Hi. I’m Alex Oo from the Centre for Education Statistics and Evaluation. With me on this podcast is maths teacher Eddie Woo from Cherrybrook Technology High School. We’re here to talk maths, teaching, and specifically what practices that Eddie uses in the classroom to make sure that all students learn effectively.

ALEX OO: Thank you for coming Eddie.

EDDIE WOO: Oh, it’s great to be here Alex.

ALEX OO: So, I saw your Australian Story, and on it there you had your two teacher mentors. One was agriculture and one was for music. Why maths? Why teaching maths?

EDDIE WOO: There are two answers to this question of why mathematics. The first one is just a practical one. So I went into teaching, I wanted to pursue this from around - Year 11 and 12 is where it sort of crystallised in my mind - and I thought, look, I want to marry up two things: what I’m good at, and also what I think matters in life, and it’s tricky to find those as a teenager at school.

I quickly realised that I love to see people learn. I love to see people grow. It’s what gravitated me towards secondary, because I feel as though you walk into high school, and you’re this tiny little blob with a bag bigger than you are, and you don’t know how to do anything, let alone make decisions for your life. And then by the time you leave, you’re an adult, you’re making choices, you’re putting yourself on a trajectory to decide the course of your life, which is quite amazing. I love seeing that change, and so, number one, teaching.

But I sort of didn’t know really what subject I would go towards. I thought, well I’m good at English and history. I enjoyed being in my music and agriculture classes with some of my best teachers, but for me, I went to Uni and I was at the enrolment day, and the Associate Dean of the University of Sydney he walked along and he looked me up and down, he looked at my transcript for all my subjects, and he said ‘you should be a maths teacher you know, you’ve obviously got a background that you can do this, there’s this immense need’. And because I just wanted to be in a place where I could serve students, serve a community and be maximally useful, that’s the direction that I went in.

But aside from that practical reason of, alright well I guess here’s where I can be beneficial to people, the longer I’ve taught mathematics, the more I’ve come to see it’s a thing of immense practical usefulness. It’s a lens for seeing the world and gaining new perspective on things, and it also is, in its own way, beautiful, a thing to be appreciated. There are patterns all around us that just kind of fly past us and we don’t notice them, but mathematics gives us the tools to understand what’s really going on.

ALEX OO: So a big thing is about what matters, and what’s going on, so maybe you can tell me more about why you feel maths is important, say, why do you think something like calculus is important? How does that explain our world?

EDDIE WOO: So we live in a world that Galileo Galilei, he said that mathematics is the language with which God has written the world, and regardless of what you think about how the world came to be, it’s an irreconcilable fact that everything that you look around at is mathematical if you dig deeply enough. Some things are really obvious - you throw a ball through the air and it traces out a parabola, and it’s quite remarkable that such a complicated physical process should be modelled by such a simple mathematical object. But you can dig further, I mean, you think about the world economic markets, and the amount of mathematics that goes into understanding how currencies work and how financial risk is managed, and how the GDP of a country affects things like the social wellbeing of all of its people. And then we could go on and on about day-to-day, you know, you’ve got to make financial decisions, making sure you’re not getting ripped off on your mortgage or your electricity bill, getting a good deal at the shops. The list is just endless. I feel like every sphere of life is touched by mathematics.

ALEX OO: You mentioned some stuff around economics and the importance of maths to that. Now there’s a lot of talk about that people get worried about the future and economic downturns, et cetera, and there’s a lot of talk about the changing job market and the need for 21st century skills. How does maths relate to that? Is maths still relevant when we’re talking about these 21st century skills?

EDDIE WOO: I think mathematics is more relevant than it’s ever been. I mean, if you go back to ancient Greece - people also forget that everyone knows the name Pythagoras, it makes people shake sometimes, they think ‘oh, bad memories’ - but we forget that the fact that we all know that name is quite astonishing, that mathematics, uniquely, is something that is global, covers all of history, and so therefore that we have built our society on mathematical knowledge and techniques. I mean, just as an example, thinking about how we all carry out credit card transactions over the internet. People often don’t realise that actually, the way your credit card number and all the vital security information that goes into that, it makes its way across the other side of the world by the biggest game of Chinese whispers you’ve ever heard of. Every single internet server tells the next server what your number is. How on earth does that stay secret and private? The answer is mathematics and cryptography. So I feel as though today, more than ever before, mathematics and numeracy matter for the skills that people need to function in everyday life.

