Siobhan:

I'd like to acknowledge that this episode of the Teach NSW Podcast was recorded on the homelands of the Darug people. I'd like to pay respect to Elders past and present, and extend that respect to all Aboriginal and Torres Strait Islander peoples listening today.

Opening credits:

Welcome to the Teach NSW Podcast, a podcast by teachers for teachers. I'm Shannon, and I'm Siobhan.

Siobhan:

Welcome back to another episode. Today we're really excited to have Juliana on the couch. Welcome. Tell you a little bit about Juliana. She's had a very dynamic career as a primary school teacher and definitely began to develop a passion for numeracy throughout her time teaching in the classroom. This led Juliana to her current role as a K - 6 numeracy advisor, where she supports schools more broadly in improving numeracy outcomes. Today, Juliana joins us to share her top tips for embedding evidence-based numeracy practices into the K - 6 classroom. Welcome.

Juliana:

Hi, guys. Thanks for having me.

Shannon:

You are so welcome. And I am so excited as well because I, too, have a passion for numeracy. Didn't always start that way. So this is exciting. As a student, I was very reluctant with numeracy, all things mathematics. But I had some wonderful teachers. And then it was funny because then becoming a teacher, I felt like it was my job now that I didn't, like the little Shannon of the world didn't, I didn't want any of my students to feel that way. So I really developed that passion. Yeah, I'm excited to unpack all that today.

Juliana:

I'm in good company. This is going to be great.

Siobhan:

And I’m here to learn. Looking forward to it.

Shannon:

So, we would love to kick off. We like to do this with all of our guests. Just a nice little warm-up and ease into it, a Teacher This or That. So I'm going to kick us off with the first one. School sport or PSSA?

Juliana:

PSSA. I had some great fun teaching cricket.

Shannon & Siobhan:

Cricket?

Juliana:

I know.

Shannon & Siobhan:

Wow.

Juliana:

You're as shocked as my family was. Cricket because my mum just always watched it in the summertime. So I knew enough about it and more than others. So that made me the cricket coach and then I just took it for a ride. So, yeah. PSSA.

Shannon:

Amazing.

Siobhan:

I love that.

Shannon:

I love that. That's really cool. I've done a cricket like gala day, not of, you know, skill or talent or anything. They really just needed someone to go and I was willing and able. And may I say I was very out of my depth, but I had a good day. And the kids were so happy to like explain to me what was going on

Juliana:

Let me just tell you, I had more skills than some of the kids but some of those kids were amazing. So, I was just like, 'You coach the team.'

Siobhan:

Yeah.

Juliana:

'I'll learn from you.'

Siobhan:

I love that.

Shannon:

Well you don't have PSSA.

Siobhan:

No, but we do sometimes go off-site for sport in schools. So I would say like my favourite off-site sports were definitely rock climbing. What else did we do? We had like beach volleyball. We used to walk, like do power walking,

Juliana:

Oh, yeah.

Siobhan:

Which was great. My skillset, yep. ‘Kids keep up with me.’

Shannon:

Yeah, get the heart rate going.

Siobhan:

Yeah, as I power walk along the esplanade, so yeah. I would say off-site sport is really engaging. But you mentioned cricket and I just had a flashback to, in Year 3 or something, I wrote a speech and I remember delivering it, and I got like all the way through to the regionals or something. And the speech was so basic, but it was like ‘basketball is the best sport to play’. And so it was like I would diss every other sport. And I remember the line for cricket. I was like, 'Who would want to play cricket? It's like watching grass grow.’

Juliana:

Well, it's like standing still for a significant amount of time. So it's a bit like a lazy sport but I can't say that because my husband plays cricket.

Shannon:

Oh, my goodness. All right, the next one. Excursion or theme day?

Juliana:

I'm going to go with theme day purely because like from the beginning you're in your own space, you can take it to the enth degree and just have a ball.

Shannon:

What was like your favourite theme day?

Juliana:

Um, I would have to go

Shannon:

Are we talking Crazy Hair Day? Are we talking like Jersey Day?

Juliana:

Oh, there was one Jersey Day that I have to bring up because I was fortunate enough to teach in the same school as my best friend at a particular time where both of our countries were playing each other

Shannon & Siobhan:

Oh, wow.

Juliana:

In one of the games. Anyway, it was just so much fun, because we wore our jerseys to school and

Shannon:

The rivalry.

Juliana:

The whole school knew about our rivalry. It was just fantastic. So that Jersey Day is particularly memorable, but it was just perfectly timed

Shannon:

Yeah.

Juliana:

And we got to bring a little bit of, yeah, our little tiff into the school.

Shannon:

Yeah, I love that. I actually really loved Jersey Day as well because my background, like my parents are from Ireland. So, I'd always wear an Irish rugby jersey in. It was just so much fun like explaining to the kids about, you know, where you come from and your country. And I'd talk about like how good the Irish rugby team was and it was always a lot of fun. Like you sort of see a different side to kids when you start

Juliana:

Yeah.

Shannon:

Bringing in sport.

Juliana:

It has a bit of storytelling.

Shannon:

Yeah.

Juliana:

You know, you can take, yeah, take it as far as you want, which is nice.

Siobhan:

Who won by the way? Your team or your best friend’s team?

Juliana:

I don't even remember because,

Shannon:

The rivalry took over.

Juliana:

The rivalry, the whole game, I think it even ended up in penalties or something. It was a soccer game. And somebody got sent off for biting another player, and they got a red card, anyway.

Shannon:

Scandal.

Juliana:

Very big scandal. So, it was like we argued the whole way to school because we drove to work together that day and then it just continued the whole day. And then kids were getting involved, and who's in the right and it was fantastic. Didn't even matter who won actually. I think it was more about, should they have got a red card? Should they have done that? I can't believe they did that.

