Hi, I’m Mark Scott, Secretary of the NSW Department of Education. Welcome to Every Student, the podcast where I get to introduce you to some of our great leaders in education. Today I am with Michelle Tregoning, our leader of mathematical professional learning K-12 for the NSW Mathematics Strategy. Michelle is an experienced primary school teacher and has led numerous high impact professional learning opportunities across NSW including building numeracy leadership. Before she started working with the NSW Mathematics Strategy she led numeracy for our Early Action for Success program working directly with 507 schools across NSW.
Hi Mark, how are you? Thanks for having me.
Good to have you onboard to talk about mathematics. There is a big new maths strategy launched here in NSW and there is a real sense that we want to increase student engagement and participation in maths and rates of students doing maths for the HSC and it seems to be very much a focus of everyone at the moment.
I am interested that you are leading the strategy for us but as a student you really didn’t see yourself much as a maths person and didn’t really have a positive experience with maths. How have you got to be leading the strategy for us?
In some ways I think it is good luck and a little bit of mismanagement perhaps on my behalf but in a really fortunate way. You are right I was a really, when I look back a disaffected young person at school. I felt that school really wasn’t a place for me, mathematics in particular was something I was really nervous about. I found it incredibly hard to remember which formula you were meant to apply on which occasion. I really wanted to know why and how things worked and at the time the best practice wasn’t necessarily built around these ideas of supporting conceptual understanding for students.
I had a few different opportunities in life before I came into education so when I came to start teaching the thing I was most nervous about was the teaching of mathematics. I was incredibly concerned that my students would leave the classroom feeling like I did about mathematics, that it wasn’t a place for them, there was nothing inside of that for them. Because I have always really enjoyed research, my background originally was in psychology and history, I just went to the research to find what it is that I could do better for my students.
My first year of teaching, within about three or four weeks, I had gone to the students with a great confession and I said to them look I don’t really know what I am doing and the kids were very kind to me and they said “that is okay, we like you and you are doing a really good job, keep going”, I said “what I’m seeing is when we come in and we are learning about things the same kids that understood it at the beginning understood it at the end and the students that are still finding it tricky at the beginning are still finding it tricky now”. For me that is indicative that something is not quite working.
I went and read this research and this guy says maybe we should try this. How about we become research partners and we look at what the research says and we test this out in our classrooms and you and I, you are my research assistants and we are going to see what works. One of my students said to me “do we get to wear lab coats” and I said “of course we do”. I went down to Big W in the afternoon and bought lab coats and this how we worked together where we would look to the research, I would talk to the kids about it and then we would work with them on getting really effective feedback from them about what was working and what wasn’t working and what worked for who.
My principal came into my classroom in my first year of teaching, just happened to come in and be bringing a message, she was watching what I was doing and she then asked me to share this with the staff that I was working with. I did and then the next year we have a consultant come in to work at the school and a colleague said to me “you really need to show Brian Tickle, who is a maths consultant, what you have been doing in your classroom”. I said, “I can’t do that, I’m too nervous, he’s Brian Tickle!”
She said “either you tell him or I do, which is less embarrassing?”. I shared with him the work that we had been doing with the students in the classroom and that created the snowball, he then invited me to start working and presenting at conferences around Australia and it just kept getting bigger until Peter Gould who was the Leader of mathematics for New South Wales, we used to refer to Peter as “Obi Kenobi", a really incredible leader of mathematics. He retired and I was asked to his office and he said to me that he was retiring and he would like me to consider filling in for in his retirement in Early Action for Success. I said to him, “oh gosh Peter, I can’t do that, I can’t be you”, he said “that’s okay Michelle no-one can be me just do what you would do given this opportunity and these challenges. That is how it happened.
That is a big Star Wars moment. I like the other Star Wars line the line of Yoda “Do or do not. There is no try.” You dived in and you have made this your own. Why is this such a challenge for us? We spend more time thinking about maths, engagement with maths students, understanding of maths than we do of almost every other subject combined. Why does maths have such a bad wrap or why have we been so challenged to engage in maths?
