because these questions really are emerging in classrooms often. So that fifth category is asking questions that encourage students to engage with the reasoning of other students. Many people refer to these as talk moves. For example, if we think about these talk moves that teachers use in their classrooms or that we need to use more often in our classrooms, an example would be, 'Who could add on to what Mateo just said?' Or another example would be, 'Could someone describe or put into their own words the strategy that Jasmine was just telling us about?' Those talk moves are the ones that really get students to listen to and start to have conversations with each other.

Mike: It's interesting because what comes to mind is, there are multiple reasons why that's such an important thing to do in the classroom. In addition to engaging with the reasoning, what it makes me think is it also gives the teacher the opportunity to position a child who may potentially have been marginalized as someone who has math knowledge or whose ideas are valuable.

DeAnn: As I was thinking about talking with you today, Mike, I got thinking about that same idea, which is how do we use questions to position students as capable and as having mathematical authority? And I think this is actually a new area in mathematics education that we need to explore in research further. Just by saying, 'Can you repeat what Jasmine just said?' I'm actually marking her idea as probably something we should all listen to and consider more deeply.

Mike: Absolutely.

DeAnn: I definitely agree that we can use questions to position students as capable in math classrooms, which is something that's greatly needed these days. And that also helps students develop a more positive math identity in themselves and even fosters their math agency and capability in the classroom.

Mike: So, for me at least, personally, my perspective on questions really changed after I read the '5 Practices for Orchestrating Productive Mathematics Discussions' that was written by Margaret Smith and Mary Kay Stein. And after I read that, I really found myself investing a lot more time in preplanning my questions. So, what are your thoughts about whether or how teachers should approach preplanning questions?

DeAnn: In the five practices model, the first practice is to anticipate. This involves anticipating student responses to the kind of key math task of the lesson, and also planning questions so that you, as the teacher, are ready to respond to your students.

Mike: Uh-hm.

DeAnn: Practice of anticipating is preplanning. And I would strongly suggest having those questions written down on a piece of paper so that we are ready to refer to them during the lesson, because it's going to keep us on track, and it's going to give us those tools to help press students to talk more about the mathematical ideas that we want to surface.

Mike: I think part of what really is illuminating for me is, we're anticipating how students might think, and then really, we're digging into what's a response that can help advance their thinking regardless of the angle that they're coming at the task from. So, it's, in some ways, what we're talking about preplanning questions, is really kind of a differentiation strategy to some degree.

DeAnn: Perhaps we want to talk a little bit more about the use of the math teaching practice talks about asking both assessing questions and advancing questions?

Mike: Yeah.

DeAnn: So, let's dig into that a little bit.

Mike: Yeah .

DeAnn: The teaching practice from NCTM says we should be using purposeful questions to both assess and advanced students' reasoning and their sense-making about important math ideas and relationships. So, assessing questions are those that really draw out students' current understanding and strategies. And then advancing questions are those that really move students forward in their thinking and understanding—and pushes or presses them or pulls them along towards those learning goals for the lesson. So, that has probably been one of the main things that has really evolved in my thinking in working on 'Principles to Actions,' is thinking more deeply about these assessing questions and the advancing questions that we need to be posing in our classrooms.

Mike: It strikes me that of the two—they're both important. But it may be that planning advancing questions is the more challenging task for an educator. Talk to me a little bit about preplanning or thinking in advance about advancing questions.

DeAnn: Certainly. So, first as we think about assessing questions, those tend to be more the recalling information, probing student thinking.

Mike: Uh-hm.

DeAnn: As teachers, I think we're pretty good at that. We can all say, 'Well, how did you think about that? How did you figure that out?' But the advancing questions are much more difficult because that means we, as teachers, have to know: Where are we going with this task and what's the math we want? So, in thinking about this … Or, for example, I was recently working with a group of teachers. And what they did is they worked in grade-level groups and even preplanned the questions they were going to use in an upcoming lesson. And it was really true that yes, assessing questions they had. But we took a lot of time to kind of unpack and think about these advancing lessons. So, I'm going to kind of share, like, three steps here to think about this.

