Beth Kobett, EdD, Practical Ways to Build Strength-Based Math Classroom

Mike Wallus, Vice President for Educator Support


What if it were possible to capture all of the words teachers said or thought about students and put them in word clouds that hovered over each student throughout the day? What impact might the words in the cloud have on the student’s learning experience? This is the question that Beth Kobett and Karen Karp pose to start their book about strength-based teaching and learning. Today on the podcast, we’re talking about practices that support strength-based teaching and learning, and ways educators can implement them in their classrooms.

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Mike Wallus: What if it were possible to capture all of the words teachers said or thought about students and put them in word clouds that hovered over each student throughout the day? What impact might the words in the clouds have on students’ learning experience? This is the question that Beth Kobett and Karen Karp pose to start their book about strengths-based teaching and learning. Today on the podcast, we're talking about practices that support strengths-based teaching and learning, and ways educators can implement them in their classrooms. 

Mike: Hey, Beth, welcome to the podcast.

Beth Kobett: Thank you so much. I'm so excited to be here, Mike.

Mike: So, there's a paragraph at the start of the book that you wrote with Karen Karp. You said: “As teachers of mathematics, we've been taught that our role is to diagnose, eradicate, and erase students' misconceptions. We've been taught to focus on the challenges in students' work rather than recognizing the knowledge and expertise that exist within the learner.” This really stopped me in my tracks, and it had me thinking about how I viewed my role as a classroom teacher and how I saw my students’ work. I think I just want to start with the question, “Why start there, Beth?”

Beth: Well, I think it has a lot to do with our identity as teachers, that we are fixers and changers and that students come to us, and we have to do something. And we have to change them and make sure that they learn a body of knowledge, which is absolutely important. But within that, if we dig a little bit deeper, is this notion of fixing this idea that, “Oh my goodness, they don't know this.” And we have to really attend to the ways in which we talk about it, right? For example, “My students aren't ready. My students don't know this.” And what we began noticing was all this deficit language for what was really very normal. When you show up in second grade, guess what? There's lots of things you know, and lots of things you're going to learn. And that's absolutely the job of a teacher and a student to navigate. So, that really helped us think about the ways in which we were entering into conversations with all kinds of people—teachers, families, leadership, and so on—so that we could attend to that. And it would help us think about our teaching in different ways.

Mike: So, let's help listeners build a counternarrative. How would you describe what it means to take a strengths-based approach to teaching and learning? And what might that mean in someone's daily practice?

Beth: So, we can look at it globally or instructionally. Like, I'm getting ready to teach this particular lesson in this class. And the counternarrative is, “What do they know? What have they been showing me?” So, for example, I'm getting ready to teach place value to second graders, and I want to think about all the things that they've already done that I know that they've done. They've been grouping and counting and probably making lots of collections of 10 and so on. And so, I want to think about drawing on their experiences, A. Or B, going in and providing an experience that will reactivate all those prior experiences that they've had and enable students to say, “Oh yeah, I've done this before. I've made sets or groups of 10 before.” So, let's talk about what that is, what the [name] of it [is], why it's so important, and let's identify tasks that will just really engage them in ways that help them understand that they do bring a lot of knowledge into it. And sometimes we say things so well intentioned, like, “This is going to be hard, and you probably haven't thought about this yet.” And so, we sort of set everybody on edge in ways that set it's going to be hard, which means, “That's bad.” It's going to be hard, which means, “You don't know this yet.” Well, why don't we turn that on its edge and say, “You've done lots of things that are going to help you understand this and make sense of this. And that's what our job is right now, is to make sense of what we're doing.”?

Mike: There's a lot there. One of the things that I think is jumping out for me is this idea is multifaceted. And part of what we're asking ourselves is, “What do kids know?” But the other piece that I want to just kind of shine a flashlight on is there's also this idea of “What experiences have they had—either in their home life or in their learning life at school—that can connect to this content or these ideas that you're trying to pull out?” That, to me, actually feels like another way to think about this. Like, “Oh my gosh, we've done partitioning, we've done grouping,” and all of those experiences. If we can connect back to them, it can actually build up a kid's sense of, like, “Oh, OK.”

Beth: I love that. And I love the way that you just described that. It's almost like positioning the student to make those connections, to be ready to do that, to be thinking about that and providing a task or a lesson that allows them to say, “Oh!” You know, fractions are a perfect example. I mean, we all love to use food, but do we talk about sharing? Do we talk about when we've divided something up? Have we talked about, “Hey, you both have to use the same piece of paper, and I need to make sure that you each have an equal space.”? I've seen that many times in a classroom. Just tweak that a little bit. Talk about [how] when you did that, you actually were thinking about equal parts. So, helping students … we don't need to make all those connections all the time because they're there for students, and children naturally make connections. That's their job (chuckles). It really is their job, and they want to do that.