Shannon:

All the controversy. I love it. And what about you? An excursion or a theme day?

Siobhan:

Ah, I love a good excursion.

Shannon:

Yeah?

Siobhan:

Yeah, just fun, getting out. You see the kids in a different light as well, like outside of the school grounds. It's, yeah, interesting to see.

Juliana:

You haven't taken Kindergarten on an excursion, have you?

Siobhan:

Oh, yeah. No.

Juliana:

That might change your view on it.

Siobhan:

I'd be putting hi-vis vests on them all and having them all hold onto a rope or something like that.

Shannon:

Everybody pull out your number, please, buddies.

Siobhan:

Yeah, yeah. Bit different in high school.

Shannon:

Well, a bit fitting for the next one, because I've got Kindy or Year 6?

Juliana:

Please, do not make me, do I have to choose?

Shannon:

You do. It's a This or That. There's no fence sitters in this game.

Juliana:

Do you know coming out of uni, I would've said Kindy.

Shannon:

Yep.

Juliana:

And then I got thrown onto Year 6 for 3 years in a row and fell in love with it. But my most recent experience have been with Kindergarten and I loved it. So I have to say Kindy. Right now, me, current me, says Kindy.

Shannon:

Yeah.

Juliana:

It's just the pace at what they learn and the way that you can shape the way that they think about something, particularly maths and numeracy, because no one's really tapped into that in that way, specifically maths and numeracy. So, it was really cool to be the first person to shape how they thought about numbers or,

Siobhan:

Oh, I love that.

Juliana:

‘What am I supposed to do with this one?’ It was just, it was a whole bit of fun doing that. So I have to say K.

Shannon:

I've never thought about it like that. Like, someone, the first person, like, the first teacher. Like obviously, you know, some of them come, not obviously, I shouldn't say, but some of them come and they're already reading. They can write a little bit. But tapping into that numeracy and unearthing, like, those little, like their mental strategies and how they're actually figuring things out and making it make sense for them, yeah. I've never taught Kindy like year, from beginning to end, but now you say that, I'm like really excited that I want to go and do it. But I'd have to answer and say Year 6 for me. Again just because I haven't had that, like I've had Year 1 exposure, but I think it's quite different than that first year of school. And I take my hat off to all Kindy teachers who weather Kindy Term 1 because that's special, very special individuals and wonderful teachers.

Siobhan:

When we visited some of the central schools on the Beyond the Line trip, I actively put my hand up and was like, you know, as a high school teacher, I want to be in a Kindy room. Like let me go and observe them. And it was just the best. And I was so, not shocked, but just like surprised at how many activities the teacher had planned, because like, they can only get through a certain amount of time before they lose their attention span. And I was like, 'Oh, this is just incredible.' And like, oh, the teacher was just amazing. And I had one kid who like really latched onto me and wanted my help with everything, and I was like, 'Yeah, this is just the best. It's the best experience of my life.'

Shannon:

Can you feel that way about your Year 7s, too?

Siobhan:

They don't necessarily latch onto you in Year 7 but,

Shannon:

Different bond.

Siobhan:

Yeah. Different type of bond, for sure.

Shannon:

I feel like we've asked this question like to both of us and it's, like you were saying, like when you came out of uni, you had a different answer. I feel like us as well, our answer changes depending on

Juliana:

Yeah. And I mean

Shannon:

What we remember or what we're talking about at the time. But that's the cool thing about teaching, like you've got so much in the bank after a couple years on different classes that, you know, different things align with you at different times in your life.

Siobhan:

Well, tell us a little bit about yourself, Juliana, in terms of how did your love for teaching begin?

Juliana:

I don't know where it began because to be honest, I always knew I was going to be a teacher. Always.

Shannon:

I love that.

Juliana:

There was a small, small moment in time where I thought,'Could I do high school maths teaching?' Because maths, it didn't come easily to me, but it just always made sense to me. And if it didn't, I had a lot of fun making it make sense. Strange if you're not a numeracy person I know, but, and like, I’d spend some lunchtime talking to, you know, the struggling kid in my class, and I remember him and his face still now, and he said, 'I just don't understand what the teacher's saying.' And this was like, I think, maybe Year 9 or Year 10 maths. And I was like, 'Come here. Let me talk about it.’.

Siobhan:

‘Let me, let the pro explain this to you.’

Juliana:

And it wasn't even, it was kind of like explaining it 2 levels down from where it was at and then building back up. And as a teacher now I can probably explain that. At the time, I didn't know that's what I was doing. But, yeah, if you had asked me in primary school, I definitely would've said teacher. I just knew, I don't know. I think it kind of suits and aligns with like my values. I like to be challenged but I like to just hang out with people. Like, I don't know. It just kind of suits who I am.

Shannon:

Yeah. Aligned to your ethos.

Juliana:

Yeah.

Shannon:

Love that. No, that's really cool. And then, so you went and did your degree and you came out. And what did that look like, first year of teaching?

Juliana:

First year of teaching, I don't know who explained it to me, but they were like, 'You need to be really firm, but really fair.' And if kids can see that, from the very beginning, you've got them. And then once I felt like I got that under control, the next person sort of said to me, 'The more engaging your learning is, again, behaviour management kind of just falls into place.' So then I started focusing on how quality the learning was. And then I just had fun. And then that's when, yeah, I got put on Stage 3 for 3 years in a row. And by the third year, I was like, 'Oh, this is, now I'm starting to feel good about this.' But I reckon it took me about 3 years to feel like, 'Okay, yeah, I'm in the right place. Yeah, I'm in the right place.' And in between that, I went overseas and taught for a short amount of time as well. So I was trialling new things and learning just about learning and what students do and what they really engage with. And, yeah, that was it. And then I, yeah, like I said, I always knew numeracy was my thing. But from teaching on Stage 3 for a little while, I did some numeracy intervention roles. So that took me all across K - 6, which was super fantastic because I knew I loved Kindy. But then when I got to work with the Kindy kids who by Term 3 just still weren't, you know, counting past 12 or didn't have one-to-one correspondence, all those sorts of things. I was like, 'Okay, I need to know what the evidence is and I need to help these kids.'

