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Announcer: You’re listening to the Fizzics Ed Podcast. For hundreds of ideas, free experiments, and more, go to fizzicseducation.com.au. And now, here is your host, Ben Newsome.

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Ben Newsome: Yes, welcome again for another Fizzics Ed Podcast. Glad to have you again wherever you are in this world. We are talking about STEM, and importantly, we’re talking about the M in STEM today as we hang out with Michaela Epstein, who is the founder of Maths Teacher Circles, where she has worked with over 700 primary and secondary teachers from all over the place to share expertise and uncover new different teaching ways to make mathematics meaningful and, frankly, fun for students of all ages. Now, she has a strong background in teaching mathematics. She used to serve as the president of the Mathematical Association of Victoria and on the council of the Australian Association of Mathematics Teachers. She has a background and a half when it comes to making mathematics really meaningful for students. And today, we’re going to have a real bit of a fireside chat, so to speak, and learn just how she goes about her thinking for teaching maths. So, without further ado, let’s listen in to Michaela and find out just what she does with Maths Teacher Circles.

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Announcer: This is the Fizzics Ed Podcast, for all about science, edtech, and more. To see 100 fun free experiments you can do with your class, go to fizzicseducation.com.au—that’s fizzics spelled F-I-double Z-I-C-S—and click 100 Free Experiments.

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Michaela Epstein: Yes, yes, I consider myself pretty lucky that I get to play around with maths ideas and talk to teachers every day. Like you say, it’s such an important part of learning, and I think the more that we can have great mathematical conversations and bring teachers together to uncover great maths ideas, the better.

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Ben Newsome: No, absolutely. So, I’ve gotta ask, how did you get into this sort of thing?

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Michaela Epstein: So, I have a secondary teaching background. And I suppose reaching even further back, I’ve always had a love of maths. And I was inspired by my Nonna when I was growing up. She always shared fun games with me, puzzles, logic problems, card games. And so to me, maths was always this fun thing, like, you know, challenging and surprising and interesting. And so when I started teaching, I really wanted to pass that on to my students. But I suppose reality struck, and I faced what most teachers face, which is this enormous spread of confidence, interest, capabilities in a maths classroom.

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Michaela Epstein: And especially in the early years, I felt really frustrated because I didn’t feel like I had the skills and the tools at my disposal to really adequately reach out to all of the students in my class. And so I wanted to learn from other teachers, and that’s kind of led me down the path to where I am today to provide spaces where teachers can come together to enjoy maths and share their expertise with one another.

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Ben Newsome: Oh, fantastic. I mean, making it real, it matters. I mean, how many times—I mean, a lot of our friends, family, and everywhere else, when they talk about mathematics, sadly, it’s not always in the greatest light, which is a sad thing when you think about it because I mean, it’s like fundamental to everything. Everything seems to work with behind it all. I mean, how do you combat that?

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Michaela Epstein: Yes, that is the lifelong question, Ben. And I wish I had a straightforward answer for how you combat it because I see that it’s this deeply ingrained phenomenon in our culture around people’s fear and attitudes towards maths. But I guess I see that there are some small things, some small steps that we can take that actually go quite a long way. For example, helping parents to understand how their language matters. So if they didn’t feel like they were successful with maths at school or they don’t feel like they have a good grasp of it now, they can use that to actually empower their kids to help their kids to see that, “All right, well, maybe this is tough, but let’s look at this together. Let’s see how we can overcome it and find out more together.”

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Michaela Epstein: So, you know, parents have a role to play. Teachers obviously have an enormous role to play. And for teachers, I always see that some of the small things are around sharing interesting maths ideas, fun maths ideas, and helping students to see that it’s not always a black-and-white subject, but it’s actually quite a colourful one where there are interesting puzzles and problems to uncover and you can actually be quite creative with it. And I think that’s an idea, creativity, that’s not often associated with maths, but it deserves to be. And it can really help people to see maths in a different light.

