Dr. Hala Ghousseini, Math Talk in Kindergarten & Beyond
ROUNDING UP: SEASON 1 | EPISODE 16
Kindergarten is a joyful, exciting and challenging grade level to teach. It’s also a time when educators can develop a set of productive norms and routines around discourse that can have a long-lasting effect on students. On today’s podcast, we talk with Dr. Hala Ghousseini, a professor at the University of Wisconsin, about building a solid foundation for math talk in kindergarten and beyond.
Mike Wallus: Kindergarten is a joyful, exciting and challenging grade level to teach. It's also a time when educators can develop a set of productive norms and routines around discourse that can have long-lasting effects on students. On today's podcast, we talk with Dr. Hala Ghousseini, a professor at the University of Wisconsin, about building a solid foundation for math talk in kindergarten and beyond.
Mike: Welcome, Hala. We're really excited to have you on the podcast today talking about math talk in kindergarten.
Hala Ghousseini: Thank you very much for having me. This is exciting. I love this topic, and the chance to really talk about this with you is great.
Mike: Well, I feel the same way. I spent eight of my 17 years teaching kindergarten, so I've been dreaming about a podcast like this for a long time.
Hala: (laughs) I can imagine the magic of kindergarten just because it's a time where people think that they know what to expect, but literally you don't know what to expect with children in kindergarten.
Mike: You started to hint at the first thing that I hope to talk about. I would love to talk about norms. This feels so important because the norms and the culture that we set in kindergarten, from my perspective, those might be some of the first messages students receive about what's valued in a mathematics classroom. And I'm wondering if you could talk just a bit about the norms that you think are important. I mean, perhaps what it looks like to support them in kindergarten.
Hala: Absolutely. And I just want to situate a little bit some of the things that I have been studying and thinking about. When I think of math in kindergarten, it very much exists within the learning altogether that happens in kindergarten; whether it's social-emotional skills, whether they're learning about other subject areas. So, when I think about the norms, I think often of them as embedded within the fabric of what's happening in kindergarten. In the research that we've done, we've seen it happening at two levels. One in relation to what we would call “norms related to what's conceptual,” or what [people might] call more like the disciplinary aspects of norms. So, some of the things that we've seen is, first of all, centered on children's thinking. The idea that first as an individual in class, that I'm a contributor to everyone's understanding. So, the way that is typically continuously communicated by the teacher, in the sense that it's important to share our thinking. And it's important to share it, not just because I'm the teacher and I asked you to do it, but because it's going to contribute to everyone else's learning.
Hala: My learning as the teacher, others learning in the classroom. And we've seen examples from teachers where often, as they're asking students to get ready to go into their small groups, they would always say, “Remember, it's important to show our thinking and our work because we want to help someone else learn it.” You want to help the class understand this idea better. And even with the use of representations, resources, those were all really in the service of helping someone make their thinking explicit so that someone else is going to understand it or use it or build on it. So, I'll give you another example. The idea of saying, “Remember, we want to listen now to Hala share her thinking because we want to think how we make sense of it, what Hala is helping us think about.” So, those were the typical expressions or things that teachers would say in building these norms in the classroom.
Hala: The other norm, when it comes to the social aspects of the norm, was really this explicit work on the sense of the collective as an intellectual community. The idea that we are in this together. It's not about me and you as the teacher, but it's about the us. What do we make of it? How do we really flag certain things that may help the group process and think about something? And those were also done constantly across the times we’ve spent in these classrooms, in the way teachers would really point to something that may help us as a group later. “Hey, look at this, this might help us later in the way we’re going to work on certain ideas together.”
Mike: Well, I do want to ask you about something else that really struck me when I was reading the article. So, you and your co-authors talked a great deal about orienting students to and then encouraging the use of resources to communicate their thinking. That really hit me as a person who used to teach these young kiddos. Can you talk a little bit about what this looks like?
Hala: Yes. This drew our attention, given where kindergartners are in their language development. They bring a lot of language from home that actually is going to be essential to build on in explaining the reasoning, talking about their thinking, reacting to someone else’s thinking. So, we started thinking about the way students’ think and the way their language that they bring with them becomes a resource that they could use. So, encouraging them that, yes, that is one way you can explain your thinking, so that really they find that language that is going to give them an entry point into the collective as an intellectual community. The second thing in relation to resources, also availing in the classroom. We’ve noticed these teachers that—besides the fact that you have, like, a number line or a hundreds chart displayed on the board or even the physical tools that usually typically students play with—how those become things that the teacher points to and says, “Wow, you know what you're doing.”