Shannon:

Can you elaborate a little bit about what that looked like in your school for your school context? Like, what was numeracy intervention?

Juliana:

Numeracy intervention. So sometimes that looked like withdrawing small groups of students and working really intensively for a short amount of time on a particular skill, like one-to-one correspondence. Or, you know, these kids can't get past 120 when they're counting. And, you know, there's specific things that we can do with them, but most importantly it's just manipulating materials, lots of practise, things like that. But then I'd also work with them and their classroom teacher in the classroom so that they were always transferring back across contexts and things like that. So I got to do a lot of team teaching, which was great, because I learnt so much from other people. And we got to collaborate and say, 'This is working. This really isn't.' So, it's kind of like an informal leadership role at the same time, you could say, because that kind of led me into this numeracy coaching space. And I've always maintained that, which I'm really lucky, so even though I've been mostly a classroom teacher in my school space, the leadership team has always given me some sort of capacity to do numeracy coaching. Whether that's just people coming in and watching me do what I do, which is just awesome because it was with my students, and like, you know, I know exactly where they've come from and where we are building to and things like that. But I also got to team teach with them or just have some planning time, which is so, so helpful. And they're just like, 'I'm really stuck with this,' or, 'I've got this group of students that just doesn't seem to be moving from, you know, A to B. What are some things we can try?' And we just dive into the syllabus together, look at the evidence and then try something. And, yeah, it's been, I've been really fortunate to be given those opportunities throughout my career as well.

Shannon:

Yeah and really cool to have had those opportunities that align so closely to your passion as well. Like I think that that's half the battle, isn't it really? When you have a passion in a space and you work with a colleague who, you know, is so driven by the, you know, their inherent passion for numeracy, literacy, whatever it may be. Working alongside someone like that is quite infectious, I think, as like a colleague as well. So having the opportunity to co-teach with you in a, you know, team teaching environment or co-plan, for example, that would've been really beneficial, I would imagine.

Juliana:

Yeah and I mean, like, I came and went to different schools and things like that and different spaces. And when I went back and found that there were other people who had, like you just said, had caught onto this, you know, I don't know what the word is, this passion for figuring out things and a better way to do things and getting it right for students so that there wasn't that struggle, it was so lovely to see that other people had that passion. And now that my eyes are open to, you know, a whole lot more schools and a whole lot more people, it's really nice to see that, that is evident across the system. And there are opportunities for people to really dive into their passion and share that with others.

Shannon:

So, in your current role as a K - 6 numeracy adviser, what would you say some of, what are your main goals within that role? What are you working towards?

Juliana:

Really, in a nutshell, if I could put it into a sentence maybe, it's really providing teachers with knowledge, so through professional learning, I guess, about the evidence in a really practical way so that they walk away from whichever, you know, form the professional learning is, whether it's a resource, or it's a video, or it's a face-to-face something, that they walk away saying, 'I know exactly what I'm going to do because, and I know that it's going to work for my students because.' So really trying to say, you know, 'This is the evidence and I know what to do, and I want to try something tomorrow because you kind of inspired me to think I can do better.' And the same with resources, I guess. So really engaging resources that can shape the way that students think about mathematics and numeracy. Because we do a lot of stuff in the classroom and it doesn't mean that that stuff is the right thing or it's going to help us in the long term. So it might give us a little bit of success today, but the way that we think about a particular concept can really shape the way that we learn something in one, 2 years’ time.

Shannon:

Yeah, I think for me, like a couple years into my career, I was lucky enough to be able to lead the key learning area of mathematics across K - 6, which was really wonderful. As part of that, I did a lot of professional learning which was really cool. So, it's still a current professional learning, I'm pretty sure, correct me if I'm wrong, across the department, it was the Big Ideas.

Juliana:

Yeah.

Shannon:

Yeah, and I, because I was on Year 5 and 6 at the time, so the one for K - 2 was Starting Strong. And that was like a, I think it was like a 20-hour PL. We did it over a couple weeks, over the year actually, I think. And we did it in a small group, so it was really wonderful having teachers at my school that I could bounce ideas off. But what I really liked about that and what you’re saying is there were really practical things that I could immediately bring back into my classroom. And I got sort of the space to be able to trial them with my students and then in turn talk through with our wider staff, what worked well and, you know, what was really beneficial for my students and how they resonated with that. So that's something that I think the department's done a really wonderful job, having people like you, you know, who are coming fresh out of classrooms into roles within the educational support staff, be able to like bring those practical skills. There were so many hands-on activities as well that I just, you know, wouldn't have even thought of doing with my students for, you know, multiplicative thinking, for example, or additive strategies, or something like that. Stuff that wasn't even in my realm. And just being able to be showcased that and have access to the resources to bring it into my classroom was really, really beneficial for me.

Juliana:

And I think most people who would've done a similar professional learning to that would say the same thing. And the best thing about that one and others similar to it is that it reveals student thinking so well. So, yeah, they're great tasks, but we are learning so much about the students through those tasks. So even though we, you know, I say we try and include things that are really practical to walk away with, but they're really specifically selected so that not only are they helping students to learn something, they're also helping us to understand students' thinking really well, so we know what to do next. Yeah, that professional learning is one of many that does that really well.

