Ryan Flessner, What If I Don’t Understand Their Thinking? ROUNDING UP: SEASON 3 | EPISODE 15

“What do I do if I don’t understand my student’s strategy?” This is a question teachers grapple with constantly, particularly when conferring with students during class. How educators respond in moments like these can have a profound impact on students’ learning and their mathematical identities.

In this episode, we talk with Ryan Flessner from Butler University about what educators can say or do when faced with this situation.

BIOGRAPHY

Ryan Flessner is a professor of teacher education in the College of Education at Butler University in Indianapolis, Indiana. He holds a PhD in curriculum and instruction with an emphasis in teacher education from the University of Wisconsin–Madison; a master of arts in curriculum and teaching from Teachers College, Columbia University; and a bachelor of science in elementary education from Butler University. Prior to his time at the university level, he taught grades 3–7 in Indianapolis; New York City; and Madison, Wisconsin.

RESOURCES

Nearpod

Pear Deck

GeoGebra 

Magma Math

TRANSCRIPT

Mike Wallus: “What do I do if I don't understand my student’s strategy?” This is a question teachers grapple with constantly, particularly when conferring with students during class. How we respond in moments like these can have a profound impact on our students' learning and their mathematical identities. Today we'll talk with Ryan Flessner from Butler University about what educators can say or do when faced with this very common situation. 

Welcome to the podcast, Ryan. Really excited to talk to you today.

Ryan Flessner: Thanks, Mike. I'm flattered to be here. Thank you so much for the invitation.

Mike: So, this experience of working with a student and not being able to make sense of their solution feels like something that almost every teacher has had. And I'll speak for myself and say that when it happens to me, I feel a lot of anxiety. And I just want to start by asking, what would you say to educators who are feeling apprehensive or unsure about what to do when they encounter a situation like this?

Ryan: Yeah, so I think that everybody has that experience. I think the problem that we have is that teachers often feel the need to have all of the answers and to know everything and to be the expert in the room. But as an educator, I learned really quickly that I didn't have all the answers. And to pretend like I did put a lot of pressure on me and made me feel a lot of stress and would leave me answering children by saying, “Let me get back to you on that.” And then I would scurry and try and find all the answers so I could come back with a knowledgeable idea. And it was just so much more work than to just simply say, “I don't know. Let's investigate that together.” Or to ask kids, “That's something interesting that I'm seeing you do. I've never seen a student do that before. Can you talk to me a little bit about that?”

And just having that ability to free myself from having to have all the answers and using that Reggio-inspired practice—for those who know early childhood education—to follow the child, to listen to what he or she or they say to us and try to see. I can usually keep up with a 7- or an 8-year-old as they're explaining math to me. I just may never have seen them notate something the way they did. So, trying to ask that question about, “Show me what you know. Teach me something new.” The idea that a teacher could be a learner at the same time I think is novel to kids, and I think they respond really well to that idea.

Mike: So, before we dig in a little bit more deeply about how teachers respond to student strategies if they don't understand, I just want to linger and think about the assumptions that many educators, myself included, might bring to this situation. Assumptions about their role, assumptions about what it would mean for a student if they don't know the answer right away. How do you think about some of the assumptions that are causing some of that anxiety for us?

Ryan: Yeah. When the new generation of standards came out, especially in the field of math, teachers were all of a sudden asked to teach in a way that they themselves didn't learn. And so, if you have that idea that you have to have all the answers and you have to know everything, that puts you in a really vulnerable spot because how are we supposed to just magically teach things we've never learned ourselves? And so, trying to figure out ways that we can back up and try and make sense of the work that we're doing with kids, for me that was really helpful in understanding what I wanted from my students. I wanted them to make sense of the learning. So, if I hadn't made sense of it yet, how in the world could I teach them to make sense of it? And so we have to have that humility to say, “I don't know how to do this. I need to continue my learning trajectory and to keep going and trying to do a little bit better than the day that I did before.”