Once upon a time, people didn’t need to be literate, and it was only a very small class of society, the scribes and people who were in (inaudible) and they were copying out books. They needed to be literate, and the rest of us just survived, just by aural communication. Then the printing press came along and just shattered that paradigm. It introduced a whole new world where if you were not literate, you could not function. That’s the world we live in now, and I think that the same is true of mathematics, that everything around you, almost everyone has a mobile phone sitting in their pocket, which is so deeply mathematical, you know, the fact that its mathematics is disguised from us is a tribute to how effective it’s been designed, but the mathematical reality is still there. So I think those 21^st century skills make mathematics even more important than they were before.

ALEX OO: So we’ve been talking about maths. Let’s talk a bit more about teaching. So, maybe the first one is, what’s the best part of teaching?

EDDIE WOO: Wow. That’s a really hard question to answer, because there are so many parts of teaching that I love, in fact, this is my tenth year teaching. I feel like every year, I discover a new thing that I love, which is important, because teaching is also really hard. So one thing that I love, I can’t remember who actually this quote is attributed to, but it puts this contrast really perfectly. The quote is: ‘the best thing about teaching is that it matters. The hardest thing about teaching is that it matters every day’, and I love that that keeps in contrast the fact that, you know what, I get to interact with, in the course of a normal day 100 to 150 kids, and I know that I’m making an enormous difference to their understanding of how the world works, their concept of themselves, and their understanding of ‘what am I capable of’.

I teach students frequently who have this belief that, you know, maths is hard, it’s not my kind of thing, and so I’ll give this a go, but I don’t expect to be any good at it. And I love shattering that misconception because I deeply believe everyone can do mathematics. There are some people who have an amazing gift, you know, some people can climb Everest and not all of us are going to reach those heights, but we can all enjoy that process of learning the deep (inaudible) pattern behind something, and the great satisfaction of being able to solve a problem. So I love all of those aspects.

I think even the hardest thing about it, that it matters every day, is part of the attraction, you know? I never walk into work and go through the day and then leave thinking ‘well, that was a waste of time’. Every moment that I’m standing in front of kids, every time that I’m at my desk trying to wrap myself around the information that helps me teach my students best, or the kind of skill I’m trying to communicate to them, I’m keenly aware of how much of a difference that makes every day.

ALEX OO: So yes, it is important that it matters every day, and that means it’s difficult, like sometimes you’re going to not make a difference. So how do you make sure you make a difference in your teaching? How do you make sure that your students are learning? That your teaching is effective?

EDDIE WOO: When I think about being an effective teacher, I think the first thing that this comes back down to is relationship. No significant learning can happen without a significant relationship, and so when I contemplate ‘okay, what’s going to make sure this lesson is going to land on students, it’s going to remain with them, it’s going to develop them as mathematicians and also gain a better understanding of the world and be better citizens in the world?’, the first thing it comes down to is, ‘okay, how am I managing the relationship between you and I as co-learners in this space?’

So I like to make sure that I’m knowing my students really well, I mean that’s a really simple fact that often escapes peoples’ attention. People don’t care how much you know until they know how much you care, so making sure that I establish rapport and that I know students. I mean, this is a really urgent thing when we think about how much students are going through high school, often just being a number, you know? ‘I got this test result’, ‘I don’t really draw peoples’ attention in class’, ‘when I go out into the workforce this is going to be even more true of me’, and so knowing each individual, knowing their strong points, knowing what you want to extend them on, and knowing the areas they need to work on, I think that’s just the bedrock. Nothing else can happen without that, no matter how good your craft knowledge is, how great your understanding of the field or theory is, you’ve got to make that relationship work.

ALEX OO: So that sounds like something that could be generalised across any key learning area, whether it’s English or science, or whatever. So does maths need to be taught differently, or is it all about relationship and that’s universal to teaching?

EDDIE WOO: I think that the first piece about teaching mathematics effectively is, full-stop, teaching effectively. So there are definitely common threads that run through all of the KLAs, but I do think mathematics is unique. I mean, mathematics is the only area of knowledge at all where, once you prove something, that it’s true, that the logic demonstrates it, it’s true forever. Every number in the world, every whole number in the world can be written as the sum of four squares. It doesn’t matter what it is. It was proven true by Lagrange centuries ago, and it’s still true today. It’s why we learn about Pythagoras and Euclid, all the things they established. Unlike knowledge in science or history or any other domain of knowledge, is always changing. So I think reckoning with that, almost eternal truth in mathematics, does mean that you have to teach it differently, and there are also aspects of logical thinking which are quite special to mathematics.