Shannon:

Yeah, and it's that whole working mathematically, right? Like that's running concurrently alongside our content, for example. So just being so mindful of students and articulating what they're learning and how they're doing and the different strategies they're using. And, oh my goodness, across the class of 30, like, the different strategies that you'll get, it was just like a surprise every time.

Juliana:

Yeah and I mean, the higher you go up into primary, sort of the wider that gap’s getting. You still have students who are using those really naive strategies and you have to notice that and then figure out, 'Okay, how am I going to get them up to this sophisticated level that they should be at because, hey, I am sending these kids to high school and there's some things they really need to know.' So, yeah, noticing that student learning as soon as possible, and through tasks, like not always assessment for assessment's sake, just really classroom noticing and leveraging from that.

Shannon:

So, coming back to that, are there some specific strategies that you sort of like hold as your holy grail almost? So, ones that, some key strategies that you have in your teacher toolkit that you know that you can just whip out, K - 6?

Juliana:

Yeah, I think if, it's tricky to say one particular strategy, but if I could nail it in one sort of concept or teaching practice, I think the way that we question in a classroom is really important because it still forces the students to do the thinking, but we can really shape that toward exactly what that learning goal was. And I think a lot of people think that questioning is sort of like, 'Yeah, I can do that.' And, I mean, I thought I could do that. And then the further you delve into it and practise and plan, you realise, 'Wow, there's such great opportunity in here for assessment,' but also for like, you know, mathematics is about creativity and reasoning. So, the way that we ask questions in a classroom,

Shannon:

Those probing questions.

Juliana:

Yeah, really shapes like the attitude students have towards the task. So, you know, ‘What if you could change the number in this question, what would the number be?’

Shannon:

Yeah, those open-ended.

Juliana:

Yeah and giving them the, you know, that ownership to say, 'Hey, I can make this problem work for me. It's not this too-hard-basket question that I don't know what to do. I'm just going to have a guess.' My favourite thing is like the student who says, you say, 'What's 13 times 12?' And they said, 'Oh no, didn't learn that. Can't tell you.' I'm like, 'But what do you wish those numbers were? What do you wish those numbers were?' And then they'll say something like, you know, 'I know 12 tens is 120.' 'Well, that's great. What else do you know that can help you here?' So just really fine-tuning their minds into, ‘What do I know that can help me here? What's the same and different from something I've seen before? And then how does that help me?’ And then that sort of channels them into that whole concept of generalising understanding, which everything could be so much simpler if they thought about it as these generalised understandings as opposed to discrete collections of information.

Shannon:

Yeah, instead of compartmentalising all of the information, like, 'Okay, you say, oh, I didn't learn that, but let's, like, bring it back to multiplicative thinking. Like, how do you know the answer to 12 times 10? Like, what strategies did you use?’ Sometimes it's about bringing them to the realisation that, 'Hey, they actually did, they don't just know it, they've actually applied some mathematical thinking to get themselves there.’ And I love that journey for a student when then they have that moment, they're like, 'Oh, yeah, you're right, Miss. Like, I used this, this and this strategy and that's how I know the answer.'

Juliana:

Yeah.

Shannon:

That for me is like the golden moment as a teacher.

Juliana:

Yeah, and I mean, it seems simple. But it's really, like, I know I said questioning is probably a teaching practice, but even before that, like you've really got to invest in time to build that culture of, 'I can ask a question here. Like, I have no idea what she's saying. I have no idea what this problem is asking me. The first thing I should do is ask a question.' So having that culture and that can be in Kindergarten too, like, it's beautiful in Kindy because they'll ask you questions about things that are totally unrelated at the same time.

Shannon:

They've got a lot of questions.

Juliana:

They've got a lot of questions. But really channelling them to align with what your learning goal was, is something that takes a bit of time to set up in a classroom, but so rewarding to have that culture of curiosity. That culture of, 'I can ask a question, or I can get this wrong, and someone's going to help me.' Like this is what our classroom's about, and we're going to talk about it because that's the other reason I would say questioning is always in my toolkit. And I have those sort of key questions that you can always ask because you really want a classroom that is talking all the time. And I don't mean the teacher. I know we’re good at that. But I mean,

Shannon:

You don't say,

Juliana:

Where they're talking about very specific things related to what the goal was.

Siobhan:

So, is there a place that, you know, beginning teachers or teachers new to the career can go to, to, you know, get a list or set of questions that they can ask as part of their numeracy lesson?

Juliana:

Yeah, well, funnily enough, recently we thought the same thing. Like, why isn't there something that a teacher can just grab to ask really good questions? And, I mean, every teacher has their own little collection. But we as a numeracy team just developed a lesson advice guide around questioning. So there's specific questions that you can plan. And that's the other thing that we've really made prevalent in the lesson advice guide, is that you really have to plan your questions. Even though you can be a really skilled teacher and really are confident, planning your questions can really be beneficial. So, there's questions for before, during, after, questions that can help you to summarise the learning, questions that can help you, you know, connect student learning within a classroom. And then there's questions that are really beautiful for assessment opportunities as well. So, there's a lesson advice guide, but a lot of the stuff that I was doing back when I was in classrooms was from reSolve. They have amazing resources.

Shannon:

reSolve is fantastic.

Juliana:

Yeah. And it was focused on reasoning at the time and those resources are still available. We still refer to them all the time. And, like, they're simple questions of, ‘Can you give me an example of that? And then can you give me another one?’

Shannon:

Or justify.

Juliana:

Yeah, justify it.

Shannon:

Oh, my students, we had, there was a running joke in my classroom. 'We know, Miss, you're going to ask us to justify. You want to know how I got the answer?'

Siobhan:

So predictable.

Shannon:

I'm like, 'Yes, I do. Enlighten me.'

Juliana:

I mean, the same thing works in Kindy. So like, even though you’re probably referring to a

Shannon:

5, 6.

