Raylene Park

Welcome to the EAL/D conversations podcast. My name is Raylene Park. I'm the EAL/D Education Advisor for K-6 with the NSW Department of Education. Today, I'm joined by Noel Maddern, Numeracy Advisor Primary and Anette Bremer, EAL/D Literacy and Numeracy Advisor. Welcome Noel and Anette.

Noel Maddern

Thanks Raylene. Great to be here.

Anette Bremer

Thank you very much Raylene and I'm looking forward to this opportunity.

Raylene Park

Today we are going to be talking about supporting EAL/D learners in numeracy. We hear lots about numeracy across the KLAs, could you please explain the difference between numeracy and mathematics?

Noel Maddern

Yeah, that's a really important question, Raylene. The simplest way for us to think about the difference between numeracy and maths is that numeracy is applying maths to real life situations. There's a great little simple quote that we often use, that numeracy is maths in action. That idea of maths in action applying maths to a real life circumstance. So for example, financial maths is one of the most common areas we think of, with numeracy being able to deal with money calculations as we need to everyday life. We're all dealing with money, so numeracy is a perfect example of numeracy, where we're applying our mathematical skills to money. Another simple thing, lots of things in real life with measurement simple thing like you might be moving the furniture around in your house and one way to do it is to just start moving cupboards and bookcases and whatever and discovering that it doesn't quite fit and you've got to change it all over again, or you could actually do some measurement and calculations beforehand and work out how it's going to fit and that would be an example of numeracy. Basically anything we're applying maths to a real life context.

Anette Bremer

Yeah. Thank you very much, Noel. And I'd just like to add that we can have some examples of maths in a real life situation and the one I want to talk about is the way maths is enmeshed in culture. And I want to relate a story. I was lucky enough to hear at a conference where Di Siemens, who many of you who are maths teachers, will know about, and she talked about her experience to working with the Yolngu people of Arnhem Land and particular, she was working with schools around the concept of subitising, which we all know is a very important math concept in number sets. So the schools were struggling in the sense of how to get the kids to understand the idea of subitising. Until they came across what was a known number within the culture, and that was the known number of the number of eggs in an emu clutch, and once there was a cultural reference and the and the kids already could subitising because they knew exactly how many emu eggs were in an emu clutch. Then the kids got the concept and could apply it to other ways of subitising, which we often do in our culture in base 10 or in 12.

The second thing Raylene I wanted to speak to you talked about numeracy across the curriculum, and I just wanted to talk about the importance of this because numeracy is everywhere and what we mean about numeracy across the curriculum is, the use of maths or numeracy concepts or maths in real life outside of the subject maths. Now those of us who are school teachers can think of multiple examples of this, for instance science where kids have to measure ingredients or fluids for experiments. In geography, you're often reading scales on a map, looking at a timeline, history again, there's the use of timelines to represent historical periods, and in English, as an English teacher myself, we look at a range of informative texts and which we read a variety of visual representations of data, and you can have a graph, you can have a table or some sort of chart, so there is numeracy moments embedded in all KLAs as it is embedded in in real life and it's important that we think about this as teachers of EAL/D students.

Noel Maddern

And can I just add Raylene? There's a really important reason why we want to make this distinction between maths and numeracy when we think about the sorts of assessments that we have in schools, so the NAPLAN numeracy assessment, for example, it is a numeracy assessment, so it's assessing the application of mathematics to scenarios to real life situations. You don't get in a NAPLAN numeracy assessment, a question like 42 takeaway 17, just as a bold calculation question, all the questions are tied up in a scenario because it is testing numeracy, it's testing the application of mathematics.

So EAL/D students need to be able to read and understand the scenarios. And as teachers, we've got to realise that assessments like NAPLAN assessment for instance, because it's a numeracy assessment, there's going to be language and cultural demands that are going to challenge our EAL/D students.

Raylene Park

Thank you, Anette and Noel, for outlining the difference between numeracy and mathematics, and the crucial role numeracy plays across all KLAs. What general advice can you offer teachers to support EAL/D students effectively in developing numeracy skills?