I like to think that the big question that students need to constantly ask themselves is ‘why?’ Mathematics can become the learning of a set of algorithms and steps without any knowledge of why does this matter? What is the significance of what I’m actually working out? Why do I do this step after I do this? For me, the penny really dropped, in terms of my understanding of mathematics and my relationship to it, when I started to recognise that understanding why, thinking about every single step, and not settling for anything less than full comprehension, is when mathematics really made sense to me. So I think that that’s kind of the key to effective mathematics teaching, beyond just effective teaching in the classroom.

ALEX OO: Okay. If it matters so much, if there’s so much importance to maths, why do so many people give up on it? Why is there a fact that so many people call themselves just not a maths person, I don’t do maths. Why?

EDDIE WOO: There are a lot of pieces that go into why so many people have this aversion to mathematics, and I think it’s a cultural aversion too, it’s become a thing. If you are making a movie and you want to make someone look like they’ve had a terrible experience at school, you show how mean their maths teacher was and how bad an experience they had in that class. It’s just kind of emblematic of peoples’ difficulties with the subject, and I think that’s the first key. Mathematics is hard. It’s not easy, it doesn’t come naturally. We didn’t evolve to be good at mathematics the same way we evolved to be natural language learners. A lot of the things in mathematics are counter-intuitive, and are abstract, which are not the normal media that we deal with, so I think just the difficulty of it is the first piece.

The second piece I’d probably add to that is that one of the side effects, one of the problems of having mathematics be this enormous body of knowledge is that, because it’s a body of knowledge and it’s coherent, if you’re missing a piece, if times tables just eluded you, then you’re going to have trouble with fractions, and then you’re going to have troubles with decimals and percentages and the whole thing unravels. Or people say ‘oh, I was fine with mathematics until they started putting letters in the mix’. Well if algebra is challenging to you and you never crossed that line where you suddenly get what’s actually happening and that it’s just the mathematics of working with numbers when you don’t know what the numbers are, if you check out at that point, well you’re not going to be able to progress. You’ll be trying forever to put together a jigsaw when you don’t have all of the pieces. So I think that interconnectedness of mathematics is both its strength, that everything informs everything else, which is amazing, it’s why it comes up everywhere in the world, but it’s also what makes it difficult to learn. If you’re missing one piece, it becomes very difficult to get back on the horse.

I think I’d probably add a third and final piece, which is that mathematics is often not reckoned with as a very personal subject. I think people even say, it’s entered our vernacular to say someone is ‘cold and calculating’ if you want to get across that someone is impersonal and cruel, but I actually believe that mathematics is a deeply personal subject. The struggle to understand why something works. The satisfaction that you get when you solve a problem and it finally clicks for you and you can explain it to someone else. All of those processes, I think, speak to the fact that mathematics is a personal, it’s a creative pursuit, and often mathematics is not learned that way, which makes it difficult when students run up against difficult things and they don’t have the emotional or psychological resources to develop resilience in problem solving, to think about another perspective on how to solve this problem. Once people get that though, I think the world becomes their oyster.

ALEX OO: So you’ve been talking a lot about your teaching methods in some of the answers you’ve been giving, so let’s get inside that black box, like Dylan Williams would say, and let’s just talk more about your practice and pedagogy. So maybe we’ll start with those ‘non-maths’ people. How do you help those students with low self-perceptions, low expectations of their own maths ability and achievement, how do you help them? I remember I saw – on your Australian Story I heard you talk about helping those non-maths students, and there was this point where you were talking about ‘let’s go back to where you did understand’, and before you were talking about the importance of different steps, like of the sequencing – asking that ‘why’ for every step, so maybe you could tell us, is that how you help these kids, these non-maths kids, by really laying it out, structuring it out, and giving them the why?

EDDIE WOO: I think I’d probably point to two particular things that I’ve felt are the real bread and butter that if you’re missing these things then you’ve almost got no chance at really reaching out and connecting with someone who views themselves as a so-called ‘non-maths’ student.

The first thing is something that you’ve just alluded to, which is people don’t start out having an aversion to mathematics. You don’t have to teach a kid that it’s fun to count, you know? I know someone, again this is a quote, I can’t remember where it comes from, but ‘music is the joy that our soul feels when it’s counting and doesn’t know that it’s counting’. And so I think that there’s something deep in our DNA that resonates with us, but where we start to get that negative attitude is where we realise oh, I can’t do this, I find this hard, it’s discouraging getting bad results, and that kind of thing, and I feel like I have no access to the help that I need. So the first thing is coming back to that point where, you were on the wagon once upon a time, where did you fall off? Let’s go back to there. Because it’s really an exercise in frustration to try and build from your current position, you’re a Year 10 student, you’re meant to be learning this Year 10 maths, if from primary school you never really got past, okay, how do fractions and counting numbers actually relate to each other? Well everything else is going to flow from that. So I think firstly, going back to whichever point it is, and that’s challenging, you know?