I think part of the challenge is that there is an identity crisis for mathematics. It is typically perceived as you are good at mathematics because you are the first person to the right answer. Whilst being able to recall and use number facts and formula is a critical component to mathematics it’s like if you try and look at the world through the lens of a microscope. You would miss seeing mountains, you would miss seeing the ocean, and you’d miss the broad picture. It relates back to this historical narrative around mathematics in particular, that when I went to school it was all about computation or following computation so this is what I am expecting to see. We know an awful lot more now about research. It is about getting those messages out to our schools and our teachers and then because there is such a tricky emotional space around mathematics because you are either good at mathematics because you are the first person to the right answer or you’re bad at mathematics because you are not the first person to the right answer. It means inside of a room of 30 kids there is two students potentially that are positioned to feel successful.
When we start to broaden our perspective of mathematics, when we see it as it is defined, as the science of thinking and reasoning, when we acknowledge that being able to recall and use number facts is equally as meritorious as having the tenacity to sit inside problems and to embrace cognitive dissonance and sweaty brains and really critical for learning, we can start to create different opportunities for everybody to feel successful in classrooms which allows for engagement to happen.
It means for our teachers and our parents that are really disrupting this historical narrative that we have told around mathematics and we need to really carefully nurture and support our teachers into seeing that mathematics is a place for them so that they can help afford that to their students.
There is so much in that. Previously on the podcast I spoke with Eddie Woo and Eddie of course means that you are only the second most famous maths teacher in NSW Education, I know you work close with Eddie. Eddie is very dismissive of that concept of maths people and non-maths people. You will hear that language in almost every classroom around the state at different times with kids and then also their parents and possibly even their teachers putting that tag on themselves that they are not a maths person.
What are our strategies? Talk a little bit more about the strategies you have developed to change that mindset in classrooms?
From a maths strategy perspective one of the things that we are doing is as much as possible. We have our big pieces of work and the desire of sustained ongoing professional learning on projects that we will be working with teachers as of next year and moving forward that comes with coaching support. We are really borrowing from the work of Paul Cobb and his colleagues that led large scale reform of system wide growth in mathematics in the US and he talks about really solid professional learning, it has to be connected to cycles of enquiry and cycles of enactment. It is not just knowing about the research and seeing how that plays out in our context but being supported and nurtured into enacting that in your classroom practice, to then come back and reflect again and move forward. To borrow from Dylan Wiliam he talks about that we are in the business of trying to form and change people’s habits and that is really hard to do without someone being with you at the moment, that you are sometimes speaking about mathematics in a way we want to shift or bringing a task into kids in a classroom that will perpetuate this messaging about mathematics.
It is these big initiatives but for us as well we are looking for all the microscopic moments, the fissures and the cracks that we can get ourselves into. We have reached out to the sport unit in Thinking While Moving so that we can refine just some of those really small semantic shifts that have insignificant impact on the way we talk about mathematics. It is really carefully interrogating the way we talk about mathematics in things like the Everyday Maths Hub. We are ruthless with the red pen when things come through to us for feedback about making sure that the messaging is neutral and positive and welcoming so that everybody sees this opportunity for mathematics for them.
Part of the critique has been that maths in school is very skills based and that students lack that conceptual knowledge to be able to deal with that. Talk a little bit more about your strategies at play around that.
The National Council of Teachers of Mathematics published some work recently about eight effective practices for the teaching of mathematics. One of the eight that they talk about is using conceptual understanding for the basis of procedural understanding. This is a real flip for a lot of our teachers who typically, there is this view of if you just teach the kids this first then you give them the problem that they can solve it in. What all of the research evidence is showing us now is that the problem solving, the reasoning, the challenging task becomes the space for our explicit teaching to take place and that what we need to be doing is building kids capacity for conceptual thinking and understanding. The reasons for that is because then when I have conceptual understanding my knowledge and my awareness is much more robust. When we rely on things like memorisation of procedures or number facts, my brain perceives that I am in a high pressure situation it is corrosive, my memory starts to not work as well.
When we can build concepts what we are actually doing for kids is changing their brains, we are supporting the development of Schema theory and the connection of ideas and it means that if I am under this pressure situation I am suddenly asked in front of people to solve seven nines and I now can’t remember that number fact, because I know seven tens I can now use that as the basis to work out seven nines really effectively.
To build conceptual understanding we use a framework from Tom Lowrie and his colleagues at Canberra University around creating really powerful experiences for students to see the mathematics at play. That then becomes the anchor for the language, then we start to play around with different ways of representing and exploring these ideas by mathematical modelling in various representational competencies, from there we link into the symbolic.
Typically what happens with mathematics is we move straight to the symbolic and we miss these early phases that are really critical in the development of conceptual understanding.
