(Duration: 39 minutes 23 seconds)

Jackie Blue – My name is Jackie Blue and I'd like to begin this afternoon, we'd like to begin this afternoon by acknowledging the many different traditional lands that we're gathered upon to participate in this session. I would like to pay my respect to Elders past, present, and emerging and extend that respect to any of our Aboriginal colleagues who are joining us today. I'm joining you this afternoon from the land of the Dharug people and I'd love to invite you to share the lands you're gathered on this arvo in the chat.

We are joined by a number of leaders in our wider mathematics team this afternoon. As I said, my name is Jackie. We're also joined by Michelle Tregoning and Ayesha Ali Khan. Over to you, Ayesh.

Ayesha Ali Khan: Good afternoon everyone. Thank you so much for joining us for our first In Conversation session of our online lecture series. We'll jump straight into it, so over to you, Michelle.

Michelle Tregoning: Good afternoon everybody. Welcome to our first In Conversation of 2021. We're so excited to be joined by Associate Professor Catherine Attard, who is an associate professor in primary mathematics education and also the Deputy Director of Research within the School of Education.

I've been really fortunate to have worked with Catherine in a number of research projects actually over the years, I first came to meet Catherine in a project with Western Sydney University around student engagement, which is what we'll talk with her about today. But also, we did some really fun work with financial literacy with some students in Year 6.

So, Catherine, thank you so much for coming to join us today. We're really thrilled that you're here and we're really excited that we can talk to you about some of the things that we really love. Mathematics and engagement in mathematics with you and with our communities across NSW, so welcome, Catherine.

Catherine Attard [Associate Professor, Mathematics Education, Western Sydney University]: Thanks, Michelle and thanks for the opportunity. I just love talking to teachers about the stuff that I'm passionate about; engagement in mathematics. So, I really appreciate this opportunity.

Michelle: So we thought we would just start by asking you by way of introduction in a way of how did you come to research engagement in mathematics?

Catherine: It started when I was a teacher in a school teaching Year 6 for several years. And so, I started my very first research project in my Masters course and I looked at engagement and motivation of boys specifically, and ways to improve that in year 6 and then that led me to do a whole lot of reading around student engagement and it led me to my big research question around the influences on engagement as students make that transition. So yeah, that's where it started, and it still continues today.

Michelle: That's such a powerful entry point, isn't it? When you see something and get curious and want to learn more about it, It's also really powerful message. I think just in there too, Catherine and how we continuously learn. And, you know, even though you started researching this a long, well not a long time ago, but few years ago now, but there's still opportunities to continue to learn and grow and refine your understanding as knowledge and research shifts as well.

Catherine: As teachers, I think it's our responsibility to always be reflecting on the things that we do in our classrooms and conducting our own research. So, whether it's action research in the classroom or whether it's research data in a higher level, you know, as further study, I think it's really critical to develop ourselves as teachers.

Michelle: I've always liked how Bob Lingard talked about having research dispositions.

Catherine: Yeah absolutely.

Michelle: Catherine in education we typically about hear the word engagement, well, not typically but often we hear the word engagement being used synonymously with participation. From your research in this field, what's something you wish every learner, which in our view includes our teachers, our leaders, our educators, our communities, our students knew about engagement in the field of education? 

Catherine: I wish everybody knew how important it is, how critical it is and how much engagement actually impacts on a person's life, not just in the in the present time, when they are at school, but in their future lives as well. Jeff Munns made a comment in one of his papers around making the choice around freedom so you know if we're engaged, we're going to invest in what we're learning in, and it's going to give us choices and freedom later in life.

But if we are disengaged, that means that we make this choice, and sometimes we don't realise we're making the choice to opt out. And that then impacts on our freedom down the track. So, I think we need to understand how important it is and how it influences our lives. But we also need to understand the complexities around engagement and that it's not just participation. It's much deeper than that.

Michelle: Do you have a model of what that looks like exactly?