Juliana:

5, 6 example, I used to play 4 corners with my Kindys and say, you know, 'Which one do you think it is and why?' And then they'd have to convince each other to move corners and things like that. And it was an interactive sort of argument, you could say. And, like, that's just a really simple, ‘Do you agree or disagree? Why, why not? And convince me.’ If you just said to students, ‘Convince me.’ The amount of reasoning that they have to bring into it is so different to answer, move on, answer, move on, which is what we would typically see in a lot of classrooms. Because, you know, we all feel that rush to get through content and things like that.

Shannon:

Well, it all stems back to like we were talking about before, like that all those working mathematically skills, like they’re the skills that you're embedding through your lessons. Like, you were just talking about your reasoning, your justifications, things like that. And the things that students, those skills they need to apply to all strands,

Juliana:

Yeah.

Shannon:

All content areas.

Juliana:

And coming back to even communicating.

Shannon:

Oh yeah.

Juliana:

Getting them to reason using like, you know, show me. Like whether that's, you know, gesturing, or drawing, or using manipulatives in the classroom. Just that extra layer of representation not only supports their understanding, it gives us an eye into exactly what they were thinking. Because they could have the right answer for the wrong reason and reveal a really important misconception. So just asking that extra layer really reveals so much. But it also helps the other students in the classroom connect what they're thinking to what you are thinking.

Shannon:

On one of the opportunity classes that I had, I had quite a few students, because with an opportunity class, they sit, select, no, they sit an opportunity class test, sorry. And then they can come from neighbouring schools. So, I would often, in that Year 5 class that I had in particular, I'm thinking of, I had a lot from all different schools. So you don't really know, you just don't really know how they've been taught or where they've come from. They all come with different ideas, you know, like any new class, I suppose, but in particular when they've all come from different contexts, I suppose. I had a lot of students that were very apprehensive to use concrete materials when it came to mathematics. And I'm a big concrete materials, I was a big concrete materials teacher, loved a tangram, get the dominoes out, the cards any chance I get, like, loved it. I was, whiteboards, my go-to, loved them. Why? Because you're in Year 5. Why do you think you are above using a whiteboard? Show me you're working out, let's go. So, I was always a big believer in like mixing it up. But I had so many students and I spent a lot of time at the beginning of the year sort of setting up that expectation and teaching why I use manipulatives in the classroom. And showing them why it's okay to be able to use maths, use concrete materials, sorry, to understand numeracy. And it took a little bit of time. And the same thing was quite prevalent with apprehension when we would do, you know, per se, maths games. They'd say, 'Oh, but we're just playing.' I'd say, 'Okay, let's break it down. What strategies did you just use to win? Like, let's talk about it.' And it all boiled down to that communication. And I was really trying to get that out of them because a lot of the time they were really great. They loved an algorithm. But justifying and explaining and reasoning and sort of communicating that mathematical thinking was a challenge. So that was where I felt like I had to spend a lot of time and unravel those sort of misconceptions that they had about using concrete materials.

Juliana:

Yeah and I think that's like an important understanding for teachers as well, is when we remove concrete materials, that's because students have probably got to a point of abstracting that particular idea. But every time there's a new piece of learning, at the heart of mathematics is representing that and doing it in a concrete way, and then getting to some form of pictorial representational idea, then we can abstract it because mathematics is quite abstract as we know it. But pulling it always back and going forward and back through that whole like, sort of progression of concrete, pictorial and abstract is so important. And like you said, many teachers would think that that's, you know, K - 2 focused. But that's at the heart of mathematics and that's true to high school teachers that I'm fortunate now to work alongside. And see what Year 7 and 8 students, in particular, benefit from doing. And then they learn so much from seeing what, you know, we are doing in upper primary and then making those connections. And leveraging what materials are available or even representations like a bar model or something like that. But, yeah.

Shannon:

Very cool.

Siobhan:

I just want to say, shout out to all the primary school teachers. I just think that there's a lot of language around, you know, these subjects or these topics, and it's, yeah, quite inspiring to see like how much you both love your curriculum areas and how much you love teaching numeracy. So good for you guys.

Shannon:

Big passion. Big heart for the numeracy.

Juliana:

I think we’ve convinced her. We've almost swayed her into primary and

Shannon:

I'm trying.

Siobhan:

If I asked the question to you, what would you say to somebody like me, why should numeracy be my business? Why should I care and know about it in my context?

Juliana:

I almost want to throw a question back to you and say, do you realise how much numeracy you use today?

Siobhan:

Of course.

Juliana:

And how important it is to be positive about it? And that's why I think it's everybody's business. Because if it's nobody's business, it becomes a really tricky thing. And it becomes this hard thing that we just want to ignore and things like that. And I totally respect that. It doesn't always feel like a fun and confident space for teachers or students, but it can be.

Shannon:

Yeah.

Juliana:

Right? And you just have to tweak a few things and it's so beautiful and creative. And the students really, really engage as soon as you make those few shifts. And even if you just change your mindset, it changes the way you select tasks, it changes how much talk you embed. So, it's everybody's business because it's everywhere.

Shannon:

Yeah, I mean, we think of our day-to-day lives. And that was like my one thing that I loved doing with my students when they'd be like, 'When are we going to use this in real life?' And I'm like, 'Well, sit down. Let me tell you. Who went to the canteen at lunchtime? What did you have at the canteen? How did you pay? You paid with money. How did you know how much your item was going to cost? What strategies did you use for that?' So, yeah, absolutely.

Juliana:

Oh, even like I have a great story of people missing flights, and this is adults,

Shannon:

Missing flights.

Juliana:

Who run successful companies, who miss flights because of 24-hour time.

Shannon:

Yeah. Well, I believe it.

Juliana:

So, I mean, like, it's everywhere.

