School leaders play a vital role in providing every student in New South Wales public schools with a great education and the best start in life. They have a positive impact in classrooms and on their staff. They guide teacher development and engage their communities. Here at the NSW Department of Education's School Leadership Institute, our mission is to support all NSW public school leaders by providing world-class, evidence-informed leadership development programs and resources.

Our podcasts will explore the key issues and challenges of school leadership. Hosted by Joanne Jarvis, the director of the School Leadership Institute, tune in and listen to our guests and colleagues share their expertise, insights and wisdom on leading with purpose and impact. Welcome to our Leadership InFocus series.

Joanne Jarvis

Hello and welcome to episode 23 of the Leadership InFocus podcast series. I'm Joanne Jarvis and I'm the Executive Director of the NSW Department of Education's School Leadership Institute. I'm joined by Eddie Woo. Eddie leads the Teacher Growth team, a statewide instructional leadership initiative for the NSW Department of Education. Alongside his work delivering pedagogical learning and supporting pre-service teachers as a Professor of Practice at the University of Sydney, he continues to teach mathematics at Cherrybrook Technology High School, reflecting his deep commitment to practitioner-led professional learning.

Together, we will explore how educational expertise can be deliberately developed and mobilised to strengthen mathematics teaching across a school through deeper collaboration, more meaningful feedback and richer professional learning. So welcome Eddie.

Eddie Woo

Thank you so much for having me. A pleasure to be here.

Joanne

It's a pleasure to have you here, Eddie. Before we jump into the questions, just to set the scene. Educational expertise is about strong pedagogical knowledge and teaching practice, the knowing how students learn, how to teach effectively, and how to translate that across a whole school.

And research tells us this is built through collaboration with leaders learning alongside their teachers, and focusing on what's actually happening in classrooms. And this is especially important, I think, in mathematics, where teacher confidence and expertise can vary considerably and have a decisive impact on student learning. And the knowledge, priorities and actions of leaders is really do shape the quality of teaching and the outcomes that students achieve.

So with that in mind, Eddie, tell us about where your passion for mathematics came from and why you're still teaching as a mathematics teacher.

Eddie

Jo, when I think about that question, I'd probably position this with two different answers directionally. One in front of me and one behind me. So I think about in front of me all these brilliant teachers, educators, mentors, leaders who I've grown from and have developed me over the years.

I've been extremely thankful to have people who've modelled for me what effective and inspiring teaching and leadership look like. And that's always been something that I aspired to, which I always thought would be incredible. And what a privilege to be able to take up that mantle myself. And that's something which I've seen ahead of me, that I followed in the footsteps of brilliant other leaders who've mentored me, coached me and built my capacity.

But then I also think about what drives me from behind, if you like, to change the metaphor, the wind in my sails. And I know we're going to come back to this many times throughout the conversation, but it's really about the students who I've taught over and over again, who either have excited me by the possibilities of what it's like to be a teacher and leader in schools, and for me to realise by looking at the influence I get to have on them and saying, wow, this is what I can be capable of if I'm doing my work effectively. What a difference it makes, not just in academic outcomes, but in life outcomes.

And equally, I think it's important to acknowledge there’ve been plenty of moments where seeing those students has actually pulled me up short. And as a leader who's constantly learning, I've realised at different points throughout my journey, here's a place where I definitely need to develop. There's a lot more strengthening, there's a there's a deficiency in what I'm doing here and I owe my students to do that work, to put in that discipline, to learn broadly, acknowledge where I've got some areas that need development and that has always been, I think, the strongest motivation for me to continue in that journey, and help develop other teachers along the way as well.

Joanne

You've covered so much turf just in that first response. I mean, you've talked about the importance of mentoring, which in my own career has been so critical, all these years later, I still stay connected with my mentors. And you've also talked about the connection of mentoring and your ability to reflect on your own practice to strengthen your educational expertise.

You know, that sense that we never stop learning, we're always growing, we're always trying to improve. And also, you've connected that back to your moral purpose for, you know, what is it that the students really require from me? And how can I deliver it the best way I can?

So let's explore a little bit more then the notion of the expertise in mathematics and how, as a leader in a school, you support the growth of expertise not only in yourself but in the colleagues that you're leading.

Eddie

The first thing I'd say is that even though I know I began my teaching journey thinking about developing in the way that you've just described and becoming an expert teacher, I very much looked at it through the lens of, very much like the syllabus. I'm thinking back to a few syllabuses ago where the mathematics service was broken into two columns, and it was students will learn about, and students will learn to.

So there was conceptual knowledge, and then there were these skills that we wanted to develop. Now, of course, that's a very helpful lens to use. But I've come to realise as I've matured as a leader and I'm still plenty of room to grow, that knowledge and skills are only two of the dimensions that that are important here .\I've read a lot and seen a lot and amassed a lot of deeper understanding of what I'm doing. And I have deepened and broadened my pedagogical toolbox, as it were, for all of the different things that as a teacher, I want to use my professional judgement to balance in the classroom based on what concept and skill we're learning and what my students need at that particular moment.

But I've come to realise more and more Jo that there's this relational aspect, that knowledge and skills just doesn't really cover. And of course, teaching is at its core, it is this wonderful learning relationship between us and our students, between us and our classes, between us and our colleagues and our leaders.

And for me to think about becoming an educational expert only through the lens of knowledge and skills and me developing that as an individual, I think, misses out an important part of now the lens that I take and with the team that I lead, it is very much about understanding where people are at in the dynamically shifting, journey of expertise and saying, where can I take you to the next step? Why, in this particular setting, in this particular context, is this a skill or a strategy we really want to master, or something that we haven't quite learned how to do successfully or effectively? How does that then match up with the research and evidence base that that we need to grow at that point of need?