DeAnn: One, you really need to know the math learning goals for the lesson because the advancing questions need to be about the mathematics students are learning. Two, it's helpful to work through the math task that the students are going to be doing in the lesson cause that's going to help you anticipate and approach the task and think about, 'OK, what might be happening in their work?' And then third, we can preplan those questions that should be specific to the task, to the anticipated student work, and most importantly to the mathematics.

Mike: Uh-hm.

DeAnn: If you can do that with someone, it's so invaluable to brainstorm and bounce ideas off each other.

Mike: I was thinking about what you were saying. And it's striking the difference between an advancing question that's, as you said, about the mathematics that we're trying to advance, versus a question that might move a child toward mimicking a strategy for a right answer right now, but that isn't actually in the long-term advancing the mathematics that we want. That really, for me, is jumping out as something that … it's a line that we want to help people see the difference between those two things, particularly in the moment. And I think that's why, as you were talking, DeAnn, the idea of, let's write some of these things down so that we have them on hand. Because in the moment it's often difficult to make those kinds of judgements when you're in a public space with a whole bunch of children in front of you. That's a superhuman task at some times (chuckles). So, there's certainly no stigma to writing it down. In fact, it's a strategy that makes a ton of sense for teachers.

DeAnn: Yeah, definitely agree. There's nothing wrong with having those questions on a piece of paper, on a clipboard, carrying that with you, pausing, taking a moment. 'What might be some questions I want to ask here?' I mean, asking questions is really a skill we develop as teachers, and we need to use tools and resources to, kind of, help us.

Mike: Well, I was going to say, the other thing that's really hitting me, DeAnn, is the connection between the learning goal and the question; how clearly we see the learning goal and the different levels of progression that kids will make as they're approaching the learning goal. And advancing means recognizing the meaning of a child's thinking at a given time and thinking about what's the next move, regardless of where they're at. Move children toward that deeper understanding.

DeAnn: Yeah. Perhaps it would be helpful if we share some examples.

Mike: Let's do that.

DeAnn: All right. So, assessing questions—as we were talking, it's like, 'Tell me about your thinking? Can you explain your picture to me? Can you tell me about the tape diagram you drew and used to solve this problem?' Just getting into that kid's thinking and where they're currently at. But then the advancing questions really move students' thinking forward. As you were saying, kind of along this continuum. So, we have to be ready to guide them, kind of step by step, to kind of scaffold that thinking, right? So, I might ask a question, 'What equation could you write for that problem?' Maybe they got the answer, but what would be an equation they could write? Because perhaps my learning goal is to help them make a connection between those different representations, the context and the equation. I might see that a child has written an equation, but then I might say, 'Could you label what each of those numbers means in your equation?' Because I really want to make sure they understand the mathematical meaning of each of those numbers.

Mike: Absolutely.

DeAnn: Just asking kids questions, like 'How are your strategies similar or different?' That's also going to make them think a little more [deeply]. So, all of these advancing questions, really the goal is sense-making and more depth of understanding.

Mike: That totally makes sense. I'm wondering if we can pivot a little bit and talk about the types of teacher moves that might accompany an assessing or an advancing question? What might I do after I ask an assessing question, as opposed to say, asking an advancing question?

DeAnn: So, with assessing questions, the goal of them is really to understand where the student is currently at. So, I would ask an assessing question, and as the teacher I would stay and listen. So, we could assume students are working individually or small groups.

Mike: OK.

DeAnn: So, I might ask an assessing question of a child or a small group and stay and listen because I'm trying to figure out, really to understand, what they did (chuckles) and why they did that. Whereas an advancing question, I would be more likely to pose the question to the individual child or small group and then walk away and say, 'I'll be back in a minute or two to see what you've done or what you're thinking about.' So, it's kind of like giving them time to pause and ponder and consider that question.

