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Raylene Park

Welcome to the EAL/D Conversations podcast. My name is Raylene Park, and I’m the EAL/D ÌÇÐÄvlog¹ÙÍø Advisor for K–6 with the NSW Department of ÌÇÐÄvlog¹ÙÍø. Today, I’m joined by Noel Maddern, Numeracy Advisor – Primary, and Anette Bremer, EAL/D Literacy and Numeracy Advisor, for the second part of our series on numeracy for EAL/D learners.

In part 1, Anette and Noel explained the difference between numeracy and mathematics, shared advice on supporting EAL/D learners to develop mathematical knowledge and vocabulary, and provided examples of high-challenge, high-support numeracy teaching.

In today’s episode, Anette and Noel will build on that discussion by exploring explicit mathematical language teaching and effective strategies for developing EAL/D learners’ numeracy skills.

So, with all of that in mind…

What do all teachers need to know about mathematical language, and how can they explicitly teach the required language across the KLAs?

Anette Bremer

Thank you Raylene. I noticed you use the word mathematical language and I first of all would like to point to some resources we have here in NSW, which is the NESA glossary, which is a fantastic tool and the two excellent teaching guides which accompany both the primary school and the high school maths syllabuses. But there is more to maths language or the language of maths than what's in the NESA glossary, which is why I would point you to those two NESA teaching guides on the language and vocabulary of mathematics.

And in particular there is a lot of words that we use in a numeracy context which are have multiple meanings and so therefore there is a huge need for explicit teaching.

So that's the first thing you've mentioned it in your question, but we need to think about explicit teaching, and we need to think about those words, which are homonyms, which means the same name but a different meaning, and one of the ones I like to use it as an example is the word product.

And when you say the word product to your typical teenager, they think of something they put in their hair, which is fair enough, because that's what we call that stuff. However, a product obviously is something very different in the maths classroom, but it's also very different in a commerce classroom as well.

And one of the things as teachers of numeracy across the curriculum, we are aware of those multiple meanings and we know that the context defines the meaning we're going to draw upon when we listen to those words or comprehending that that language. But an EAL/D learner may not be aware of multiple meanings and not be aware of the context to the same extent, so teaching multiple meanings of what we would call a tier two word is very important. So the NESA glossary has a list or a compendium of Tier 3 words like denominator, division, those sort of typical maths language, they're important and we tend to teach them explicitly or KLA teachers or teachers of KLAs teach those, because that's the language of your field. It's the Tier 2, Tier 2 words that we really need to think about, but with our EAL/D learners, they come to school with significant less amount of English language and English language vocabulary. And one of the particular tricky things in a numeracy context can often be what's called Tier 1 or sight or everyday words. So they're often those little words that we use to construct a sentence and are absolutely essential for meaning making in any kind of text.

In a numeracy context, some of the little words we might want to think of that do need to be pointed out to our kids, and we need to demonstrate the difference would be something like of and off. If we're working in percentages.

Well, I could say what is 20% of a kilo?

Or I could say I'm buying some oranges and there's 20% off the marked price. Very different mathematical calculation that you have to do. The whole question is conceptually different and it's a small word that we comprehend readily and understand it in context but we'll have to be explicitly teach taught to some, but not all but some of our EAL/D learners.

So the best way to teach Tier 1 words is when you're doing the actual numeracy teaching. So you're teaching it in context so they can see, for example, what's the difference between of and off when you're working with percentages. One of the ways we can explicitly teach we can do what I've just done and you can stop to explain and that's great. But there's a whole lot of other tools that we can use as well and I like to use visuals because I find that they work for my students. And so I would point to something like a Freya model, which if you're in NSW public schools you can find on the digital learning selector which allows our kids to have examples and non examples and provide definitions. There's an excellent reverse Freya model up on the digital learning selective, which is using a numeracy example, so you might want to have a look at it. Another one that works really effectively and again uses visualisation and actually can use all the language modes are Think Board. And so this allows students to make multiple representations of a word problem and that sort of feeds back to Noel's strategy of the three reads. So a student could have a number sentence in the middle of a Think Board. And then draw a picture of the think board. Write a word problem of the Think Board. Do some skip counting for perhaps to solve the answer of the number sentence in the middle of the of the Think Board.

Noel Maddern

Can I just add one thing on to your answer there, Anette, when you mentioned of and off, it made me think about the importance of making connections. When we teach language as well I might be doing a lesson on percentages and I need to explain the meaning of the word of and I know that off is not going to come up until next week when we take do percentage discounts, but rather than teaching of this week and then waiting until next week to teach off, if I teach both of them together, that's actually easier for students to understand. When we teach vocabulary in isolation with here's just one word easy to forget. But when we make connections between words, it's actually easier to remember both of them than it is to just do one at a time.

Raylene Park

Thanks, Anette and Noel, for sharing strategies to explicitly teach mathematical language, using visuals like Frayer models and Think Boards, helping EAL/D leaners make connections between related terms, and highlighting some great departmental resources available. This way, EAL/D learners are learning the maths and the language together. So now my final question for today is, can you discuss some effective strategies for developing EAL/D learners numeracy skills?

Noel Maddern

Yeah. Look, there's, there's lots of great strategies we can use. I think I'll restrict myself to two broad categories. The first category I'll talk about is the use of visuals and concrete materials. And then I'll also talk about how we can help students to use talk in maths and numeracy.