Remediation has always been a problem in schools because our syllabus sort of has this drumbeat march to it, where it’s like, well you’ve got to move on, you know, because we have a responsibility to make sure we hit every single syllabus dot point. I think that that is true, but at the same time, if you are teaching something but students aren’t learning it, then I think that that’s really a pointless exercise. So coming back to students’ knowledge, where they have an established set of skills, is the first point where you think, okay, if success is the first ingredient of engagement, I need you to feel that you’re getting this and that you can do this, let’s build from there.

The second major thing is making sure students feel that they have the opportunity to ask questions. Again, this is a problem that somewhat rises up from the fact that a mathematics classroom, particularly in a secondary context, is often a streamed classroom, and there’s a lot of research that’s been done both for and against having ranked or ability groups within a class, or the classes themselves. I think that one of the problems with doing that is that you can very quickly find yourself in a class where everyone else around you just seems to be working at the same pace, and it’s not yours. Something has gone wrong, you’ve had some absence or you’ve come in from some other school or some other jurisdiction, and you’re just not really understanding what’s going on, but everyone else seems to be understanding everything fine.

In that kind of environment, it’s very difficult to put your hand up and say ‘uh, I don’t really understand what’s going on, this concept isn’t really connecting with me, can I get a bit of help?’ So it’s really important to connect with students who’ve had a negative experience by helping them see, oh, help is accessible, help is available and it’s not going to make me feel stupid for asking a question.

I don’t think anyone has anything against numbers or patterns or shapes. I think people don’t like feeling dumb, and if the way they learn mathematics gives them that experience, then that’s where that negativity develops. So connecting back to prior knowledge, providing access to an easy place where they can ask questions and get answers that make sense to them, and different perspectives on the same question because the first way and the second way didn’t connect, those I feel are the keys.

ALEX OO: Yeah because I saw on your Australian Story that there was actually a little snippet where you were talking to a student and you started giving feedback on a very specific method, like that you need to multiply both sides by 750, which was the exact quote, so is that your usual way? Is that how you make – how do you avoid students feeling like they can’t ask that question, that they can’t be looking like they’re dumb? How do you – what is the way, because I know sometimes people praise ability, sometimes people praise effort, and other people, what some of the literature says is about praising method, so how do you make sure that, or give instruction on method? How do you make sure that they feel comfortable to ask the right question through your feedback?

EDDIE WOO: In terms of growth mindset and Carol Dweck’s work and Jo Boaler’s work on making sure that there’s an understanding that we’re not trying to reward you if you’re just that naturally talented person. We’re trying to reward the effort that you apply yourself with. I definitely think that piece is there, and I’ve seen the difference that it makes when a student thinks of themselves as, okay, I’m a hard worker, that’s why I’m valued in this classroom, that’s why my contributions are important. I think that’s definitely an important piece.

For me personally, what I think has gained the most currency in the classroom is actually something a little bit different, which is the way that I question students in class. Questioning, I think, is a very undervalued skill. I know there’s that joke where someone asks a Rabbi ‘why do you ask so many questions?’ and the Rabbi’s response is ‘what’s wrong with asking a question?’ I think that that sort of Jewish way of developing understanding by almost that Socratic sort of a way of getting at peoples’ knowledge and expanding it by questioning, I feel that’s the key.

So as an example, in my classroom, I almost never answer questions. I almost never answer questions. Students will say ‘I don’t get this’, and I’ll respond with ‘okay, can you explain to me, why is it that you can do this part, but then this part goes wrong? You answered this question before and everything worked fine. Can you tell me what’s different about this question that makes the wheels fall off?’ And then they’re suddenly put in the position of ‘oh yeah, I know how to do this, I’m the expert at this, okay well let’s try to dissect what’s happening in this new question’, and then they start to work out ‘okay, this is different, oh I didn’t notice that before’.

