Latest / Rounding Up / What If I Don't Understand Their Thinking? with Ryan Flessner

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What If I Don't Understand Their Thinking? with Ryan Flessner · Rounding Up

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What do I do if I don't understand my student's strategy?
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This is a question teachers grapple with constantly,
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particularly when conferring with students during class.
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How we respond in moments like these can have a profound impact on our students'
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learning and their mathematical identities.
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Today we'll talk with Ryan Lesner from Butler University about what educators
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can say or do when faced with this very common situation.
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Welcome to the podcast, Ryan. Really excited to talk to you today.
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Thanks, Mike. I'm flattered to be here. Thank you so much for the invitation.
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So this experience of working with a student and not being able to make sense of
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their solution feels like something that almost every teacher has had.
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And I'll speak for myself and say that when it happens to me,
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I feel a lot of anxiety. And I just want to start by asking,
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what would you say to educators who are feeling apprehensive or unsure about
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what to do when they encounter a situation like this?
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Yeah, so I think that everybody has that experience.
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I think the problem that we have is that teachers often feel the need to have
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all of the answers and to know everything and to be the expert in the room.
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But as an educator,
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I learned really quickly that I didn't have all the answers and to pretend like
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I did put a lot of pressure on me and made me feel a lot of stress and would
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leave me answering children by saying, let me get back to you on that,
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and then I would scurry and try and find all the answers so I could come back
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with a knowledgeable idea.
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And it was just so much more work than to just simply say, I don't know.
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Let's investigate that together. Or to ask kids,
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that's something interesting that I'm seeing you do.
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I've never seen a student do that before.
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Can you talk to me a little bit about that?
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And just having that ability to free myself from having to have all the answers
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and using that Reggio inspired practice for those who know early childhood
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education to follow the child,
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to listen to what he or she or they say to us and try to see.
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I can usually keep up with a seven or an 8-year-old as they're explaining math
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to me. I just may never have seen them notate something the way they did.
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So trying to ask that question about show me what, teach me something new.
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The idea that a teacher could be a learner at the same time I think is novel to
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kids and I think they respond really well to that idea.
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So before we dig in a little bit more deeply about how teachers respond to
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student strategies if they don't understand,
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I just want to linger and think about the assumptions that many
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educators, myself included might bring to this situation.
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Assumptions about the role,
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assumptions about what it would mean for a student if they don't know the answer
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right away.
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How do you think about some of the assumptions that are causing some of that
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anxiety for us?
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Yeah. When the new generation of standards came out,
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especially in the field of math,
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teachers were all of a sudden asked to teach in a way that they themselves
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didn't learn.
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And so if you have that idea that you have to have all the answers and you have
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to know everything,
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that puts you in a really vulnerable spot because how are we supposed to just
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magically teach things we've never learned ourselves?
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And so trying to figure out ways that we can back up and try and make sense of
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the work that we're doing with kids.
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For me that was really helpful in understanding what I wanted from my students.
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I wanted them to make sense of the learning.
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So if I hadn't made sense of it yet,
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how in the world could I teach them to make sense of it?
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And so we have to have that humility to say, I don't know how to do this.
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I need to continue my learning trajectory and to keep going and trying to do a
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little bit better than the day that I did before.
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I think that teachers are uniquely and they're always trying to do better,
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but I don't know if we necessarily are taught how to learn once
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we become teachers. We've already learned everything we have to do now.
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We just have to learn how to teach it to other people.
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But I don't think we have learned everything that we have to learn.
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There's a lot of stuff in the math world that I don't think we actually learned.
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We just memorized steps and kind of regurgitated them to get our a plus on a
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test or whatever we did. So I think having the ability to stop and say,
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I don't know how to do this, and so I'm going to keep working at it,
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and when I start to learn it,
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I'm going to be able to ask myself questions that I should be asking my
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students.
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And just being really thoughtful about why is the child saying the thing that
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she is? Why is she doing it the way that she's doing it?
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Why is she writing it the way that she's writing it?
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And if I can't figure it out,
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the expert on that piece of paper is the child himself,
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so why wouldn't I go to her and say, talk to me about this.