One of the interesting things, one of the challenges in education of course is that everyone is an expert because everybody went to school. Just thinking through what you are saying there, there would be some that would say “look seven nines we all had to learn seven nines, it wasn’t fun back then, it shouldn’t be fun now, just sit and do it”. I remember sitting at school and you would hear the chanting of the times table from classrooms up and down the corridor.
What you are saying though as I hear it is students will still know what seven nines is, they still get there but they get there in a way that is more engaging and is more likely to make the learning embedded and sustainable over time. You are making sustainable mathematicians.
You talk about the need to encourage students to wrestle with this because in order to do it the way you are doing it something might be hard and we are almost trained if something is hard or difficult to avoid it rather than dive into it. How do you work on the psychology of engagement around dealing with complexity and times when the answer doesn’t come quickly?
One of the things that we do talk with students about a lot is this idea of having a sweaty brain. I was fortunate enough a number of years ago to be part of a research project with the team at Western Sydney University around student engagement and we tussled with this problem of we know things like student engagement is defined as thinking hard, feeling good and seeing relevance in your learning, and when all of those three things are happening simultaneously for a child that is when we can say they are engaged. The only way to know that actually is to ask them.
I was working at Fairfield Public School at the time, 96% of students came from an EAL/D background. We really tussled with this idea of how do we talk to kids about how cognitive challenge, feeling good about their learning and relevancy and how do we specifically do it through this potential language barrier as well. One day as happens we had this great ‘aha moment’ and we started to talk to students about cognitive challenge is a bit like when your brain is out for a run. When you are out for a run you start sweating and what we want our brains to feel like today is that they are out for a run or we would say things like, today what we are doing is really practicing and cementing of these skills and understanding. We want you to feel like you are out for a walk but not sprinting uphill. Let me know if we have mismanaged the right level of challenge inside this task.
This started to work really well and in the end with the students we designed this thing called the sweaty brain climb where it is an image, a vocabulary climb that we use to develop knowledge of language with students that moved from my brain feels like it is sitting down watching TV fully chilling out to it is now sprinting uphill and in fact the opposite is I feel like I have fallen off the cliff and I am sweating because I have gone too far down the other side. We use this with our students, we use it with kids across K-6, we are now using it with students in secondary and we found that was really powerful in talking to the students about getting them a common language to be able to talk about how challenging they were finding something and where we had wanted or intended them to sit.
Alongside of that we have also explored with students what does it mean to learn and what does learning feel like. There is that critical importance of building growth mindset and the knowledge around when you are learning you should feel a degree of discomfort, this is a good thing and if it is too uncomfortable and you have fallen off the edge of the sweaty brain climb then we will help you manage that location but if all you ever feel is that your brain is sitting down pretty much watching television at school, that is not what we are here for. We really work with our teachers and our students around how important it is to embrace the sweaty brain because that means that we are learning today and that is what we are here for, we are in the business of learning.
The brain it’s said is the most complex object yet discovered in the universe and if you are a primary school teacher you may have 25 or 30 of those growing brains in your class and each of them are on a separate learning journey. I have often wondered part of the challenge in mathematics is it does quite often rely on sequential learning, you are building on a foundation that’s been previously built to move to higher levels of insight and understanding and if there are gaps in knowledge, if students are away, if they didn’t really get it then that hampers their ability to continue to build upwards but it also erodes their confidence.
How should teachers think and what role do you think assessment plays in giving us genuine insight in identifying where those gaps are and retrospectively building that foundation so that students can then move on with confidence?
I think assessment plays a critical role, in fact you can’t separate quality teaching and skillful equitable teaching in mathematics from assessment. It is about asking the right questions. Last year with Early Action for Success schools and a couple of years before that spent a lot of time working in partnership with Professor Dianne Siemon, out of RMIT, Di and her team led a really large scale project where they looked up what fundamentally are the things that are critical for things to have. She says what are lines in the sand? What are these big ideas that are so foundational to student understanding that if students don’t have these that we should be moving all of our resources to support students in the development of those skills and understandings, because this is foundational.
It started because they were looking at what is happening in Year 9 mathematics where we start to see this drop of student achievement and what they found was that the critical blocker was students’ capacity to move into multiplicative thinking. Then they mapped back and they said what is the foundation for multiplicative thinking and they found that place value knowledge and not a superficial knowledge of place value where you can say there is a two in the ten’s place in 526 but where you can really think flexibly about numbers and you can do something really nerdy in the research where they talk about renaming with confidence so it means I can look at 32 and know there is three 10s and two 1s but I can also say that there are two 10s and twelve 1s or one 10 and 22 1s. I have this real flexibility of number and that as the mathematician I know that I am charge of them too.