Mike: So, the other bit that I want to pick up on is the subtle way that language plays into this. And one example that really stood out for me was when you examined the word “misconception.” So, talk about this particular bit of language and how you might tweak it or reframe it when it comes to student learning.

Beth: Well, thank you for bringing this up. This is a conversation that I am having consistently right now. Because this idea of misconception positions the student. “You're wrong, you don't understand something.” And again, let's go back to that [...] “I've got to fix it.” 

But what if learning is pretty natural and normal to, for example, think about Piaget’s conservation ideas—the idea that a young child can or can't conserve based on [...] the arrangement. So, you put [...] you know, five counters out, they count them and then you move them, spread them out and say, “Are they the same, more, or less?” We wouldn't say that that's a misconception of a child because it's developmental. It's where they are in their trajectory of learning. And so, we are using the word “misconception” for lots of things that are just natural, the natural part of learning. And we're assuming that the student has created a misunderstanding along the way when that misunderstanding or that that idea of that learning is very, very normal.

Place value is a perfect example of it. Fractions are, too. Let's say they're trying to order fractions on a number line, and they're just looking at the largest value wherever it falls—numerator, denominator, I'm just throwing it down. You know, those are big numbers. So, those are going to go at the end of a number line. But what if we said, “Just get some fraction pieces out”? That's not a misconception 'cause that's normal. I'm using what I've already learned about value of number, and I'm throwing it down on a number line (chuckles). [...] So, it changes the way we think about how we're going to design our instruction when we think about what's the natural way that students do that. So, we also call it “fragile understanding.” So, fragile understanding is when it's a little bit tentative. Like, “I have it, but I don't have it.” That's another part, a natural part of learning. When you're first learning something new, you kind of have it, then you’ve got to try it again, and it takes a while for it to become something you're comfortable doing or knowing.

Mike: So, this is fascinating because you're making me think about this kind of challenge that we sometimes find ourselves facing in the field where, at the end of a lesson or a unit, there's this idea that if kids don't have what we would consider mastery, then there's a deficit that exists. And I think what you're making me think is that framing this as either developing understanding or fragile understanding is a lot more productive in that it helps us imagine, “What pieces have students started to understand?” and “Where might we go next?” Or like, “What might we build on that they've started to understand?” as opposed to just seeing partial understanding or fragile understanding from a deficit perspective.

Beth: Right. I love this point because I think when we think about mastery, it's all or nothing. But that's not learning either. Maybe on an exam or on a test or on assessment, yes, you have it or you don't have it. You've mastered or you haven't. But again, if we looked at it developmentally that “I have some partial understanding” or “I have it and … I'm inconsistent in that,” that's OK. I could also think, “Well, should I have a task that will keep bringing this up for students?” so that they can continue to build that rich understanding and move along the trajectory toward what we think of as mastery—which means that “I know it now, and I'm never going to have to learn it again.” I don't know that all things we call mastery are actually mastered at that time. We say they are.

Mike: So, I want to pick up on what you said here because in the book there's something about the role of tasks in strengths-based teaching and learning. And specifically, you talk about “the cumulative impact that day-to-day tasks have on what students think mathematics is and how hard and how long they should have to work on ideas so that they make sense.” That kind of blows me away.

Beth: Well, I want to know more about why it blows you away.

Mike: It blows me away because there's two pieces of the language. One is that the cumulative impact has an effect on what students actually think mathematics is. And I think there's a lot there that I would love to hear you talk about. And then also this second part, it has a cumulative impact on how hard and how long kids believe that they should have to work on ideas in order to have them be sensible.

Beth: OK, thank you so much for talking about that a little bit more. So, there's two ways to think about that. One is, and I've done this with teams of teachers, and that's [to] bring in a week's worth of tasks that you designed and taught for two weeks. And I call this a “task autopsy.” It's a really good way because you've done it. So, bring it in and then let's talk about, “Do you have mostly conceptual ideas?” “How much time do students get to think about it?” Or are students mimicking a procedure or even a solution strategy that you want them to use or a model? Because if most of the time students are mimicking or repeating or modeling in the way that you've asked them, then they're not necessarily reasoning. And they're building this idea that math means that “You tell me what I'm supposed to do; I do it; yay, I did it.”

And then we move on to the next thing. 