Mike: This is fascinating because I wonder if for a lot of people that might feel counterintuitive, that you would pose the advancing question and walk away. Tell us a little bit more about the why behind that choice.

DeAnn: Our goal really is to help students become independent math learners in the classroom. By asking the question and then saying, 'I'll be back in a couple minutes; think about that or show me what you've done,' we want them to be able to figure out how to proceed with a task on their own so that they don't become dependent upon us as teachers. But they really develop that agency in themselves to try things out, whether they're right or wrong, but at least that they're making some progress in the task.

Mike: You know what it makes me think, DeAnn, is that asking an advancing question and walking away might feel foreign to the educator, and it might at least initially feel kind of foreign to the child as well. But over time, it will start to feel like the culture of the classroom, and the child will actually get to a point where it's like, 'Oh, my teacher believes that I have the ability to think about this and come up with an idea.' And that's a real gift to a child. It does what you were talking about earlier, which is: Question sets the culture and helps children think about what is it to be learning about math.

DeAnn: Yeah. We've also talked about that other type of question to encourage students, to engage with the reasoning of each other. That also really helps with those advancing questions and that tone in the classroom. Cause you could ask a question as a teacher and then say, 'Why don't you talk with each other for a while about this?' Or ask one student to explain to another student some of their ideas. So, we can, again, use those talk moves when students are working in partners in small groups to learn from each other.

Mike: I'm struck by the idea that this conversation we're having about questioning is also really pretty tightly connected to, how do we support children when they need to engage with productive struggle? And I'm wondering if you could talk about the connection between high quality advancing or assessing questions, and helping kids manage and engage in productive struggle at the end.

DeAnn: Thinking back to 'Principles to Actions,' we identified eight high-leverage teaching practices for mathematics. And one of them is using purposeful questions. But another one is supporting productive struggle. So, the connection I think you're kind of alluding to here, Mike, really is they go hand in hand. We can use our questioning to encourage students to persevere in the mathematics that they're doing. But those questions, again, [mean] we are, first of all, trying to understand where the student is at by asking those assessing questions. And then we can encourage them to kind of, like, this bridge, right? With those advancing questions we're trying to get them to consider some of the mathematical ideas that might actually not even be on their horizon for them right now. So, if we say, 'How could you put this fraction on a number line?' Or 'How do you know this fraction is greater than or less than one?' We're asking a question to really make that math idea visible and to get them to consider it. And then we're pausing and giving them time and space to consider it and figure out how to proceed on their own. If I, as a teacher, tell them what to do next, that means I'm owning the math, I'm being the authority, and I'm not valuing struggle as part of the learning process.

Mike: Mm, yes. Yes, absolutely. Well, before we close, I want to dig into one more question type. And this is the one that I think really is just kind of transcendent. It transcends the task at hands and digs into students' understanding of big ideas. And it's the one that you would describe as making mathematics visible. Can you talk a little bit about the importance of these types of questions and perhaps some examples that would help people kind of envision what they look like in an elementary classroom?

DeAnn: So, you asked about these questions [that are] really making the math visible. As I think about that, what comes right to mind is a fascinating study conducted by Michelle Perry and her colleagues. They actually looked at the questions and examined very closely the questions teachers ask in a first-grade classroom for mathematics. And they compared the questioning of teachers in Japan, Taiwan, in the United States. Well, unfortunately they found that teachers in the U.S. ask significantly [fewer] questions that require high-level thinking than in Japan and Taiwan. In fact, teachers in those countries tend to ask questions that transcend the problem at hand. I love that phrase . The question goes beyond the surface of the task to really transcend that problem at hand, to get at the underlying math ideas, math concepts, and connections that we want students to make. And they found that teachers in Japan and Taiwan went beyond the surface to really make the math visible for students to consider. And really kept students engaged at higher cognitive levels of thinking.