Catherine: I certainly do. Ok, so this might be a good time to actually to just step into a diagram, a way that I think about engagement. And this is not the model, I think this comes before the model, so I'm just going to share my screen.

[On screen: Defining engagement. The three dimensions of engagement are: cognitive, operative and affective.]

Catherine: I think first of all it's more of a definition, so if we think about engagement as not just being ‘on task’ but much deeper than that and being ‘in task’ and being a multi-dimensional construct so there are three dimensions that come. These dimensions come from my research, but also the research of others and basically the first one is that cognitive engagement. So, students thinking really hard about the mathematics and reflecting on the mathematics and on their learning of the mathematics.

Second dimension is the operative, so, that's linked more to the participation element, and it's not just participation with others or with concrete materials. It sits around participating with the mathematics itself, so, that's really critical, and you see in my PowerPoint slide I've written group discussions, practical, relevant classroom activities, but also homework tasks because often we do really great things in our classrooms, but that doesn't translate into the tasks we ask students to do beyond the classroom and you know, homework implies it's working at home, but also it should be work around the home. You know, highlighting the mathematics that's in students' everyday lives is really critical and sometimes we miss that really important opportunity to link mathematics with real life and make it relevant to students rather than, you know, homework as almost a punishment. And you know, just repetitive tasks. That sends really negative messages about mathematics.

That third dimension is the affective domain, and that's really important. It's not just about liking maths, it's about valuing the mathematics, so we want our learners to be able to visualize themselves as users of mathematics in their immediate lives, but also in their future lives. And this is one of the big challenges in maths education, is that children can't see themselves using mathematics down the track. They opt out, they then opt out in senior secondary years, and then that closes up a whole lot of opportunities for them in their lives beyond school. So, you asked about a framework and I do have a framework that's split into two sections and it's if you could think about it similarly to the way that we think about Maslow's hierarchy of needs. At the base of the hierarchy is pedagogical relationships, so those relationships that we developed with our students... oh, I forgot to show you my moving diagram there around the three dimensions of cognitive, operative, and affective.

[On screen: Diagram of overlapping circles to indicate the relationship between operative, cognitive and affective elements]

Catherine: When those three elements come together in the classroom, that's when we get substantive engagement with mathematics and a really simplified way of thinking about this is having students thinking hard, working hard, and feeling good about learning mathematics, and that's translatable to teachers as well, and the way that they teach in the way that they are engaged in the teaching of mathematics. We want teachers to be thinking hard, working hard, and feeling good about teaching mathematics and knowing that they can influence students for the long term. So back to my framework.

[On screen: The Framework for Engagement with Mathematics: Pedagogical Relationships. In an engaging mathematics classroom, positive pedagogical relationships exist where these elements occur: teacher awareness, pre-existing knowledge, continuous interaction, constructive feedback and pedagogical content knowledge.]

Catherine: I was saying that the foundation for engagement is pedagogical relationships, and positive pedagogical relationships. So, you know, in a nutshell, it's about how well we understand our students as learners of mathematics, not just as individuals but as learners, and being aware of their needs, understanding what they bring into the classroom in terms of past experience, cultural experience, all of those sorts of things. Providing opportunities for that continuous interaction. So being able to have those conversations with your students about mathematics and allowing them to have conversations with each other about mathematics, constructive feedback is absolutely critical, and, I mean, feedback is probably not the right term for what we do.

We need to be feeding back, but we need to be feeding forwards as well, so that's absolutely critical. And this is a really important one: Having the right pedagogical content knowledge. So, really as teachers we need it. We have a responsibility to know the mathematics, to understand the curriculum, to understand how students learn the mathematics and the best ways of teaching all the elements of mathematics. So that's absolutely critical. And those are those really important foundations.

Once we have that once we know our students, we know our maths, we know how to teach it, then you bring in all the bells and whistles around, you know, the things that we do in the classroom, those pedagogical repertoires that we bring into our classroom and the way that we work with our students. So, tasks that are challenging and those challenging tasks have to be challenging for every learner in our classroom. But understanding that what's challenging for one student may be out of reach for another, so being able to find tasks that are able to be differentiated, or tasks that self-differentiate like rich tasks are really important. Tasks that are relevant.