So these are the things that are at the foreground of my mind when I'm thinking about a school leader who's helping to build the capacity of their staff.

Joanne

You've really defined andragogy in practice, haven't you? Because we talk about the pedagogical needs of students and that's pretty much laid out in the syllabus. And we, you know, our job as leaders and teachers is to interpret that.

But what you've really highlighted is the importance of leaders understanding their staff and recognising that andragogy is about saying, what is the particular problem of practice that you need to be addressed right now? And how can we develop that with you? And you're more likely to get the buy-in from staff when you do that. Has that been your experience as well?

Eddie

Absolutely, Jo. I mean, I think about the fact that there's that wonderful quote, who dares to teach must never cease to learn, which I know you know and you prize. And I'm sure many of our listeners have heard as well. But I want to acknowledge that, that's something which I think resonates with so many people, but it doesn't, the quote itself, I mean, it's very pithy and delightful, but it doesn't at all spell out if I'm a leader and I want to engender that attitude and that posture in the staff who I have the responsibility to lead, how do I do that?

I mean, it's obviously not simply by saying, I know what I want them to do to help my students. They don't know how to do it yet. I'm just going to tell them and then hope, cross my fingers that everything will work out. I mean, that's such a, I'm using that as an example because as an early leader, I didn't know any better, and I wondered why my leadership approaches were just not gaining traction, buy-in as you mentioned.

And that's why I think that relational understanding, being able to take that time to get an accurate view of reality, of what's going on in my colleague’s classroom, why is it that they're perhaps struggling with a certain thing. Or even after I've explained to them, here's what I think might really help, they might, for one reason or another, not want to adopt that practice or strategy.

What's going on underneath that? You know, as Vivian Robinson says, what's the theory of action that's driving the decisions that a teacher makes? I used to beat my head against a brick wall, not understanding, not knowing how to do that work of comprehending what was going on inside of a teacher's mind and heart. And I view that work as more and more important the longer I'm a leader.

Joanne

Well, I'm sure that as, our listeners, listening to your wisdom here, you have identified a problem that many of them would be grappling with right now. And, you know, that is, how can they work with a staff to bring them on board to really improve practice when perhaps they’re confronting some resistance?

And you've just talked about understanding the theory of action which is such an important component of that. What's your best advice on, on how they seek to understand that theory of action and what's underpinning the perception of resistance? Because it's not always, in my own experience, it's usually not resistance per se. It's a level of angst about what, you know, they're being asked to do.

Eddie

I think about the image I met, I can't remember how many years ago it was Jo, but it was in a very different context. And it was the anger iceberg. And it was me thinking about, you know, is it, you know, related to trauma informed practice with our students and so on, and what we may see above the surface. And in this context, we're talking about perhaps our teachers who are resisting the idea that we, as the leader, want to be implemented in the school, but there's so much going on underneath the surface.

And as you point out, probably resistance is I mean, that's such a surface way of looking at it. And it can be apprehension. It can be change fatigue. It can be frustration or just a lack of the mental and emotional energy to do this. I'm yet to meet a teacher who wants to do a bad job for the students.

Joanne

Me either

Eddie

That moral purpose is consistent across all of us. So if there's a disagreement about what we think might be best, you know, actually digging into that is so important. So back to your question about what might be helpful to leaders. I think about, for instance, the work of Moore who talked about the chasm when you when you're trying to get past, you know, there's people who are always going to be quick amongst your staff to adopt a practice early.

Those people who once they see it a couple of times, they develop mastery. And they're easy to bring on board with something. And then there's this chasm of trying to say, well, how do we bring that across all of our staff? How do we change the culture and not just, you know, make sure these are some practices you're only doing because I'm really requiring you to do that. How do we move past that compliance approach?

And I think about how it's that difference between I'm looking at something and even the novelty of it is interesting and exciting, or I want to try new things versus that large proportion, the biggest proportion of of us who, I mean and this is the way us human beings evolved, we need some modicum of social proof to decide that actually, this is worth investing our time in.

And I think that it is, as a leader, reading a book or going to a conference or hearing a talk. It's a great place to start. But it often disguises so much of the emotional energy that needs to be invested. Which we, I think, as people in complex work environments have learned to be really judicious about, say, I'm only going to invest in this if I really clearly see the value. If I walk past a classroom of a colleague of mine and I think, wow, that's not a practice, I would have thought of trying out.

But that's really working with that Year 8 class. I taught them in Year 7 last year, and I know there are some real characters in there. this might actually be worth my time and investment. But seeing that, which might take days, weeks to for that to actually occur is miles away from just sitting in a faculty meeting, seeing a lovely PowerPoint slide deck up the front and being said, okay, now go off and do this.

So acknowledging I guess that there’s that time to understand what it is that people need, and give them an experience in which they can become persuaded of the value of trying it themselves. And then, of course, after the first time when it's probably not going to go perfectly, having the resilience to then try and implement again and try it a different way with a different class. All those pieces of the puzzle of the advice I'd give to someone who's trying to work toward that buy-in.

Joanne

I mean, all of that makes perfect sense to me. And what you're really talking about, I think, is the way leaders shape the conditions for that to occur. But there's a reality around, somebody walking past say that fabulous class that's just really engaged in mathematics, and I think I taught them last year, but they seem to be so much more engaged than when I taught them. What do you suggest a leader does to deliberately create those conditions where that teacher then feels comfortable to say, can I come and watch you teach? Or I noticed what you were doing with that class. Tell me a bit more about it. Because there's a lot of courage in being able to seek that kind of feedback from a colleague, isn't there?