So in terms of concrete materials and visuals, one of the things we really need to make sure is that we don't rush to the abstract. We have a tendency to think that the symbolic representations of things is the most important, and we've got to get students there, and we got them there as quickly as we can. But we really need opportunities for students to play with concrete materials to see visuals really build that conceptual understanding. So having concrete materials on hand in the classroom so students can use them at the point of need. So we might have been doing something with place value. We've used some base 10 materials and then we stack them away in the cupboard and then we expect them to be able to do everything with number without the materials anymore. Why not have them on trolley in the middle of the classroom? so whenever there's a need where something could be explained better with the base 10 materials, they're there, they're on hand at point of need. Similar to concrete materials, the sorts of tools we use that like number lines for instance, like it might not be actually concrete, but it's something that is a tool that students can use in multiple situations to help build that better understanding. Other visuals like bar models. If you haven't seen bar models before, there's some great resources on the reSolve website, on bar models, and there's now somethings in our math syllabus around bar models that can be great for doing calculations and really seeing the size of the numbers in a question. So a question with lots of words and lots of numbers can be confusing when you first read it, but by then taking the information in the question and drawing it in a consistent way with a bar model that shows the relative size of the numbers in the question can be really powerful in simplifying what can be confusing for an EAL/D student when they first read a question.

Visuals with multiplication. Again, we get very quickly rushed towards multiplication facts or multiplication algorithms or things with multiplication that are all symbolic when there's so much richness in using visuals like arrays and then region models and an open area model and an open area model for multiplication, if we teach that well in primary school, that's going to serve students well right through high school as well, you can use array open area models for multiplication with algebraic multiplication. And even if you're teaching extension maths in stage six, you can use an area model for multiplication and do away with the need for polynomial division like visuals can be so powerful in building conceptual understanding and helping our students to really understand what's going on when they're attempting to do different questions. Basically, any visuals or tools that support that conceptual understanding or that helps simplify word problems.

I said it'll also talk about talk, could talk about talk all day, but a few key things that are really good to help students to use in a maths class or when they're looking at numeracy in another KLA talk moves is a great resource. If you go to the universal resource hub and just search on talk moves, you'll find a number of resources there. If you haven't seen them before, talk moves, there's seven main categories of types of talk. Really simple and really simple little explanations as to what they are when you would use them. So for example, turn and talk is one of the seven.

Really great strategy to use. You might have shown a question in class. You might have gone through three reads or you might be wanting students to do the three reads, so they might do it on their own and then you can say turn and talk to a partner. And so the first thing they do, their first communication is non-threatening with a peer. And rather than answering in front of the whole class and maybe being wrong, I can have a conversation with one other person and we can sort of suss out if we're both on the same page or not that turn and talk really powerful. Adding on Revoicing. Revoicing is a great one for EAL/D students to be able to have the opportunity to rephrase something. It might be a question they've read, or the teacher might have said something and then getting them to put it in their own words. So talk moves really simple resource to use, easy to find on the universal resource hub, and you can use with students straight away.

Another aspect of talk extended IRF. If you're familiar with IRF initiation, response and feedback, we're asking a student a question. You're getting a response from the student, then you're giving them feedback. Extended IRF is to go that one step further. So I might ask a student a question about a graph and they might say, well, the bits go up and so I might give them some feedback on go up and then I might ask them what are some other maths words that we use for go up and they may or may not know of the word increasing. If they do, then that's great. If they don't, then I might teach them the word increase.

And then ask them again later on. So how could we reword your answer to use some more maths vocabulary, and they might then be able to say, well the columns increase so that back and forth conversation rather than just I'll ask a question, you'll give me a response and I'll give you some feedback. Now we'll move on from that feedback. Now let's go again. Let's ask the question again. And can you rephrase your answer using more sophisticated vocabulary.

The last thing I'll say touched on what Anette mentioned earlier about the use of home language. There's so much cognitive load for EAL/D students when they're trying to understand words and text. They're trying to understand the maths they're trying to understand, the numbers, the graphs, the diagrams, giving them the opportunity to discuss with one another if there's more than one student in the class that share that same home language to use the home language to focus on the maths, focus on the parts that they can discuss in not have language as a barrier in the way really important and really powerful. Yes, we want students to learn English, but it's really powerful to allow them to build their understanding in their own language, reduce that cognitive load, and gradually we can transition to them learning language, learning language takes time, and if we're wanting to teach maths and language at times, it's best to give them the opportunity to not have to worry about the language. Use your own language and now you can focus on the maths. So whether it be talk moves, whether it be extended IRF, whether it be number talks, use of home language, talk in numeracy in math's really important.

Anette Bremer

I'd just like to chime in and endorse what Noel has said, especially about the use of home language. Those of us who are in NSW and teach NSW syllabuses know that NESA has a statement about the use of home language as a learning tool.

And we shouldn't underestimate the use of home language in as a learning team, Absolutely as Noel said, we need them to learn English because that is the language of instruction. But what students can do, who have that mathematical in numeracy knowledge in their home language is work on that and learn it through that in the classroom at the same time as teachers, we're teaching them the English language that they will need to talk about it in English, at a later stage.

Raylene Park

Thank you so much both of you. There was some great tips you both shared and I just wanted to say a big thank you for joining us today and sharing your knowledge and expertise around numeracy for EAL/D learners. You've helped unpack some of the research, explore their whys and the how and provided really great, like practical strategies and resources to support EAL/D learners in their classroom. So big thank you again for joining us today and I hope you have a great day.

Noel Maddern

Thanks very much Raylene.

Anette Bremer

Very much appreciated, Raylene.