So, where we can, linking maths to real life. And we know not all mathematics is easy to link to real life. So also promoting a love of mathematics for itself. You know, number puzzles, all sorts of things. The joy of finding a pattern, whether it's in spatial concepts or whether it's in number, is really important. Sometimes we should just enjoy mathematics for mathematics, not just because it's something that we do when we go shopping, or in cooking and all that sort of thing. You know, giving kids choice is really important in terms of engagement. A variety of tasks. Kids get sick of doing the same thing day in and out you know, and I'll use the example of textbook lessons. You know nothing could be more boring or even having a subscription to an online maths program, which is the same day in, day out. I mean that is really detrimental to student engagement.

Having deep conversations about mathematical concepts and also student-centred technology, which I can talk about a little bit later on in a little bit more depth. So, students are engaged with mathematics when it's a subject they enjoy learning, they value maths and see its relevance and they see its connections, and I think something that's really important to say here is that students are not going to see connections on their own. We actually have to help them see those connections and so one of the most important things about engagement in mathematics is how teachers interpret and enact the curriculum. So yeah, I think I think I've answered your question, Michelle.

Michelle: Yeah, you definitely have, and I think one of the things I found really powerful for me, Catherine, is actually the power of having a really rigorous research-based framework that you can trust, and what a framework like yours offers us, is an opportunity to make sense of those things that are working for students, but it also then allows us the opportunity to reflect as well and look for, where are the opportunities for me to continue growing my practice? Where are my, you know, blind spots? Because we all have them, and it gives us a common language, you know, for those of our schools and our communities to be talking about practice.

Catherine: Absolutely. And you know, even when you do get a framework as a teacher, I think it's really important to not see it as something that's fixed and I still don't regard my framework as perfect because there are things that I've been thinking about in recent times that either need to be added as a different element or tweaked because you know, as an example, I'm thinking about student agency with mathematics and there is some research around agentic engagement, which doesn't really fit with the way that I'm thinking about it.

But I'm thinking about how students use mathematics, because of their engagement, to do something in the world to change the world and make it a better place. So, giving them agency. And I think that is either a product of this framework. Or it needs to be woven into the framework and I, you know, it's something that I'm struggling with at the moment in terms of where it might fit, but I'm really interested in that, it's giving kids agency and it's an interesting concept.

Michelle: I was reading something last week from the National Council for Teaching Mathematics, the NCTM, and I had not heard that phrase this before, but the idea of students being knowers, doers and sense makers in mathematics and that link between agency and identity and how critical that is for building mathematical understanding.

Catherine: Absolutely, yes, yes sense makers. But also, I think added to that is problem solvers and problem finders. And that where the agency comes in, you know, we're using the mathematics to actually, find problems in our world and actually solve them before they become critical. It's really interesting, Like, COVID has helped me think about well, you know, the relevance of mathematics and how a lot of the way that our experts in the world have solved or have begun to deal with this is through mathematics. So, there's probably never been a better time to highlight how important understanding mathematics, and be able to do mathematics is, in terms of solving world problems.

Michelle: You'd make our secondary folk really happy in particular with that because they would then talk about the role of mathematical modelling inside as a really important problem-solving strategy for all of us actually, as we navigate online. But Catherine, you sort of alluded to the idea of the role of engagement and technologies, and I, I wonder if you could talk a little bit more to us about the role technologies can play in supporting engagement of students in mathematics.

Catherine: Technology can work both ways. It can lead to disengagement or it can lead to engagement. What we found in more recent studies is how technology has been able to support and promote pedagogical relationships, which is the foundation of engagement as I said earlier. So particularly in secondary schools, this is pre COVID and then during COVID, what we found was that a lot of schools are using learning management systems as a repository I guess for resources, for teaching and learning resources, but also as a way for kids to, I guess, keep their work, keep a record of their work, a way that teachers are starting to engage with students in terms of marking their work, giving feedback, and what that's done, it has it's opened up a whole world for teachers and for students and some of it's positive, some of it's negative.