Eddie

You’re so right Jo. And I have to, you know, freely confess that example I just gave, really, it doesn't convey how much thought, care, and I don't know if this word is going to rub people up the wrong way, but the engineering that has to happen behind the scenes to create something like that, that you know, oh, this just happens to occur. Of course, actually as leaders, we don't have the luxury of just waiting for this to happen by coincidence.

I guess I'm thinking a lot about the creation and the cultivation of psychological safety amongst our teams. And I know that in numerous schools that my team has partnered with and supported, it's been interesting to us. You know, in the first few weeks, one of the things that I always tell my team, particularly newer team members who they're just getting on the road of instructional leadership, they’ve maybe had a few tastes of it, but they haven't had a lot of experience yet.

And one of the things that I will quickly remind them is that we have two ears and one mouth, and we really shouldn't be rushing in there with a wrecking ball before we even know what's going on with our staff. What historical, baggage, I feel like is the right word that they bring. The number of times that one of my team members will be in a school and the word observation will be uttered, and a sort of, cold wind blows through the staff room, and you can feel the emotions.

Number one, sort of depress people down is they think, oh, here we go again. This is what's going on. Or the all the way around. There's this anxiety that wells up in people because of the experiences that they have had over time, either with a past or even a present leader. And so acknowledging all those things, knowing some of those, I hope it doesn't sound too, insensitive to call them trigger words.

But once you know them, you realise actually that building a psychological safety, it takes time, it takes sensitivity. And it also, we've found, is something that can only be built once people have a clear sense in their mind that. We often as a person who I'm thinking particularly of a new leader who comes into a space and they're getting a handle of their staff.

We somewhat need to earn that respect and not just respect, as in certainly the people looking up to us, but earn people's treating us as someone who is for them and is on their side and is not trying to point a finger at them or come down on them and and ask them, require them to comply on certain things.

We're actually there to support them and help them become the best teacher they can be for the sake of their students. And there are lots of little things. We often call them on our team, you know, the quick wins, the little things that we can drop into a conversation. They don't require some formal gathering of the whole team, of the whole faculty and just be dropped into a conversation that helps to see, oh, Jo, you're here to help me out.

You want to understand what I'm about, and you want to give me practical suggestions that will help me do my job better. Those little things get currency in the bank is what we find, for helping earn and develop that psychological safety and help people feel. You can be safe and comfortable in being open to me about the things that you're apprehensive about. Your own identity as a teacher is really out there on the line when you're being open about your own practice. So it's really important not to take shortcuts on that.

Joanne

It sounds to me that when you are in those schools and what a joy and privilege that must be to go in and work with others, with that intent to say, I'm here to support you. I believe in you and and in your capacity to grow and develop as a as a teacher. Because you chose mathematics, you know, there's a passion for it. It sounds like you are really strengthening their sense of efficacy, because you're going to strengthen their mastery of teaching particular concepts.

So, okay, you've gone into the school, they're getting a sense that Eddie’s here not to judge me, but to help me. How do you know, what are the steps? What would it look like? You know, for the people listening to this, they're going to be doing it with their own staff as well. And, you know, we take for granted that, you know, we build psychological safety.

And we know that that comes from having conditions for feedback, that there's a sensitivity around that. There’s a seeking of feedback before giving it. There's all of those things. What would it look like?

Eddie

I think the first thing to acknowledge is that it's going to look and feel and sound very different across settings and contexts.

And I'm always very wary of how many approaches I've been shown, told. And someone says, this will revolutionise everything. This is, go through step one, two, three and four and everything will end up rosy at the end. And I've tried and failed that enough times to realise.

I mentioned early on in our conversation about some of those teachers and leaders who mentored me, and I'm so delighted that I had people like Ian Woodhouse and Gary Johnson and Steve Henry. These are people who I look up to and admire and respect. But I'm also not anything like Ian or Carrie or Steve and I have to lead as a function of my personality. And even though there are skills that I've adopted from them, I had to make them my own.

So I guess I'm, through this sort of long prologue, I just want to caution anyone who's listening to think Eddie told me to do these three things, but then they didn't work.

Well, you know, your mileage may vary. I guess probably, in light of that, now, to more directly come to your answer. The place where I often begin is to try and understand the way I heard it said once was, the pebble in my teacher’s shoe. I could come in as a leader, and I could even take, you know, weeks, months to develop my vision for what this school, what this team needs. And I could present it in a compelling and a clear and inspiring way. And I could even be right about every aspect of what I've seen, diagnosed, and think might be the path forward.

But if I come in doing that, even if I am quote unquote correct in my assessment and in my thinking of what we should do next, there's very little I can do if that's the first thing that I'm proposing to prevent teachers from thinking Eddie’s just come in with this agenda. He thinks he knows better than we do. I've been in this context for X number of years, months, and I really don't think he has this right. By the way, I may be right, but that doesn't mean that they might not still think that. And that perception, while it may be inaccurate, can still be real and will absolutely affect the way that teacher is then going to respond to what I as leader think might be helpful.

And so that's why I love taking the pebble in a teacher's shoe, because every teacher for the classes they teach, for the students they work, with has something they think could be done better in their own practice.

There's something which I know with this class, I really struggle to get this student or these group of students engaged. Or, you know, I know they work really hard on this, but I can’t motivate them to do that. And if I can start at that point, if I can work out all right, I have now developed an understanding of a thing that you want to do, and I may not be able to snap my fingers, wave a magic wand and solve that problem. But this comes back to what I was mentioning before about convincing and persuading and not just being an image of, but really being on the side of my staff and being able to say I care about the things that you care about. Help me understand them. Let's think about whether there are some tools that can help us make progress on that.

