Supporting Multilingual Learners During Number Talks with Jana Dean & Heather Byington

What might it be like to engage in a number talk as a multilingual learner? How would you communicate your ideas, and what scaffolds might support your participation?

Today, we're talking with Jana Dean and Heather Byington about ways educators can support multilingual learners' engagement and participation during number talks.

Heather Byington has taught all grade levels over the span of her 27-year career as a bilingual public educator. She currently teaches middle school mathematics and English language support classes in Lacey, Washington. She is also a student at Washington State University pursuing a PhD in Mathematics Education.

Jana Dean currently serves as CEO of the Mathematics Education Collaborative and supports a fantastic team of middle school math teachers in North Thurston Public Schools. Her research focuses on the intersection of content learning and language learning.

Number Talks and Multilingual Learners article from Mathematics Education Collaborative by Jana Dean

Judit Moschkovich research

Math Between Us blog

"Number Talks: A Whole Class Routine for Learning Language for Learning Mathematics" article

Mathematics Education Collaborative website

jdean@mec-math.org Jana Dean email

Mike Wallus: Welcome to the podcast, Jana and Heather. I am so excited to be talking with you both today.

Jana Dean: Good morning. Yeah, thanks for having us.

Heather Byington: Thanks so much for having us.

Mike: Absolutely.

Jana, before we begin talking about the ways that teachers can support multilingual learners during number talks, I wonder if you can offer a working definition that would help educators visualize what a number talk actually looks like.

Jana: Yeah, I'd be happy to do that. A number talk in terms of how we worked with the routine in this project consisted of the teacher providing some sort of visual prompt, starting either with a visual pattern of dots or a computation problem. And then the students get wait time, time to think about how they might solve that problem. And then as they share their strategies, the teacher records and asks them questions about their reasoning for why they approached the problem in the way that they approached it. The teacher creates what I like to think of as a visual mediator of student ideas. So the students' ideas become visible as they share them. So children who are listening can listen to the dialog or conversation between the person sharing and the teacher, but the ideas actually become visible as they're being shared. And the teacher always verifies with the student whether or not they've been understood. And the goal is not for the student to be right, but for the teacher and student to understand each other.

Mike: That's really helpful. Heather, is there anything else you'd add to that?

Heather: In terms of the way that we worked with it with multilingual learners and increasing their opportunities for engagement in the routine, we always gave them an option of talking to a partner and rehearsing their answer before they volunteered to share with the whole group. We prioritized calling on multilingual learners if they volunteered. And we also did a final reflection at the end. So those were some enhancements that we added onto the routine.

Mike: I think that's really helpful and I'm excited to talk a little bit more about the details of those, Heather.

One of the things that really struck me as we were preparing for this conversation was reading about the ways that some of the multilingual learners you worked with, how they described their experience during number talks. And it helped me to see the experience from their perspective and rethink some of the ways that I'd facilitated number talks in the past. And I'm wondering if you could share a bit about some of the feelings students told you that they were experiencing.

Jana: Yeah. One of the things we suspected before we started was that as a language learner myself, talking about ideas that you're just forming in a language you're in the process of learning can be really intimidating. It's very challenging. So they were nervous. And when I interviewed fourth graders about their experience in number talks, even facilitated with language acquisition in mind, they talked about how much courage it took them to share their ideas.

They also talked about and could very keenly remember moments when they had made a contribution that their teacher made use of or a time when they made a contribution that another student made use of later. So there was a lot of pride they felt in having shared their ideas once they found ways to do that.

They also talked about how much easier it was to share our ideas than it was to share my idea. And so if, for instance, we had given them the opportunity—and like Heather said, we almost always gave them the opportunity to talk with a partner—they would often share using the pronoun "we." "This is how we thought of it." And we picked up on that and began to ask them if it was OK to attribute a group of students with a unique idea rather than an individual. And that was also consistent with many of their home cultures. It's not every culture in which individual contributions are elevated, but rather when you dare to speak, you're definitely speaking for the group, for a collective. So that collective understanding was really important.

There was one child, and I'm really curious about how representative he was of many. He always talked to the same friend, and every time he shared, he, I'm going to say, nailed it. He really had it figured out what it was that he was going to say. And there was one particular day when he did a beautiful job sharing, and I asked him about that day and he said, "To be honest, that day I really didn't want to share, but I knew my teacher wanted to hear my idea, so I did anyway." And so there's that element of love and respect for their teacher that I think was also really motivating for them.

Heather: Yeah. Can I add something quickly to that?