I think that teachers are uniquely self-critical and they're always trying to do better, but I don't know if we necessarily are taught how to learn once we become teachers. Like, “We've already learned everything we have to do. Now we just have to learn how to teach it to other people.” But I don't think we have learned everything that we have to learn. There's a lot of stuff in the math world that I don't think we actually learned. We just memorized steps and kind of regurgitated them to get our A+ on a test or whatever we did. 

So, I think having the ability to stop and say, “I don't know how to do this, and so I'm going to keep working at it, and when I start to learn it, I'm going to be able to ask myself questions that I should be asking my students.” And just being really thoughtful about, “Why is the child saying the thing that she is?,” “Why is she doing it the way that she's doing it?,” “Why is she writing it the way that she's writing it?” And if I can't figure it out, the expert on that piece of paper is the child [herself], so why wouldn't I go and say, “Talk to me about this.”? I don't have to have all the answers right off the cuff.

Mike: In some ways, what you were describing just there is a real nice segue because I've heard you say that our minds and our students' minds often work faster than we can write, or even in some cases faster than we can speak. I'm wondering if you can unpack that. Why do you think this matters, particularly in the situation that we're talking about?

Ryan: Yeah, I think a lot of us, especially in math, have been conditioned to get an answer. And nobody's really asked us “Why?” in the past. And so, we've done all of the thinking, we give the answer, and then we think the job is done. But with a lot of the new standards, we have to explain why we think that way. And so, all those ideas that just flurried through our head, we have to now articulate those either in writing on paper or in speech, trying to figure out how we can communicate the mathematics behind the answer. 

And so, a lot of times I'll be in a classroom, and I'll ask a student for an answer, and I'll say, “How'd you get that?” And the first inclination that a lot of kids have is, “Oh, I must be wrong if a teacher is asking me why.” So, they think they're wrong. And so I say, “No, no, no. It's not that you're wrong. I'm just curious. You came to that answer, you stopped and you looked up at the ceiling for a while and then you came to me and you said the answer is 68. How did you do that?” A child will say something like, “Well, I just thought about it in my head.” And I say, “Well, what did you think about in your head?” “Well, my brain just told me the answer was 68.” 

And we have to actually talk to kids. And we have to teach them how to talk to us—that we're not quizzing them or saying that they're wrong or they didn't do something well enough—that we just want them to communicate with us how they're going about finding these things, what the strategies are. Because if they can communicate with us in writing, if they can communicate on paper, if they can use gestures to explain what they're thinking about, all of those tell us strengths that they bring to the table. And if I can figure out the strengths that you have, then I can leverage those strengths as I address needs that arise in my classroom. And so, I really want to create this bank of information about individual students that will help me be the best teacher that I can be for them. And if I can't ask those questions and they can't answer those questions for me, how am I going to individualize my instruction in meaningful ways for kids?

Mike: We've been talking a little bit about the teacher experience in this moment, and we've been talking about some of the things that a person might say. 

One of the things that I'm thinking about before we dig in a little bit deeper is, just, what is my role? How do you think about the role of a teacher in the moment when they encounter thinking from a student that they don't quite understand […] yet? Part of what I'm after is, how can a teacher think about what they're trying to accomplish in that moment for themselves as a learner and also for the learner in front of them? How would you answer that question?

Ryan: When I think about an interaction with a kid in a moment like that, I try to figure out, as the teacher, my goal is to try and figure out what this child knows so that I can continue their journey in a forward trajectory. Instead of thinking about, “They need to go to page 34 because we're on page 33,” just thinking about, “What does this kid need next from me as the teacher?” 

What I want them to get out of the situation is I want them to understand that they are powerful individuals, that they have something to offer the conversation and not just to prove it to the adult in the room. But if I can hear them talk about these ideas, sometimes the kids in the classroom can answer each other's questions. And so, if I can ask these things aloud and other kids are listening in, maybe because we're in close proximity or because we're in a small-group setting, if I can get the kids to verbalize those ideas sometimes one kid talking strikes an idea in another kid. Or another kid will say, “I didn't know how to answer Ryan when he asked me that question before, but now that I hear what it sounds like to answer that type of a question, now I get it, and I know how I would say it if it were my turn.” 