For me, I want to begin there before I ever get anywhere near within ten feet of, here's what I think might be the vision that solves the problems here. I'd suggest that to any staff member who's trying to get on that journey.

Joanne

It's such a strengths-based approach, isn't it? Taking what's working well and amplifying it rather than looking at the deficits. And that therefore builds the confidence, which is what I was going to ask you about, because we often hear, you know, this saying, I could never be a maths teacher. I was hopeless at mathematics, you know, how often must you hear that every time you convey to someone that you're a mathematics teacher.

Eddie

All the time.

Joanne

How do you build confidence with mathematics? Not only with staff, but with the students. Beyond you know what you've just described so beautifully about amplifying what's already working well and, you know, strengthening that. How do you build confidence?

Eddie

Confidence is both one of the simplest and most mysterious things. I think, you know, and mathematics is one space for it. I often get asked, you know, if I'm say for example, at a conference, I've just given a keynote presentation, and some will say, how do you do that confidently in front of your colleagues? Hundreds of people. That seems terrifying to me.

And on one level, as I mentioned, developing confidence is exceedingly simple. Confidence comes from repeated success and an assurance of the things that we know. And if we can think about anything at all that we are confident to do. At the moment I'm thinking about my daughter learning to drive, and she is not confident.

And she looks at me just getting into the car effortlessly, you know, starting off the engine and then off I go, navigating this very complicated and dangerous space. Frankly, that's what it's like to drive a car. But we forget about that because for the hundreds and thousands of times we have done it successfully, we develop this sense of, I can do this. Even if something comes up that I have, I'm not entirely anticipating. I can respond, I know what to do in that space.

And so there is a point at which at first we must get over that initial hump. Because if confidence comes from repeated success, the place that confidence does not come from, it is some magical process happening before we actually begin, fail, try again. There is no shortcut around starting and going through that bumpy beginning. But then I think that, you know, all the places where I've developed and experienced success in a repeated way, they came from me saying, all right, I'm going to try this out. I'm going to experiment with it a few things.

It's probably going to be a bit rough at the beginning, but I've got a trusted leader. I'm going to ask Jo to come in with me. I'm going to ask her to watch and see the things which I'm going to be too cognitively overloaded to observe about my own teaching or my own leadership practice. And then I'm going to dissect this with Jo afterwards.

I'm going to have someone who I trust and who I know and who knows me, and I can use her as my parachute. I know that Jo's going to help me out. She's going to give me some helpful advice. And so seeking that I think is really vital. And then the taking that commitment, I mean, I'm going to expect Jo that you're going to give me some homework, you're going to tell me some things that I probably didn't want to hear, because we naturally become defensive when we are trying to work on something that we're not very good at.

You know, just behind me, our listeners can't see it, but I have this big shelf of books.

Joanne

I can see it

Eddie

Because I've done homework on every time someone like yourself or other colleagues have said you should, this is the place where you need to develop. Go and read this. Take all of this learning that's been encapsulated over the decades and distil down to this, take that, go and do some work, and then let’s come back and try this again.

And that's where that repeated success and then the confidence grows out of that.

Joanne

It’s great advice. It's that confident humility, that term that Adam Grant uses, that embrace the certainty of uncertainty and adopt that growth-oriented mindset that says, I want to do better and I want to grow. And the best place to do that is learning from others and working collaboratively, which I think as teachers, we can do better, you know, the interdependence of learning from each other. And you've just highlighted how important that is in growing one's confidence in mathematics.

I think that's a good point. To end. The first part of this two-part episode. In the second part we’ll unpack the importance of explicit teaching in mathematics and other subjects, discuss how leaders can guide their staff towards engaging with the latest educational research, and explore some different elements of teaching practice.

The second part is available now on the School Leadership Institute website or Spotify. Thank you for listening.

School leaders play a vital role in providing every student in New South Wales public schools with a great education and the best start in life. They have a positive impact in classrooms and on their staff. They guide teacher development and engage their communities. Here at the New South Wales Department of Education's School Leadership Institute, our mission is to support New South Wales public school leaders by providing world-class evidence-informed leadership development programmes and resources.

Our podcasts will explore the key issues and challenges of school leadership. Hosted by Joanne Jarvis, the Director of the School Leadership Institute, tune in and listen to our guests and colleagues share their expertise, insights and wisdom on leading with purpose and impact. Welcome to our Leadership InFocus series.

Joanne Jarvis

Welcome back to Part 2 of Episode 23 of our Leadership in Focus podcast. I'm joined again by Eddie Woo. Eddie leads the Teacher Growth team at the New South Wales Department of Education, is a professor of practice at the University of Sydney and is also a teacher at Cherrybrook High School. We're continuing our discussion on strengthening mathematics teaching through deeper collaboration, more meaningful feedback and richer professional learning.

Eddie, the mission of the School Leadership Institute is the provision of world-class, evidence-informed, future-focussed leadership development programs and resources to support leaders at every stage of their career. A really key focus from that mission is the evidence-informed component. We don't want to do anything unless it is grounded very much in the literature, so that we are informed by best practice as much as we possibly can be.

With that in mind, what do you think the role of being evidence-informed looks like for leading the teaching of mathematics?

Eddie Woo

This is such a wonderful and important question. The first thing I want to say is that for those people who are listening, almost by virtue of the fact that they are listening to this podcast, you're going to be, dear listener, someone who I think would really resonate with and align with Jo, the vision you just described of our teaching and leadership, aligning and being informed by the research and evidence base.

But it's also worth noting that we lead many teachers, perhaps the large proportion of our teachers who might never listen to a podcast like this and actually would be quite reluctant or feel like it is not worth their investment of time to pick up a book or look up a research article, get into a journal and say, what does this have to say about my practice.