I often have to tell pre-service teachers when I’m mentoring them, you know, the person who’s doing the talking is the person doing the learning, so if you’re busy explaining, in some ways it doesn’t matter how clearly you put an idea or a skill, if you’re the one talking, you’re the one who’s most active in constructing understanding. So questioning students, often putting some wrong working in and then saying to the student ‘wait, what went wrong, can you explain to me where I’ve gone wrong?’ and putting them in the position of ‘oh, silly Mr Woo, what were you doing? I knew what you were doing wrong’. That’s one of the most important ways that I’ve found has been effective at developing a student’s self-concept of ‘yes, I am a mathematician, I can question this process. It’s not just because the teacher said or because the back of the book agrees with my answer’, and in fact I think it’s just as important to do that with the really quick, gifted students, as well as the students who are struggling, because I think that questioning them and saying ‘do you really understand why that answer is that you’ve got, like I mean, you’ve got the right answer, good for you, can you explain the rationale for why? Can you explain why the process you did arrived at that answer?’ and what that often does is reveal a superficial level of understanding.

So I feel like questioning is kind of, for me, that secret thing which I was never told, but I discovered is so powerful in the classroom.

ALEX OO: Yes, questioning is a really powerful form of feedback, especially because you’re questioning so much around what exactly is happening in this process, so it’s really specific about the maths and the things that they’re meant to be learning, but at the same time empowering them, giving them those high expectations to be really able to move forward and to believe in them and keep learning. But towards the end you started talking about how you’ve had a few different students, like you’ve had, you know, those non-maths students who are now doing great, and you’ve had somebody who’s gotten 100 in one of their HSC courses, right? So with all these different students, is there – are you trying to teach them differently? Like, or is it, you said questions you use for everyone, but are there different ways you might pose those questions? Or how do you change your teaching in general to be more personalised, to make sure every student is learning?

EDDIE WOO: I think that one of the ways that classroom and curriculum differentiation can work in the classroom is that there has to be that time where you break out and you’re not doing something from the front of the room. That you have that opportunity to have conversations with each individual, seeing what’s going on there, that you check their books. I often have struggled in the past with, you know, you get to know in a class of 30 students the really, really bright buttons, the ones who are constantly putting up their hands, like ‘sir, I’m going to die if you don’t let me answer this question’. You also quickly, you know, work out who are the people who are distracted, trouble makers, all that kind of thing. And then there’s this kind of wide open middle. Students who don’t necessarily gain your attention or stand out in any particular way. One of the ways that I’ve overcome that, because I feel like that individual knowledge is so important to making sure everyone gets a good, positive experience, is I like to say look, in a single lesson we have 53 minute periods here at Cherrybrook, and so 53 minutes, if you take out time for kids to arrive, kids to pack up, time to explain stuff, you hardly get 30 seconds to actually chat to each kid.

Something I’ve adopted, which I’ve found has been really helpful over the last few years, has been saying okay, I have 24 students in my class and I’m going to really struggle to have a really meaningful conversation with all 24 of them every single lesson. That’s going to be immensely challenging, so what I do, it’s so simple and yet it’s changed the way that I’ve known my students so much, is that I’ll say every lesson I’m going to pick out three particular kids. I’ll just go alphabetically down the roll, that will be fine, and I’m going to say no matter what happens today, no matter how quiet or reserved or what kind of activity we’re doing in the classroom, I’m going to make sure I have a decent conversation where I ask questions, where there’s real interaction with those three kids. And what that does is, obviously it gives me the opportunity to interact with the whole range of kids, but also pushes me as a teacher. A teacher’s job, you’ve got spinning plates constantly, all the time. Something’s always happening, there’s all these processes you’ve got to manage in the classroom, and so you’re a human being, it’s difficult to remember, okay I’ve got to try and hit that kid, and the one who hasn’t really said anything for a couple of weeks, and are they late again for the seventh time in the last fortnight. Doing something like this and making sure you have a regular, systematic way of getting to every single kid, knowing them well and having a deep knowledge of where they’re at and what they need to move forward, I’ve found has been enormously helpful for getting across the bulk of kids, many of whom need help but you wouldn’t know otherwise, because they want to fly under the radar. They don’t want to draw attention to themselves.

ALEX OO: That’s great. So maybe on that, like, how else do you understand your students, understand your students’ learning needs? So you’ve got this system of making sure that you have these great conversations with each of these students and that’s a great form of, let’s say data, basically, on these students through these conversations, observations and questions and all that kind of stuff, but like, what else do you do in order to understand your students? To understand every one of your students? Like, maybe formative, what’s a formative assessment you might use, or things like the exercises you might get them to do, you know, all that. What would you use?

