Dr. Zandra de Araujo, Enhancing Tasks for Multilingual Learners

Mike Wallus, Vice President for Educator Support


How can educators take concrete steps to enhance tasks for multilingual learners? That’s the subject of today’s podcast. Today we’ll talk with Dr. Zandra de Araujo, the Chief Equity Officer at The University of Florida’s Lastinger Center for Learning about three ways to enhance tasks for multilingual learners and how to implement them in an elementary mathematics setting. We’ll also discuss practical strategies and resources for supporting multilingual learners regardless of their age or grade.

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Mike Wallace: How can educators take concrete steps to enhance tasks for multilingual learners? That's the subject of today's podcast. Today we'll talk with Dr. Zandra de Araujo, the chief equity officer at the University of Florida's Lastinger Center for Learning, about three ways to enhance tasks for multilingual learners and how to implement them in an elementary mathematics setting. We'll also discuss practical strategies and resources for supporting multilingual learners regardless of their age or grade. 

Mike: Hey, Zandra. Welcome to the podcast. 

Zandra de Araujo: Thanks for having me. I'm excited to be here. 

Mike: I'm super excited to be talking to you. So, I'd love to just start with a quote you and your coauthors wrote. You say, “Rather than focus on language before mathematics, research shows that multilingual learners both can and should develop mathematical knowledge and language proficiency simultaneously.” Can you talk a little bit about that statement and share some of the research that informs it? 

Zandra: Sure. So, basically, if you think about learning a new language, you need to use it to get better at it. And so, in the past, people were more likely to put language first and to hold off on academics until students learned English. And what we've learned since then from brilliant scholars like Judit Moschkovich and others, is that we should simultaneously grow math alongside language development. And there's a couple of reasons for that. One, it helps improve your math learning and your language learning at the same time, which is great. It doesn't put you below grade level for your math learning because you're waiting to catch up with English first. And we know that proficiency in your first language also will lead to better proficiency in your second language in math and other areas. So, there's only benefits really. 

Zandra: And also, if you think about kids who are native English speakers, they're also learning how to talk about mathematics in school and how to use math language. And so, you might as well do it with the whole class and practice discourse and use good multimodal representations and communication skills to enhance everybody's language learning and math learning because you learn through and with language. And so, you can't really put language—or mathematics—on hold completely for kids. It's just not the right thing to do. 

Mike: I loved where you said you learn through and with language. 

Zandra: Um-hm. 

Mike: Could you just expand upon that? Because it really feels like there's a lot of wisdom in that statement. 

Zandra: Yeah, I mean, the way that we learn is we listen, we participate, we talk, we discuss. We have to communicate ideas from one person to another. And it's this communication—and communication is not just in one language in one way. And language is more expansive than that. And we need to think about that. And the way you communicate what you've learned is through language. Or you show it visually. But usually as you're showing, you're gesturing and communicating in maybe nonverbal language communication. So, I think we forget that math is inherently language based as we communicate it in schools and as we typically experience it in schools. 

Mike: Thank you. I want to shift a little bit and talk about the three types of enhancements that you and your coauthors are talking about. So, using and connecting multiple representations, thinking through language obstacles, and contextualizing concepts and problem-solving activities. And what I'd like to do is take time to discuss each one of these. So, to begin, can you talk a little bit about what you mean by using and connecting multiple representations? 

Zandra: Sure. I tend to put things in my own frame of learning a second language. So, if you think about when you travel to a country that you don't speak the language fluently, you probably do a lot of gesturing. You look for signs that don't have words in that language, necessarily, if you can't read it. You might draw something—you might do a lot of things. So, visuals and representations are very helpful when we're learning something new or trying to understand something that we already understand, we just can't communicate it. So, in mathematics, a lot of our representations are serving that purpose. They allow us to learn things in a more deep way. 