And so I think one of the elephants in the room that I want to acknowledge is that I'm sure I'm not the only person out there who, when I was at university training initially to be a teacher, I've looked at the voluminous readings that I was given by my lecturers and tutors with suspicion is probably an understatement, and I thought to myself, how relevant or important or worthwhile is this? You've given me this, this enormous ream of papers to read, and this is a very important part, I don't yet have the experience in the classroom of the problems that all of this research is trying to solve. So most of this is somewhat meaningless to me, because I need to get into the classroom, into schools, and encounter the things that the phenomenon that you're talking about and then say, oh, this is why you've introduced this model or this framework.

I think that there are plenty of teachers in our schools today who still have that scepticism, that critical attitude. And when you add on to that, the absolute time poverty that every school teacher feels who, you know, gets home, perhaps, you know, looks after family, tidies up the house a little bit, gets dinner on the boil and then gets ready for their second lot of work at 7 or 8 in the evening and and they're thinking, Eddie, you're suggesting I spend more time on reading something which I don’t even know if it’s going to be relevant. I just think it's important to acknowledge that actually, that is an extremely common experience for the teachers who we lead and so it would be naive to think, hey, I'm reading this, this is amazing, I'm just going to give this to my staff and expect them to have the same emotional and cognitive experience of thinking, oh, I'm going to change what I do tomorrow because of what I've read here.

So I guess in that light, I'm thinking a little bit of maybe it's a strange metaphor for people to take on, but, Jo, I attended an agricultural high school from years 7 to 12, and as a consequence, I spent a lot of time understanding the, anatomy and physiology of farm animals. One of the facts that many people will know is that a cow has four stomachs. And the reason why they have four stomachs is so that they can digest all of the grass that they eat. And I kind of think of educational leaders as we are, some of those stomachs for the staff that we lead in taking this vast evidence and research and being able to digest, break down, identify the parts that are going to be the most relevant, useful and in contact and intersection and overlap with a particular setting and context of our teachers and our staff. And being able to say, here's a kernel of something that I think might actually be useful to you. I've thought about, ‘Joe, you’ve talked to me about a specific class or a particular concept that you're trying to teach effectively. I've read this, and I think this might be really well suited to give you another perspective on that. I'd love to give this to you. And would you would you mind telling me your thoughts about this next week?’ Or ‘here's a podcast’ or whatever it happens to be.

I think that that's a really important role that we as leaders have for not, using research and evidence a bit like a stick to hit our colleagues over the head with, but to actually give them a taste and I really mean that, develop a taste for our colleagues to be able to engage with that world themselves but acknowledging that that actually can be a very difficult world to enter and to access, especially if you throw someone in the deep end. So I think that's a great privilege for us, but we want to acknowledge those challenges and be real about the time and the accessibility challenges that are there, so that our teachers can embrace this for themselves.

Joanne

I mean, what you've said makes a lot of sense. And if you want to take a slightly different analogy, none of us would want to go to a doctor that hasn't, kept themselves up to date with research and evidence before they offer a diagnosis. I would like to think that no teacher in our system, isn't up to date with the best practice that enables students to achieve their best outcomes as well.

So I think it is an important component of us, and we are a highly skilled and a highly knowledgeable profession, and we should be proud of that and not lose sight of the value of being informed by research and evidence. So I really appreciate your response to that, Eddie. So, Eddie, explicit teaching is a really important focus for the New South Wales Department of Education.

What do you see its role in teaching mathematics more effectively?

Eddie

Certainly, in terms of teaching mathematics, explicit teaching is the beating heart of how we can learn mathematics in the most effective way. I am amazed by the fact that from kindergarten through the Year 12, we effectively teach young people centuries worth of mathematical progress and innovation that mathematicians have come up with, over the ages around the world.

I love how international mathematics is and how some of the oldest names that anyone will study in schooling are not in ancient history, but in mathematics, Pythagoras, Euclid. One of the wonderful things about mathematics is that it's timeless. Once something is true in mathematics, it is true forever. So, if we learned it 5000 years ago, we can still teach it today.

And what that means is, one of the critical consequences of that is that, if we want to learn mathematics effectively, there are two arms to this. Students need to experience for themselves the inquiry and discovery process of ‘how can we identify a pattern or an algorithm, or a solution to this particular problem that we care about?’

But at the same time, it would be doing students an incredible disservice if we said, I'm just going to let you hopefully work out on your own you know what the principle of strong mathematical induction is? I just expect you, 14-year-old child, to discover this off your own bat. That's not going to be a helpful or efficient way to do things.

And so explicit teaching comes in as this tool that allows us to cover these, well, literally millennia, actually, of mathematical concepts that we've developed over time, and help students adopt that and learn that and own that for themselves. What I would say, though, in addition to that, is that is vitally important for us to have a nuanced understanding of what explicit teaching is.

I often think to myself that mathematics is the easiest subject to teach badly, because you can think, oh, look, there's a there's a formula and I can put it up on the board and I can say to my students, I can model for them very effectively. Here's where you put each number, and magically the right answer will appear every single time and it is you can turn the handle and and get the the right answer and it's, it's very assuring in that way.

Joanne

And if you don't know, and also if you don't know you can ask BOB.

Eddie

Yeah. Back of book, has helped many generations of students, myself included. And I suspect you too Jo, but the problem is, though, that if we simply say, okay, and this is just an example I want to give because I see it a lot, if I just model this particular process for my students and then, you know, guide them through a process of them adopting it for themselves and let them have independent practice.