Hala: This might help us think about this idea. So, let’s remember that what struck us was that, when students were explaining their thinking, we rarely saw a student asking for permission to go and use something to come and support their thinking. We saw that they were really going to things and bringing them. So that was a norm in that class. That kind of intersects with the idea of normative ways of working. You can just go and reach it. You don’t have to get that teacher’s permission to do it. I think one more thing I’ll say about resources. We’ve noticed the teacher, typically if a student used a particular resource that supported them in their thinking, when they’re sharing, they make sure to actually highlight it, lift it up in what the student is saying so that others see that those resources could be contributions to supporting the reasoning in this class.
Mike: So, boy, there’s a lot there. I think the first thing that really hits me is this idea that part of the culture that you want to establish, is that the resources are available and it’s contingent on the teacher saying, “Yes, you can go get that right now.”
Hala: Absolutely. And it’s a way of socializing the students to be aware of what’s in their classroom that is actually part of what’s supporting their learning. You know, there is a thing that I always work on when I’m working with teachers, this idea that, you know, children are sensemakers. And we tend to think of children as sensemakers beyond just mathematics. Of course they are, but also they’re sensemakers as learners in general. So, we treat them as sensemakers in the way as teachers. We owe it to them to explain to them why, for example, we’re asking them to do something. And we say, “So, I want you to show your work—not just to please me, because this contributes to the collective work in this way.” And we reinforce this message continuously. Similarly, the idea of what’s in our class, like, when we see, for example, base ten blocks. I have a few things in this corner. The idea that these are there to also support our learning. So, we treat them as sensemakers in the sense—these are all shared tools for our classrooms. So, that's kind of how we think about it in relation to the orienting to resources.
Mike: I want to check my own understanding. I was struck by the way that you talked about the way that the teacher positions the materials. It seems like a pitfall—I know that I have fallen into at different points in time is—using the materials to set a conversation up in a way where children might come away thinking, “Oh, that’s the way to do it,” which is very different from, I think the way I heard you describe it. It was more like, this is a tool that can help us think about, for future reference. I just wanted to call that out because I thought I heard that, but I wasn’t exactly sure if I was interpreting that accurately.
Hala: Thank you for mentioning that. I think what you’re really referring to is what often happens, especially when we use some manipulatives, let’s say, or resources or tools. Where the idea becomes that the tool equates what it means to do or to reason, like, as if the idea is within the tool and/or the representation, etc. And I think the idea that there is a lot of choice. So, one of the things for example, that we are currently studying is in kindergarten classrooms, the nature of the use of multiple representations. There’s one question, “How often can students come up with their own representations?” They invent the representations. How often can they go on their own to draw on certain tools to represent an idea? Those say something when it’s actually coming from the student, where you can follow up with questions and say, “So, tell me why you use this? Like how do you see it in this one?” And that’s the work that we saw teachers do often, is that they’re orienting the resources but then they’re orienting to resources as supporting reasoning.
Hala: And there is the question of why, pressing students. There is a nice example that I always love to think about, especially with kindergarteners using multiple representations and their own choices. Of course, students come to class with various fluency in academic language, vocabulary, etc. So, there was an instance where the teacher was asking the students, “If we’ve been in school for 129 days, in how many days like that number 29 is going to, we are going to get another 10?” And they were working with bundling sticks and other things. They focused on the number nine as 9 ones. And how many more ones till we get another 10? Then the teacher asks the class, “Well, is there another way we can think about how many more days till we get to another 10?”
Hala: “Can we use the number 29 altogether?” And a student raises her hand, we call her Gloria, and actually points to the number line above the whiteboard and says, “One twenty-nine, 130.” And the teacher says, “What do you mean by those two?” That literally points to it: 129, 130. So, what the teacher does, she presses Gloria to explain more and says, “Tell us a little bit more. What do you mean by 129 and 130?” Then Gloria actually sees that just looking at the number line as a representation—we call it a language proxy—to help her really explain her thinking, according to Gloria, wasn't enough for her. She actually goes back to the hundreds chart. She points at 29, makes a hop, and says, “One jump and we get to 30.” So, we see this is just as a small example of where the student is really using their agency in deciding on the representation, and the teacher then helps the class try to see the connection that Gloria was trying to make between this representation. We think this is important for not only this grade level, but whenever we use multiple representations. The power of multiple representations is in helping the students see the conceptual connection between them. So, that's where I would caution all of us when we are doing this, to try to make sure we are focusing on the conceptual piece that the representation is allowing us to see.
Mike: I think part of what you had me thinking about is The Math Learning Center and Bridges. We have kind of hung our hat on this idea that visual representations are a powerful tool. But the caution that I always feel is, if those visual representations just turn into another version of an algorithm that's more like geometric or visually laid out, then we are not advancing the kind of classroom culture or discourse or thinking that we want, right? That it really is to expose the big ideas. And I think that's what I take, particularly from that example is, the visual actually served as, like, a tool that helped them find the language to describe the concept rather than just as, like, a here's how you do it. Does that make sense?
