Dr. Victoria Jacobs, Examining the Meaning and Purpose of our Questions ROUNDING UP: SEASON 3 | EPISODE 12

Mike (00:03): The questions educators ask their students matter. They can have a profound impact on students' thinking and the shape of their mathematical identities. Today we're examining different types of questions, their purpose and the meaning students make of them. Joining us for this conversation is Dr. Vicki Jacobs from the University of North Carolina Greensboro. Welcome to the podcast, Vicki. I'm really excited to talk with you today.

Vicki (00:33): Thanks so much for having me. I'm excited to be here.

Mike (00:36): So you've been examining the ways that educators use questioning to explore the details of students' thinking. And I wonder if we could start by having you share what drew you to the topic.

Vicki (00:47): For me, it all starts with children's thinking because it's absolutely fascinating, but it's also mathematically rich. And so a core part of good math instruction is when teachers elicit children's ideas and then build instruction based on that. And so questioning obviously plays a big role in that, but it's hard. It's hard to do that well in the moment. So I found questioning to explore children's thinking to be a worthwhile thing to spend time thinking about and working on.

Mike (01:17): Well, let's dig into the ideas that have emerged from that work. How can teachers think about the types of questions that they might ask their students?

Vicki (01:24): Happy to share. But before I talk about what I've learned about questioning, I really need to acknowledge some of the many people that have helped me learn about questioning over the years. And I want to give a particular shout out to the teachers and researchers in the wonderful cognitively guided instruction or CGI community as well as my long-term research collaborators at San Diego State University. And more recently, Susan Sen. This work isn't done alone, but what have we learned about teacher questioning across a variety of projects? I'll share two big ideas and the first relates to the goals of questioning and the second addresses more directly the types of questions teachers might ask. So let's start with the goals of questioning because there are lots of reasons teachers might ask questions in math classrooms. And one common way to think about the goal of questioning is that we need to direct children to particular strategies during problem solving.

(02:23): So if children are stuck or they're headed down a wrong path, we can use questions to redirect them so that they can get to correct answers with particular strategies. Sometimes that may be okay, but when we only do that, we're missing a big opportunity to tap into children's sense-making. Another way to think about the goal of questioning is that we're trying to explore children's thinking during problem solving. So think about a math task where multiple strategies are encouraged and children can approach problem solving in any way that makes sense to. So we can then ask questions that are designed to reveal how children are thinking about the problem solving, not just how well they're executing our strategies. And we can ask these questions when children are stuck, but also when they solve problems correctly. So this shift in the purpose of questioning is huge. And I want to share a quote from a teacher that I think captures the enormity of this shift.

(03:26): She's a fifth grade teacher, and what she said was the biggest thing I learned from the professional development was not asking questions to get them to the answers so that I could move them up a strategy, but to understand their thinking. That literally changed my world. It changed everything. So I love this quote because it shows how transformative this shift can be because when teachers become curious about how children are thinking about problem solving, they give children more space to problem solve in multiple ways, and then they can question to understand and support children's ideas. And these types of questions are great because they increase learning opportunities for both children and teachers. So children get more opportunities to learn how to talk math in a way that's meaningful to them because they're talking about their own ideas and they also get to clarify what they did think more about important math that's embedded in their strategies and sometimes to even self-correct. And then as teachers, these types of questions give us a window into children's understandings, and that helps us determine our next steps. Questioning can have a different and powerful purpose when we shift from directing children toward particular strategies to exploring their mathematical thinking.

Mike (04:54): I keep going back to the quote that you shared, and I think the details of the why and kind of the difference in the experience for students really jump out. But I'm really compelled by what that teacher said to you about how it changes everything. And I wonder if we could just linger there for a moment and you could talk about some of the things that you've seen happen for educators who have that kind of aha moment in the same way that that teacher did, how that impacts the work that they're doing with children or how they see themselves as an educator.