Shannon:

I believe it.

Juliana:

And it's really important.

Shannon:

Yeah. No, absolutely. I love that. And I'd like to talk a little bit more about, well, like as you said, numeracy can be that sort of thing, that can be a little bit scary sometimes. Particularly like even for me, as I shared earlier, like it was challenging for me as a student. But I think then coming into teaching, I was so focused on differentiating in the right way for my students so that they didn't feel like they didn't have, you know, or they weren't able to, they didn't get it. What would be your advice for a beginning teacher around differentiation? I know we could sit here for 3 hours and talk about it, but.

Juliana:

Honestly, I know this is going to sound like a really simple answer to a really complicated topic, but knowing your students and then knowing the mathematics.

Shannon:

Yeah.

Juliana:

Right? So having those 2 things. And then it's really about sequencing and bite-size chunking the learning, so that it seems manageable and right at their level, and then making those connections constantly. And the other thing I would say in terms of differentiation, that is probably the easiest tool in your toolkit, is to always go back to concrete and pictorial representations. And that's for every layer of learning. So even if you have your high-achieving students who always do want to default to the algorithm, that's going to trip them up sometimes. But also, it comes down to efficiency and having that conversation. So, there are different layers of differentiation, but knowing how to support your learners and eventually, you know, bridge that gap to that more sophisticated layer of understanding is really important. It's at the heart of what we do. Now our students know how they learn and know our content so that we can get them there.

Shannon:

Yeah, absolutely.

Siobhan:

So, I'm learning. Concrete representations are?

Juliana:

Concrete is something you can hold in your hand and manipulate.

Siobhan:

Okay.

Juliana:

So, you know, in a classroom, if we were teaching place value, for example, that might start with paddle pop sticks. Then we might move on to something like the MABs. You know those hundreds, tens and ones that you would've used? And then we've even got like something really similar for decimals that high schools can use, well, Stage 3 teachers and high schools can use. Because being able to connect our understandings to something concrete that we've manipulated is really important. But then being able to represent that because, you know, we want to get to this abstraction sort of phase and have that mental model. So we talk about mental computation all the time. But we can't expect this amazing, efficient mental computation strategy if we haven't modelled that. Even if it's like something like an open number line. So that would be a picture, technically. And, you know, your whiteboards in Stage 3 are perfect for that. And just showing how, you know, jumping between numbers that we know can help us to solve a problem more efficiently. So, there's a whole heap of things that sit in different contexts. So, like for addition and subtraction, you might do different things to multiplicative thinking as we were talking about before. And there's certain pictures that are more, they afford more learning than others. So that's another thing that teachers have to be conscious of. There are a lot of manipulatives available, there are a lot of pictorials, especially in this whole digital world. But knowing which one is the right one for the particular content that you are teaching is really important as well.

Shannon:

Yeah. Fantastic. I remember one year when we were doing whole numbers, I had a very advanced Year 6 class. And they were working well beyond Stage 3 outcomes for whole number. And I remember we were looking at like elevators and talking about like negative numbers and negative floors, and it just like opened up this whole world. And all I did was, I did a number talk and I put an elevator, and I had the different, like, floors up the top like in red, little numbers. And just the conversation that came out of that number talk, talking about negative numbers. 'Okay, where else, you know, do we use negative numbers?' They'd talk about temperature. Like those conversations, using a picture, sometimes you don't even think that it's going to sort of soar in the way that it does, which is a really cool thing to be able to, and I think it took me a few years to be able to have the confidence as a teacher because that can be a scary thing, because it's quite open-ended.

Juliana:

Yeah. Yeah.

Shannon:

And I think, you know, knowing your students and knowing where they can take it sometimes and then they go beyond, you're like, 'Wow. Incredible.'

Juliana:

Yeah, and that's an important thing that you said you know your students and you know where they're going to get to from looking at that image. So, you know, anticipating what you think your students are going to do based on where they're coming from and where you want them to get to is a really tricky craft, I would say. But a really important part of what we do so that we can do beautiful things and know that they're going to get us to that same learning goal rather than, you know, what we might default to because we are a little bit anxious of just letting it be a discussion.

Shannon:

Yeah, for sure. It was a big lesson for me as well, having students who were working beyond that Stage 3, those Stage 3 outcomes. I had to have an awareness. You know, I'm primary trained, K - 6 trained, but I had to have an awareness of my Stage 4 where my students were going to. And I think that is so valuable for you to be able to look ahead, because we do it really well, you know, K - 6. But it's like that jump into high school, we're not familiar with that. But it was really eye-opening and beneficial for me to see, you know, where my students were headed next and sort of like where they were sitting.

Juliana:

Yeah and I would say that's even important, even if your students aren't attaining above stage level in Stage 3, just having that like hierarchical knowledge. It's the same as knowing where your Kindy kids are going to in Year 6. And being able to communicate with them why this is important now, but also why it's important for what you're going to learn or how it's important in the world you're going to live in and things like that.

Shannon:

Yeah, and from a high school perspective, you know, would you sort of, when you have your Year 7s are you looking back at Stage 3 outcomes at times to sort of pin-point?

Siobhan:

Yeah, I would actually say more relevant to that would probably be like the cross-curricular aspect that you can embed, I suppose. Like a lot of people get subject specific, but it's like there are a lot of elements of numeracy in like a standard English lesson, for example, within assessments that we have, whether they're formative or summative. Like I've done many a project where I've asked students to add up or calculate a certain number or amount of things or look at a historical timeline and, yeah. I think I would like to do it, like a personal goal of mine would be able to embed it in a less tokenistic way, I suppose. But it's always good as a starting point.

Juliana:

I feel like, I don't know your subject?

Siobhan:

English.