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Ben Newsome: That’s interesting when you say creativity because I remember we were speaking actually just prior in the green room, we were talking about a past guest, Asha Rao. Hi, Asha, if you’re listening, love your work. But she did mention creativity as well. I mean, creativity, I mean, people have their own take and I mean, in a lot of ways, just the very essence of being creative is even defining the word. But being creative in mathematics, I mean, what does that look like? Does it look like using different strategies to solve said problem? Or what does that look like to you?

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Michaela Epstein: Yeah, good question. I think quite often it is around using different strategies. And what’s important when you have creativity is that you have a problem that students want to solve. That motivates the creativity and inspires students to find different solution paths.

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Ben Newsome: I’m smiling just now just thinking about my little ones. Okay, they’re only little at timestamp right now; they’re 13 and 10. But they all right now, they love doing this, school did this number busting when they were very, very young, like Kinder and Year 1. And just different ways we can play with this couple of integers. They loved doing that, until, you know, kids start to then layer their issues around mathematics. It does come up. But initially, they love playing with strategies and seeing if they can get the 20 different ways we can divide 20, or whatever it was.

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Michaela Epstein: Yes. Yeah, and it’s really interesting that you bring up this example, Ben, of when your kids were younger. And I think often we see in the earlier years of school some really clever, creative maths ideas. And then there’s a challenge as students get older and older, where there’s so much curriculum content to just get through and pressures that teachers are under.

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Michaela Epstein: And also combined with that, maybe a misconception or a common perception that we think older kids don’t like those sorts of activities anymore or, you know, they’re too old for it. But I actually think that older kids sometimes do like to just play around, and there’s no harm in introducing that playfulness and, you know, letting them go.

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Ben Newsome: Oh, totally. I mean, as you were saying that, I was just thinking about some of the memes that you see on Instagram around especially engineering. “When in doubt—this is for all the engineers listening—when in doubt, PV equals nRT. No matter what, it just does.” They’ll just go into this simple, this formula so that they go, “Look, if we can’t work it out, at least start throwing stuff into a formula and see what sticks.” So, it’s like this initial start. But I mean, okay, it’s said in some glib humour, but it’s a start. I mean, sometimes like you hit this blank wall. I mean, I know I’m not a spectacular mathematics student, but at least making a start will get the brain going a little, I feel.

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Michaela Epstein: Yeah, yeah. There are a couple of questions that I’ve learned from others over time that are a really lovely way to start a maths problem and kind of very much linking into what you’re saying. So, if you imagine that, you know, we could present students with something that might typically seem really boring, like an algebraic equation that they’re working at. And you ask them the questions: “What do you notice? What do you wonder?”

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Michaela Epstein: And what you’re doing there is you’re getting students to slow down their thinking and you’re also honouring their insights and the perceptions, and you’re saying that it’s not just in this problem about laying out your working in a particular way, but there are some subtle things going on. Let’s have a think about it. Let’s see what you notice. Let’s connect it to other areas of maths and other problems that you’ve done. And I think when there are those opportunities to just slow down and to wonder and to think a bit more broadly, you can bring in that creativity and you can bring in that more kind of also intrinsic interest, I think.

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Ben Newsome: Oh, totally. I mean, I remember speaking with Steve Sherman, who runs a group called Living Maths out of South Africa, quite a while ago—it’s one of the back catalogue episodes. But he was talking about how he had a student who would stare out the window the whole time during his lessons. And he did find out that this kid was hyper-interested in stuff that was happening outside. And so he would then layer mathematics questions over what the kid was actually interested in. I mean, let’s be honest, the kid wasn’t paying attention in the main lesson; he wasn’t at all. But he was able to pull the kid back into the fold, so to speak, by talking the kid’s language, and that sort of worked.

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Michaela Epstein: Yeah, yeah. It is interesting. So with Maths Teacher Circles, we have all sorts of different guest presenters who come to our professional learning sessions, and I do a lot of work with them in the lead-up. And these are consultants, and academics, and classroom teachers. And what they do is they choose a problem to run with a very diverse group of teachers: primary teachers, secondary teachers, new teachers, super experienced teachers, all of that.