In terms of positive aspects, this technology has broken down the walls of the classroom and given students access to the mathematics resources and sometimes to their teachers beyond that timetabled classroom lesson, which is really important. That does a couple of things. What that does is give the message that mathematics is not bound to the classroom, so that's really critical. It's allowed teachers to get to know their students in a different way, and that was really enhanced in many cases during COVID where teachers used technology to actually keep in touch with their students, etcetera, during that lock down period. But then again, you know that was detrimental to others where it wasn't used well, so, I think the key message here is when you're using technology you need to use it very carefully and very thoughtfully. And, look, another way that technology does enhance engagement, is it offers new ways of seeing mathematics and working with mathematics.

What we've found is in primary schools it's used very differently to secondary settings. In primary schools, teachers tend to use things like screen-casting, more generic tools to capture mathematical thinking, which is absolutely brilliant. It's something that, you know, we couldn't do as well before having all of these mobile devices in our classroom, so asking students to actually record their thinking as they're working is quite powerful.

You know, prior to that, we had kids writing in books, but we couldn't capture what was going on in their heads. So, you know, that allows teachers to actually develop those pedagogical relationships at a deeper level because they can see what's going on in their heads and are able to respond to that. Secondary teachers are tending to use it either through those learning management systems, but also there are more dynamic tools that they're using, and so they're actually focusing on providing different representations of mathematical concepts where that doesn't happen as much in primary.

You know, one of the negatives is that sometimes primary schools subscribe to programs because they have the technological devices there, and these programs almost lock them into teaching in a certain way. So, and those programs don't always reflect best practice either, or good mathematics. So, it's really critical that teachers are critical of what they do or what they use and how they use it, and having that really strong purpose. I do have another framework and I don't know if this is an appropriate time to show you.

Michelle: No, please do because that was going to be my follow-up question because I know that you also just recently published a book with Professor Kath Holmes at Western Sydney University about optimizing student engagement and technology in enabling mathematics engagement. And I know there's a framework in there and a pyramid, and we would love you tell us more about that as well.

Catherine: It's one of my favourite things at the moment. Look, I have to say that doing research is really satisfying when you can come up with frameworks that are useful for teachers and schools and also useful for other researchers as tools for analysis. So, this framework, I'm really proud of, and it came about because I've always been concerned about the struggle of teachers having to deal with new devices or new software one at a time, individually.

So, you know, IPads came out, how do we use these IPads? What's the best practice? Whatever. And my goal in life is to prepare teachers to teach with any type of technology at any time. Just understanding what are the critical elements that we need to consider before we use that technology. So, Kath and I came up with this pyramid and I've got an actual model here.

[On screen: Catherine is holding a 3-dimensional pyramid model]

Catherine: Isn't it beautiful?... and so, what the pyramid is, and I'll show you a PowerPoint slide in a minute, but basically, we've got the base of the pyramid, which illustrates the influences on technology use. And what it does is acknowledges that every single school and every single classroom is unique, which means there's not a recipe book for effective technology use. It's about understanding your context, your community, your culture, and the commitment of the school before you even think about using it in your classroom.

If you understand this, and the school has a good idea of where it sits in terms of the influences, then things can be done to improve things within an individual classroom. Then we've got the sides of the pyramid. So, I'll show you my screen because that might help.

[On screen: The Technology Integration Pyramid (Mathematics)]

Catherine: So, there's the base in the top left-hand corner and then we've got the four elements that I think every teacher needs to consider each time they plan to use technology. And, you know, it might sound clunky if you have to think about four things every time, but what it does if you start to do it that way then it builds a habit and it becomes just part of the way that you practice thinking about these four things and, look, there's no particular order, but I always think that it's important that if we’re teachers of mathematics, to begin with the mathematics. Because sometimes that gets lost in technology use.