Zandra: So, if you think about—I can show you something like the number five written out. I can show you five unifix cubes—I could show you five tally marks. Those are all different representations that very young children experience. And we're trying to communicate the same concept typically, of five; like the total set of five, the cardinality of five things, typically. And so, kids, when they experience all these different things in different ways, and we connect explicitly across them, it really helps them to understand something in a new or different way. But also, for students who are acquiring English, it allows them to connect the visual with their home language that they're thinking in their brain. And they probably have the words for it in their home language. They may just not understand just the spoken word. But when you see a representation, you have more ideas to anchor on. 

Mike: Yeah. As you described that, you can see how critically important that would be for multilingual learners and how much that would both support them and allow them to make the connections. 

Zandra: Um-hm. And it's not just for multilingual students. I can't imagine the number of times I've been in a classroom and a teacher might model something with base ten blocks and maybe draw a representation of base ten blocks on the board and then never take the extra step to explicitly link it to the numerals that it… 

Mike: Um-hm. 

Zandra: …They're representing—or the bundles and things like that. But those connections are what we're hoping kids will make. And so, explicitly linking those things and talking across them—and, “How do you see five here? And how do you see five here?” is really important for all students. But it's especially beneficial if you're still acquiring the language of instruction. 

Mike: Absolutely. So, let's shift gears and talk a little bit about language obstacles. So, as a monolingual English speaker, this is an enhancement that I'd really like to understand in more depth.

Zandra: (laughs) As a monolingual also, uh, English speaker that grew up in a Portuguese-speaking household and someone who is trained in mathematics teaching and learning and not in language teaching and learning specifically, this was very interesting to me, too. Essentially, it seems intuitive that you would take away language if that's an obstacle. And that is the main obstacle that students who are acquiring English in school are facing. It's not necessarily that they're below grade level in math. Sometimes they are. But many times they're not. They might be above grade level. But there are specific potential needs for support around English-language proficiency or acquisition. And so, when we think about language obstacles, it's those things that get in the way of learning the mathematics. And there's kind of two ways that you could address them: One is you remove them all, and then two is you scaffold up so that they can access it. 

Zandra: I'm more in favor of that approach where we scaffold and try to help further their language alongside their mathematics. Because that goes through the very first thing we talked about, is that you're enhancing and developing English alongside mathematics. But there are some times where there's just unnecessary obstacles that are really getting in the way of understanding what you're trying to do in mathematics. And that's kind of what we provided in the article is the list of some of these things. So, for example, a low-frequency term, and we give an example in the article, if you say “perusing a menu,” a lot of children do not use that in their day-to-day language, English language learners or otherwise. And so, we might just say “looking at the menu.” It's conveying the same meaning, but it's a more common, frequently used term. 

Zandra: So, more students will understand what that means. They're not getting hung up on this word. They're able to actually pursue the math task. Again, you could also say, like, “Perusing. Oh, that's a new word. It means like ‘looking’ or ‘reading,’ you know, ‘looking over.’” And that is certainly an option, but sometimes you just need the kids to understand the task that you're providing, and you don't want to do so much language development on things that are not really going to impact their math. So, as teachers, we make these decisions every day, and I think sometimes we can make these decisions just to eliminate some potential obstacles. There's a lot of other words. A lot of my colleagues and my coauthors have written about words with multiple meanings. Like “table.” If you're new to English and you hear “table,” you're probably going to think of the most commonly encountered table in your life, which is probably like a kitchen table or a table… 

Mike: Um-hm. 

Zandra: …at school and not a mathematical table, which is different. And so, uncovering these things, thinking about them as somebody who's a monolingual English speaker is really important because it just passes by us because it's normal to us. But we need to put ourselves in the shoes of these children as well. 

Mike: Yeah. I think what it really made me think about is structurally there's lots of challenges if you're trying to make meaning of them for the first time. Like words that have multiple meanings jump out. I found that part of the article really helpful. It helped me see issues with the language structure that having just kind of learned it naturally, they're invisible, right? 

