Latest / Rounding Up / Inside Out: Examining the Meaning and Purpose of our Questions wit Dr. Victoria Jacobs

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Inside Out: Examining the Meaning and Purpose of our Questions wit Dr. Victoria Jacobs · Rounding Up

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The questions educators ask their students matter.
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They can have a profound impact on students' thinking and the shape of their
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mathematical identities. Today we're examining different types of questions,
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their purpose and the meaning students make of them.
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Joining us for this conversation is Dr. Vicki Jacobs from the University of
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North Carolina Greensboro.
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Welcome to the podcast, Vicki. I'm really excited to talk with you today.
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Thanks so much for having me. I'm excited to be here.
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So you've been examining the ways that educators use questioning to explore the
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details of students' thinking.
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And I wonder if we could start by having you share what drew you to the topic.
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For me,
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it all starts with children's thinking because it's absolutely fascinating,
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but it's also mathematically rich.
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And so a core part of good math instruction is
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when teachers elicit children's ideas and then build instruction based on that.
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And so questioning obviously plays a big role in that, but it's hard.
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It's hard to do that well in the moment.
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So I found questioning to explore children's thinking to be a worthwhile thing
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to spend time thinking about and working on.
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Well, let's dig into the ideas that have emerged from that work.
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How can teachers think about the types of questions that they might ask their
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students?
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Happy to share. But before I talk about what I've learned about questioning,
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I really need to acknowledge some of the many people that have helped me learn
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about questioning over the years.
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And I want to give a particular shout out to the teachers and researchers in the
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wonderful cognitively guided instruction or CGI community as well as my
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long-term research collaborators at San Diego State University.
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And more recently, Susan Sen. This work isn't done alone,
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but what have we learned about teacher questioning across a variety of projects?
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I'll share two big ideas and the first relates to the goals of
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questioning and the second addresses more directly the types of questions
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teachers might ask.
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So let's start with the goals of questioning because there are lots of reasons
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teachers might ask questions in math classrooms.
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And one common way to think about the goal of questioning is that we need to
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direct children to particular strategies during problem solving. So if
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children are stuck or they're headed down a wrong path,
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we can use questions to redirect them so that they can get to correct answers
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with particular strategies. Sometimes that may be okay,
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but when we only do that,
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we're missing a big opportunity to tap into children's sense-making.
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Another way to think about the goal of questioning is that we're trying to
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explore children's thinking during problem solving.
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So think about a math task where multiple strategies are encouraged and
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children can approach problem solving in any way that makes sense to.
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So we can then ask questions that are designed to reveal how children are
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thinking about the problem solving,
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not just how well they're executing our strategies.
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And we can ask these questions when children are stuck,
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but also when they solve problems correctly.
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So this shift in the purpose of questioning is huge.
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And I want to share a quote from a teacher that I think captures the
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enormity of this shift. She's a fifth grade teacher,
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and what she said was the biggest thing I learned from the professional
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development was not asking questions to get them to the answers so that I
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could move them up a strategy, but to understand their thinking.
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That literally changed my world. It changed everything.
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So I love this quote because it shows how transformative this shift
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can be because when teachers become curious about how children are thinking
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about problem solving,
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they give children more space to problem solve in multiple ways,
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and then they can question to understand and support children's ideas.
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And these types of questions are great because they increase learning
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opportunities for both children and teachers.
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So children get more opportunities to learn how to talk math
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in a way that's meaningful to them because they're talking about their own ideas
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and they also get to clarify what they did think more about important
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math that's embedded in their strategies and sometimes to even self-correct.
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And then as teachers,
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these types of questions give us a window into children's understandings,
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and that helps us determine our next steps.
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Questioning can have a different and powerful purpose when we shift from
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directing children toward particular strategies to exploring their
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mathematical thinking.
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I keep going back to the quote that you shared,
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and I think the details of the why and kind of the difference in the
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experience for students really jump out.
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But I'm really compelled by what that teacher said to you about how it changes
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everything.
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And I wonder if we could just linger there for a moment and you could talk about
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some of the things that you've seen happen for educators who have that kind of
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aha moment in the same way that that teacher did,
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how that impacts the work that they're doing with children or how they see
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themselves as an educator.
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That's a great question.