So, we have to actually offer kids the opportunity to learn how to engage in those moments and how to share their expertise so others can benefit from their expertise and use that in a way that's helpful in the mathematical process.

Mike: One of the most practical—and, I have to say, freeing—things that I've heard you recommend when a teacher encounters student work and they're still trying to make sense of it, is to just go ahead and name it. What are some of the things you imagine that a teacher might say that just straight out name the fact that they're still trying to understand a student's thinking? Tell me a little bit about that.

Ryan: Well, I think the first thing is that we just have to normalize the question “Why?” or “Tell me how you know that.” If we normalize those things—a lot of times kids get asked that question when they're wrong, and so it's an [immediate] tip of the hat that “You're wrong, now go back and fix it. There's something wrong with you. You haven't tried hard enough.” Kids get these messages even if we don't intend for them to get them. So, if we can normalize the question “Tell me why you think that” or “Explain that to me”—if we can just get them to see that every time you give me an answer whether it's right or wrong, I'm just going to ask you to talk to me about it, that takes care of half of the problem. 

But I think sometimes teachers get stuck because—and myself being one of them—we get stuck because we'll look at what a student is doing and they do something that we don't anticipate. Or we say, “I've shown you three different ways to get at this problem, different strategies you can use, and you're not using any of them.” And so, instead of getting frustrated that they're not listening to us, how do we use that moment to inquire into the things that we said obviously aren't useful, so what is useful to this kid? How is he attacking this on his paper? 

So, I often like to say to a kid, “Huh, I noticed that you're doing something that isn't up on our anchor chart. Tell me about this. I haven't seen this before. How can you help me understand what you're doing?” And sometimes it's the exact same thinking as other strategies that kids are using. So, I can pair kids together and say, “Huh, you're both talking about it in the same way, but you're writing it differently on paper.” And so, I think about how I can get kids just to talk to me and tell me what's happening so that I can help give them a notation that might be more acceptable to other mathematicians or to just honor the fact that they have something novel and interesting to share with other kids.

Other questions I talk about are, I will say, “I don't understand what's happening here, and that's not your fault, that's my fault. I just need you to keep explaining it to me until you say something that strikes a chord.” Or sometimes I'll bring another kid in, and I'll have the kids listen together, and I'll say, “I think this is interesting, but I don't understand what's going on. Can you say it to her? And then maybe she'll say it in a way that will make more sense to me.” Or I'll say, “Can you show me on your paper—you just said that—can you show me on your paper where that idea is?” Because a lot of times kids will think things in their head, but they don't translate it all onto the paper. And so, on the paper, it's missing a step that isn't obvious to the viewer of the paper. And so, we'll say, “Oh, I see how you do that. Maybe you could label your table so that we know exactly what you're talking about when you do this. Or maybe you could show us how you got to 56 by writing 8 times 7 in the margin or something.” 

Just getting them to clarify and try to help us understand all of the amazing things that are in their head. I will often tell them too, “I love what you're saying. I don't see it on your paper, so I just want you to say it again. And I'm going to write it down on a piece of paper that makes sense to me so that I don't forget all of the cool things that you said.” And I'll just write it using more of a standard notation, whether that's a ratio table or a standard US algorithm or something. I'll write it to show the kid that thing that you're doing, there's a way that people write that down. And so, then we can compare our notations and try and figure out “What's the thing that you did?,” “How does that compare to the thing that I did?,” “Do I understand you clearly now?” to make sure that the kid has the right to say the thing she wants to say in the way that she wants to say it, and then I can still make sense of it in my own way. It's not a problem for me to write it differently as long as we're speaking the same language.

Mike: I want to mark something really important, and I don't want it to get lost for folks. One of the things that jumped out is the moves that you were describing. You could potentially take up those moves if you really were unsure of how a student were thinking, if you had a general notion but you had some questions, or if you totally already understood what the student was doing. Those are questions that aren't just reserved for the point in time when you don't understand—they're actually good questions regardless of whether you fully understand it or don't understand it at all. Did I get that right?