Zandra: Yeah. I had a colleague at Missouri that taught ESOL classes, and that was her area. And she said, “You say a big, red ball, but you don't say a red, big ball in English.” And I was like, “Oh yeah, it's like they're both adjectives, but we do have patterns that I've never really thought about.” But they are common, and you hear them in people that are acquiring the language that like, “Oh, it's not how I would say it.” “Why not?” And you don't know these rules if you weren't trained in this area. I also had a former graduate student who said—he was Korean—and when he came, he said it was confusing because “no, yeah” means “yeah.” But “yeah, no” means “no.” And it's similar type things that we say, and we don't understand. And ever since he told me that, I'm like, “Oh yeah, I totally get that.” And I say it all the time, and I just never noticed how confusing that definitely is. 

Mike: So, I'm really excited about this last bit, too. I really want to talk about the importance of context and talk a little bit about how context impacts learning, particularly for kids at the elementary level. If I'm an elementary educator using a curriculum, what's your sense of what I might do to build context into my students' mathematical experience? 

Zandra: So, context helps us make sense of things because we can relate it to our actual uses or things we're familiar with and use that as a sensemaking tool. So, it's kind of similar to representations in some ways. In elementary school, we're very fortunate that there's so many things that the kids come in contact with because we tend to teach all subject areas in our classrooms. In elementary, we do a lot of counting, for example. And there's so many things that we can count. Or we've been counting every day that we can tie into. That's why a lot of teachers like to use calendar math and things like that because it's interesting, it's something the kids are familiar with. And so that context allows them to think through how they do it in the real world and connect that thinking with the mathematical reasoning, which is really powerful. 

Zandra: It also is just more interesting to the kids. I think they like it when it's something… I mean, if you want to see a kid get really excited, figure out what their pet's name is and make a problem about their pet doing something. They get really excited because it's, like, personalized to them. And it's not a real deep, meaningful connection. It's not super culturally relevant necessarily, just putting a cat or dog's name in a task. But it's the idea that you're connecting to something that is interesting and matters to the kids, and that they can use that for reasoning and sensemaking. And that's what we ultimately want. 

Mike: I'm going to mine what you said for another nugget of wisdom. You said at the beginning, context is a reasoning tool. Did I capture that correctly? 

Zandra: Um-hm. Yeah, absolutely. I think I can reason far better with something that I can actually play out and think through the process that I do. And I can connect it to the real world, and then I can think about, like, “Oh, what did I actually just do?” Because some things are pretty automatic that we do every day, and we don't know that they're connected to math or could be. And when we reason through it, it really helps us to reason a little deeper. There's been a lot of math studies—most of them are older now—but about kids who did math in the real world as jobs. Maybe they were, like, working after school when we had real money, (laughs) physical money, more frequently, and they could do all these calculations very easily. But they struggled with school mathematics that was decontextualized. So then, as teachers learn how to bring in the context they're familiar with, they know how that works and then they can connect it, the representation to the symbol. So, it's all kind of connected, all three of these enhancements at the end of the day. 

Mike: Yeah, that makes a lot of sense. So, before we finish, Zandra, I'm wondering if you can point listeners to any kind of additional resources that you think would help them take the conversation that we're having and maybe add some depth to their understanding.

Zandra: Sure. So, any three of my coauthors’ work is great to find online. Fortunately, I think all three of them consult with the EL Success Forum. It's elsuccessforum.org, I believe. That is a group that has put together amazing banks of resources for teachers and people that work in schools around English language learners, in particular. So, that's a great one that I point a lot of people to. I have a Grassroots Workshop that I made that's on teaching mathematics with English learners that you could find online. And I think beyond that, there's a number of great resources through TODOS: Mathematics for ALL, which is a professional organization. They're an affiliate of NCTM, and they have some amazing resources as well. 

Mike: That is fabulous. Thank you so much for joining us, Sandra. It has really been a pleasure talking. 

Zandra: Yeah, likewise. Thanks for having me. I appreciate the opportunity to share about this. Something I'm super passionate about, and I'm always happy to talk about. 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.