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Michaela Epstein: And so they have a challenge of finding a problem that will be broadly accessible. But I also tell them to choose something that they themselves are curious about. And when you have a problem that you have interest in, then you pass on that interest and that enthusiasm that you have to others so much more richly. And that problem is far more likely to be taken in and for those who are listening to it and learning about it for the first time to run with it in many different directions.

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Ben Newsome: Oh, for sure. I mean, I could imagine if I was pulled into that group. One of the things that blew my mind when I was in early high school and it still breaks my brain in some ways: you can have something with the same perimeter but the area’s different. What? How does that work? It’s not intuitive. Like when you look at a plane and you understand the mechanics of how the thing flies, but that doesn’t mean I like it, you know? Like it’s weird, and maths is filled with these little strange things that happen.

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Michaela Epstein: Yes, yes, that’s it. So, you know, take two numbers and add them together. What happens? What do you notice about the result? Now keep one of those numbers the same and choose another number. Now see what happens. What’s happening with whether they’re odd or even? You know, whether they’re multiples of other numbers? You just take very everyday instances of things and you can find such rich results.

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Ben Newsome: For sure. I was just thinking about the poor parents. I mean, a lot of us are children of the ’70s, ’80s, and ’90s, or maybe older. But we’ve got the kids and they’re going through and they’re seeing new strategies. So, like every other discipline, new things come up and new ways of teaching said things come up. And the constant feedback is, “I don’t understand the strategies.” They’ve gotta learn just like the students do. How do you sort of work with the parents when it can seem almost alien when they’re going, “Hang on, I used to do long division in a different way”? How do you work with the parents on that side?

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Michaela Epstein: Yeah, it’s tough. And I think part of this conversation is around seeing that maths has to be done in a particular way. And what’s interesting is that there are reasons why parents and older people were taught things the way they were taught them back in the day, because often that was the most efficient way most of the time if you took that strategy.

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Michaela Epstein: However, what we’ve come to realise and what curriculum writers and teachers have come to realise more recently is that just because a strategy is most efficient doesn’t mean that the student understands it or doesn’t mean that it’s going to work in every instance of a problem.

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Michaela Epstein: So in maths at the moment, there’s this lovely layering of the curriculum with something called the proficiencies: problem-solving, reasoning, understanding, and fluency. And it’s all about getting students to think in different ways and develop their understanding and their flexibility with how they do maths. So we want students to be able to approach different problems and not just go, “Oh, this is the one way I’ve been taught; I have to do it that way,” but to be able to think critically—which will be the best approach to take? And if you think about it, that’s actually a lifelong problem-solving skill.

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Michaela Epstein: When young people, outside of the classroom, beyond school—whatever problems they’re tackling in life—we want them to be able to look at a problem and think, “What instances can I compare this to? What tools do I already have available? What makes the most sense here?” rather than just copying and pasting something that they’ve seen before that may not match the situation in any way at all.

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Ben Newsome: Oh, totally. And I’m going to get this wrong, and I’m happy to get things wrong because I don’t mind because I’ve got a growth mindset. But I was thinking about the movie Hidden Figures as you were talking about how if I go back to first principles from over a thousand years ago—whatever it was—if I apply this idea, I can solve the trajectory to the moon.

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Ben Newsome: And I can’t remember what version of mathematics it is, so feel free to say, “Ben, what are you doing?” But I love how the whole little snippet of that particular movie was the brain ticking into overdrive and trying multiple different ways to solve a problem—frankly, with chalk and a slide rule—and to solve something that was spectacularly difficult but using something that was geometrically designed and thought out over a thousand years ago to solve a problem then. That’s a point in case of there are many different ways to cut that pie up.

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Michaela Epstein: Yes, yes, that’s it. And the most complex problems in the world haven’t been solved for a reason, and that is purely that the existing strategies that we have don’t work. So if you’re going to solve new, tough problems, you need to be able to think differently. And like you say, often that means going back to first principles and undoing your thinking and being patient with yourself and all of that.