So one aspect of that, I think that idea of a student sharing because it meant a lot to the teacher, we also tried to utilize individual conferring with students as much as possible and gave them opportunities to confer with us, whether it was just checking in briefly before the number talk started, encouraging them or maybe telling them, "Hey, you can share the idea with me after the number talk if that feels more comfortable to you." So it's giving them multiple opportunities to do that and encouraging them to share their thoughts.

Mike: What I appreciate about what you all are doing is even in this initial part of the conversation, really getting specific about the practices and the way that those practices played out for kids. And I think as an educator, one of the things that I've come to over all my years teaching is the need to have humility and also continue to be a learner. And that sometimes really leads me to questions about intent versus impact.

Heather, I wonder if you could talk about the parts of the number talk routine or facilitation practices that may have unintentionally provoked some of the anxiety that kids were experiencing.

Heather: So for multilingual learners, when I think about what they will need, the supports that they may need to be able to engage in a routine like a number talk, I think about first the processing time that they might need to understand and think about different ways of solving that prompt. And then I think about their understanding of the prompt. And then the other thing I think about is their ability to communicate their thoughts and ideas with others. So naturally, if it seems like there's a lot of pressure because of time, if they don't have much time, if they feel that pressure to do that processing and think of those ideas and share them quickly, that may provoke anxiety because this, of course, is still a language that they're still developing. So that ability to share with a partner and rehearse those ideas and process that with a partner, that really becomes, as Jana mentioned, more of a team effort.

And then being able to rehearse the words that they're going to use and the way they're going to convey that message and communicate it to others, that again reduces the anxiety because it's a lot less pressure to share my thoughts and ideas with one person than with a whole group. And if I share those thoughts with one person and they seem to understand what I mean, then now I might feel confident enough to share with more people. So I just think that naturally when it's a time constrained activity, that that naturally can provoke anxiety.

Mike: Yeah. I mean, that absolutely makes sense. I will say as a child who was not quick, even in my first language, the impact of that was profound, let alone trying to both process in a language that I was learning and feel like I was under pressure to produce an idea and describe it. That absolutely makes sense.

Jana: I want to back up a bit and quote something that you said, Heather, partway through our working together, which was that Heather had some familiarity with number talks before we started working together, but had a healthy skepticism as well. And at one point she said that she wondered if we might not actually be hurting students when we are facilitating a routine that they cannot find entry into. And so it became really like a guiding light or principle of our work together to work hard to help them find entry into the routine. And something that I didn't realize until a year after we began working together and I was really closely tracking the experiences of the multilingual learners themselves—and this is kind of back to your question about intent and impact—when we listen to children's mathematical ideas with the intent of not correcting them, trying to figure out what's right and what makes sense to them, we have to ask them questions about what their ideas are. And for many of the multilingual learners, engaging in that process itself was a huge lift language-wise. So I'm not just going to be able to say the answer or tell my teacher my strategy; I'm going to have to stick with my teacher until my teacher actually gets it. And a few of the multilingual learners that I followed over the course of a year actually said to me, "I don't like it when my teacher doesn't understand me." So while we absolutely, 100%, our intention is golden. It is about understanding them. But putting them in that position of that negotiating meaning with us until we do understand takes a great deal of trust on the part of the student. And so it's on us to develop that trust so that they're willing to do that with us.

Mike: I think that's a good segue because Jana, going into this, you mentioned three big ideas as starting points for supporting multilingual learners. One was negotiated meaning, one was the notion of voluntary sharing, and the last was the idea of using ambiguity as a resource. And I wonder if we can start this next part of the podcast with having you describe each of these for the listeners.

Jana: Yeah, absolutely.

Voluntary sharing means I've made a commitment to not ever put you on the spot as a student. And so any one of us who has learned a second language—which I've learned a couple, none of them to a super high level—but most people can relate to, say, standing in line in a grocery store and rehearsing what you're going to say so that you ask for the bag you want rather than the receipt that you don't want. There's a process in coming to speak, and I think there's a process in coming to speak publicly for just about every learner, especially about ideas that you're in the process of forming, but that pressure—and I've had many, many students over the year thank me for being the kind of teacher in a kind of classroom where they knew that I wasn't going to call on them unless they had volunteered to share. So the level of distraction, I think that that, again, well-intentioned pressure causes, is absolutely not worth it, and especially not for our multilingual learners.

Negotiated meaning really is the process of coming to understand each other, and we do it all the time. Unfortunately, often in classrooms, we end up in discourse routines that are actually not about teachers understanding students. They're about teachers asking questions for which students are supposed to have answers, which then the teacher evaluates. So what I would argue that the number talk routine turns that discourse pattern, which is often called I.R.E.—initiate, respond, evaluate—absolutely on its head. The child volunteers their idea, the teacher responds by trying to understand it as best they can, and then the student is the evaluator of whether or not the teacher actually understood them.