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I think it's freeing in some way
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because it changes how educators
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think about what their next steps are.
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Every teacher has lots of pressures from standards and sometimes
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pacing guides and grade level teams that are working on the same page,
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all sorts of things that are a big part of teaching.
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But it puts the focus back on children and children's thinking and
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that my next steps should then come from there.
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And so in some ways,
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I think it gives a clearer direction for how
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to navigate all those various pressures that teachers have.
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I love that. Let's talk about part two.
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Sure.
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So if we have the goal of questioning to explore children's thinking,
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how do we decide what questions to ask? So first of all,
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there's never a best question.
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There are many questioning frameworks out there that can provide lots of ideas,
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but what we've found is that the most productive questions always start with
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what children say and do.
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So that means I can't plan all my questions in advance,
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and instead I have to pay close attention to what children are saying and
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doing during problem solving. And to help us with that,
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we found a distinction between inside questions and outside questions.
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And that distinction has been really useful to us and also usable even during
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instruction.
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So inside questions are questions that explore
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details that are part of inside children's current
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strategies.
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And outside questions are questions that focus on strategies
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or representations that are not what children have done and may even be linked
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to how we as teachers are thinking about problem solving. So I promised an
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example,
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and this is from our recent research project on teaching and learning about
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fractions.
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And we asked teachers to think about a child's written strategy for a fraction
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story problem.
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And the problem was that there are six children equally sharing four
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pancakes, and they need to figure out how much pancake each child can get.
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So we're going to talk about Joy's strategy for solving this problem.
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She is a fourth grader who solved the problem successfully,
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but in a complex and rather unconventional way.
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So I'm going to describe her strategy as a reminder.
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We have six children sharing four pancakes.
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So she drew the four pancakes.
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She split the first three pancakes into fourths and distributed the pieces to
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the six children, and that works out to two fourths for each child.
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But now she has a problem because she has one pancake left and fourths aren't
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going to work anymore because that's not enough pieces for her six children. So
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she split the pancake first into eighths and then into 20 fourths
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and distributed those pieces.
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So each child ends up receiving two fourths,
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one eighth and one 24th. And when you put all those amounts together,
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they equal the correct amount of two thirds pancake per child.
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But Joy left her answer in pieces as two fourths,
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one eighth and one 24th,
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and she wrote those fractions in words rather than using symbols.
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Okay, so there's a lot going on in this strategy.
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And the specific strategy doesn't matter so much for our
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conversation, but the situation does.
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Here we have a child who has successfully solved the problem,
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but how she solved it and how she represented her answer are
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different than what we as adults typically do.
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So we ask teachers to think about what kind of follow-up conversation would you
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want to have with joy? What types of questions would you want to ask her?
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And there were these two main questioning approaches,
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what we call inside questioning and outside questioning.
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So let's start with outside questioning.
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These teachers focused on improving Joy's strategy.
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So they ask follow-up questions like,
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is there another way you can share the four pancakes with six children?
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Or is your strategy the most efficient way you could share the pancakes?
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Or is there a way to cut bigger servings that would be more efficient?
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So given the complexity of Joy's strategy,
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we can appreciate these teachers' goals of helping joy move to a more efficient
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strategy.
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But all of these questions are pushing her to use a different strategy.
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So we considered them outside questions because they were outside of her current
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strategy. And outside questions can sometimes be productive,
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but they tend to get overused. And when we use them a lot,
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they can communicate to kids that what they're actually doing was wrong and that
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it needs fixing. So let's think about the other approach of inside
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questioning.
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These teachers started by exploring what Joy had done in all of its complexity.
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And they ask a variety of questions. Usually it started with a general question,
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can you tell me what you did?
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But then they zoomed in on some of the many details. So for examples,
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they've asked how she split the pancakes. They offered questions like,
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why did you split the first three pancakes into four pieces?
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Or Tell me about the last pancake.
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That was the one that she split into eights and 20 fourths.
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Or they might ask about how she knew how to name each of the fractional amounts,
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especially the one 24th,
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because that's something that many children might've struggled with.
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And then there were questions about a variety of other details.
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Some of them are hard to explain without showing you a picture of the strategy,
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but the point is that the teachers took seriously what Joy had done and
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elevated it to the focus of the conversation.