Vicki (05:28): That's a great question. I think it's freeing in some way because it changes how educators think about what their next steps are. Every teacher has lots of pressures from standards and sometimes pacing guides and grade level teams that are working on the same page, all sorts of things that are a big part of teaching. But it puts the focus back on children and children's thinking and that my next steps should then come from there. And so in some ways, I think it gives a clearer direction for how to navigate all those various pressures that teachers have.

Mike (06:14): I love that. Let's talk about part two.

Vicki (06:17): Sure. So if we have the goal of questioning to explore children's thinking, how do we decide what questions to ask? So first of all, there's never a best question. There are many questioning frameworks out there that can provide lots of ideas, but what we've found is that the most productive questions always start with what children say and do. So that means I can't plan all my questions in advance, and instead I have to pay close attention to what children are saying and doing during problem solving. And to help us with that, we found a distinction between inside questions and outside questions. And that distinction has been really useful to us and also usable even during instruction. So inside questions are questions that explore details that are part of inside children's current strategies. And outside questions are questions that focus on strategies or representations that are not what children have done and may even be linked to how we as teachers are thinking about problem solving.

(07:26): So I promised an example, and this is from our recent research project on teaching and learning about fractions. And we asked teachers to think about a child's written strategy for a fraction story problem. And the problem was that there are six children equally sharing four pancakes, and they need to figure out how much pancake each child can get. So we're going to talk about Joy's strategy for solving this problem. She is a fourth grader who solved the problem successfully, but in a complex and rather unconventional way. So I'm going to describe her strategy as a reminder. We have six children sharing four pancakes. So she drew the four pancakes. She split the first three pancakes into fourths and distributed the pieces to the six children, and that works out to two fourths for each child. But now she has a problem because she has one pancake left and fourths aren't going to work anymore because that's not enough pieces for her six children.

(08:23): So she split the pancake first into eighths and then into 20 fourths and distributed those pieces. So each child ends up receiving two fourths, one eighth and one 24th. And when you put all those amounts together, they equal the correct amount of two thirds pancake per child. But Joy left her answer in pieces as two fourths, one eighth and one 24th, and she wrote those fractions in words rather than using symbols. Okay, so there's a lot going on in this strategy. And the specific strategy doesn't matter so much for our conversation, but the situation does. Here we have a child who has successfully solved the problem, but how she solved it and how she represented her answer are different than what we as adults typically do. So we ask teachers to think about what kind of follow-up conversation would you want to have with joy?

(09:23): What types of questions would you want to ask her? And there were these two main questioning approaches, what we call inside questioning and outside questioning. So let's start with outside questioning. These teachers focused on improving Joy's strategy. So they ask follow-up questions like, is there another way you can share the four pancakes with six children? Or is your strategy the most efficient way you could share the pancakes? Or is there a way to cut bigger servings that would be more efficient? So given the complexity of Joy's strategy, we can appreciate these teachers' goals of helping joy move to a more efficient strategy. But all of these questions are pushing her to use a different strategy. So we considered them outside questions because they were outside of her current strategy. And outside questions can sometimes be productive, but they tend to get overused. And when we use them a lot, they can communicate to kids that what they're actually doing was wrong and that it needs fixing.

(10:29): So let's think about the other approach of inside questioning. These teachers started by exploring what Joy had done in all of its complexity. And they ask a variety of questions. Usually it started with a general question, can you tell me what you did? But then they zoomed in on some of the many details. So for examples, they've asked how she split the pancakes. They offered questions like, why did you split the first three pancakes into four pieces? Or Tell me about the last pancake. That was the one that she split into eights and 20 fourths. Or they might ask about how she knew how to name each of the fractional amounts, especially the one 24th, because that's something that many children might've struggled with. And then there were questions about a variety of other details. Some of them are hard to explain without showing you a picture of the strategy, but the point is that the teachers took seriously what Joy had done and elevated it to the focus of the conversation. So Joy had a chance to share her reasoning and reflect on it, and the teachers could better understand Joy's approach to problem solving. So we found this distinction between inside and outside questioning to be useful to teachers and even in the midst of instruction because teachers can quickly check in with themselves. Am I asking an inside question or an outside question?