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Michaela Epstein: I think it’s wonderful. I love being in that headspace and the challenge of problem-solving. I think it’s a really beautiful space to be in, particularly when you can just be patient with yourself and see that the challenge isn’t about your own failing as a person; it’s actually just a natural part of working your way through something that’s quite tough.

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Ben Newsome: Interesting. Actually gets me thinking about the applicability of the work done in the maths circle that could be done in corporate circles. That whole headspace around “Let’s see if we can solve a problem even if we’re uncomfortable with it.”

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Michaela Epstein: Yes, yes, you’re absolutely right. There’s probably a lot of application here.

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Ben Newsome: No, that’s awesome. So just curious, if you had to get helicoptered back into a classroom, what grade do you like teaching out of all of them?

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Michaela Epstein: Oh, good question. So, yeah, I mostly taught in the middle years, like junior secondary. I actually reckon I would love Year 5 or 6. Kids are really sophisticated thinkers and I’ve got a young niece and nephew. My own daughter’s only one year old at the moment, so I’m still kind of—she’s not quite at that stage of explaining heavy mathematical ideas yet. But my niece and nephew, I’m constantly surprised by what they can do at a very young age. And so I would love to work with that primary, upper primary level and just explore territory that I think previously I didn’t have an expectation that they would be able to do. But I think I would try and approach that differently.

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Ben Newsome: I really like that. I mean, we are bound by said curriculum like all of us educational practitioners. However, I care about “What can you do?” like now. And that can be a very broad range. Age becomes irrelevant at some point. I mean, if we think about if someone’s never seen something, whether it’s robotics or whatever it is, they’re starting at the base level even if they’re 50 years old.

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Ben Newsome: It’s irrelevant what can you do currently. And there’ll be some kids who are eight years old who are beyond proficient; they’re hyper-into it. They know exactly what they’re doing. And it’s kind of like, I think that’s just the really the part to work with is when we know what they’re—not just—it’s not a cognitive capability, it’s just “Can they do a thing?” and “Where’s the point where it gets fuzzy? Where does it get grey? Where does it get difficult?” That’s the part we’re going to work on. And that’s different for every learner.

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Michaela Epstein: Yeah, yeah, that’s it. I was actually working with some primary teachers from across Victoria the last couple of days, and they were shown this activity, and I was sitting there watching that gets you to think about the idea of arithmetic with integers using the concept of walking a plank.

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Ben Newsome: Okay.

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Michaela Epstein: So it’s like you imagine you’re on a pirate ship and you’re walking either towards the sharks in the water or back onto the boat. And it’s a very concrete context, and in this activity, you roll a dice and the dice tells you whether you’re facing forwards or backwards and how many steps you make. But as you engage in it and play around with it, you start doing exactly the same processes as when you’re doing integer arithmetic.

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Michaela Epstein: And in this session, we learned how kids in, you know, Year 4 or something can do this super fluently, and they’re the sorts of questions that kids four years later in Year 8 just struggle with. And so what it highlighted to me was how the way we present things really matters, and the context can turn students off or it can actually make ideas that seem complex much more straightforward.

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Ben Newsome: Oh, totally. I was just bringing myself back in time to when I was in Grade 3 or Grade 2, one of the two. And being explained greater than and less than. And our teacher was really simple. It was like, “Just think of the symbols as a crocodile, and the crocodile is hungry and it just wants to eat the bigger thing.” That’s all it is. And to this day—I’m 44—and I still think of the crocodile. Because it’s so simple. You know what the crocodile—”I’m going to eat the bigger thing.” I’m cool with that. I mean, perhaps I probably need deeper understanding, but you know what? It works.

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Michaela Epstein: And I love this example and I love that you said that you still use it, Ben, because sometimes we can be a bit cynical when we hear these examples. We’re like, “Oh, yeah, this isn’t real learning. Students at some point need to learn the formal symbols or explanations or whatever.” And it’s like, well, maybe, but the pathway to that is connecting with things that are within their realm of understanding. And if that’s crocodiles eating things, then so be it.