Juliana:

English. Okay. I was going to say data is everywhere, right? And data is, like in our world at the moment, is so important. It's everywhere. And that's one of the things that people can really leverage across the curriculum. Including in our other KLAs besides, you know, always thinking numeracy and mathematics are intertwined. But, yeah, data's a really nice space to talk about things and just, you know, taking all the labels away from a graph, for example and just say like, ‘What are you noticing? What could this be about? What do you notice about the differences and things like that?’ And then you slowly reveal the labels and the axes and things like that. Just really simple across the curriculum and it's everybody's business.

Siobhan:

Yeah, I've actually found when I worked at a selective high school, the uptake for students taking extension mathematics in comparison to extension English, like the mathematics classes were higher. So, I actually tried to play to that. And I would do things like, you know, ‘How many times does the word, ‘hadst’, in this Shakespearean text come up across the whole text?’ Whatever it may be. But getting them to look at it from a data lens as well, it actually draws them into your subject. Because, again, I know my students and I know what they like. So, I think, yeah, you can use it to your advantage a lot of the time as well. So, if I was ignorant to the practices or strategies of numeracy, I may not have included that in my classroom. So I think, yeah, I'm an advocate for it's everybody's business.

Shannon:

And that cross-curricular?

Siobhan:

Yeah, it's of advantage to your students and to you as well, because I'm getting a greater result. My students are more engaged in my lesson as a result of me adding a bit of a mathematical lens.

Juliana:

Yeah, we had some Stage 3 boys who just wouldn't engage with writing when I was teaching Stage 3. So we did interest-based writing groups and we did sport reports. And one of the best things we did was they had to analyse data from a particular game or sport that they were interested in and then turn that into like a cool headline and then turn that into a paragraph and things like that. And that was a really nice crossover between data and writing.

Siobhan:

Love that.

Juliana:

Yeah.

Shannon:

Very cool.

Juliana:

And, I mean, I learnt a lot about sport in that. But

Shannon:

We’re all learning together here Julie.

Siobhan:

The cricket coach over here.

Shannon:

Yeah, yeah.

Juliana:

Cricket coach, of course. But, yeah, knowing your students, it's more than just knowing where they're at in their learning but also what interests them so that you can leverage from that.

Shannon:

Yeah. I love that. That's a really good like little example. I know you've just sort of off the cuff

Juliana:

It was fun.

Shannon:

Thrown us a story. But that's something that someone could do in their classroom.

Juliana:

Yeah, yeah.

Shannon:

It's very beneficial.

Siobhan:

Love that.

Shannon:

So now back into your role, your current role, as numeracy adviser, what do you love most about it?

Juliana:

Oh, there's a lot that I love. But I'm going to have to put it down to the people that I work with. It's so nice to work in a space where people are as passionate as a particular thing as you are and just so eager to learn. So, you would assume that we're in this space because we want to lead a particular thing, which we do. We lead it across NSW. We lead professional learning. We lead resource development and things like that. But we're also in this space where we want to learn about a particular set of evidence. And that mindset is so nice. And I'm with colleagues who are just trying to improve numeracy for every kid in NSW. That's the best part about my role, the people that I get to work with.

Shannon:

That's really nice.

Siobhan:

What about that larger impact as well? You know, what you were saying earlier, I can help, you know, or have some, a bit of numeracy intervention with these 28 students, for example. But now you're working at like a scale or system, like, have you seen your impact more broadly in this role?

Juliana:

Yeah, it's really nice. And you mentioned multiplicative strategies before. And one of the very first things I did when I came into this role was transform what should have been a face-to-face learning into an online-blended course because of COVID. And the amount of teachers that have passed through that course and change their mindset and the way that they teach multiplicative strategies is just amazing. And we have amazing evaluations. But even just, you know, you bump into someone, and they're like, 'I know your name,' or, 'I know your face. You spoke about multiplicative strategies, you know, during that learning from home period.' There were a lot of professional learning opportunities for teachers. So, I think a lot of people got to fine tune what they were doing at the same time as unfortunately working from home. And multiplicative strategies is something that has become, even though numeracy's like my little baby, multiplicative strategies is the other thing where, you know, people sort of associate me with that because of that course and all these other little assets that have come from that. And it just starts to shift the way that people do things. And like, I can't ask for anything more than that, is just to get inside teachers’ brains to say, 'Can I do this better for my students every time they go to do something?'

Shannon:

Yeah, how cool to see that like system level, like just stand back and be like you had a hand in, you know, developing that professional learning and so many teachers would come through that. And similar to me going through that professional learning, then I bring that back at a whole-school level. Like you just have such an impact on so many students and you don't really think about it, I suppose, when you're in the thick of it, creating the professional learning.

Juliana:

And it's tricky. I mean like classroom teaching is so rewarding. And at this level, it's actually a little bit hard to see the student impact directly. It takes some time. And most of the time, you're dealing with teachers and adults. So, yeah, there's been some nice opportunities to get out in schools and work with students and start to see that shift, which is really, really nice. But mostly, yeah, we’re working with teachers.

Siobhan:

Yeah. Nice. And what sort of practical tips would you give to a teacher who is looking to enhance the numeracy outcomes of their class? Like do you have a go-to hub or resource, or some top 3 tips? What are you thinking?

Juliana:

Let me think about this.

Shannon:

Because we’re big advocates for the Universal Resources Hub as a, you know,

Juliana:

That's great.

Shannon:

First cab off the rank.