Hala: Exactly. I think the tool here is a way for them… The difference is that they're using it not to apply the reasoning, it's not an application. That's kind of where I see it. Don't just come and show me how like, like base ten blocks can represent a number. Base ten blocks are used as a way to support a mathematical idea, not just to apply, like, to show you and show you how something looks like on a hundreds chart. Actually going back to the hundreds chart, to the hop between 29 and 30, was in the service of really explaining what they meant by 130, 129, 100—there is a hop. That's what they were talking about in class that when you, you're counting by ones, you're actually now, you got no more 9, 10—9 ones—you actually have one more. And now you could bundle it, and it's your extra 10. So, it's all couched in the history of working with these representations, like how these students experienced the work as to not just, “Hey, come, let's represent the numbers.” Or there was more talk about, like, those key ideas that the students were talking about.
Mike: What you're making me think about is that there's an overall pattern that I want to explore in the context of kindergarten, which is that, as a field, in my mind, one of the things that I wonder about is whether we have almost explicitly thought about communicating our thinking as something that happens in the verbal realm. And the more that I've been in the profession is, that we need to broaden that, particularly when we're talking about young children in pre-K and kindergarten. And I'm wondering, in your mind, what broadening out communication might look like, particularly in kindergarten?
Hala: That's a great question. And I would link it again, like, whenever I think about the norms, the resources, I see them literally as a triangle with other things working together. Especially critical at this young age is verbal and non-verbal communication, or really, assets for the students to express their thinking and communicate with others. And that's where, in a way, the resources become the mediators of this, with non-verbal—we call them language proxies—is that they become ways of helping the communication without necessarily waiting for that correct vocabulary or the specific language. And I think the more we honor various ways of participating and contributing to the learning of the collective, the more students are going to be able to make improvements, and to make connections, and to show us what they know, rather than thinking it's too difficult for them to do something maybe because they don't have that particular, specialized language that someone is looking for.
Hala: We actually think of kindergartners in the way they're really acquiring this new—not only the verbal language, so that they become more proficient in it—the academic language. And actually, if you come to think of it, every student in math class, in a way, is a language learner, especially the idea of what does it mean to explain one's reasoning? And when we are thinking about certain ways that schools go, they want to follow, for example, the Common Core standards and what they expect in terms of providing evidence, supporting it. That's actually a language learning process. And there is actually literature about supporting bilingual students and multilingual students in classrooms—helps us a lot think about how we could support learners in the early childhood span. And most recently I was reading an opinion piece by Tim Boals at the WIDA at the University of Wisconsin. I just actually highlighted a few things in what he said in his opinion piece, which is basically about what it takes to make sure that multilingual students encounter opportunities to learn.
Hala: So, in a parallel way, it makes me think what it takes for opportunities for early childhood learners and kindergartners to learn. I just highlighted a few elements that might be one of the resources I share with you in the end, in case someone is interested in them, about what school programs could do to ensure that multilingual learners have opportunities to learn. One of them is actually the idea that always encourage the can-do kind of stance, that you can do it. It's not too difficult for you, like, even in the choice of tasks. How this guides us for kindergartners is that—let's not just give tasks that allow kindergartners even to skip count on a number line. Actually using tasks where they can reason and think about why something is true, would be something they can do. So, thinking about not what they can't do because they're restricted with what they know with numbers, etc.—it's actually what they can do.
Hala: So, the idea of designing tasks that leverage what they know, that they could really show you the way they're reading a situation, what they know about the situation, and really leverage the resources they have to explain their thinking. My favorite in terms of what he lists in terms of opportunities for multilingual learners, is this idea of building academic identities, where he says that this is much more than merely teaching content knowledge and skills. It's about learning to communicate and think like people who work in those academic or vocational areas. That's all of us can do. And opening possibilities for reasoning helps our kindergartners develop really mathematical identities early on that we know are going to impact their opportunities to learn later. And that's what research shows.
Mike: So, in the third part of your article, you talk about the idea of narration. And I'm wondering if you could explain narration in this context and then talk a little bit about why it's particularly helpful for young learners?
Hala: So, let me explain what we meant by it in that article. It's literally when—because students may not have that facility to explain their thinking articulately, elaborately—it's when the teacher actually supports them by recapping what they said to the class. And on top of it, building on it and setting it up for further articulation or investigation. So, we try to distinguish here—that's why we're trying to revisit the word “narration” because we don't think of it just as revoicing. We think of it as a way where the teacher is highlighting something the student did and, often, we see it in exchange. It's highlighted not only in terms of the verbatim words that they used or the actions that they took. Highlighting why this is really helping in the task that we are working on together, and then follows it. It positions it in a way where, now this is what Gloria did.
