Part 4 of our conversation with Deborah Ball, math education expert and researcher at the University of Michigan

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Here is the transcript.

– Hi, and welcome to another #PLtogether Lounge Talk, I’m Adam Geller, founder and CEO of Edthena, and I am thrilled to be joined again by Deborah Ball. She is a professor at the University of Michigan School of Education, she is a researcher with a long history of looking into math education and is also still a practicing math teacher, and we’re gonna be talking today a little bit more about the actual teaching of math. Deborah, thanks so much for joining us.

– Glad to be here.

– So, a lot of teachers are working to adjust instruction for a variety of different reasons, and that looks a lot of different ways. I think there’s a assumption, which is not true, which is everybody’s gonna be doing Zoom teaching. I think maybe more true, a lot of people might do some teaching on recorded videos and get those videos to parents and kids in various ways. So I’m curious how you’ve been thinking about adjusting the actual teaching for this new kind of way of teaching. And I know there’s a lot of complexity in teaching, but let’s maybe break it down for folks so they can start to kind of decompose, in some ways, their own practice. So let’s start with talk. ‘Cause I know that the talk within math is so critical, what you’re saying as a teacher to drive student thinking and I’m curious what you’ve learned so far, related to how talk needs to adjust, given that we may not be live with students anymore.

– Yeah, it’s a really interesting question, because it’s two kinds of talk, at least. One is the talking we do when we’re trying to either pose a question or explain something or probe children’s thinking. It requires some really careful attentiveness and attunement when we’re not close, and can’t see their bodies and their hands, and we can’t use things. I was watching a teacher yesterday teaching something, synchronously but on Zoom, to very young children and you almost could feel that she was trying to explain something with her hands tied behind her back, because these little kids really needed probably a basket with objects in it to understand what she was talking about, and I think she knew that too, but it’s not so clear how to do that. Yeah, she could have a basket and film it, but they’d actually have to feel it, see it. So I think being more aware of the fact that normally, when we do this well, we’re communicating lots of modalities, and we need to be pretty careful about what we’re expecting we can reduce to just talk. So there’s our talking and realizing, especially if we videotape or video record things and hand them off, that our language really matters. I mean, I’m just constantly aware when I ask a question, or I explain something, that I can easily use a word that just confuses the children, and then we’re surprised, you shouldn’t be surprised when in fifth grade, or in eighth grade, they’re confused, but they actually came from things that we say when we’re not carefully hearing ourselves. I’m really struck with how many confusions children develop about fractions just because we use language a little bit carelessly. We already know the content so we’re not aware, that really matters when you call it “parts” on a number line, they’re not exactly parts, and so the children start counting the tick marks, when in fact they should be counting the intervals and the distance from zero. So things like that are gonna get harder when we don’t have a whiteboard, I mean, you can have a whiteboard on Zoom, or film it, but we’re gonna lose some of that ability to be really careful and we won’t get the pushback immediately from children to realize that they might not be understanding us, so it’s a moment where, probably, when we have a full time, and I don’t know anyone will have time, but to practice a little more how we’re explaining something. I was working with just one child the other day on something related to linear equations which is a little outside my normal space, it’s like an eighth grader. But I realized that just formulating the question I wanted to ask him was really hard, I was trying to get him to explain that once you graph a line, all the points on that line are solutions to the equation, and I knew what I wanted him to understand about it, but I could not figure out how to ask a question, to see whether he actually was understanding that in addition the points he had happened to plot, that every point on that line was a solution to the equation, I just couldn’t think of how to ask it. So it was an interesting example of many in my life where I kind of know what I’m talking about, but I don’t know how to ask it, and I think it’s that much harder when I’m not together with a student, I can’t quickly sketch something, but another kind of talk that I think your question makes me really aware of, that I’ve been worrying about is that one reason we have public schooling is so that children are interacting with one another, and hearing one another’s ideas. And in my own teaching, up to this point, a lot of what I do is try to figure out how to get kids oriented to one another, and using one another’s ideas, so the class is developing a trajectory of a problem. It’s really different to work with just one child. That tutoring situation, or whatever you want to call it, is actually very different and a very different learning opportunity. Sometimes we thought that it’s a better learning opportunity, and it may be in some ways, but mostly it loses a whole dimension of learning, which is what you learn from hearing other people’s ideas, and what the teaching role is in orchestrating that. I think we’re gonna have to learn what that looks like, to have small groups of children who aren’t in the same space learning to hear one another, listen, they’re gonna need some support in learning how to do that, but if we don’t do that, we’re gonna be missing a big part of what school is for, school can’t all become sort of broken down to be one-on-one teaching, or one-on-mom teaching or one-on-grandmother teaching, or whatever, that’s a whole different thing. So, I think your question about our position, but also the opportunities to interact with talk, we have to think imaginatively in this space, and it’ll be good for us going forward, whatever mix of teaching we do, but we need to be much more aware of talk, and what a role our own and their talk plays in their learning.