Mike (11:49): Well, I have so many questions about inside and outside questions, but I want to linger on inside questions. What I found myself thinking is that for the learner, there are benefits for building number sense or conceptual understanding. The other thing that strikes me is that inside questions are also an opportunity to support students' math identity. And I wonder if that's something that you've seen in your work with teachers and with students.

Vicki (12:14): Absolutely. I love your question. One of my favorite things about inside questions is that children see that their ideas are being taken seriously. And that's so empowering. It helps children believe that they can do math and that they are in charge of their mathematical thinking. I'll share a short story that was memorable for me, and this was from a while ago when I was in graduate school. So I was working on a research project and we were conducting problem solving interviews with young children. And our job was to document their strategies. So if we could see exactly what they did, we were told to write down the strategy and move on. But if we needed to clarify something, we could ask follow up questions. I was working with a first grader who had just spent a really long time solving a story problem. He had solved it successfully, and he had done that by joining many, many, many unifix cubes into a very long train.

(13:10): And then he had counted them by ones multiple times. So he had been successful. I could tell exactly what he had done. So I started to move on to the next problem. So this young child looked at me a little incredulous and simply asked, don't you want to know how I did it? And he had come from a class where his math thinking was valued, and talking about children's thinking was a regular part of what they did. So he couldn't quite understand why this adult was not interested in how he had thought about the problem. Well, I was a little embarrassed and of course backtracked and listened to his full explanation. But the interaction stuck with me because it showed me how empowering it was for children to truly be listened to as math thinkers. And I think that's something we want for all children.

Mike (14:00): The other thing that's hitting me in that story and in the story of joy is mea culpa. I am a person who has lived in the cult of efficiency where I looked at a student's work and my initial thought was, how do I nip the edges of this to get to more efficiency? But I really am struck by it how different the idea of asking the student to explain their thinking or the why behind it. I find myself thinking about joy, and it appears that she was intent on making sure that there were equal shares for each person. So there's ways that she could build to a different level of efficiency. But I think recognizing that there's something here that is really important to note about how and why she chose that, that would feel really meaningful as a learner.

Vicki (14:44): I agree. I think what I like about inside questions is that they encourage us to, that children's thinking makes sense, even if it's different than how we think about it. It's our job to figure out how it makes sense. And then to build from there.

Mike (15:03): Can you just say more about that? That feels like kind of a revelation.

Vicki (15:08): Well, if we start with how kids are thinking and we take that seriously and we make that the center of the conversation, then we're acknowledging to the student and to ourselves that the child has something meaningful to bring to this conversation. And so we need to figure out how the child is thinking all the kind of kernels of mathematical strength in that thinking. And then yes, we can build from there, but we start with where they are as opposed to how we might solve the problem.

Mike (15:49): If you were to offer educators a universal inside question or a few sentence frames for inside questions, is it possible to construct something like that that's generic or do you have other advice for us?

Vicki (16:02): So that's a nice trick question. I wish it were that easy. I don't really think there are any universal inside questions. Perhaps the only universal one I can think of is something like, how did you solve this problem? It's a great general open-ended question. That's a good starter question in most situations. But the really powerful questions generally come from noticing mathematically important details in children's strategies. So a sentence stem that has been helpful in our work is, I noticed blank, so I wonder blank. Obviously questions don't have to be phrased exactly like this, but the idea is that we pick something that the child has done in their strategy and ask a question about the child's thinking behind that strategy detail. And that keeps us honest because the question absolutely has to begin with something in the child's strategy rather than inadvertently kind of slipping into our strategy.

Mike (17:04): Vicki, what do you think about the purpose of outside questions? Are there circumstances where we would want to ask our students an outside question?