Mike: Heather, I was hoping we could go granular on a couple pieces that I heard you talk about too. You talk a lot about something very practical, the value of predictability, and I wonder if you can talk about how predictability impacted students and what does that mean for the teacher?

Heather: Absolutely.

When facilitating these number talks with this goal of engaging multilingual learners or helping them find those entry points, I found it helpful as a facilitator to utilize similar types of approaches to statements I would make during the routine, and then similar ways of asking students if I was seeing things the way that they were seeing them. It seemed to help the students that we were really hoping to engage to feel more comfortable with what was happening in the routine and to lean in more to that engagement. So I think that that is one thing as a facilitator to be aware of.

Jana, can you think of anything else that we haven't talked about yet?

Jana: There's the whole knowing the rules of the game aspect of really any classroom routine or instructional routine. So if the student knows how this thing goes, whatever "this thing" is, then that lifts off some of the cognitive load in terms of participation because they don't have to be figuring out how to participate. Judit Moschkovich writes about this a lot in her research, and I think she calls it the "sociocultural aspect of learning mathematics," and she uses the word "ecological". So the environment itself really matters. And in community, our social environment is made up of all kinds of routines. So I think that part of it is important. My favorite metaphor for it is learning a new card game. The first time you play the game, it is no fun because all you're doing is trying to figure out how the cards move, how the turns go, what the rules are, and how you can play. You can't do any strategy at all. But then as you learn the game, then you can really engage in it in a thoughtful way and have fun with it. So I really think that classroom routines are like that and not only for multilingual learners, but I have the privilege of being an instructional coach now in a middle school and have seen teachers engage in routines that I can tell are 100% soothing of trauma that students have as they come into the classroom, just because they know what to expect. So not only are those kinds of regular routines really helpful for multilingual learners, but they're also trauma-informed teaching. And when I say "routine," it can be easy to misunderstand and think it's boring. It has to be an open-ended routine so that something inside it that is engaging and fun can happen.

Heather: There are a couple of other things that occurred to me in terms of the students participating in the routine. I know that they started to see that we were elevating the status of gestures in terms of the communication to be another way to visualize the thinking in terms of the processing for themselves, but also a way to help others see what they were seeing and to understand their ideas. So that was one aspect of the routine that they could count on, that they could utilize gestures if needed, and that we would reinforce that. If they didn't have a mathematics label for the terminology that would typically be used in that conversation about those mathematics ideas, they could rely on describing what they understood, and then either I, the teacher, the facilitator, or another student, providing those words and the opportunity to practice that specific mathematics language within that routine. So those were some other things that were predictable and happened across all of the different number talks that happened, no matter what the prompt was.

Mike: You're making me think that part of what a teacher might do in response to this conversation is really to think about some of the things that they want to make normal, right? Like this notion of using gestures is both normal and accepted and valued. The idea that you are going to use rough draft, informal language, and that's OK, and that's a way that we get to more technical language of mathematics, and that's normal. And so thinking about what are the things that I want to become normal and predictable for kids, maybe homework recommendation number one for an educator that might be listening in.

Heather: So another thing that was predictable was the utilization of color-coding. And this is something that many teachers probably do already. But we did, when we were recording the students' ideas, we used different colors for each student, and that made it more accessible. Again, it was a support for our students to be able to distinguish between different chunks of information on the board as they were looking at each other's responses and reflecting on those responses. So really reading that.

Mike: Can I ask for a clarification on that, Heather?

Heather: Absolutely.

Mike: I think what you mean is that you use different [colors] to represent different students' contributions. So if a student shared something, you might write it in red, and if it was a different student, it might be in green. And then you can distinguish what contribution each student made.

Heather: Yes. Yes, that was a predictable aspect of the routine, as well as Jana had mentioned earlier, attributing the ideas to students using their initials. And if multiple students contributed to that idea and the original person who was sharing said that, yes, they would like to attribute more people, then we included all the people's initials who contributed to that idea that was shared in that number talk for that idea, that communication.

Mike: Speaking of contribution, I want to name something that we talked about in our preparation for this that seems incredibly simple but felt like it was really significant. You all talked about the importance of the teacher consistently—not just once, not just a handful of times—but consistently, on the regular stating to kids that they wanted to hear from all students. And I wonder if you can just talk about what did this sound like to make that happen and what was the impact on kids? Jana, I think this is one I'd love for you to start with.