Ryan: Yes. I think that's exactly the point. One thing that I am careful of is, sometimes kids will ask me a question that I know the answer to, and there's this thing that we do as teachers where we're like, “I'm not sure. Why don't you help me figure that out?”—when the kid knows full well that you know the answer. 

And so, trying not to patronize kids with those questions, but to really show that I'm asking you these questions, not because I'm patronizing you. I'm asking these questions because I am truly curious about what you're thinking inside and all of the ideas that surround the things that you've written on your paper, or the things that you've said to your partner, to truly honor that the more I know about you, the better teacher I can be for you.

Mike: So, in addition to naming the situation, one of the things that jumped out for me—particularly as you were talking about the students—is, what do you think the impact is on a student's thinking? But also their mathematical identity, or even the set of classroom norms, when they experience this type of questioning or these [types] of questions?

Ryan: So, I think I talked a little bit about normalizing the [questions] “Why?” or “How do you know that?” And so, just letting that become a classroom norm I think is a sea-changing moment for a lot of classrooms—that the conversation is just different if the kids know they have to justify their thinking whether they're right or wrong. Half the time, if they are incorrect, they'll be able to correct themselves as they're talking it through with you. So, kids can be freed up when they're allowed to use their expertise in ways that allow them to understand that the point of math is to truly make sense of it so that when you go out into the world, you understand the situation, and you have different tools to attack it. 

So, what's the way that we can create an environment that allows them to truly see themselves as mathematical thinkers? And to let them know that “Your grades in other classes don't tell me much about you as a mathematician. I want to learn what really works for you, and I want to try and figure out where you struggle. And both of those things are important to me because we can use them in concert with each other. So, if I know the things you do well, I can use those to help me build a plan of instruction that will take you further in your understandings.” 

I think that one of the things that is really important is for kids to understand that we don't do math because we want a good grade. I think a lot of people think that the point of math is to get a good grade or to pass a test or to get into the college that you want to get into, or because sixth grade teachers want you to know this. I really want kids to understand that math is a fantastic language to use out in the world, and there are ways that we can interpret things around us if we understand some pretty basic math. And so how do we get them to stop thinking that math is about right answers and next year and to get the job I want? Well, those things may be true, but that's not the real meaning of math. Math is a way that we can live life. And so, if we don't help them understand the connections between the things that they're doing on a worksheet or in a workbook page, if we don't connect those things to the real world, what's the meaning? What's the point for them? And how do we keep them engaged in wanting to know more mathematics? 

So, really getting kids to think about who they are as people and how math can help them live the life that they want to live. Creating classroom environments that have routines in place that support kids in thinking in ways that will move them forward in their mathematical understanding. Trying to help them see that there's no such thing as “a math person” or “not a math person.” That everybody has to do math. You do math all the time. You just might not even know that you're doing math. So, I think all of those ideas are really important. And the more curious I can be about students, maybe the more curious they'll be about the math.

Mike: You're making me think that this experience of making sense of someone else's reasoning has a lot of value for students. And I'm wondering how you've seen educators have students engage and make sense of their peer strategies.

Ryan: Yeah. One of the things that I love to see teachers doing is using students' work as the conversation starter. I often, in my classroom, when I started doing this work, I would bring children up to the overhead projector or the document camera. And they would kind of do a show and tell and just say, “I did this and then I did this, and then I did this thing next.” And I would say, “That's really great, thank you.” And I'd bring up the next student. And it kind of became a show-and-tell-type situation. And I would look at the faces of the other kids in the room, and they would kind of just either be completely checked out or sitting there like raising their hand excitedly—“I want to share mine, I want to share mine.” And what I realized was, that there was really only one person who was engaged in that show-and-tell manner, and that was the person who was sharing their work.