And I think that sometimes we have to really do some self-talk about this. I show what I value and what I believe in those decisions that I'm making on a daily basis. And even if I say, “It's so important for you to reason; it's so important for you to make sense of it,” if all the tasks are, “You do this and repeat what I've shown you,” then students are going to take away from that, that's what math is. And we know this because we ask students, “What is math?”, math is, “When the teacher shows me what to do, and I do it, and I make my teacher happy.” And they say lots of things about teacher-pleasing because they want to do what they've been asked to do, and they want to repeat it and they want to do well, right? Or do they say, “Yeah, it's problem-solving. It's solving a problem; it's thinking hard. Sometimes my brain hurts. I talk to other students about what I'm solving. We share our ideas.” We know that students come away with big impressions about what math means based on the daily work of the math class.

Mike: So, I want to take the second part up now because you also talk about what I would call “normalizing productive struggle” for kids when they're engaged in problems. What does that mean, and what might it sound like for an educator on a day-to-day basis?

Beth: So, I happened to be in a classroom yesterday. It was a fifth grade classroom, and the teacher has been really working on normalizing productive struggle. And it was fabulous. I just happened to stop in, and she stopped everything to say, “We want to have this conversation in front of you.” And I said, “All right, go for it.” And the question was, “What does productive struggle feel like to you, and why is it important?” That's what she asked her fifth graders. And they said, “It feels hard at first. And amazing at the end of it.” Like, you can't feel amazing unless you've had productive struggle. We're taking away that opportunity to feel so joyous about the mathematics that we're learning because we got to the other side. And some of the students said, “It doesn't feel so good in the beginning, but I know I have to remember what it's going to feel like if I keep going.” I was blown away. I mean, they were like little adults in there having this really thoughtful conversation. And I asked her what … she said, “We have to stop and have this conversation a lot. We need to acknowledge what it feels like because we're kind of conditioned when we don't feel good that somebody needs to fix it.”

Mike: Yeah, I think what hits me is there's kind of multiple layers we consider as a practitioner. One layer is, “Do I actually believe in productive struggle?” And then part two is, “What does that look like, sound like?” And I think what I heard from you is, part of it is asking kids to engage with you in thinking about productive struggle, that giving them the opportunity to voice it and think about it is part of normalizing it.

Beth: It's also saying, “You might be feeling this way right now. If you're feeling like this”—like, for example, teaching a task and students are working on a task, and trying to figure out how to solve it, and it's starting to get a little noisy, and hands start coming up, stopping the class for a second and saying, “If you're feeling this way, that's an OK way to feel,” right? And, “Here's some things we might be thinking about. What are some strategies?”—like [sort of refocusing] them on how to get out of that instead of me fixing it—like, “What are some strategies you could think about? Let's talk about that and then go back to this.” 

So, it's the teacher acknowledging. It's allowing the students to talk about it. It's allowing everybody … It's not just making students be in productive struggle, or another piece of that is ‘Just try harder.” That's not real helpful. Like, OK, “I just need you to try harder because I'm making you productively struggle.” I don't know if anyone has had someone tell them that, but I used to run races and when someone said, “Try harder” to me, I'm like, “I'm trying as hard as I can.” That isn't that helpful. So, it's really about being very explicit about why it's important. Getting students to the other side of it should be the No. 1 goal. And then addressing it: “OK, you experienced productive struggle, now you did it. How do you feel now? Why is it worth it?”

Mike: I think what you're talking about feels like things that educators can put into practice really clearly, right? So, there's the front-end conversation, maybe, about normalizing. But there's the back-end conversation where you come back to kids and say, “How do you feel once this has happened?” “It feels amazing.” This is why productive struggle is so important because you can't get to this amazingness unless you're actually engaged in this challenge, unless it feels hard on the front end. And helping them kind of recalibrate what the experience is going to feel like.

Beth: Exactly. And another example of this is this idea of … so, I had a preservice teacher teaching a task. She got to teach it twice. She taught it in the morning. Students experienced struggle and were puffed up and running around, so engaged when they solved it. Beyond proud. “Can we get the principal in here? Who needs to see this, that we did this?” And then she got some feedback to reduce the level of productive struggle for the second class based on expectations about the students. And she said the engagement, everything went down. Everything went down, including the level of productive struggle went way down. And so, the excitement and joy went way down too. And so, she did her little mini research experiment there.

Mike: So, I want to stay on this topic of what it looks like to enact these practices. And there are a couple practices in the book that really jumped out at me that I'd like to just take one at a time. So, I want to start with this idea of giving kids what you would call a “walk-back option.” What's a walk-back option?

Beth: So, a walk-back option is this opportunity once you've had this conversation—or maybe one-on-one, or it could be class conversation—and a walk-back option is to go look at your work. Is there something else that you'd like to change about it? One of the things that we want to be thinking about in mathematics is that solutions and pathways and models and strategies are all sort of in flux. They're there, but they're not all finished all the time. And after having some conversation or time to reason, is there something that you'd like to think about changing? And really building in some of that mathematical reflection.