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I don't have to have all the answers right off the cuff.
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In some ways,
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what you were describing just there is a real nice segue because I've heard you
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say that our minds and our students' minds often work faster than we can write,
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or even in some cases faster than we can speak.
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I'm wondering if you can unpack that. Why do you think this matters,
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particularly in the situation that we're talking about?
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Yeah, I think a lot of us, especially in math,
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have been conditioned to get an answer.
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And nobody's really asked us why in the past.
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And so we've done all of the thinking,
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we give the answer and then we think the job is done.
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But with a lot of the new standards, we have to explain why we think that way.
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And so all those ideas that just flurried through our head,
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we have to now articulate those either in writing on paper or in speech,
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trying to figure out how we can communicate the mathematics behind the answer.
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And so a lot of times I'll be in a classroom and I'll ask a student for an
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answer and I'll say, how'd you get that?
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And the first inclination that a lot of kids have is, oh,
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I must be wrong if a teacher is asking me why so they think they're wrong.
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And so I say, no, no, no, it's not that you're wrong. I'm just curious.
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You came to that answer,
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you stopped and you looked up at the ceiling for a while and then you came to me
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and you said the answer is 68. How did you do that?
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A child will say something like, well, I just thought about it in my head.
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I say, what did you think about in your head? Well,
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my brain just told me the answer was 68.
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We have to actually talk to kids and we have to teach them how to talk to us
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that we're not quizzing them or saying that they're wrong or they didn't do
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something well enough that we just want them to communicate with us how they're
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going about finding these things, what the strategies are.
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Because if they can communicate with us in writing,
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if they can communicate on paper,
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if they can use gestures to explain what they're thinking about,
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all of those tell us strengths that they bring to the table.
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And if I can figure out the strengths that you have,
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that I can leverage those strengths as I address needs that arise in my
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classroom.
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And so I really want to create this bank of information about individual
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students that will help me be the best teacher that I can be for them.
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And if I can't ask those questions and they can't answer those questions for me,
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how am I going to individualize my instruction in meaningful ways for kids?
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We've been talking a little bit about the teacher experience in this moment and
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we've been talking about some of the things that a person might say.
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One of the things that I'm thinking about before we dig in a little bit deeper
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is just what is my role?
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How do you think about the role of a teacher in the moment when they encounter
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thinking from a student that they don't quite understand it yet?
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Part of what I'm after is how can a teacher think about what they're trying to
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accomplish in that moment for themselves as a learner and also for the learner
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in front of them? How would you answer that question?
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When I think about an interaction with a kid in a moment like that,
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I try to figure out, as the teacher,
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my goal is to try and figure out what this child knows so that I can continue
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their journey in a forward trajectory.
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Instead of thinking about they need to go to page 34 because we're on page 33,
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just thinking about what does this kid need next from me as the teacher.
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What I want them to get out of the situation is I want them to understand that
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they are powerful individuals,
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that they have something to offer the conversation and not just to prove it to
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the adult in the room, but if I can hear them talk about these ideas,
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sometimes the kids in the classroom can answer each other's questions.
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And so if I can ask these things aloud and other kids are listening in,
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maybe because we're in close proximity or because we're in a small group
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setting, if I can get the kids to verbalize those ideas.
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Sometimes one kid talking strikes an idea and another kid or another kid will
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say, I didn't know how to answer Ryan when he asked me that question before,
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but now that I hear what it sounds like to answer that type of a question,
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now I get it and I know how I would say it if it were my turn.
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So we have to actually offer kids the opportunity to learn how to engage in
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those moments and how to share their expertise so others can benefit from their
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expertise and use that in a way that's helpful in the mathematical process.
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One of the most practical,
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and I have to say freeing things that I've heard you recommend when a teacher
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encounters student work and they're still trying to make sense of it,
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is to just go ahead and name it.
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What are some of the things you imagine that a teacher might say that just
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straight out name the fact that they're still trying to understand a student's
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thinking? Tell me a little bit about that.