Anette Bremer

So if we're thinking about EAL/D learners and numeracy, the first general advice is the same. When we think about EAL/D learners and any area of the curriculum, which is that English language learning. Why you're learning the curriculum takes a significant amount of time and that we need to be aware that each student develops the English language proficiency according to a whole range of factors, including what level of English language proficiency they come to school.

The amount of prior schooling which we know in our some students is rather limited. Their home language and their home language, literacy and numeracy skills. So there's a whole lot of factors that we always got to keep in mind in the numeracy context, and this is also important in the maths classroom in particular because one of the things that has really interested me is Whiteford's research, published as is mathematics, a universal language, and Whiteford notes the importance of students first mathematics, and in that article Whiteford claims that a student's first mathematics is just as important as a student's home language because the first mathematics, just like the home language of a student, brings a range of knowledges and ways of doing things.

So we can start thinking about students who have got mathematical and numeracy experience in another language and culture bringing those attributes or dispositions into the classroom. So to know about our students and what they bring to learning is incredibly important. So some of the things that might be apparent in the classroom is, for example, notation may not be universal. We often think of mathematics as a universal language, but we know it is done differently in different cultures and the way you say numbers, of course, is not universal. Each language has a different way of saying language numbers. For example, we have the teen numbers, other cultures put the second-place value number first and then have the first-place value number. So that's a different way of conceptualising the number and may influence the way they demonstrate mathematics knowledge and numeracy knowledge in the classroom. We should welcome what students bring to the classroom and explore these differences in any particular numeracy context, including in the mathematics classroom.

So what I'm really talking about is the Australian Professional Standards for Teacher for teachers, which every teacher in NSW public schools should be aware of. And I'm referring to the first two standards in the Australian Professional Standards for teachers, which is know your learner and know how they learn and know your content and how to teach it. So in the context of EAL/D learners, we need to know what they're bringing to learning in terms of their English. Their English language proficiency and knowledge of literacy, but also their home language, knowledge and knowledge of literacy, as well as their numeracy knowledge in both of these.

We need to know about their prior educational experience, what we need to do also is need to know how to teach numeracy or mathematics in a way that is accessible and is linking to what the students are bringing to learning. So some students will bring incredibly strong mathematics in that more abstract sense to the classroom, but we'll need a lot of English language learning to attach the words and the concepts to what they already can do in their home language. Other students, as alluded to previously, may have very good numeracy skills. They may have grown up in a refugee camp or something like that, and have used to, you know, division of food rations, bartering at the market, organising all sorts of things that that is numerate but do not understand how we do numeracy in mathematics at in a NSW public schools, nor have the language to describe the numeracy skills that they're displaying.

Raylene Park

Thank you, Anette – such an important reminder that EAL/D learners bring rich mathematical knowledge and lived numeracy experiences from their home language and culture. As teachers, understanding their language proficiency, prior schooling, and numeracy backgrounds helps us build on what they already know and make learning more accessible. Building on that can you share some examples of what high-challenge, high-support numeracy teaching looks like for EAL/D learners?

Noel Maddern

You know, first of all in terms of high challenge, I mean our high challenge comes first and foremost from our syllabuses. Our syllabus documents are a wealth of information and there is an expectation on where our students need to be. But there's great support in the syllabuses also in terms of teaching advice, examples and so on. So the high expectation first comes from the syllabus, but then we also have a number of different assessments. So for instance already mentioned, we have the NAPLAN numeracy assessment, we have check in assessments, we have HSC minimum standards, we have the HSC exams. So there's assessments that give us a good indication of the high expectations or the high challenge that we need to meet for our students. In terms of high support, numeracy, teaching lots of different ideas.