When kids don’t have this robust place value knowledge what comes before that is this idea of trust in a count or a number sense. What we do with our teachers is use assessment tools that dig into what do the students have in terms of their number and operational sense. What do we know about their place value knowledge, what can we see in their multiplicative thinking, and then use that to target teaching.
There has been a lot written about girls participation rate in STEM and it is still very interesting to look at the analysis of HSC results and the extension maths classes again, what is the participation rate of girls doing maths in Year 11 and 12 and extension maths. Just as you look at it as part of the maths strategy, are there any special things that we need to be thinking about as far as the engagement of girls in maths is concerned?
I think one thing is being able to see yourself in the field. I was working out in Wilcannia last year and one of their SLSO’s told this beautiful story, she was a student growing up in Wilcannia and we were comparing stories of how disaffected we were in our own high schooling and she was saying that she didn’t think school was for her, there was no place for her in it. It wasn’t until an Indigenous woman came in who was a scientist, that came to visit the school where she realised that someone like her from background and her culture could be a scientist. It always has stuck with me of how you theoretically know how important it is to see yourself near it or reflect it in spaces but that story really sat in my belly. I think that part of the solution is being able to show our students and our parents and our broader community that we are genuinely serious at every aspect of learning in NSW there is a place for you in it and to do that we need to be representing those groups be they women, be they young students from refugee backgrounds, be they students from Aboriginal backgrounds. I think that is part of the solution and I think the department has a good focus on trying to achieve that goal.
Another part of it I think goes back to earlier parts of our conversation around how critical language and semantics is. Anne Prescott and her team at UTS did some really interesting research work around the ways that women talk to girls about mathematics and they found that one of the most detrimental, yet entirely intended to be helpful, things that a female role model can say to a young female student is it is “okay darling I was bad at that too”. It allows permission for us to go that isn’t a place for me and it is delivered in such a nurturing way that we are both now confident by that point.
I am sure for some of our teachers need to deal with that too. It is a real challenge being a primary school teacher. If you are a high school teacher you teach in the subject areas of your passion, you can walk away from areas that weren’t of great interest to you or you didn’t feel as successful in and if you are a primary school teacher you need to teach it all and that means that even if you never saw yourself as a mathematics person you need to become one and you need to be able to model that to students. A continuing important part of the professional development work that you are spearheading for us in all of this.
Finally for the parents who are listening into this podcast how do they send those right messages and what is the thinking behind this Everyday Maths Hub that you have been associated with developing?
It is in the title that mathematics is everyday and it is everywhere. One of the most beautiful things, I was working at a school where they had some parent/carer sessions and the students helped us lead them. One of the first things we asked our parents/carers to do was to write down all the things you have done today, what are all the jobs you have done and then we collected them up on the whiteboard and then we went through and showed them all the mathematics in each of those tasks. Things like getting the kids ready for school in the morning and we showed them where the mathematics was, if they paid the bills we showed them where the mathematics was and that’s part of the goal of the hub is to be able to show our parents that not only is there a space for you in mathematics but in fact without mathematics we can’t function.
Mathematics empowers and underpins us no matter what we want to do or where we want to be. That when we are heading out somewhere with our family we are using mathematics to get us there on time. When we are creating and when we are doing art or we are building something at home, we are using mathematics to empower us into that. We can talk about mathematics when we are hanging the clothes out on the line or when we are preparing lunches in the morning, that it is everywhere and it is incredibly beautiful and creative and you can do really simple things like going along for a walk and collecting sticks and coming home and ordering them and having really rich beautiful mathematical discussions with your child because it is everywhere for you.
You can find more about that on the department’s Everyday Maths Hub. Michelle I want to thank you for your time today listening to you at how many researchers you have invoked, I know as you lead this maths work for the NSW Department of Education you are tapping into the leading global thinkers in this work as we try and create an environment where every student is flourishing, where every student is improving, where every student is confident about maths and able to apply this mathematical insight across all their learning in a way that really sets them up for a vibrant future.
Thanks for your leadership and thanks for your commitment and thanks for your passion for mathematics and thanks for joining us today on the Every Student Podcast.
Thank you for having me.
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Thanks again and I will catch you next time.
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