– I’m very tempted to go down this path of thinking about the impact of students not being in schools, and not being able to talk to each other. That sounds like a big box to open, so I wanna go back to the teachers teaching, and you kind of talked about the precision and the amount of time and it made me think about if let’s say the, quote, unquote “lesson” that a teacher is handing off in a recorded format or maybe even a video-based format for live, synchronous teaching is only five to ten minutes now, instead of what used to be 50 minutes. It may be the case they need to adjust to thinking, well, it’s still gonna take an hour to plan those five or ten minutes because you’re gonna need to really think, “What is that exact question I’m going to ask?” Or, “What is the precise language I’m going to use?” because it’s not that video is a one-shot opportunity, but in some ways, you’re pointing out the risk of the students picking up the slightly imprecise version of the truth from the adults, and them not being able to discern that… And we won’t have multiple opportunities to go back and kind of reshape and re-hone the way that we’re explaining to them over the course of that 50 minute lesson. You described the kind of challenge with the hands-tied-behind-your-back feeling, when it’s not as simple as recording a whiteboard, or recording that physical movement of some object potentially. But I do think there is this very real question of representations in math, I know that that’s an important aspect of planning and teaching. So, sure that whiteboard isn’t the best solution, but should we be really thinking carefully as math teachers that we need to have more whiteboard-style representations in these videos? Because talking heads aren’t gonna cut it, right?

– Yeah, I think it’s a place to do some real thinking. Obviously there are videos out there where you can see them all the time, if you just go out and look, you can find people explaining all kinds of things, with fraction bars and number lines, but just that alone is worth looking at really carefully, because do you do it in front of the kids so they can see how you’ve made a drawing? I do a lot of work with fifth graders on learning to identify fractions as numbers on the line, ’cause that’s become kind of an important idea that we didn’t teach very well in the past, and I could make a perfect drawing of a number line from zero to one, and I could already have it labeled, and then hold it up and film it, but actually they probably need to see me have an open number line and mark the intervals, and then carefully show that I’m looking at the interval from zero to 1/3, or the interval from zero to past one to 7/3, so I’m gonna have to be really thoughtful of how I’m orienting my hands so that I’m going a direction that looks like it’s going the right way for them. Like I hope I’m doing that correctly for you right now, but it matters, right? And then we’ve, I think historically, when we’re in class, often been kind of casual about some of our drawings. And that in its own right has created misconceptions, so when we draw a circle in class, we often don’t really draw circles, we draw something that’s sort of a circle, and we know that it’s meant to be a circle, but then we’re surprised that children don’t really understand that a circle is all the points equal distance from the center. Because we’ve been calling all kinds of things circles. So, the coordination between our talk, which we were just talking about, and making a drawing while talking, this is real in face-to-face teaching, but I think when we’re making video recordings, we’re gonna have to think even more carefully about how we orient it, how visible is it, are we doing it in front of kids, I don’t mean to scare us all, but being aware that our slight casualness with that, kids can pick that up, and understand things that we don’t mean them to be understanding, and I think you’re right. What do we do with the fact that we’ve been relying on base 10 blocks, and counters, and chips, and yeah, there are probably nickable things that people are developing or that already exist to do that online, but not quite the same thing as building something with base 10 blocks and seeing how big is a million, that’s an amazing activity. We could draw that, we could show an animation of it, still not gonna be the same thing. So re-imagining how create those experiences, do kids need to have some of these objects at home? How would we supply that? Everything may not have to be able to be flattened into this online world.