Mike: That is fascinating. What it reminds me of is, I think it was Jim [James] Hiebert and [James] Stigler wrote about the idea of the mathematics classroom as a cultural activity, in that there's this kind of underlying script of what it means to be a student or a teacher in a mathematics classroom. And I think what we're really talking about in some ways is the role of questioning in building a different vision of what a mathematics classroom is or what it means to be an educator of mathematics.

DeAnn: Yeah. I think that ties right back to our earlier sharing about productive struggle. We think if students don't know the answer quickly that it's our job to step in and tell them how to do it.

Mike: Uh-hm. We're almost coming full circle though, in the sense that I think the promise of high-quality questioning—be it assessing or advancing—is that we're really, by considering the ways that students might think about a task and then considering the ways that you can assess that and advance their thinking from wherever they may be, we really are helping teachers see a different way. And I think that's the power of what you're describing when you talk about strong questioning, DeAnn.

DeAnn: Yeah.

Mike: So, we talked a little bit about what to do next. But I would love for you to take a moment to weigh in on the question of wait time. What are your thoughts about wait time and its value and how that can work in a classroom to support children?

DeAnn: So far today, we've been talking a lot about like the types of questions that teachers ask. But the implementation of those questions is also something we need to think a little bit more about. So, [there are] two types of wait time. Wait time is when I ask a question as a teacher, and how long do I wait until I call on a student? The research on wait time really shows that as teachers, we tend to wait less than a second.

Mike: That's incredible.

DeAnn: Yeah. We provide no processing time to our young learners to really formulate those ideas in their head and then be able to share back. So, just by reminding ourselves to pause for 3 seconds makes a huge difference in the learning that goes on in a classroom. Those 3 seconds, what happens is we find out that more students will respond to our questions. The length of students' responses increases. And those questions or those responses from students where they say, 'Oh, I don't know,' decrease. So merely waiting 3 seconds makes a huge difference. And as teachers, we just don't deal well with silence, and thinking time, and processing time. So, I think it's always a good reminder to just monitor the amount of time we give students to process ideas after we ask a question.

Mike: You know, as a person who works in math education, when I'm at a dinner party or in mixed company with people, and I ask them, 'Tell me about your memories of elementary school mathematics.' There are a few common things that always come up. One is typically, as I'm sure won't surprise you, the idea of memorizing my facts. And the other theme that kind of goes along with that is this sense that I wasn't good at math because I didn't know the answer right away. And the connection I'm making is, maybe that's because we didn't give you enough time to actually process and think. If we simply expand our time and give kids 3 seconds or 4 or 5, rather than 1, how different would that experience of mathematics be for children? How many folks would actually feel differently about mathematics and maybe, perhaps, not associate mathematics with just being the first and being the fastest to find the answer.

DeAnn: So, again, we're talking about using our questioning to kind of establish that tone and the expectations in the classroom about what it means to learn and do mathematics. And we shouldn't be in such a hurry (chuckles) for students to respond. We as adults need our processing time. Our young learners, [who] are first encountering many of these new ideas in mathematics, we need to give them time to think and to process and make connections before we expect them to respond to any of our questions.

Mike: The piece about 1 second is just so striking . It's odd because I suspect people imagine that by coming back that quickly, they're actually supporting the child. But you're actually doing the opposite (chuckles). You're teaching them: One, if you haven't had it in a second, what's wrong with you? And then two: You're also fostering dependency. It's fascinating how, what I think comes from a desire to help, is actually debilitating.

DeAnn: It really speaks to the need to reestablish not only norms for students in our classrooms, but really for ourselves as teachers.

Mike: Definitely. Well, I just wanted to say thank you so much for this conversation. It's really been a pleasure to have you join us and hopefully we'll have you back at some time in the future.

DeAnn: And thank you, Mike. I've really enjoyed talking about the importance of purposeful questions for teachers to consider more deeply in their classroom practice.

Mike: This podcast is brought to you by The Math Learning Center and the Maier Math Foundation, dedicated to inspiring and enabling individuals to discover and develop their mathematical confidence and ability.