Juliana:

That's been our little project for a little while. And that has some really great stuff inside of it. But I think the tricky part is, you know, we give teachers all these beautiful resources, but the craft and the thinking behind it sort of gets lost on them. So then, you know, they want to pick up a resource and use it and then what do they do next? So, I think my 3 tips would be, number one is really fine tune like top 5 questions and always have them in your bank. So, like something that is about same and difference. So, ‘What's the same? What's different?’ Something that really focuses on generalising. So, like, ‘Can you think of another example and another?’ So, I would encourage teachers and I got this from another podcast I was listening to a couple weeks ago, is to write down your top 5 evergreen questions and have them, because planning for questioning is so important, but we don't always have the time to do it. But if you have these 5 that always work and always relate to your, oh, not your, but to the heart of the definition of mathematics and numeracy, then do that.

Shannon:

And, you know what, go a step further, put them on the wall.

Juliana:

Yeah, yeah, 100%.

Shannon:

Let's put them up on the wall. A visual.

Juliana:

Yeah. 100%. You know, then the students have this expectation that they're going to be asked to answer these questions in this way, not just yes/no, correct/incorrect. The other thing I would say is to bring back your materials and your pictures, not your pictures, get your students to draw and represent their thinking.

Shannon:

Visuals.

Juliana:

Yeah, bring back those visuals at all stages for all content areas. So, so important.

Shannon:

If I was, you know, lesson planning, for example, thinking about my programming, is there like a go-to place that I can get really reliable, practical resources?

Juliana:

Yeah, like you said, the Universal Resources Hub is fantastic. The other thing we have are some lesson advice guides. So there's stuff on using number lines, there's stuff on questioning, there's one on the literacy and language for numeracy and mathematics, which we know is so important. So, there's a couple of different avenues. And then the other one that I would really say is helpful is we call it the Interview for Student Reasoning.

Shannon:

Oh, the IfSR.

Juliana:

The IfSR. I was going to say it as IfSR but I wasn’t sure if everybody would know.

Siobhan:

IfSR, of course, my favourite.

Shannon:

Siobhan is feeling very left out over here.

Siobhan:

No, I’m fine.

Shannon:

We can talk about it later.

Siobhan:

I love the IfSR.

Juliana:

I didn't use the acronym on purpose, just in case. The Interview for Student Reasoning. It's really fascinating because when we were out there filming and trialling that assessment, students thought that they were incorrect because we asked, ‘How do you know?’ They were so used to only being asked that question when they were incorrect, rather than you’re always expected to prove your answer and reason with it was really, really interesting. So, I would say have a look at that as a beginning teacher or a teacher who hasn't dabbled in that space before. And just choose some questions so you can really find out what your students are thinking and what misconceptions they might have. Because it's really fascinating that those questions have been really carefully selected around content areas. So, yeah, dabble in that space, and there's a whole heap of resources that go alongside them so that you can really target your teaching accordingly as well.

Shannon:

Fantastic. Thank you. I think they’re some really like practical things. Obviously, I'm a bit passionate about them all as well. I don't know if that's shining through or not.

Juliana:

Yes.

Shannon:

But I think, yeah, that's a really good place and space to start because it can be overwhelming. There are so many resources out there but the department does a really good job of like honing in on the really quality evidence-based resources for our beginning teachers and early career and current teachers, really anyone.

Juliana:

Yeah.

Shannon:

Because it's everyone's business as we've touched on.

Siobhan:

Agreed. I'm interested to ask you, before we close off today, what would you say to your pre-service teacher or early career self in your approach to numeracy? You know, what you know now, what would you say to that person then in your approach to numeracy?

Juliana:

Work really hard at the beginning of each year to get that culture right. Because you can't introduce a set of questions or a task, like the ones we've been talking about, if you don't have that culture set up in your classroom where everyone's expected to be able to reason with that particular answer at any time. And they're not, like, it doesn't feel onerous. It feels like, ‘I get to tell you why I did this hard thinking, you know?’ And that is true for any classroom, K - 12, I would say. So really invest in that time so that your students have those high expectations and want to talk about what they're doing. And it's not this closed off, correct/incorrect, sort of atmosphere.

Shannon:

Fantastic. Well, thank you so much for joining us, I've had a great time.

Siobhan:

I'm loving it.

Shannon:

It's been really good. Like, yeah, it's really wonderful. As I mentioned before, like you are so passionate and it really shines through. So it's lovely to have someone on the couch to talk all things numeracy. So thank you.

Siobhan:

We'll take you times 1,000 in our schools.

Juliana:

I was just saying, I might talk to Shannon offline after this for a little bit..

Siobhan:

Have a little one-to-one where you can talk about mental computation strategies.

Juliana:

And multiplicative.

Siobhan:

And multiplicative.

Shannon:

It gets me going.

Siobhan:

I've got 2 new strategies in my word bank now.

Shannon:

I'm going to do some quiz, a quiz, an assessment after this.

Siobhan:

I'll know it.

Shannon:

Summative, potentially. I'm thinking summative would be the right one.

Siobhan:

Concrete, pictorial, I've learnt it all.

Juliana:

Amazing. If that's all you walk away with today, I'm pretty happy with that.

Siobhan:

I've learned it all.

Shannon:

I love it. Well, hopefully our listeners got lots out of this as well. I know if I was a beginning teacher, I'd be hearing so many buzzwords, meta language, like we talked about before. But, you know, with our new curriculum and the new syllabus that's been rolled out, it's very much the talk of the town and the education space at the moment. So, it's very, it's pivotal. So, thank you so much for joining us. We hope you enjoyed this episode. If you did, share it with a friend, share it with someone you know who will benefit because numeracy is everyone's business. And we'll see you next time. Thanks for listening.

Siobhan:

Bye.

Shannon:

Thank you for tuning into the Teach NSW Podcast where we explore the dynamic world of education. Don't forget to follow, like, and subscribe to be notified when new episodes become available. You can find us on social media via our handle @teachNSW. Until next time, keep learning, keep teaching, and keep making a difference. The Teach NSW Podcast is a podcast by the Teach NSW team from the NSW Department of Education.