EDDIE WOO: Understanding students I think is, in some ways, the chief art of a teacher, and it’s very challenging because it’s a personal thing, the relationship with the kids, and what matters to them and what motivates them. It’s difficult because it’s not quite a science and every kid is unique and different when they walk in the door. So I think that firstly, making sure that I have substantive conversations with them, making sure I see them in contexts outside of the classroom. All of these things contribute to understanding, alright, what’s important to this student, what is it that will be the part of their life that I can connect to mathematics and help them to realise, oh this is worth doing, you know? It’s very frequent for me to work with students who have no interest in proving that triangles are congruent to one another and understanding the sufficiency conditions for different categories of quadrilaterals, but if I can say well you know what, those of you who are heading into a trade, this trigonometry is going to be so important to you, or those of you who are trying to design something in textiles because you’re really interested in that design aspect of things, I can say these will be the bits of financial mathematics, or you know, proportion and ratios and measurement that are going to be important to you doing your job effectively and being a great craftsman or craftswoman. All those kinds of things happen as a result of knowing our students, and knowing them outside the context of the classroom. So I think those things are really important.

I also reckon that the assessment that I do with students in formal structures, their big exams, their big ticket assessment tasks twice a year, and also the regular little tasks are so vitally important. So I think that I gain a lot out of making sure students are regularly being exposed to, okay, this is what it means to articulate my understanding and express it. Yes, I get it, I know how to answer the question, but can I explain it to others? So putting students in that position of being almost a peer teacher helps me as I watch them actually teach through something, that gives me a real sense of ‘do you actually understand this or not?’ I often tell kids there’s understanding to answer the question, to get to the right number at the end, and then there’s real understanding of what this is about and why it actually works, and that kind of understanding is not often revealed, or you know, unmasked as being you know, fake, until you put a student in the position of, hey, can you get up, show me this on the white board, or get into pairs, get into groups of four, explain that question, you can prepare, take as much time as you like to wrap your head around the question, but then I want you to stand there, be ready to take questions, be ready to be scrutinised in terms of your understanding. I feel like those are the most effective mechanisms for assessments that I can use in my classroom from day to day.

ALEX OO: So it’s not just the old school worksheets. You’re really trying to get them to really delve into the problem, really try to be able to become such experts that they could explain it to anyone. So that’s one of the big processes. Okay, so that’s all the information that you’re gathering about your students that helps you understand your students. So how do you make sure that your – how do you respond to that? How do you change your teaching with response to new information? So one of the things you mentioned was that you know, you try to understand the students outside of the classroom context and then once you understand what they’re interested in, then you can relate how maths relates to that, say through the triangles and through them applying to trade. So, like, what are other ways that you change your teaching when you find out new things about your student?

EDDIE WOO: Teaching is an endlessly creative profession, because when you’re in the classroom you really can do things any way that you want, and so I like to think that once I have a good grasp of, here’s where my students’ strong points are, here are the parts of mathematics that they enjoy, I can take those, I can accentuate them and the parts that they struggle with, once I know what they are, I can make sure I’m providing additional support underneath those areas. So as a perfect example, algebra is a struggling point for a lot of Year 7 and 8 students. They first encounter it and then they either get it really quickly – ‘oh this is just like patterns that I’ve looked at before’, or they learn it as a set of rules that are sort of arbitrary and they don’t really understand why, but if you do this with the brackets and you multiply both things then you get the right answer at the end. So if I understand quickly, alright students are struggling with this, then I’ll adapt the way that I explain things as I move forward.

One of the things that I love doing is demonstrating that every algebraic expression can be represented with a picture. It doesn’t matter how complicated it is, obviously it can start to get a bit tricky, but this goes all the way back to when the ancient Greeks were doing a lot of their work with numbers, they wouldn’t have said algebra the way we do, but they were constructing things, they were trying to construct, you know, irrational numbers and solutions to polynomials, they would do that all with geometry, and that’s why to this day, a pair of compasses and a straight edge are a necessary set of tools in every mathematics student’s repertoire. We get this connection between numbers and geometry from them, and even though now we’ve sort of left that behind in many ways, one of the reasons why it’s so useful is that if you can say to a student ‘okay A plus B, put them in brackets, two different numbers, any numbers you like, square that, A plus B, all squared’. The number of students who will say ‘that’s A squared plus B squared because there’s two things and you square them’, is countless. However, it is so simple to overcome that misconception by saying, ‘okay, you talked about something that was squared. Let’s draw a square. Let’s make that A plus B. It’s a square, so let’s make this A plus B. What emerges? There’s the A squared, there’s the B squared, but there’s these extra things, there’s these ABs. There’s two of them that are there which escaped your attention before’.