I'll just focus on a couple to begin with now. And in particular, I'm thinking about strategies that help students to unpack those challenging questions in external assessments, and particularly challenging for EAL/D students when they've got to cope with the language demands, the cultural demands, as well as the mathematics behind the numeracy questions. So one fantastic strategy we can work on with students is the idea of three reads. So we might present a question from past assessment and put it up in the classroom and encourage students to read through it three times and each time with a different focus. Our first focus is just about understanding the situation, so don't worry about any numbers, calculations, anything. Just thinking about what is the situation, what's actually happening, what's the story that's being told in the question. Then the second read we go through and we read about, we read the numbers and think about well, what are the size of quantities that are being represented in the question, what numbers actually give us more information about the scenario that we read about in the first read and then the third read is when we finally get to the point about planning a response. How are we actually going to answer this question. Apart from anything else, just slowing down and reading something three times is one way that we can really help our EAL/D students to meet that high challenge, and we can support them and show them a strategy that helps them to think clearly and slowly through what's going on in the question. And this can be something that you can do in the class with students, but you can teach them to do it so they can then take the strategy into an assessment as well.

Second strategy I'll mention is similar but slightly different. The idea of Notice and Wonder and a Slow Reveal of Questions. Now, one way you can do this I like to do this by getting a past assessment question, putting it on a PowerPoint and then making a whole heap of white rectangles that I put over the top of parts of the question and then animate the PowerPoint so that the boxes are slowly removed and so you can control the parts of the questions that the parts of the question that you show the students and so to begin with there might be just the first opening part of the first sentence, that all it is. And so we just what do you notice? What do you wonder? And they can say, well, the question must be about something just very basic. What do you notice? What do you wonder about the most simple information in the question. The other good thing about notice and wonder is it's non threatening. A student can notice and wonder anything they like. They can say it's in blue text is what I noticed and that's correct. Like there's no wrong answers to it and so everyone can be part of notice and wonder and be thinking about the things that they see.

Gradually you show more and more of the question and each time you show something new again, what do you notice? What do you wonder? And you'll start to notice and wonder more things as more of the question is revealed. I like to leave the numbers as the last thing that I reveal, and then my question just before that would be what numbers would we like to see here. And so they might say, oh, it'd be good if the numbers were 5and 10 because that would make the question easy.

And so then you can think about how to answer the question with easy numbers. And finally, the final reveal is the whole question including the numbers and the numbers might be 4.7 and 93 and something really tricky. But we've already thought about the scenarios, the information in the question that tells the story. We've thought about how to do the question with easy numbers and so by the time we then get to the whole question being revealed, we can then go and use all that information. So both those strategies three reads and slow reveal notice and wonder are all about slowing down and thinking about what a question is about and it reduces the cognitive load for students as well. If you just present one big question, lots of text. Maybe there's a diagram, there's numbers, there might be a table. There's so much to take in at once. If we can slow our EAL/D students down and just think about specific things as we go through, we reduce that cognitive load and they can cope with the demands of the language as well as the mathematics behind the numeracy question.

Raylene Park

Thanks for sharing such excellent examples of high-challenge, high-support numeracy teaching. I particularly enjoyed your example of the Three Reads strategy – it immediately brought to mind Gibbons’ concept of message abundancy, which highlights the importance of presenting key ideas in multiple ways. This enables EAL/D learners to repeatedly see, hear, and use the same information, helping them consolidate both language and conceptual understanding.

I also really appreciate the Notice and Wonder and Slow Reveal approaches. These strategies provide EAL/D learners with valuable processing time, which is especially important as they often need to code-switch between their first language and English while engaging in mathematical problem-solving.

In this series, both Anette and Noel clearly explained the distinction between numeracy and mathematics and shared excellent advice for teachers of EAL/D learners. They reminded us that EAL/D students bring rich mathematical knowledge and lived numeracy experiences from their home languages and cultures. As teachers, developing an understanding of each learner’s language proficiency, prior schooling, and numeracy background allows us to build on what they already know and make learning more accessible and meaningful.

Thanks for listening to the part 1 of our two part series on Numeracy for EAL/D Learners. Join us next time for part 2, where we’ll discuss how to explicitly teach mathematical language and explore effective strategies to support EAL/D learners in developing their numeracy skills.