Jana: Yeah, absolutely. It is simple. All you say is, "I'm so glad to be with you today. And let's remember that while we may not hear from everyone today, it's our goal to hear from almost everyone over the course of the week." And if you as a teacher have made a commitment to voluntary sharing, it's essential to say that, to really tell them that you do want to hear their voices. You need to tell them that. Otherwise, they're not going to know that you want to hear their voice. And like I shared a little while ago, there was one student who actually said to me, "I didn't want to share that day, and I knew my teacher wanted to hear from me, and so I did." And then in reflecting back on that share, to get at students' perspectives on what number talks have been like for them—they were fourth graders, only 10 years old. I showed them video of themselves participating in the number talk, and you should have seen the smile on that kid's face. The pride he had in having taken that risk because his teacher wanted him to. People rise to the expectations that we have for them, 100%, maybe not 100% of the time, but if we don't have that expectation, they don't get to choose to rise to the expectation. And you can't make anyone talk when they're not ready to talk yet.

Mike: Heather?

Heather: I also think that part of that goes back to something that we were talking about a little while ago, and that is establishing the norms in the community of learners. And in addition to communicating that to the whole group, our goal is to hear everyone's ideas over the course of the week. Something also as simple as when they were getting ready to do a pair-share and rehearse their thoughts with each other before launching into the whole-group discussion, also reminding them, "Hey, make sure that we're taking turns when we're sharing in that pair." So again, just to reinforce that we value everybody's contribution, we value everybody's voice and everybody needs to have a turn.

Mike: Can you say more about why it's important to offer kids the option to talk with a classmate before they do any whole-group sharing? Why does that matter so much, particularly for multilingual learners? And either one of you, feel free to jump in and take this.

Heather: I'll start. My understanding is that when the originators of these number talks created this idea that they wanted, that idea of agency and giving students choice was really an important priority to them. And so I feel like part of the rationale for that is to give students choices as often as possible in this routine to elevate students to co-learners with the teacher. So I feel like that's kind of where it starts.

Mike: Jana, is there anything you want to add to that one?

Jana: Well, we've already mentioned the value of rehearsal before sharing with the whole group, but there's also another aspect of it that we may not have touched on yet, which is: As that person listens to us and we actually negotiate meeting and clear up ambiguity, we feel seen, heard, and understood. And if I feel seen, heard, and understood by Heather, it's going to be easier for me to share my idea with Mike, who I don't know quite as well as I know Heather. And so there's really a relational aspect of it that is about feeling understood.

Mike: I want to ask another question about something that feels eminently practical. You all talk about recommending that educators call on multilingual learners early in number talks. And I wonder if you could say more about the why behind that recommendation.

Heather: So as a learner of a new language, I may only have one way of explaining my thinking about that problem or the way that I'm seeing that. And if I have taken that risk and I've raised my hand, if somebody else answers first or maybe two other people answer first, maybe they've taken the only way that I knew to answer and share my thinking about this prompt. So for me, as a facilitator in that setting, that was really important for me to prioritize those volunteers if they raise their hand and call on them as one of the first contributors. I've also seen in some classes that I've been in, some math classes, if a student is not yet fluent in English, sometimes their classmates think that they don't know math, that they don't have ideas to share in math. So I also think that calling on those students first also, again, sets the norms in this community of learners that, again, we all have valid and valuable ideas to share.

And so Jana and I saw in particular with the pair-shares, we saw students starting to choose to work with students who still spoke primarily another language. And Jana captured on video where she had a student who didn't speak Spanish and a student who primarily spoke Spanish and they were sharing ideas with each other in that pair-share to get ready for the whole-group discussion. And honestly, I think that that worked more effectively because of that idea that everybody has valuable ideas to share. So I also think that that was another part of that idea of calling on those students first and making sure that they had a lot of opportunities to share their ideas.

Mike: Yeah. I'm really glad you mentioned that. You're making me think about this notion called positioning, meaning that the choices that we make—whether they're spoken or unspoken, like who we call on first or who gets called on more—they are sending a message to students. And often that message may not be the one we intended. So in this case, it really does show how the choices that you all were making in calling on multilingual learners early, it may have disrupted some narratives that people could have formed about how much those kids had to contribute to a mathematical conversation. I'm so glad you shared that.

Jana, I want to ask you this next question. It's something that, if I'm not mistaken, Heather brought up earlier, and I wanted to dig into it a little bit more if we could. You referenced the value of making gestures something that's a normal, accepted, valued practice, and I want to take a bit of time to clarify that. Perhaps for some folks who might not have a clear picture in their own mind of what we mean by that, can you say more about what we mean by gestures and maybe some examples of the ways that gestures either help students to communicate or even how they contributed to the conversation that was happening during the number talk where there might've been something that was lost if gestures weren't in play?