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Ben Newsome: Totally. Okay, you know what? Those people listening in, I challenge you. How many days are in May? And now how many of you start thinking about the old song about “30 days hath September, April, June…”? I bet you a bunch of you do it right straight away. I still do it. You smile, so I suspect you do it.

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Michaela Epstein: I was thinking about my knuckles, actually.

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Ben Newsome: Oh, you do the knuckle thing! I know the knuckle thing. I do remember those. But there—okay, perfect case in point: two different ways to achieve the same answer.

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Michaela Epstein: Yeah, yeah. And two different ways that are in no way connected to the scientific concept of time.

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Ben Newsome: That’s right. That’s right in different calendars, definitely. But that’s the point. So righto, so I mean, flicking back to the sort of work that you do, this is it. If we’ve got different strategies that might get us to the end goal, great. And the more tools in the kit, you’re going to have more chances of doing it.

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Michaela Epstein: That’s exactly right. It reminds me there’s some work by Professor Di Siemon. She’s a researcher in maths education. And she’s written about how any model that you use in mathematics, it’s got limited value. So it can do a whole lot to bridge students’ understanding, but at some point, there will be examples and problem situations where that model doesn’t work.

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Michaela Epstein: Now, that doesn’t mean that that model isn’t relevant or useful. It just means that you need to be aware of those limitations and be ready to draw in new models. And I think it’s exactly the same for, you know, the rhyme about the months of the year or about crocodiles eating or whatever it is. Like, they will all play their role in helping us to understand new things.

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Ben Newsome: Totally. And I love this. So with that in mind, if you had to sit in another maths circle right now and you had a bunch of different teachers pop in the room and they’re all going, “I don’t know which strategy to teach; I’ve got all these things coming at me,” what would be your advice to ease their minds around this thing with teaching tools and mathematics?

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Michaela Epstein: Great question. My number one advice for teachers is to go out and do the maths yourself. There are a couple of reasons for this. Firstly, when you do some maths like the problems, the tasks, whatever it is that you’re going to present to your students—when you do it yourself, you will automatically develop a far deeper understanding of that content. You’ll understand the successes that your students will inevitably have as well as the challenges. You’ll start to think about the strategies that they’ll use, and you’ll then through that be able to empathise with their situation and be more prepared with, you know, extra questions and prompts for your students when you go into the classroom.

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Michaela Epstein: I think the next step also with that is not just do the task yourself but also to invite your colleagues to do it. Because there you have the multiple strategies. I promise you, spend five minutes in a meeting and collectively do a problem like 27 times 5. Now ask that problem to 15 different teachers, and you’re guaranteed to get close to, if not that many, different strategies. And I think that’s the fascinating and awesome thing about maths. And, you know, you and your students will have a really rich experience through questions like that.

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Ben Newsome: I love it. I was actually just thinking just then, it’s really just a game. It’s like a game with numbers. If you approach it from that way, it’s like, “How can we do this this way?” which is fun.

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Michaela Epstein: Yes, look, I secretly think that sometimes the less seriously we take maths, the better. I think, you know, we see that maths is very important, and it is. But it’s also great fun, and we should have as much fun with it as we can.

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Ben Newsome: Yeah, oh, I love it. That’s awesome. Hey, how do people get in touch with you?

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Michaela Epstein: So they can head to the Maths Teacher Circles website, mathsteachercircles.org/fizzicsed. And they can find out more about what’s coming up. We run regular sessions throughout the school year and you can join us through a circles membership. You’ll have time to do maths and explore fascinating problems and talk about interesting teaching strategies with other teachers. You can also follow us on social media, Maths Teacher Circles on Facebook and on Twitter.

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Ben Newsome: Excellent. No, definitely, definitely reach out. Do they have to be Australian-based?

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Michaela Epstein: Oh, absolutely not. So, thank you, COVID! We run our sessions online, and we actually—it’s amazing the great collaborative tools that are available. So we have people who join from literally all over the world, including some of our presenters. And our sessions are also recorded, so if the timing doesn’t quite work for you, then you get the recording afterwards as well as all of the goodies that come with the session.