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Well,
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I think the first thing is that we just have to normalize the question why or
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tell me how you know that if we normalize those things.
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A lot of times kids get asked that question when they're wrong,
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and so it's an immediately tip of the hat that you're wrong.
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Now go back and fix it. There's something wrong with you.
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Haven't tried hard enough kids get these messages even if we don't intend for
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them to get them. So if we can normalize the question,
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tell me why you think that or explain that to me,
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if we can just get them to see that every time you give me an answer whether
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it's right or wrong, I'm just going to ask you to talk to me about it.
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That takes care of half of the problem.
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But I think sometimes teachers get stuck because, and myself being one of them,
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we get stuck because we'll look at what a student is doing and they do something
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that we don't anticipate or we say,
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I've shown you three different ways to get at this problem,
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different strategies you can use, and you're not using any of them.
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And so instead of getting frustrated that they're not listening to us,
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how do we use that moment to inquire into the things that we said obviously
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aren't useful? So what is useful to this kid?
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How is he attacking this on his paper? So I often like to say to a kid,
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huh, I noticed that you're doing something that isn't up on our anchor chart.
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Tell me about this. I haven't seen this before.
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How can you help me understand what you're doing?
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And sometimes it's the exact same thinking as other strategies that kids are
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using. So I can pair kids together and say, huh,
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you're both talking about it in the same way,
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but you're writing it differently on paper.
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And so I think about how I can get kids just to talk to me and tell me what's
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happening so that I can help give them a notation that might be more acceptable
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to other mathematicians or to just honor the fact that they have something novel
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and interesting to share with other kids. Other questions I talk about are,
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I will say, I don't understand what's happening here, and that's not your fault,
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that's my fault.
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I just need you to keep explaining it to me until you say something that strikes
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a chord.
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Or sometimes I'll bring another kid in and I'll have the kids listen together
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and I'll say, I think this is interesting,
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but I don't understand what's going on. Can you say it to her?
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And then maybe she'll say it in a way that will make more sense to me.
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Or I'll say, can you show me on your paper you just said that?
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Can you show me on your paper where that idea is?
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Because a lot of times kids will fake things in their head,
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but they don't translate it all onto the paper. And so on the paper,
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it's missing a step that isn't obvious to the viewer of the paper.
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And so we'll say, oh, I see how you do that.
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Maybe you could label your table so that we know exactly what you're talking
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about when you do this.
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Or maybe you could show us how you got to 56 by writing eight times seven in the
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margin or something.
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Just getting them to clarify and try to help us understand
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all of the amazing things that are in their head. I will often tell them too,
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I love what you're saying. I don't see it on your paper,
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so I just want you to say it again and I'm going to write it down on a piece of
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paper that makes sense to me so that I don't forget all of the cool things that
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you said, and I'll just write it using more of a standard notation,
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whether that's a ratio table or a standard US algorithm or something.
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I'll write it to show the kid that thing that you're doing.
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There's a way that people write that down.
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And so then we can compare our notations and try and figure out what's the thing
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that you did? How does that compare to the thing that I did?
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Do I understand you clearly now to make sure that the kid has the
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right to say the thing she wants to say in the way that she wants to say it,
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and then I can still make sense of it in my own way.
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It's not a problem for me to write it differently as long as we're speaking the
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same language.
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I want to mark something really important and I don't want it to get lost.
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For folks,
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one of the things that jumped out is the moves that you were describing.
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You could potentially take up those moves if you really were unsure of how a
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student were thinking. If you had a general notion,
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but you had some questions or if you totally already understood what the student
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was doing,
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those are questions that aren't just reserved for the point in time when you
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don't understand they're actually good questions regardless of whether you fully
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understand it or don't understand it at all. Did I get that right?
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Yes. I think that's exactly the point.
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One thing that I am careful of is sometimes kids will ask me a question that I
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know the answer to,
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and there's this thing that we do as teachers where we're like, I'm not sure.
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Why don't you help me figure that out when the kid knows full well that you know
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the answer? And so try not to patronize kids with those questions,
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but to really show that I'm asking you these questions,
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not because I'm patronizing you,
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I'm asking these questions because I am truly curious about what you're thinking
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inside and all of the ideas that surround the things that you've written on your
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paper or the things that you've said to your partner to truly honor that.