Jana: One thing I know for sure is that lately I've been learning from Heather about how some mathematical ideas are actually perhaps communicated better with gesture than verbally. And yet we have this traditional notion that there's some kind of language for expressing mathematics that's fancy and only occurs from the neck up, but that's not how we usually talk. So why would we tell people who are trying to explain their ideas that they can't use gesture as part of a person-to-person conversation? Gesture by no means keeps you from developing formal language. It actually helps you develop formal language. So one example of using gesture, it came up particularly during dot talks when we first started the routine, and the dot talks were a fabulous way to encourage and introduce that norm that gestures are welcome. But if a student is describing an array of dots and they say, "three on top," and then they use their hand to indicate it's horizontal, we would affirm, "Thank you so much for using your hands." I can tell that the three on top are in a horizontal line. And then, Heather is fabulous, and I've learned a lot about this from her at gesturing "horizontal" by bringing her hand across the space in front of her horizontally. And then everyone [says] "horizontal," and everyone gestures and says "horizontal" with them. And so we're pairing what's an academic word that is often very hard for students with any language background to remember with a physical gesture.

Mike: That's really helpful. As you all were talking about this, one of the things that I started thinking about is how there are ways that I use gestures to indicate a lot of mathematical ideas like partitioning into groups, indicating that I'm talking about a group and another group and another group, which is basically the seeds of multiplication or unitizing. How I'll gesture as a way to show that I'm combining or separating. How I gesture to show the way that I'm counting things. That all of those are ways that actually enhance what I might be saying and actually communicate that meaning more clearly both to my teacher and to the other students who are in the room.

Heather: Absolutely. Yeah. Another example of that, as you were talking about that, that I use all the time as a seventh grade mathematics teacher and we're working a lot with integers, is the idea of 0 in a horizontal hand as 0. And thinking about if that's 0 and I'm navigating between positive and negative numbers, what will that look [like] visually? And as you said, I just think that gestures are another tool for thinking and understanding and processing information and sometimes communicating that information.

Mike: Heather, I want to come back to you for something that, again, really struck me as important when we were preparing for this. You said that you recommend educators close their number talks with an opportunity for kids to make connections between strategies that emerged. And I wonder if you can just talk about: Why is it important to provide that opportunity for kids to make connections, particularly for our multilingual learners?

Heather: So first of all, I have a firm belief that development of conceptual understanding is really valuable in mathematics. And as we are engaging in this routine, in this whole-group discussion, and we're considering all these different possible ways of solving a prompt or seeing a prompt, then when we get to the end, it feels like that we should reflect on the different ideas that have been shared and draw some conclusions about what we can say across all of these different ideas as part of that development of conceptual understanding of what is happening there mathematically. In addition to that, in terms of student engagement, some of our students are multilingual learners. That was the time in the routine that they actually felt the most confident to contribute their thoughts and ideas. So maybe they didn't often raise their hand to speak in that whole-group discussion, but they did raise their hand to share something they noticed from the artifact, some kind of commonality or something that stood out to them.

So again, that was another opportunity for them to feel like they had a valid contribution, that their contribution needed to be heard. So those are a couple of good reasons why I feel like that final reflection is really important in particular for multilingual learners.

Mike: Well, Jana, before we close this conversation, I'm wondering if there are any resources that you'd recommend to a listener who wants to keep learning about the ideas and the practices that we've been discussing today. Is there anything that you could point them in the direction of, or perhaps even something that you'd invite them to try out as a first step?

Jana: Yes, absolutely. I have a couple of ideas. One would be to go to a blog I write that's called mathbetweenus.org. And I've published a short article there ["Number Talks: A Whole Class Routine for Learning Language for Learning Mathematics"] that is specifically about the adjustments we've made to the routine.

Also, I am now CEO of the Mathematics Education Collaborative, and we recently developed a grassroots workshop in making number talks meaningful. It only takes 2 hours. It's an introduction to the routine, ensuring that it's more than just something fun, but actually results in building number sense for students. It's a low-cost way for an individual teacher to get started. And then you can also go to our website at the Mathematics Education Collaborative, which is [www.mec-math.org] and reach out to us and see if you're interested in having us come to your district or your region. Or you can email me at jdean@mec-math.org. So lots of ideas.

Mike: I think that's a great place to stop. I can't thank you both enough for joining me and being willing to have such an in-depth and detailed conversation. Jana and Heather, it's really been a pleasure talking with you both. Thank you.

Jana: You're welcome.

Heather: Thank you so much.

Jana: Thanks for your curiosity.

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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