Hala: So, really it positions the student in a way where other students are now listening, are trying to see what the student is doing and saying, and then it sets the stage for further focus or deeper conceptual exploration of particular ideas. So, an example of that would be when Gloria went from 129 to 130 and went down to the hundreds chart and said, “You know, there is a hop from 29 to 30.” So, the teacher may say, “OK, here's what Gloria said so far. She picked those two numbers, she saw that they follow each other. Actually we're going to get to 130. Then she went down to the hundreds chart to really focus on that jump of one from 29 to 30.” And then she would immediately go on with a question to the group. “Now what do we do?” I think that makes it more ambitious than just simply revoicing or appropriating something that the student said, or trying to put words that they may not have used. I think positioning it for further and deeper conceptual work takes us a bit away from that.
Mike: That's really helpful. You started to address the question that I was going to ask next, which is what's the sweet spot for what you described in the article as narration? It struck me, at least as I was reading it, that over narrating, if we were defining it as kind of revoicing for kids, might impact kids in ways that are not productive. But what I hear you saying is, narration is much more than revoicing.
Hala: Absolutely. And that sweet spot that I think you are getting at is really knowing when do you do it and when do you hold off. In the sense, I don't think there is a rule, but it all goes to the teacher's ability to know: “Is there a shared language here that the students can access through what a student said?” So, knowing your students in terms of, is this something that I need to further articulate so that now they could engage productively with someone's idea? And if it's not, then actually it's just highlighting, pulling from what a student says, the valuable pieces that you think are going to be important for the continued work of the class, rather than, literally, a student says something, you say verbatim, and then you ask more questions. It's really tracking what seems to be important for the development of everyone's thinking, that collective as an intellectual community that's working together.
Mike: That's really helpful. And I think what I heard are simultaneous things that are happening. One is attending to the ideas that you want to position as important. And the other thing that really jumps is this idea that we're also positioning the child as the author of the ideas.
Hala: Yes. And you know, in later grades—we've seen teachers being able to do this in Grades 1 and 2—is often, especially when we are working early on to build that classroom talk community, that math talk community, is encouraging students as listeners to someone to say, “Did you hear something that you think is important for the way we are really working on this problem in what Mike said? So, let's listen. Was there something you have a question about, you're not certain about?” Also, distributing the work of the narration, if we want to call it that way, so it's distributed. It's not just about me, but now the class is listening and trying to pull what's important and worthy of focusing on.
Mike: I love that. Particularly that idea that you can in fact distribute the idea of narration to the class, and it doesn't just live with the teacher. It also advances that broader cultural goal that you have, which is that the students are actually sensemakers, which is the thing from the very beginning of this conversation.
Hala: Again, it goes back to the way I think about all the practices that we've talked about, to be very interconnected. It's not like we know you set up norms, you put them on a chart. You know, norms are reinforced, are renegotiated with your students through the work that you do. And there's a lot of socializing that you're doing while you're working on content. It reinforces certain ideas, it reintroduces certain ideas for others to see how they're able to access them and be part of them. So yes, I agree with you. They're all connected in that way.
Mike: Well, Hala, before we close the podcast, I'm wondering if you could share some resources with listeners who might be encountering some of the ideas we're talking about for the first time. Is there anything that you might suggest for a listener who just wants to keep thinking about this and perhaps learn more?
Hala: So, if they're interested in thinking a little bit more about representations, there is a recent article that I published with Dr. Eric Siy, who is currently at Boston University, in relation to what multiple representations mean. And how different they are from just using different representations.
Mike: Yep. We could absolutely put a link to that on the podcast notes.
Hala: Yeah. And I find the work of Dr. Amy Parks at Michigan State University. You know, she has this book called Exploring Mathematics Through Play in the Early Childhood Classroom. [It] has wonderful pieces that really could support this work in relation to the idea of reasoning in kindergarten, discourse in kindergarten. And it could happen during play. It doesn't have to happen necessarily only during academic tasks that are, like, problem-solving situations or worth problems.
Mike: We could absolutely add a link to that. And I think that's probably another great podcast that we should do relatively soon.
Hala: Yes, I find you really connecting wonderful, cohesive dots together here, which I think is really going to be helpful to the listener.
Mike: Well, I want to thank you so much for joining us, Hala. It's really been a pleasure talking with you.
Hala: Thank you very much. And it's been a great opportunity to talk about these ideas with you, and the questions are on target in terms of the things that we have to pay attention to.
Mike: Oh, thank you so much. 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.