Vicki (17:12): Absolutely. Sometimes we need to push children's thinking or share particular ideas, and that's okay. It's not that all outside questions are bad, it's just that we tend to overuse them and we could use them at more productive times. And by that I mean that we generally want to understand children's thinking before nudging their thinking forward with outside questions. So let's go back to the earlier example of Joy. Who was solving that problem about six children sharing four pancakes. And we had the two groups of teachers that had the different approaches to follow up questioning. There was the outside questioning that immediately zeroed in on improving Joy's strategy and the inside questioning that spent time exploring Joy's reasoning behind her strategy. So I'm thinking of two specific teachers right now. One generally took the outside questioning approach and the other inside questioning approach. And what was interesting about this pair was that they both asked the same outside question, could Joy partition the pancakes in a different way?

(18:19): But they asked this question at different times and the timing really matters. So the teacher who took an outside questioning approach wanted to begin her conversation that way. She wanted to ask Joy, could she partition in a different way? But in contrast, the teacher who took an inside questioning approach wanted to ask Joy lots of questions about the details of her existing strategy, and then posed this very same question at the end to see if Joy had some new ideas for partitioning after their conversation about her existing strategy. And that feels really different to children. So the exact same question can send children different messages when outside questions are posed. First they communicate to children that what they did was wrong and needs fixing. But when outside questions are posed after a conversation about their thinking, it communicates a puzzle or a problem to be solved.

(19:17): And children often are better equipped to consider this new problem having thoroughly discussed their own strategy. So I guess when I think about outside questions, I think of timing and amount. We generally want to start with inside questions, and we want most of our questions to be inside questions, but some outside questions can be productive. It's just that we overuse them. I want to mention one other thing about outside questions, and I think we often need fewer outside questions than we think we do, as long as we have space for children to learn from other children's thinking. So think about a typical lesson structure like launch, explore, discuss where children solve problems independently. And then the lesson concludes with a whole class discussion where children share their strategies and reflect on their problem solving. Will these sharing sessions serve as natural outside questions? Because children get to think about strategies that are outside of their own, but in a way that doesn't point to their own strategy as lacking in some way. So outside questions definitely have a place we just need to think about when we ask them and how many of them are really necessary.

Mike (20:34): That is really helpful. I find myself thinking about my own process when I'm working on a problem, be it mathematical or organizational or what have you. When someone asks me to talk about how I've thought about it, engaging in that process in some ways primes me, right? Because I've gotten clearer on my own thinking. I suspect that the person who's asking me the question is also clearer on that, which allows them to ask a different kind of outside question if and when they get to the point. So there's the benefit for the learner in that their clarifying their own thinking. There's the benefit in the educator who's engaging with the learner and getting just a much clearer sense of how that thinking was happening. And I suspect that leads to an outside question that's much more productive.

Vicki (21:16): It's a win-win situation.

Mike (21:18): Absolutely. This conversation has been wonderful. The challenge of having a podcast, of course, is that we've got about 20 to 25 minutes to talk about a really big idea that has profound implications for teachers. If someone wanted to pick up on the things we've been talking about today, where would you start, Vicki?

Vicki (21:38): I would encourage them to go talk to children. Children's thinking is so mathematically rich and it's so fascinating. So be curious about their thinking. Ask questions, ask those inside questions. Don't worry about asking the best question. It doesn't exist, but ask questions and then children will be your guides. They'll help you know where to go next. The other thing I would suggest is these journeys are always best done with your colleagues. And so get a colleague together and think about questioning together what we were talking about earlier with joy strategy teachers. We're looking at students' written work. That's a great place to practice. You can look at children's written work and talk together to figure out what types of conversations do you want to have with this child afterwards.

Mike (22:28): I think that's a great place to stop. I want to thank you so much for joining us today, Vicki, it has really been a pleasure talking with you.

Vicki (22:34): That was fun. Thanks for having me.

Mike (22:39): This podcast is brought to you by the Math Learning Center and the Meyer Math Foundation dedicated to inspiring and enabling all individuals to discover and develop their mathematical confidence and ability.

© 2025 The Math Learning Center | www.mathlearningcenter.org