Sometimes we get distracted by the technology, whether it's the device or the software, and you know if we get distracted, imagine how the students get distracted, so making sure that we embed this technology in good practices. It's not just all about the technology either, so focus on the mathematics. What's the mathematical purpose of this lesson? What's the mathematical purpose of using this technology? That's really critical. We then have to look at the tools that we have at hand and how they can actually enhance what we would normally do. So how can they enhance how we present a mathematical concept or how students practice using or learning a mathematical concept?

So, I'll give you an example of a way that I saw a teacher in a school news technology where this teacher really had nothing in that classroom except an Interactive Whiteboard and her personal mobile phone. So those were the tools she had. This was a fairly new school. Low socio-economic area. And you know, severely underfunded, really, in terms of technology. And so, this teacher was in Year 2 I think, or Year 1, and she basically had her Interactive Whiteboard and she used it in ways that were absolutely awesome. She used an app called Clicker, for example, to do a quick assessment of the students in her class where they didn't need individual devices. They just held up this code and it was awesome, highly engaging for the students but also she used her mobile phone during the middle part of the lesson where the kids were working, to talk to students about their mathematical thinking and do quick recordings of their thinking so that she had evidence. And you know, gathering evidence is something that's quite challenging for a lot of teachers. You know, sometimes with mathematics teachers think that you know if I have to gather evidence of work or assessment data that has to be pen and paper.

But a quick audio recording is sometimes more effective because we get at working mathematically, so that was a really good example of how this teacher looked at the tools that she had, and the way that she could best use it in the classroom. She also had kids using the Interactive Whiteboard during group time, so you know groups would come up and use an app on the whiteboard, and I guess the other end of the spectrum was, you know, a teacher that we observed in an affluent area in a very expensive private school, where she had a maths lesson that was making use of Spheros, IPads, of the Interactive Whiteboard, you know, everything, all the bells and whistles, but she did it in a really clever way in a really rich task where the technology wasn't a distraction, it was a seamless use of technology so the kids weren't distracted by the devices because it was something they used every day, and the focus did remain on the mathematics.

Of course, student engagement has to be a priority and so we have to think about those three elements, you know. Is this task using technology going to be challenging for every child in my class? Is it going to give them opportunities to interact with the mathematics or interact with each other? You know, there are questions around that that stem from, you know, the number of devices that I have and is it best to have a one to one program? Or is this task better if I have kids working around a device so that the conversation is happening and there's reasoning happening and communication happening. So, it's, you know, there are a lot of complexities around here, and of course the last side of the pyramid is the pedagogy. So how am I going to implement this task and the technology? What practices am I going to embed it in? So, I'll give you an example of you know, basic use of IPads, which is pretty typical in primary schools, where a teacher might find a maths app and use that with their students, and so, in group time the kids might engage with the app, but the teacher doesn't really know what's happened within that.

You know, the teacher might not understand that thinking that's happening, or the challenges that have happened and so to embed it in good pedagogy might mean that that teacher might ask the kids to take a screenshot of something. And then do a reflection based on that screenshot and have some really good reflection prompts based around that app or the mathematics in the app. Or even asking the students things like, you know, what mathematics did I need to know to be able to engage effectively with this app? You know, what advice could I give another child that was going to use this app tomorrow in terms of being successful? So, it's about how the teacher embeds that technology into the broader practice rather than the technology itself.

Michelle: That reminds me of John Mason, in one of his papers where he wrote once that it's not just enough to have challenging tasks, or rich tasks but the teaching has to be rich.

Catherine: Absolutely!

Michelle: And then, you know, it's not just enough to have any sort of technological tool, but the teaching around the tool also has to be rich to allow it to enable and empower further engagement of students.

Catherine: And, you know, something I often say to teachers is that you can take an extraordinary app or an extraordinary task and make it really ordinary. On the other hand, you can take an ordinary task or an ordinary app, and you can make it extraordinary. It all depends on you. It all depends on the teacher understanding the mathematics, recognizing the mathematics, or the potential mathematics in a task or an app or whatever it is, and being able to maximize the potential of a task.