If that is the only thing that I do, then sadly, an extremely common occurrence, and I'm sure our listeners will be able to empathise with this from their own learning experience, the rehearsal of an algorithm that produces the correct answer can sadly masquerade as real understanding far more often than we would like to admit. And I know from my own, particularly some of the concepts which I remember, being able to get the right answer in Year 12,

and to my horror, I discovered when I first went to teach them that I really had no idea what I was doing. I was just going through the motions and getting the right answer. So what that means is, say, for example, I just talked about modelling a process, getting towards guidance and independent practice, gradual release of responsibility, is actually an extremely, complex and dynamic process that when you look at the research, there are lots of different ways to do it that are suited to particular students, particular concepts and particular skills. And being able to say, all right, I mean, I said the beating heart, right? Being able to use this, this technique appropriately, and, and make explicit teaching come to life requires us to have a deep understanding of, of when, where and in what proportion to use any of these strategies.

So I just commend, every teacher and leader who's listening to, to take, you know, the department has produced some fantastic resources that have distilled down broad research into a really, succinct format. Use that as a launchpad, is what I commend, because there's a there's a you a cavernous world, of research to explore. They'll help us understand the strategies and techniques better and use them effectively in our classrooms.

Joanne

This is going to come from left field. We didn't talk about this before. We started this podcast together. Do you think there's a difference in the way we teach mathematics in a K to 6 setting to the way it's taught in a secondary setting? And is there a, a particular emphasis or bit of homework that you would ask of, of our listeners to really master the expertise of teaching mathematics?

K to 6, compared to 7 to 12, I suppose, in a central school it's all the way through isn’t it?

Eddie

I think the direct answer to your question is yes, there are differences. Some of those differences are fitting and appropriate, some of them aren't, though, there are distinctions between what you see in a primary and secondary setting and I'm convinced that both primary and secondary educators would benefit immensely from learning from each other, sharing practice. And what I would suggest is, firstly, there are appropriate differences. I mean, I think about, the developmental changes that are happening in a child as they move through kindergarten, up through through infants and into primary. And I'm extremely thankful that as a secondary educator, I don't need to be an expert about all of those things. I remember the first time I encountered the idea of subitising, which is instantly looking and recognising a set of numbers of something like that, of objects in front of you. That's not something I ever encountered in my teacher degree. And as a secondary teacher, I shouldn't need to be an expert at helping to recognise and develop that.

Nonetheless, it's very helpful to know that that is a skill which actually not all of my students in Stage 4 have finished all of their Early Stage 1 and Stage 1, 2 and 3 outcomes. So if I want to teach my my Year 7 students effectively, it's incumbent on me to know what happened before. And coming from the opposite direction, because mathematics is actually, we have a beautifully designed syllabus in New South Wales, I know I'm biased, but I've seen a bunch of different curriculum documents around the world, and the the coherence of our syllabus is something to be prized, but that means that for a K to 6 educator out there, you talked about homework. Having some sense of the horizon of knowledge of what you're building toward is vital. I'm thinking a lot about multiplication and division facts and the importance of automaticity in that area, and I know, listeners might probably know what I'm talking about more in a more comfortable way if I said times tables, and I'm deliberately not just calling them times tables because multiplication, division, automaticity, is a much richer idea than that, but the idea that I actually it's not an end for my students to know that 7 9s are 63. That is a means to bridge toward much deeper, more sophisticated knowledge and a primary teacher obviously doesn't need to know what differential calculus is and how to teach it, but to know that that's actually a trajectory that we're getting our students on, I think is so important and valuable.

So I think that there's a lot of bridging work to be done across primary and secondary. It's something I really enjoy doing, but we have a lot of work to do still in that space.

Joanne

And it wouldn't just be in mathematics that applies, but it makes so much sense, doesn't it? The way we respectfully, talk about the skill of teaching students K to 6, 7 to 12, or if you've got the the privilege of being in that central school and saying the whole trajectory, there's a leadership, intentionality there, I think, where recognising that that's the task of leadership in curriculum development is, a critical component of the work, I think.

I'm going to turn to a slightly different angle now. How do you know that, your staff, when they're teaching mathematics, how do you know that they're having the impact? What kinds of, evidence do you look for to know that, you know, beyond the success in, say, a test that they're really understanding mathematics conceptually, not just memorising formulas and trying to think about how to apply them, which is probably my experience in mathematics.

Eddie

I have to apologise before I say anything in answer to this question, because there's no way that I can, treat this really massive topic with anything like the breadth and complexity that it deserves. I'm really glad you asked it, though, because it is something which I know, in the early stages of my teaching career, I had an instinct that this is an important question to answer, but I really knew so little about how to appropriately know that for myself as the teacher of the 30 or the 24 students in front of me. I remember it was some embarrassment, actually, when, Dylan Williams spent some time in Australia many years ago, and he was running this professional learning, and of course, as an expert on formative assessment. One of the things he said was, please give me, you know, an indication if you're there, if you've ever in the past taught something to your students from the front of the classroom and then thought, I wonder if my students know, have that conceptual understanding that you're talking about. So, you posed a question to the class. A few students put their hands up. You picked one, and they gave the right answer, and you patted yourself on the back and felt so good about how successfully you had taught that entire class and moved on to the next idea. When in fact, by selecting a volunteer and only getting a single voice, from them, confirming something which you were already biased to hope that you had taught successfully, you really have no idea, actually, of whether, you have a view of the students understanding.

So I think that this is a critical question to answer. I think I've, you know, in referencing Dylan Williams work, there are really critical ways to, take simple strategies like mini whiteboards or vertical non-permanent surfaces and, and approaching student work in, in those, you know, by the second, by the minute ways in the classroom.