– What I’m hearing in a way is, really, you’re just setting up the kind of caution cones on the highway here, which, you’re kind of saying, “Look, it was important before “to think about these questions, “and so, it’s still important.” When you were talking about the number line, for example, I was imagining how easy it would be to pre-draw that number line and kind of swoosh it in, and you’re saying, “Wait, wait, wait, you wouldn’t do that in class, “so, why would you do that in this short video “where the amount of time that your spending, “quote, unquote ‘together’ “is even more compressed than usual.” I’m curious, we’ve talked in some ways about the communication with students that could happen in various ways. There’s another avenue to supporting younger learners, and potentially middle grade and older learners, which is thinking about how the parents could support that learning, and I’m curious, though, let’s say I’m a teacher who’s working on multiplying fractions, should I be thinking about creating a video that’s, quote, unquote “teaching” students, but also one that’s guiding parents on helping their students?

– Yeah, I’ve been wondering about this a bit. I mean, on one hand, if we are gonna be doing that, which perhaps we should be, I haven’t started trying to do that, but in the past I’ve done things that are similar. One of the big things parents will probably need from us that we don’t always have to do, is make sure that it’s clear what the point of something is. I think when we just send home activities, and I’m getting this a lot from some of my colleagues who are parents of little kids, and they’re getting things, and they’re like, “I’m a pretty well-educated person, “and I don’t really see what “was my kid supposed to be getting out of this.” They’re not criticizing the teacher, they just actually don’t… I think elementary teachers, we forget we know a lot. And it’s not obvious to someone who doesn’t teach little kids what the purpose of something is, and so, I think we’re gonna have to think a little harder about how to say, “This is the point. “This is why I want your child “to play with this or do this, “is because this is what I’m hoping they’ll begin to see.” And I think that will take some self-consciousness about explaining adult-to-adult. And of course, we’ve always done this, but I think it will require, if we’re going to go down that path, a little more of that. But I’ve also been wondering whether we couldn’t practice thinking more about, I mean, kids do all kinds of things on their own. If there’s some way that we could be designing some work that actually can be done at home that doesn’t require the parent to do it, I’m not trying to rule the parent out, it’s great when parents want to work with their kids, but parents are dealing with a lot right now. Some kids are living with people other than their parents, there’s a lot going on in everyone’s lives, and that, in fact of course, is always true, so maybe a mix of thinking how we communicate with whomever the caregivers are, and pick really carefully things that make sense to do at home, that we can clue in whoever the partner is to the kid and help. But maybe we should also be thinking of some things that can get launched that kids can get into and give the parent a chance to be just watching the kid, or maybe doing something else that the parent or the caregiver needs to take care of at that time. I want kids and their parents to have relationships and to do things, but just asking families to take on being teachers when teaching actually is a hard skill, let’s just be thoughtful about that, and not forget that children are capable of doing a lot. Just like we ask them to read on their own, and analogous things that are not worksheets that we could be asking kids to be doing that would be a little bit like, “read everyday”. What does it look like to say “math everyday”, that isn’t just “do a sheet of worksheets”? So collecting some of those that parents could launch for their kids, I think could be a really useful thing, and not be relying no the differential situations that families are in right now to become teachers.

– I think I heard something pretty important there, which is don’t think that you have to teach these things twice, once for the students and once for the parents. Instead, think about how to communicate to the parents, since they’re likely to get asked that question, “Why are we doing this?”, that the parents can understand why is this the learning activity, and then I liked that kind of guidance you offer, which is leverage those adults that are in the students’ lives, but do so judiciously because they’re busy and stressed and pulled in 300 different directions, just like everyone else is feeling, and we need to remember that. So, good advice. Deborah, thank you so much for joining us to share a little bit about how we can adapt math instruction and instruction generally. If you’re joining us for the first time, this is part of the #PLtogether Lounge Talk series, and you can find more of those at pltogether.org Deborah, thanks so much for joining us.

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