I mean, you can take a very ordinary photograph and turn it into an absolutely fantastic maths lesson. But you could just go, "Oh, look, here's a photo." And do nothing with it. So, so it's about really developing teachers and the way that they interpret, as I said before, interpret and enact the curriculum. And I truly think that the curriculum that we have is a gateway to engagement. It absolutely is. When you think about working mathematically. If we address working mathematically and use it as an umbrella over everything that we do in a math classroom, you can't not engage the students. Likewise, with the general capabilities. So, there are these lenses that we need to look through. These layers of lenses to get to the mathematics and the general capabilities, to me, are key in terms of engaging and relevant mathematics.

Michelle: I think my favourite sentence in the syllabus, I almost know it off by heart, and I might get it wrong. As students develop understanding and fluency in mathematics through inquiry, exploring and connecting mathematical concepts, choosing and applying problem solving skills and I think it also talks about techniques, communication, and reasoning in there. Look there's a lot I like in the syllabus but that's actually one of my, is that too nerdy to admit I have a favourite quote in there?

Catherine: No, no, not to me. From one nerd to another. And I like how you mentioned problem solving because I haven't talked about problem solving yet, and you know one of those things I often show teachers is those concentric circles, that diagram, that problem solving is literally at the core and problem solving needs to be at the core of how we teach mathematics. And I can't say that often enough. I guess one of the challenges is that we need teachers to really understand how to teach problem solving, and what successful problem solving looks like.

Michelle: That distinction too between how to teach problem solving, but also how to teach through problem solving.

Catherine: Absolutely. Yeah, yeah, and that's something that I really promote very heavily is teaching through problem solving rather than teaching for problem solving or teaching about problem solving.

Michelle: So, Catherine, we've got Michael Loy and Jackie Blue who have been fielding questions from our teachers around NSW this afternoon, so I'm going to hand over to Jackie and Michael.

Jackie: One of the questions that's come through the chat today is, ‘What are some of the mathematical examples of what engagement looks like when it hits one or two of those engagement domains, but not all three’?

Catherine: Ok, so an example might be playing a maths game. So, kids initially are engaged because the game is competitive, it's a bit of fun...and it's operative, so it's interactive. so, you've got the operative domain and the affective domain. But if the questions in the game are really easy, and the kids don't feel that challenge, that cognitive challenge, then they will come out of that lesson and forget what they did.

You know there won't be substantive engagement. If, though, on the other hand, the game has challenge embedded within it, and I'm thinking about as an example, my MABBLE game. That's quite challenging in lots of different ways, and the kids have to think really hard when they're making their moves. So not only is it a little bit competitive, but it's competitive in a gentle way. It's interactive and there's lots of conversation, but also the maths is challenging. Then they feel good about it and they want to come back and do it again. But if it's too easy, you know that's when you don't get the substantive engagement.

Michale Loy: Catherine, thank you. So, you just mentioned that games are one of those really nice effective strategies to really build substantive engagement inside of mathematics, have you got any other strategies that you could name, or list off that will help teachers get involved with some of this work?

Catherine: Look, I think a good strategy is to think about as I said before, teaching through problem solving and picking good problems. So, picking the right type of problem where all the students have an opportunity to achieve success. So, I think understanding your students, picking the right problem and then setting them up in the right way in the classroom is really important. So, there are times when you need to group students so that there's peer mentoring happening and there are times when you might group them according to ability. depending on how you're presenting the problem, whether it's differentiated or not. So, it comes down to a good task or a good problem, perhaps a maths investigation, and making sure that you set up the students in the right way so that there is opportunity for success.

A really nice one that I did the other day in our class and I think I tweeted about this, because I did an investigation with a Year 4/5 class and it was just a question around, ‘Do right handed people have bigger left feet?’ So, immediately, that was engaging because it was about them. Ok, so the students would like, oh, my feet, and they started to look at their feet and take their shoes off and do all sorts of things and then we had this really nice conversation about well, how are we going to work this out? What are the things that we need to measure? What do we know about measurement? How are we going to present the data so that it makes sense? So, this really simple question led to a whole lot of mathematics and not only that, the kids started to wonder about things. You know, what's the average shoe and foot size in our classroom? Was the difference between the shoe size and the foot size? And a whole lot of things.