I am definitely not waiting till the end of the week, let alone the end of the term, to do a big summative, you know, test and say, ‘oh, OK, from this exam mark, I therefore know what's going on’, and especially because again, like you mentioned before, this is definitely not only true of mathematics, but I think people mistakenly believe it often in mathematics, an exam mark is an exceedingly narrow view or lens on what a student can do, or can know.

In mathematics. I think about the, the aspect of working mathematically, fluency, understanding, problem solving, reasoning and communicating. There are some of those that can be very appropriately assessed in an individual time bound, bring no resources into the exam room test. There are some. And that's why we use them. But there are so many things. I mean, problem solving is a good example, for those listening who aren't familiar with the technical, definition for problem solving in our syllabus in New South Wales, it's about an unfamiliar, non-routine question that you've never encountered before.

So, Jo, if I've taught you how to encounter this particular problem, then do an algorithm for it. Then if I show you a question to which you know what to do, and we reproduce that algorithm, then that was an exercise, not a problem. Almost by definition, there is no way that I can set a single question in an exam that is a problem, that is unfamiliar, non-routine, for every single one of my students. Here at Cherrybrook Technology High School, we have 375 students in Year 12. Not a chance that there's a single question that not one of them encountered. And so therefore, I guess coming back to your original question, it is so important that we use things like tests as only one leg of the tripod and understanding what's going on with our students.

We should be, asking questions constantly within the classroom, doing that in individual and in group context, because something like communicating, can't be done in, in, in solitary, sort of, you know, a context like that with an individual student. And I'm also, I mean, I think about the fact that I've been recording my own classroom lessons and putting them online for about 14 years now, and I've been asked why those lesson videos are so impactful people.

I'm convinced that one of the reasons why people find them useful is because I record them with an actual class in front of me, and I'm watching their eyes and their faces and their posture as I explained, and I know if I'm going too fast or too slow, or I've said something that is completely incomprehensible, that I thought in my lesson plan looked really good.

All of that is me formally assessing second by second in the classroom. It's what every teacher does who's effective and has that that efficacy practised and rehearsed over years. So these are the kinds of things which I think help us form a holistic picture of a student and what they can do.

Joanne

Very helpful. I went to that same Dylan William talk. I've heard him speak multiple times, and I remember thinking, you know, what a powerful comment, because I taught history, and so I started putting that into practice, and I'd say, I'd ask a question, a deep question, I feel, and then I got better at just shutting up, just pausing and saying, I'm going to give you some time to think, because how often do we ask a question and expect an immediate response?

And, you know, our students need time to think, just like we do. And I'd pause, and then I use to say, and I'm going to, give you some time to think about it. I'm going to give you some time to talk to the person next to you. And then I'm going to ask you, you and you for a response. And we're going to bounce off each other. And gosh, the change to the tone of the lesson and that genuine, searching for knowledge from each other was so powerful. I just thought Dylan William made so much sense in a different context, but, to say it's the same kind of, practice, isn't it?

Eddie

And Jo, you, you mentioned briefly homework before, if anyone is listening and thinking about, well, how would I do this very specifically within a mathematic context, I can't help but think of the work of Smith and Stein, the the title of their book, that they're most known for is extremely long and awkward, but it really says everything. It's 5 Practices for Orchestrating Productive Mathematics Discussions. And I remember picking up that book off the shelf and thinking, I barely understand, this is when I was a teacher for maybe 2 or 3 years, I barely understand what that title means, let alone how I would do it. And there was a whole universe, that just you illustrated it really well there, there are some really careful and well-designed protocols that you would give to your students that enable them. It doesn't happen just by accident, we’ve got to be extremely thoughtful and conscious about how we give our students, carve out that space for them and the time to develop that thinking, articulate it, and then bring it to the fore.

Joanne

Yes. You know, another, interesting, example, I heard Professor Wayne Soya, he was, at the University of Western Sydney at the time he was presenting, and he was talking about a maths teacher that he had observed. And, you know, who had really done some outstanding work and, had students like yourself eating out of the palm of his hand.

And he said he would give a test and he'd come back, you know, coming to class the next lesson, with the results of the test, but instead of giving the tests back to the students, he would break them into groups and give them the same test as a, as a group and require that the groups actually answer the questions together, before he would then give them their individual results. And he found that, he was able to identify probably just one question that was common amongst all the groups that they're all struggling with. And then he would then use that as the basis for, extending those students to understand the concept that seem to have been missed across the class. Then he would give them a test at the end of the lesson, their test results at the end of the lesson, I thought, that's a really novel idea, because it certainly is so far away from my own experience in being taught mathematics. There's so many exciting things that you fabulous maths teachers can do to really engage students and build their confidence, and the staff who were teaching them as well.

Eddie

On what you just said, Jo, I think that that's such a powerful illustration of how it's not as though we are necessarily asking for, our colleagues, for our staff to throw the baby out with the bathwater, start from scratch, something as simple and as I'm going to say, quote unquote, traditional as a stock standard exam for a maths classroom using that sort of collaborative feedback, I'm thinking about, you know, changing nothing about the format of the test and even just saying not necessarily for all of them, but saying ‘you know what, students, I want you to retake this test and you can earn back 50% of the credit on the questions that you got wrong. I just want you to have a look, try and learn this again and then give it another go’. I mean, it's wild to me that we have crafted this school environment in which we say, ‘you can have one shot at that, and then after that, forget it, we're moving on’. Real life is not like that. Real work is not like that. And it drastically changes. And I think there's a real lesson here for not just the way we work with students, but the way we work with our colleagues. There's a real communication there of, this test is not just for me to measure and to judge you. This test is actually for us, It's for you to understand yourself better, to know where you can improve. And I do think, I mentioned that example before about observation, part of why that can be such a difficult thing for teachers is because they've actually viewed it solely as a performance management mechanism that has been put upon them, not as something for them to understand their own practice better and then grow.