Drawing a picture often helps students. For others, who don’t need that, they just want to get straight into the algebra, they want to go straight to the symbols. They don’t want to have pictures in their way. So if I can identify, alright, here’s a weak point, here’s something where you need additional support, where I want to give you another analogy, another metaphor, another perspective or entry point into this topic, that’s where me knowing my students’ strong points and weak points is really valuable.

ALEX OO: Wow. Wow. So with all of that, that all assumes that students are really engaged right? That students are willing to pay attention, that they’re willing to struggle with something that is difficult that they need not just to listen once, but to see another perspective or another step, so how do you keep them engaged? How do you make sure that, you know, that they are focussed and not disruptive, because you know, you’re a dynamic performer. You’re a great performer, but is it something more than that, like do you have any tricks of the trade, or is it something more about what I’ve heard you say, the human role, you know, about really knowing your students and that relationship, that close relationship that we were talking about before? What is it that keeps your students engaged?

EDDIE WOO: Relationship with the kids and rapport is definitely the first ingredient, you know. If you don’t have that, all you’re doing is lecturing at kids and all you would have to do is walk into a university lecture hall and have a look at the attendance rate to know how effective that is as a mechanism. Not that lecturing is unimportant, but as a tool for connecting with students and convincing them to learn, learning is a social process. The primary job of a teacher is not to convey information, but through the social environment, help students feel accountable for doing the work of learning. That’s how they’ll learn. Not by having some really flashy presentation. So definitely, relationship as a foundation and you can’t go anywhere beyond that.

However, I think what I’d add to that then is, once you have got that great relationship with students and you understand the way they, what makes them tick, and they understand that you are there for their good, you’re there to help them, not to make their life miserable and difficult, after that I find probably the most essential thing is as the teacher, being a learner and really grappling with, and not settling for a baseline understanding of, okay, well I can teach these kids enough to answer that question in the exam or the textbook, but can I go beyond that? Can I actually dig deep into this concept and understand why on earth are complex numbers important? Who cares if you can take the square root of a negative number? Why should that matter? When I think about, for example, the work that I do trying to wrap my head around a topic that is challenging for me, that has two advantages.

When I actually spend an hour trying to wrap my head around some difficult concept, number one I develop empathy for the learner, and that’s so important. I think the other thing, after relationship with the students, that really improves the dynamic within the classroom so much, so dramatically, is for the teacher to make the commitment to do the work of the learner, to wrestle over a concept that’s challenging and not settle for a basic level of understanding, or just enough understanding to answer questions in an exam or a textbook. So you know, labouring over the book and saying okay, there are five lines of working here. What’s really going on from line one to line two. What’s going on and why are they doing that? Why would they even think to do that? And just pushing relentlessly on asking the questions on every single line that you’re working out. There are two benefits I think that flow from that immediately. Number one, when you spend the time to do that work, you develop empathy with the students and you understand very intimately yes, here’s a really challenging thing about this question. I know because I just experienced it and I can convey that live sort of, yeah I didn’t just learn this twenty years ago and this is self-evident to me, why isn’t it evident to you? Having that experience in the classroom is deadening for a child, because when they find something as challenging and their teacher, the person who’s meant to help nurture their learning, is patronising to them and is just frustrated that they don’t get it, which is understandable because the teacher’s work is hard, that’s really difficult for the student to get over because then they’re going to stop asking questions. They’re going to feel like, okay, you don’t really want to help me because you don’t understand how difficult this is for me.

But the other benefit that comes from it is that when you do the work of a learner, you discover cool stuff. You realise patterns. You understand things that you won’t do if you just skim the surface. I often like to say to pre-service teachers ‘you want to be engaging? Be interested in what you’re learning. Do the work to be interested because interested people are interesting’. People can tell if you are bored and if you are bored then what hope do the students in your classroom have, regardless of your key learning area, but I feel especially for mathematics. The teacher at the front of the room or the sides of the room talking to a student and having an individual conversation, the teacher is the lens through which your students experience the subject. So if what they’re getting is something which is tired and frustrated and really quite bored with this because it’s been the same for years and years and years, then they’re going to have the same kind of experience that you’re having. So we owe it to our students to recapture that interest and that excitement in what we’re learning, because learning things is amazing. It’s a miracle what human minds are capable of, so reconnecting with that, or connecting with it for the first time, I feel is just very powerful for teachers with students.