But that to me was really engaging for all the students because even the people who the kids who are less able or you know was would struggle with the mathematics typically were able to access this task and were able to achieve success, even if it's just by measuring their foot and knowing, you know, where to place their foot against the ruler. Because the rulers didn't start at the starting point, there was a bit of a gap, so we had to talk about, well, how do we make an accurate measurement? And yet the high achievers were also very challenged because there were things embedded within that simple question that required a bit of complex thought, particularly around presenting the data you know, we talked about.

Well, ok, we've gathered all the class data after the groups had their data. And we said, ok, how are we going to present this data? What kind of graph might you use? And you know one of the higher achievers said a line graph and I said ooh, a line graph, let's think about that, you know, is it the type of data that we that is appropriate for a line graph? So, there was challenge embedded in this very, very simple task.

Michelle: I find that example really powerful because I just was taking some notes as you were talking about all of the different potential learning or mathematical goals that you could have the students inside of there, right? So, they could connect to data or measurement, aspects of whole number, addition, subtraction, multiplication, and division. Aspects of reasoning and communicating and problem solving.

And it reminds me of that idea. I think I heard it from Jo Boaler around when you broaden what the mathematics can be inside of a task, you broaden the space for every child to have an opportunity to learn and every child to have an opportunity to be successful. And I think that's a really great example about from colleagues across NSW.

Catherine: Yeah, and you know, I was thinking about this only yesterday. You know sometimes it's the simplest things. I don't think we should be reliant on resources such as books so much, you know, subscriptions to things except Maths 300, which I love. But you know the best tasks come from what's around us. Either in our world or in our classroom, you know.

They're the best things, the simplest things. It's about recognising where the mathematics is, how we can access it, and, you know, you could do that task for the secondary classroom and what would be different would be what the kids get back to you. So, you could do it in kindergarten, you could do it in Year 8, Year 9, and what you would get back is different. And that to me is like the perfect task. But it's only good if I recognise the value of it as a teacher.

Michelle: Well, Catherine, we could talk to you for a really long time and keep going, but to be honest, I now need to know whether people with right hands have larger left feet?

Catherine: I won't tell you what we found.

Michelle: We will get back to you, maybe on social media and in other forums so that you know what we discovered you in our work.

Catherine: Excellent, I look forward to that.

Michelle: Thank you so much for your time this afternoon. We're so grateful that you made time to talk with us and share your experiences and knowledge with our teachers across NSW. There's a whole lot of things I could summarise, but I think I'm going finish with maybe two points of summary, Catherine.

One being about how knowledge and understanding evolves constantly over time, and that even things like frameworks shouldn't be used so they're rigid and they crack, but they should be used with flexibility to really derive their power in our work. What that really speaks to me is in your role, your position I think, or your ethos actually, probably is a better word of being a lifelong learner and how what a great role model that is, I think our teachers across NSW.

And the second big point, is the idea that it's also not a recipe book. That you have to look to your context, you need to understand your situation in your school environment and then use all of these tools around you to make informed and intentional decisions to best support students in your context, that you look after, that are with you this year, in this space. Did I do alright?

Catherine: You did a great job. As always.

Michelle: Thank you so much, Catherine, for your time. Thank you everyone. To all of our colleagues in the field that have joined us today, we look forward for our next ‘In Conversation.’ Have a lovely afternoon!

Ayesha: Catherine today spoke about problem solving as a central idea in mathematics. Our next ‘In Conversation’ is with Doctor Kristen Tripet and that is in Term 2, Week 3. So, Thursday the 6th of May at the same time, and she will share insights on another big mathematical idea, reasoning. So, looking forward to you joining us then. Take care and see you then.

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