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Ben Newsome: There you go. Awesome. Gotta love that. There’s always a silver lining to everything.

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Michaela Epstein: Absolutely, there is.

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Ben Newsome: Awesome. Look, thank you so much for popping on. This has really been fun to have a chat.

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Michaela Epstein: Thanks so much for having me, Ben.

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Announcer: We hope you’ve been enjoying the Fizzics Ed Podcast. We love making science make sense. Why don’t you book us for a science show or workshop in your school? If you’re outside of Australia, you can connect with us via a virtual excursion. See our website for more.

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Ben Newsome: Well, I hope you enjoyed that chat with Michaela Epstein. How fun would it be to be in her classrooms learning mathematics in a way that’s meaningful? I love it. And if you want to know a bit more, head on over to mathsteachercircles.org/fizzicsed, so F-I-double-Z-I-C-S-E-D, and find out how you can get involved.

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Ben Newsome: As she mentioned, you can get involved no matter where you are around the planet. And how good would it be hanging out with a whole bunch of motivated teachers who, just like you, want to be able to make mathematics really make sense to students in multiple different ways? And that’s very much what we talked about in that chat. So, look, I hope you enjoyed this particular chat. That is the end of this particular episode. But as usual, we have more things coming up. You’ve been listening to me, Ben Newsome from Fizzics Education. This is the Fizzics Ed Podcast, and I’ll catch you another time.

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Announcer: You’ve been listening to another Fizzics Ed Podcast. We’re excited about science. Subscribe to us on iTunes to download the next episode as soon as it’s released. And don’t forget, for hundreds of ideas, free experiments, our new Be Amazing book, and more, go to fizzicseducation.com.au—that’s fizzics spelled F-I-double-Z-I-C-S.

[00:27:59]
Announcer: This podcast is part of the Australian Educators Online Network, aeon.net.au.

Frequently Asked Questions

What are Maths Teacher Circles?

Maths Teacher Circles are collaborative communities where primary and secondary educators come together to engage in mathematical problem-solving. These circles allow teachers to share their expertise, explore new teaching strategies, and rediscover the joy of mathematics in a supportive environment.

How can I help students who have a negative attitude towards mathematics?

One effective approach is to change the language used in the classroom and at home. Instead of focusing on right or wrong answers, try using prompts like “What do you notice?” and “What do you wonder?” This honours the student’s insights and encourages them to see maths as a creative, colourful subject rather than a series of black-and-white rules.

Why is creativity important in teaching mathematics?

Creativity in maths involves finding different strategies to solve a single problem. By encouraging students to be creative, we move away from rote learning and towards flexible problem-solving. This helps students understand that if one method doesn’t work, they have a toolkit of other ideas to draw upon.

Should I teach my students the most efficient strategy first?

Not necessarily. While efficiency is important, it doesn’t always lead to deep understanding. It is often better to let students explore a problem using their own models and strategies first. As they develop a concrete understanding, they can then be guided towards more abstract and efficient methods.

Can I join Maths Teacher Circles if I am not located in Australia?

Yes! Thanks to online collaborative tools, Maths Teacher Circles sessions are accessible to educators globally. Sessions are held online and recorded, so teachers from different time zones can still benefit from the expertise and resources shared during the meetings.

Extra thought ideas to consider

The Value of Adult Mathematical Play

When teachers take the time to do maths themselves—not just for lesson planning but for genuine enquiry—they develop a deeper empathy for their students. Experiencing the frustration and eventual triumph of solving a tricky problem helps educators better support students through their own learning hurdles.

The Limitation of Mathematical Models

It is important to recognise that every mathematical model has its limits. A strategy that works for whole numbers might not work for integers or fractions. Encouraging students to understand the “why” behind a model prepares them for the moment that model no longer applies, fostering true critical thinking.

Discussion points summarised from the FizzicsEd Podcast, verified and edited by Ben Newsome CF