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So Joy had a chance to share her reasoning and reflect on it,
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and the teachers could better understand Joy's approach to problem solving.
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So we found this distinction between inside and outside questioning to be useful
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to teachers and even in the midst of instruction because teachers can quickly
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check in with themselves. Am I asking an inside question or an outside question?
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Well, I have so many questions about inside and outside questions,
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but I want to linger on inside questions.
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What I found myself thinking is that for the learner,
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there are benefits for building number sense or conceptual understanding.
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The other thing that strikes me is that inside questions are also an opportunity
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to support students' math identity.
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And I wonder if that's something that you've seen in your work with teachers and
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with students.
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Absolutely. I love your question.
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One of my favorite things about inside questions is that children see that their
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ideas are being taken seriously. And that's so empowering.
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It helps children believe that they can do math and that they are in charge of
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their mathematical thinking. I'll share a short story that was memorable for me,
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and this was from a while ago when I was in graduate school.
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So I was working on a research project and we were conducting problem solving
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interviews with young children. And our job was to document their strategies.
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So if we could see exactly what they did,
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we were told to write down the strategy and move on.
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But if we needed to clarify something, we could ask follow up questions.
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I was working with a first grader who had just spent a really long time solving
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a story problem. He had solved it successfully,
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and he had done that by joining many, many,
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many unifix cubes into a very long train. And then he had
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counted them by ones multiple times.
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So he had been successful. I could tell exactly what he had done.
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So I started to move on to the next problem.
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So this young child looked at me a little incredulous and simply asked,
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don't you want to know how I did it?
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And he had come from a class where his math thinking was valued,
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and talking about children's thinking was a regular part of what they did.
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So he couldn't quite understand why this adult was not interested in how he had
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thought about the problem. Well,
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I was a little embarrassed and of course backtracked and listened to his full
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explanation.
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But the interaction stuck with me because it showed me how empowering it was for
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children to truly be listened to as math thinkers.
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And I think that's something we want for all children.
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The other thing that's hitting me in that story and in the story of joy is mea
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culpa. I am a person who has lived in the cult of efficiency where I looked at a
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student's work and my initial thought was,
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how do I nip the edges of this to get to more efficiency?
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But I really am struck by it how different the idea of asking the student to
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explain their thinking or the why behind it. I find myself thinking about joy,
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and it appears that she was intent on making sure that there were equal shares
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for each person.
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So there's ways that she could build to a different level of
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efficiency.
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But I think recognizing that there's something here that is really important to
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note about how and why she chose that,
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that would feel really meaningful as a learner.
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I agree.
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I think what I like about inside questions is that they encourage us
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to, that children's thinking makes sense,
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even if it's different than how we think about it.
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It's our job to figure out how it makes sense. And then to build from there.
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Can you just say more about that? That feels like kind of a revelation.
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Well,
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if we start with how kids are thinking and we take that
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seriously and we make that the center of the conversation,
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then we're acknowledging to the student and to
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ourselves that the child has something meaningful to bring to
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this conversation.
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And so we need to figure out how the child is thinking all
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the kind of kernels of mathematical strength in that
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thinking. And then yes, we can build from there,
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but we start with where they are as opposed to how we
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might solve the problem.
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If you were to offer educators a universal inside question or a few sentence
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frames for inside questions,
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is it possible to construct something like that that's generic or do you have
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other advice for us?
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So that's a nice trick question. I wish it were that easy.
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I don't really think there are any universal inside
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questions. Perhaps the only universal one I can think of is something like,
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how did you solve this problem? It's a great general open-ended question.
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That's a good starter question in most situations.
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But the really powerful questions generally come from noticing mathematically
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important details in children's strategies.
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So a sentence stem that has been helpful in our work is,
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I noticed blank, so I wonder blank.
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Obviously questions don't have to be phrased exactly like this,
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but the idea is that we pick something that the child has done in their strategy
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and ask a question about the child's thinking behind that strategy
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detail.
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And that keeps us honest because the question absolutely has to begin with
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something in the child's strategy rather than inadvertently kind of slipping
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into our strategy.
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Vicki, what do you think about the purpose of outside questions?
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Are there circumstances where we would want to ask our students an outside
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question?
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Absolutely.