Mike: I love that. I want to shift and talk about this next piece, too, which is “rough-draft thinking.” So, the language feels really powerful, but I want to get your take on “What does that mean, and how might a teacher use the idea of rough-draft thinking in a classroom?”

Beth: So rough-draft thinking is really Mandy Jansen's work that we brought into the strengths work because we saw it as an opportunity to help lift up the strengths that students are exhibiting during rough-draft thinking. So, rough-draft thinking is this idea that most of the time (chuckles), our conversations in math as we're thinking through a process is rough, right? We're not sure. We might be making a conjecture here and there. We want to test an idea. So, it's rough, it's not finished and complete. And we want to be able to give students an opportunity to do that talking, that thinking and that reasoning while it is rough, because it builds reasoning, it builds opportunities for students to make those amazing connections. You know, just imagine you're thinking through something, and it clicks for you. That's what we want students to be able to do. So, that's rough-draft thinking, and that's what it looks like in the math classroom. It's just lots of student talk and lots of students acknowledging that “I don't know if I have this right yet, but here's what I'm thinking.” Or, “I have an idea; can I share this idea?” I watched a preservice teacher do a number talk, and a student said, “I don't know if this is going to work all the time, but can I share my idea?” Yes, that's rough-draft thinking. “Let's hear it. And wow, how brave of you and your strength and risk-taking. [Come]over here and share it with us.”

Mike: Part of what I'm attracted to is even using that language in a classroom with kids; to some degree it reduces the stakes that we traditionally associate with sharing your thinking in mathematics. And it normalizes this idea that you just described, which is, like, reasoning is in flux, and this is my reasoning at this point in time. That just feels like it really changes the game for kids.

Beth: What you hear is very authentic thinking and very real thinking. And it's amazing because even very young children—young children are very natural at doing this. But then as you move, students start to feel like their thinking has to be polished before it's shared. And then that gives other students who may be on some other developmental trajectory in their understanding, so much more afraid to share their rough-draft thinking or their thoughts or their ideas because they think it has to be at the polished stage. It's very interesting how this sort of idea has developed that you can't share something that you think in math because it's got to be right and completed. And everything's got to be perfect. And before it gets shared, because, “Wait, we might confuse other people.” But students respond really beautifully to this.

Mike: So, the last strategy that I want to highlight is this one of a “math amendment.” I love the language again. So, same question: How does this work? What does it look like?

Beth: OK, so how it works is that you have done some sharing in the class. So, for example, you may have already shared some solutions to a task. Students have been given a task they're sharing; they may be sharing a pair-to-pair share or a group-to-group share, something like that. It could be whole-class sharing. And then you say, “Hmm, you've heard lots of good ideas today, lots of interesting thinking and different strategies. If you'd like to provide a math amendment, which is a change to your solution in addition, something else that you'd like to do to strengthen it, you can go ahead and do that.” 

And you can do it in that lesson right there, or [...] what we're finding is really powerful is to bring it back the next day or even a few days later, which connects us back to this idea of what you were saying, which is, “Is this mastered?” “Where am I on the developmental trajectory?” So, I'm just strengthening my understanding, and I'm also hearing … I'm understanding the point of hearing other people's ideas is to go and try them out and use them. And we're really allowing that. So, [...] this has been amazing; the math amendments that we're seeing students do, taking someone else's idea or a strategy and then just expanding on their own work. And it's very similar to, like, a writing piece, right? You get a writing piece and you polish and you polish. You don't do this with every math task that you solve or problem that you solve, but you choose and select to do that.

Mike: Totally makes sense. So, before we go, I have the question for you. You know, for me this was a new idea. And I have to confess that it has caused me to do a lot of reflection on language that I used when I was in the classroom. I can look back now and say there are some things that I think really aligned well with thinking about kids' assets. And I can also say there are points where, gosh, I wish I could wind the clock back because there are some practices that I would do differently. I suspect there's probably a lot of people where this is a new idea that we're talking about today. What are some of the resources that you'd recommend to folks who want to keep learning about strengths-based or asset-based teaching and learning?

Beth: So, if they're interested, there's several … so strengths-based or asset-based is really the first step in building equity. And TODOS, they use the asset-based thinking, which is [a] mathematics-for-all organization. And it's a wonderful organization that does have an equity tool that would be really helpful.

Mike: Beth, it has been such a pleasure talking to you. Thank you for joining us. 

Beth: Thank you so much. I appreciate it. It was a good time.

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