ALEX OO: So for you, all those like classroom management tricks and stuff, it’s not really about that to make sure that students are engaged, it’s really about authentically purveying the experience of learning in some senses, in that you’re trying to show that you’re excited about this learning, that you’re interested in the learning, also that you understand how difficult it is and actually authentically portray the difficulties and have the sympathy for them, and then also build those great relationships. With all that, we’ve been talking a lot about your particular teacher practice. Let’s talk about other teacher practice, because we’ve been touching on that a little bit, talking about other teachers, so you’re head teacher, how do you help your fellow maths teachers, your fellow teachers throughout the school, or you know, the pre-service teachers that you mentor, how do you help them to become the best teachers they can be?

EDDIE WOO: Helping pre-service teachers and in-service teachers to develop as educators and in their understanding of curriculum and their delivery of pedagogy is something I’m really passionate about, because like I was saying before about making a difference in the classroom, this is something that I know makes an immense difference to the impact, positively, that a teacher can have on their students.

I think there are a few different ways that come to mind when I think about it. Firstly, just getting in that classroom and observing. Watching a teacher, seeing the way they do things, and this is actually something that I’ve learned just from myself when I started videoing my lessons, and I think it’s that experience which a lot of people have, you learn what does your voice sound like when it’s from outside your head, and in exactly the same way, what do I look like when I’m at the front of the room and I’m explaining something, and I was shocked by some of the things that I realised, I do that? That looks terrible, or that’s not clear. Why on earth would I think to do that? And the answer was I didn’t think to do that, it was just instinctive and there are better ways that can be developed once we’re conscious of the way that we do things. So providing opportunities for teachers to be observed and to have constructive feedback given to them about, okay, I noticed this aspect of your lesson was great and this one just fell to pieces, let’s work on that. I think that’s the first piece.

I think the second piece is, as much as possible, providing for other teachers to come into my classroom, whether that’s through technology or just physically being in the room, seeing the way that I interact with the students. Helping people see, you know what, my way might not be the best way, but it’s another way, and having lots of tools in your repertoire and different strategies that you can take is so important for a teacher because every room that you’ve got has 30 unique people in it and requires access to a range of different strategies that you can use to help people be disciplined in their approach towards learning and understand things effectively.

So I would say those are probably my go-tos in terms of developing my own staff, constantly asking them the question of, when they come to me and they say ‘how do we do this effectively?’ Just like in my classroom I say ‘well, what’s this really about?’ I pose that question back to them, and often, teachers actually have access to, they have the resources, they have the knowledge to be able to say, oh, the best way to teach these statistics in class and the real meaning of a z-score or a regression line is to be able to say let’s have access to some real data. Let’s get data from you guys and then this will be so much more connected to you because you’ll understand its relevance to your life.

Things like that are things that we can often think through, so long as we have the time and the opportunity to workshop through those ideas with our fellow educators.

ALEX OO: Okay. So collaboration can be great, and it can be a great way to be able to improve teacher practice, and you were talking about having those constructive conversations and being able to give constructive feedback, but how do you make sure that it’s constructive and not destructive? There can be so much defensiveness and it’s just, for a teacher it can be scary letting somebody else into your classroom to be observed, to actually be judged. So how do you get around that?

EDDIE WOO: The very human impulse to receive feedback and just take that personally is something which is very challenging to overcome. I don’t think that there’s any silver bullet to actually make sure that the words coming out of my mouth are going to land on you and be received in a positive way to say, oh this is not about criticising my ability, it’s about developing me further, you know. I don’t think there’s one way that can be done, or even that there’s any particular suite of ways of doing this that is always 100% immediately successful. I think the most important ingredient to add into the way that I lead my staff to ensure that staff can hear that feedback and realise, okay, I want to take this feedback and I want to learn how to be better, is to develop that culture of being able to say, look, we’re here for the kids. This isn’t about us in the room. We are the least important person in the room. So therefore what this is really about is about doing the absolute best job we can do to ensure every student is learning, no matter where they are on the learning continuum, we’re moving them forward, we’re helping them improve, we’re helping them understand what they themselves are capable of and the kinds of heights that they can reach.

When the focus is placed on improving things for the kids, we can, all of us, take our ego, put it aside and realise, alright, yeah, I’m doing some things really well. That’s great. I’m not here to improve because I have to. I’m here to improve because I want to and I have the opportunity to, and why wouldn’t I, if I can improve the experience of students out there? I think developing that culture and constantly drawing our attention to what all teachers do, this is about doing work that benefits students. That’s the key ingredient.

ALEX OO: So I want to thank Eddie Woo, maths teacher extraordinaire, for sharing all his insights in education, teaching and especially maths. So thanks so much for coming today Eddie.

EDDIE WOO: Thanks Alex. It’s been great.