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Sometimes we need to push children's thinking or share particular ideas,
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and that's okay. It's not that all outside questions are bad,
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it's just that we tend to overuse them and we could use them at more productive
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times.
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And by that I mean that we generally want to understand children's thinking
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before nudging their thinking forward with outside questions.
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So let's go back to the earlier example of Joy.
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Who was solving that problem about six children sharing four pancakes.
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And we had the two groups of teachers that had the different approaches to
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follow up questioning.
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There was the outside questioning that immediately zeroed in on improving Joy's
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strategy and the inside questioning that spent time exploring Joy's reasoning
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behind her strategy. So I'm thinking of two specific teachers right now.
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One generally took the outside questioning approach and the other inside
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questioning approach.
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And what was interesting about this pair was that they both asked the
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same outside question,
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could Joy partition the pancakes in a different way? But they asked this
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question at different times and the timing really matters.
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So the teacher who took an outside questioning approach wanted to begin her
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conversation that way. She wanted to ask Joy,
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could she partition in a different way? But in contrast,
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the teacher who took an inside questioning approach wanted to ask Joy lots of
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questions about the details of her existing strategy,
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and then posed this very same question at the end to see if Joy
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had some new ideas for partitioning after their conversation about her
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existing strategy. And that feels really different to children.
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So the exact same question can send children different messages when
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outside questions are posed.
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First they communicate to children that what they did was wrong and needs
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fixing.
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But when outside questions are posed after a conversation about their thinking,
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it communicates a puzzle or a problem to be solved. And
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children often are better equipped to consider this new
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problem having thoroughly discussed their own strategy.
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So I guess when I think about outside questions,
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I think of timing and amount.
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We generally want to start with inside questions,
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and we want most of our questions to be inside questions,
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but some outside questions can be productive. It's just that we overuse them.
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I want to mention one other thing about outside questions,
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and I think we often need fewer outside questions than we think we do,
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as long as we have space for children to learn from other children's thinking.
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So think about a typical lesson structure like launch, explore,
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discuss where children solve problems independently.
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And then the lesson concludes with a whole class discussion where children share
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their strategies and reflect on their problem solving.
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Will these sharing sessions serve as natural outside questions?
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Because children get to think about strategies that are outside of their own,
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but in a way that doesn't point to their own strategy as lacking in some way.
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So outside questions definitely have a place we just need to think about when we
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ask them and how many of them are really necessary.
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That is really helpful.
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I find myself thinking about my own process when I'm working on a problem,
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be it mathematical or organizational or what have you.
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When someone asks me to talk about how I've thought about it,
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engaging in that process in some ways primes me, right?
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Because I've gotten clearer on my own thinking.
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I suspect that the person who's asking me the question is also clearer on that,
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which allows them to ask a different kind of outside question if and when they
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get to the point.
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So there's the benefit for the learner in that their clarifying their own
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thinking.
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There's the benefit in the educator who's engaging with the learner and getting
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just a much clearer sense of how that thinking was happening.
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And I suspect that leads to an outside question that's much more productive.
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It's a win-win situation.
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Absolutely. This conversation has been wonderful.
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The challenge of having a podcast, of course,
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is that we've got about 20 to 25 minutes to talk about a really big idea
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that has profound implications for teachers.
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If someone wanted to pick up on the things we've been talking about today,
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where would you start, Vicki?
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I would encourage them to go talk to children.
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Children's thinking is so mathematically rich and it's so fascinating.
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So be curious about their thinking. Ask questions,
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ask those inside questions. Don't worry about asking the best question.
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It doesn't exist,
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but ask questions and then children will be your guides.
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They'll help you know where to go next.
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The other thing I would suggest is these journeys are always best done with your
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colleagues.
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And so get a colleague together and think about questioning together what we
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were talking about earlier with joy strategy teachers.
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We're looking at students' written work. That's a great place to practice.
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You can look at children's written work and talk together to figure out what
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types of conversations do you want to have with this child afterwards.
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I think that's a great place to stop.
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I want to thank you so much for joining us today, Vicki,
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it has really been a pleasure talking with you.
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That was fun. Thanks for having me.
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This podcast is brought to you by the Math Learning Center and the Meyer Math
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Foundation dedicated to inspiring and enabling all individuals to
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discover and develop their mathematical confidence and ability.