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The more I know about you, the better teacher I can be for you.
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So in addition to naming the situation,
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one of the things that jumped out for me,
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particularly as you were talking about the students,
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is what do you think the impact is on a student's thinking,
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but also their mathematical identity or even the set of classroom norms when
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they experience this type of questioning or these type of questions?
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So I think I talked a little bit about normalizing the question,
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why or how do you know that?
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And so just letting that become a classroom norm I think is a sea changing
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moment for a lot of classrooms that the conversation is just different.
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If the kids know they have to justify their thinking,
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whether they're right or wrong, half the time, if they are incorrect,
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they'll be able to correct themselves as they're talking it through with you.
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So kids can be freed up when they're allowed to use their
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expertise in ways that allow them to understand that the point of math is to
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truly make sense of it so that when you go out into the world,
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you understand the situation and you have different tools to attack it.
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So what's the way that we can create an environment that allows them to truly
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see themselves as mathematical thinkers and to let them know that your
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grades and other classes don't tell me much about you as a mathematician,
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I want to learn what really works for you,
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and I want to try and figure out where you struggle.
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And both of those things are important to me because we can use them in concert
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with each other. So if I know the things you do well,
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I can use those to help me build a plan of instruction that will take you
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further in your understandings.
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I think that one of the things that is really important is for kids to
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understand that we don't do math because we want a good grade.
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I think a lot of people think that the point of math is to get a good grade or
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to pass a test or to get into the college that you want to get into,
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or because sixth grade teachers want you to know this.
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I really want kids to understand that math is a fantastic language to use out in
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the world,
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and there are ways that we can interpret things around us if we understand some
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pretty basic math.
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And so how do we get them to stop thinking that math is about right answers and
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next year and to get the job I want? Well, those things may be true.
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That's not the real meaning of math. Math is a way that we can live life.
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And so if we don't help them understand the connections between the things that
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they're doing on a worksheet or in a workbook page,
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if we don't connect those things to the real world, what's the meaning?
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What's the point for them and how do we keep them engaged in wanting to know
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more mathematics?
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So really getting kids to think about who they are as people and how math can
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help them live the life that they want to live.
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Creating classroom environments that have routines in place that support kids
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in thinking in ways that will move them forward in their mathematical
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understanding,
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trying to help them see that there's no such thing as a math person or not a
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math person that everybody has to do math. You do math all the time.
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You just might not even know that you're doing math.
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So I think all of those ideas are really important.
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And the more curious I can be about students,
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maybe the more curious they'll be about the math.
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You're making me think that this experience of making sense of someone else's
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reasoning has a lot of value for students.
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And I'm wondering how you've seen educators have students engage
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and make sense of their peer strategies?
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Yeah. One of the things that I love to see teachers doing is using students'
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work as the conversation starter. I often, in my classroom,
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when I started doing this work,
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I would bring children up to the overhead projector or the document camera,
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and they would kind of do a show and tell and just say,
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I did this and then I did this, and then I did this thing next. And I would say,
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that's really great, thank you.
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And I'd bring up the next student and it kind of became a show and tell type
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situation.
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And I would look at the faces of the other kids in the room and they would kind
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of just either be completely checked out or sitting there like raising their
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hand excitedly. I want to share mine, I want to share mine.
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And what I realized was that there was really only one person who was engaged in
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that show and tell manner, and that was the person who was sharing their work.
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And so I thought, how can I change that?
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So I saw a lot of really amazing teachers across my career,
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and the thing that I saw that I appreciated the most is that when a piece of
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student work is shared,
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the person who really shouldn't talk is the person who created the work because
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they already know the work.
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What we need to do as a group is we need to investigate what happened here on
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this paper.
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Why do you think they made the moves that they made and how could that help us
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understand math, our own math in a different way?
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And so getting kids to look in at other kids' work and not just saying, oh,
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Mike, how do you understand Ryan's work? It's Mike, can you get us started?