And so, I thought, “How can I change that?” So, I saw a lot of really amazing teachers across my career. And the thing that I saw that I appreciated the most is that when a piece of student work is shared, the person who really shouldn't talk is the person who created the work because they already know the work. What we need to do as a group is we need to investigate, “What happened here on this paper?” “Why do you think they made the moves that they made? And how could that help us understand math, our own math, in a different way?” And so, getting kids to look in at other kids' work, and not just saying, “Oh, Mike, how do you understand Ryan's work?” It's “Mike, can you get us started?” And then you say the first thing, and then I say, “OK, let's stop. Let's make sure that we've got this right.” And then we go to the kid whose work it is and say, “Are we on the right track? Are we understanding what you're …?” So, we're always checking with that expert. We're making sure they have the last word, because It's not my strategy. I didn't create it. Just because I'm the teacher doesn't mean you should come and ask me about this because this is Mike's strategy. So go and ask the person who created that. 

So, trying to get them to understand that we all need to engage in each other's work. We all need to see the connections. We can learn from each other. And there's an expectation that everyone shares, right? So, it's not just the first kid who raises his hand. It's “All of you are going to get a chance to share.” And I think the really powerful thing is I've done this work even with in-service teachers. And so, when we look at samples of student work, what's fascinating is it just happens naturally because the kid's not in the room. We can't have that kid do a show and tell. We have to interpret their work. And so, trying to look at the kid's work and imagine, “What are the types of things we think this child is doing?,” “What do we think the strengths are on this paper?,” “What questions would you ask?,” “What would you do next?,” is such an interesting thing to do when the child isn't in the room. But when I'm with students, it's just fascinating to watch the kid whose work is on display just shine, even though they're not saying a word, because they just say, “Huh.” They get it. They understand what I did and why I did it. 

I think that it's really important for us not just to have kids walk up to the board and do board work and just solve a problem using the steps that they've memorized or just go up and do a show and tell, [but] to really engage everyone in that process so that we're all learning. We're not just kind of checking out or waiting for our turn to talk.

Mike: OK, you were talking about the ways that an educator can see how a student was thinking or the ways that an educator could place student work in front of other students and have them try to make sense of it. I wonder if there are any educational technology tools that you've seen that might help an educator who's trying to either understand their students' thinking or put it out for their students to understand one another's thinking.

Ryan: Yeah, there's so many different pieces of technology and things out there. It's kind of overwhelming to try and figure out which one is which. So, I mean, I've seen people use things like Nearpod or Pear Deck—some of those kind of common technologies that you'll see when people do an educational technology class or a workshop at a conference or something. I've seen a lot of people lately using GeoGebra to create applets that they can use with their kids. One that I've started using a lot recently is Magma Math. Magma Math is great. I've used this with teachers and professional development situations to look at samples of student work because the thing that Magma has that I haven't seen in a lot of other technologies is there's a playback function. So, I can look at a static piece of finished work, but I can also rewind, and as the child works in this program, it records it. So, I can watch in real time what the child does. And so, if I can't understand the work because things are kind of sporadically all over the page, I can just rewatch the order that the child put something onto the page. And I think that's a really great feature. 

There's just all these technologies that offer us opportunities to do things that I couldn't do at the beginning of my career or I didn't know how to do. And the technology facilitates that. And it's not just putting kids on an iPad so they can shoot lasers at the alien that's invading by saying, “8 times 5 is 40,” and the alien magically blows up. How does that teach us anything? But some of these technologies really allow us to dig deeply into a sample of work that students have finished or inquire into, “How did that happen and why did that happen?” And the technologies are just getting smarter and smarter, and they're listening to teachers saying, “It would be really helpful if we could do this or if we could do that.” And so, I think there are a lot of resources out there—sometimes too many, almost an embarrassment of riches. So, trying to figure out which ones are the ones that are actually worth our time, and how do we fund that in a school district or in a school so that teachers aren't paying for these pieces out of their pocket.

Mike: You know what? I think that's a great place to stop. Ryan, thank you so much for joining us. It has been an absolute pleasure talking with you.

Ryan: It's always great to talk to you, Mike. Thanks for all you do.

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

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