We could hardly blame teachers who have been through that for years to not want to have their classrooms open to their colleagues. So there's a real, messaging there that is it's somewhat subliminal, but it actually can be, you know, redesigned and shaped to be much more positive and helpful to the people we work with.

Joanne

It's actually really exciting. I feel like I need to go back into the classroom. I think I'd be so much better, but there's an opportunity to then also, take that strategy that I discussed a moment ago and then finish that lesson to say, OK, let's now let's just pause and reflect. What what's one thing that I, I've learned today that I didn't know before, the end of the lesson? And what's something that I'm going to practice, you know, and that sort of fading forward into the next lesson. I think students would really respect and value the uncertainty of the flow of that. But whilst you're still maintaining the focus on the on the syllabus and the conceptual elements that you need to, strengthening them as well.

I sound like on this kind of, expert in mathematics, I'm absolutely not, but I just love the whole concept of growing students and getting them excited about their learning.

Can we turn to a question around, how you've built teacher agency in relation to, in relation to teaching mathematics? What are your thoughts about that?

Eddie

This to me is such an important piece of the puzzle. I'm thinking about the work of Clark and Peterson and their framework for understanding why teachers do what we do. And one of the seminal lessons that I learned from them is that, of course, a teacher cannot do something that they don't know how to do. And I'm thinking, say, for instance, this is going to date things a little bit, but if I cast my mind back about 6 years from today, we were all in the midst of trying to Apollo 13 our way to what on Earth remote learning looked like in this global pandemic, and we didn't know how to share screen or unmute ourselves or get breakout rooms sorted out. We couldn't do those things if we didn't know how to do them.

So clearly that knowledge piece is vital, and it's a big part of why so much of the professional learning that is available to teachers addresses that knowledge component. You know you can't do something if you don't know how to do it. But as a leader, we rapidly encounter the fact that there are lots of things that we and our staff know how to do, and we still don't do them. We don't want to do them. There's some reason or some motivation that's holding us back.

Clarke and Peterson talk particularly about the attitudes and beliefs that are underpinning our actions, and also just the intent. You know, if I'm in a school setting where the particular thing that I'm going for is I'm trying to maximise the the number of Band 5 and 6s that I'm getting in this particular HSC course, then if that is the sole metric on which I am being judged, then something is going to happen in the way that I invest or don't invest time and energy into those students who maybe a Band 5 or 6 is a bit out of reach, but actually I want them to finish Year 12. I want them to, a Band 3 for this student would be a raging success. Well, if the metric that I'm aiming at is just the number of Band 5 and 6s, then my intent is going to be, rather, my behaviour is going to be funnelled through the lens of that intent.

So for me that the teacher agency piece is about saying teachers are not automata, who I want to train up and say, alright, you can do this, now, off you go. I'm the leader and I want to direct you in this way.

There are obviously places, in which a leader clearly and unambiguously has to direct and say, this is something that we need to do, it's a it's a statutory requirement, it's an obligation. But I think that in terms of what really makes a difference for our students’ experience of of learning, so much of it is actually not just, I can show you how to do something, I can build your capacity in this space, but I want to help you see yourself as the agent who is actually driving and making decisions about, ‘I think this is what my students would need best. Here's how I'm going to get on the, journey of growing in myself and and growing my colleagues. I think teacher agency is so important for, you know, we were talking before about resistance, and that perhaps being a bit of a misnomer, I think some of the, it's not always the most experienced teachers, but it often is, those teachers have been in our system for a really long time and therefore have great confidence in their own practice, and therefore might be a little sceptical about a new idea or new strategy being brought to them.

For me, leveraging their agency to say you have all this knowledge and expertise, decades of it, that I would love to leverage across our entire staff body. I'm not here to just say, hey, I want you to stop doing that thing and try a new thing. I want you to share that knowledge and expertise and be an agent for changing and lifting teacher practice across our team. That, for me, is, a really wonderful way to give respect and show every teacher in our teams that they have an important part to play in raising the tide for all of the boats. So that's why I think the teacher agency is a missing component often, and it's why, as I've mentioned already in our conversation, we begin by listening because it is foregrounding the teacher in what they want to do and what they see is important, and me helping to guide that rather than just saying, ‘OK, I'm the one who has the the hands on the steering wheel’, it's about helping them, direct and drive their own journey in a way that we know it will be helpful for everyone.

Joanne

That sounds like a lovely bookend to, where we started this really enjoyable conversation. It's been such a pleasure to speak with you today to, share your insights on the expertise of teaching mathematics and all of those leadership capabilities that we need to be able to instil the confidence, the efficacy, if you like, in our teachers and our students.

I thank you very much for joining us today. Eddie.

Can I also add, that my nephew Will Jarvis, who may or may not be listening to this podcast, was very jealous when I told him I was going to be interviewing Eddie Woo, he was such a fan. He's in Year 12 at the moment. He learned so much from listening to you.

So, you have had an impact in so many ways you may or may not realise. So, thank you for all that you do. For the students and staff of New South Wales public education and across the board, I dare say.

Eddie

It's my absolute privilege and I think it is the, the joy of every teacher. Don't they say a teacher never knows where their influence ends?

And I hope I get to meet Will one day, but every single one of us who gets to educate young people has that same impact. Whether we can see it visibly, hear about it on the podcast or not.

Joanne

Thank you. It is a joy, isn't it?

For our listeners, please follow the School Leadership Institute on X. Our handle is @NSWSLI and for New South Wales Department of Education staff, you can access our leadership resources on the department's website.

And thank you for listening.