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And then you say the first thing, and then I say, okay, let's stop.
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Let's make sure that we've got this right.
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And then we go to the kid whose work it is and say, are we on the right track?
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Are we understanding what you're, so we're always checking with that expert.
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We're making sure they have the last word, because it's not my strategy.
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I didn't create it.
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Just because I'm the teacher doesn't mean you should come and ask me about this
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because this is Mike's strategy. So go and ask the person who created that.
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So trying to get them to understand that we all need to engage in each other's
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work, we all need to see the connections. We can learn from each other,
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and there's an expectation that everyone shares, right?
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So it's not just the first kid who raises his hand.
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It's all of you are going to get a chance to share.
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And I think the really powerful thing is I've done this work even with
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in-service teachers. And so when we look at samples of student work,
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what's fascinating is it just happens naturally because the kid's not in the
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room. We can't have that kid do a show and tell.
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We have to interpret their work.
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And so trying to look at the kid's work and imagine what are the types of things
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we think this child is doing? What do we think the strengths are on this paper?
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What questions would you ask? What would you do next?
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Is such an interesting thing to do when the child isn't in the room.
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But when I'm with students,
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it's just fascinating to watch the kid whose work is on display just shine,
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even though they're not saying a word, because they just say, huh, they get it.
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They understand what I did and why I did it.
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I think that it's really important for us not just to have kids walk up to the
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board and do board work and just solve a problem using the steps that they've
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memorized or just go up and do a show and tell to really engage everyone in that
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process so that we're all learning.
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We're not just kind of checking out or waiting for our turn to talk.
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Okay. You were talking about the ways that an educator can see how a student was
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thinking or the ways that an educator could place student work in front of
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other students and have them try to make sense of it.
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I wonder if there are any educational technology tools that you've seen that
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might help an educator who's trying to either understand their students'
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thinking or put it out for their students to understand one another's thinking.
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Yeah, there's so many different pieces of technology and things out there.
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It's kind of overwhelming to try and figure out which one is which. So I mean,
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I've seen people use things like Nearpod or Pear Deck,
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some of those kind of common technologies that you'll see when people do an
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educational technology class or a workshop at a conference or something.
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I've seen a lot of people lately using GeoGebra to create applets that they can
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use with their kids. One that I've started using a lot recently is Magma Math.
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Magma Math is great.
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I've used this with teachers and professional development situations to look at
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samples of student work because the thing that Magma has that I haven't seen in
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a lot of other technologies is there's a playback function.
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So I can look at a static piece of finished work, but I can also rewind.
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And as the child works in this program,
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it records it so I can watch in real time what the child does.
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And so if I can't understand the work because things are kind of sporadically
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all over the page,
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I can just rewatch the order that the child put something onto the page.
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And I think that's a really great,
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there's just all these technologies that offer us opportunities to do things
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that I couldn't do at the beginning of my career or I didn't know how to do.
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And the technology facilitates that.
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And it's not just putting kids on an iPad so they can shoot lasers at the alien
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that's invading by saying eight times five is 40 and the alien magically blows
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up. How does that teach us anything?
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But some of these technologies really allow us to dig deeply into a sample of
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work that students have finished or inquire into,
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how did that happen and why did that happen?
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And the technologies are just getting smarter and smarter,
21:19
and they're listening to teachers saying,
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it would be really helpful if we could do this or if we could do that.
21:24
And so I think there are a lot of resources out there, sometimes too many,
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almost an embarrassment of riches.
21:31
So trying to figure out which ones are the ones that are actually worth our
21:33
time,
21:34
and how do we fund that in a school district or in a school so that teachers
21:38
aren't paying for these pieces out of their pocket.
21:41
You know what? I think that's a great place to stop. Brian,
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thank you so much for joining us.
21:45
It has been an absolute pleasure talking with you.
21:48
It's always great to talk to you, Mike. Thanks for all you do.
21:54
This podcast is brought to you by the Math Learning Center and the Meyer Math
21:57
Foundation dedicated to inspiring and enabling all individuals to discover
22:02
and develop their mathematical confidence and ability.