Honeycomb hunting, Spirit levels, and more. The crew are lucky enough to be joined by the amazing Debbie Lee, Maths Lead, Year 4 Lead and teacher at Overchurch Junior School, Wirral, to chat about content strands. Which content strands need more love and exposure? What real-life maths examples can we show to children? Plus, Andy takes us to the 11th dimension, almost.
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Hi, I'm Andy Psarianos.
Hi, I'm Robin Potter.
Hi, I'm Adam Gifford.
This is the School of School podcast.
Welcome to the School of School podcast.
Welcome back to another episode of The School of School podcast. I'm Robin and I'm here with the usual suspects. Hi, Adam.
And Andy, how are you? Andy?
Hey, I'm great. Thanks for asking.
Fantastic. Well, we have a great guest on today. I love this guest. She is just so knowledgeable about so many things maths related. Debbie Lee, welcome. She is a maths lead at Overchurch junior school in Wirral. So, welcome Debbie, and feel free to introduce yourself a little bit more.
Yes, I'm maths lead. I'm head of year four and year four teacher and very enthusiastic about maths and I teach using Maths — No Problem! So, I teach maths every day. I'm fully in the classroom. And I'm here to have a chat today.
Yes. And now you're here, so thank you for coming. So, just before we started recording, we were discussing, well, the four of us were chatting about, well, all things maths. And Andy has his bee in a bonnet right now about all kinds of things he's been reading about. So, as we were discussing, we thought, "Hey, maybe we should record this."
So, we decided we'd talk about content strands for mathematics for primary schools. Now Andy, I know as much as you'd love to start this conversation-
I'd love to start.
... talking about, oh, okay, maybe-
No, no, no let's do ... Debbie, Debbie can have the first one.
Okay. Can we get Debbie to start?
I mean, it was an interesting chat actually, because you do notice as a teacher that some children shine in parts of the maths lessons that actually find other things quite hard in maths, or perhaps ... It's the same across the curriculum, where you get a child who shines in art or PE. It's exactly the same in maths. So, things like geometry in particular, shape and space. Some children find that easy and some children who find the problem-solving and the number side easy, actually don't find this part easy. So, for some children they see it and some children. So I think the different strands are quite different. So I know, Andy, you had quite a lot of questions on this.
Yeah, well, so this stems from personal interests and I think Robin was alluding to, I've been reading some pretty, I guess nerdy maths books, some written by mathematicians, some ancient texts as well, written by some of the founding fathers of mathematics. Euclid's work in particular is what's fresh in my mind right now and his work on proofs and that kind of thing. I was just thinking we have this obsession about calculation in primary school mathematics.
I think sometimes it comes from an oversimplified view of people who aren't really that familiar with mathematics, or don't have much more of an understanding, let's say, than what they learned in primary or secondary schools themselves, which is a lot of it probably in the past was calculation focused. And then that's their understanding of what mathematics is. But if you look at what's happening in the modern world right now, and particular I'm thinking about things like artificial intelligence and this explosion of mathematical concepts that are happening in the physics world and in astronomy, and all kinds of stuff.
A lot of it, I mean, obviously calculation is important, it's always important, but a lot of it has to do with what you highlighted Debbie, geometry. It seems to me like geometry is the key to a lot of these things. We don't talk a lot about it. No one's obsessed about geometry. You hear people saying that, "Oh, our kids need to know the internal angles of triangles by the age of ... " geometrical principles of ... they don't talk about that stuff. Everyone seems to be obsessed with times tables for some reason, which actually seems to me is the least of our problems, anyway. So, it got me to thinking, what are all these different strands that we teach in mathematics? Because other things that we don't really talk a lot about is things like probability and statistics and all these kinds of ... but they're so important in the modern world, but we all seem to be hyper-focused on calculation.
And now with the new Labour government, the big buzzword is financial literacy as well, which is another one. So, I just wanted to put that out there. What are these different strands that we teach of mathematics and where do they lead to and which ones are important and which ones resonate with what children and all that kind of stuff. So, I don't know, Adam, what do you think about all this?
Yeah, I think this is a hangover, excuse me, a hangover of assessing calculation, like memorise formulas, regurgitate, prove that you can memorise it because for a long time, that gave you credit, that validated you as a mathematician. So, there's one part of it, is that I think that there's a legacy of assessing calculation that being able to calculate without necessarily the application of it anywhere or being able to look around your room and apply any mathematical principle or theory to your immediate surroundings. So, I think that's part of it.
I think the other thing too is that I think ... I don't know how many people know a full-time mathematician. So, I think when you talk to full-time mathematicians, and I know a few, they're not talking about the times tables, they're not talking about ... What they're talking about is a language and something that is almost like a story, a narrative, ideas that are creative and artistic. I think that we still suffer in mathematics, an identity crisis of what mathematics is about, of how we see it and how we use it, and the curiosity it can create.
I just recently read a book, Seven Brief Lessons On Physics by a guy, Carlo Rovelli. If you've not read it, it makes it accessible. And it's some really big ideas in physics, but it's so lovely because it tells a story and mathematics underpins it, but we're not hung up on the actual mechanics and calculations of it. I think that part's missing. I think that part's missing.
Yeah, exactly. So it's like, okay, it's important to be able to add up three numbers. We know that that's important, but that in itself doesn't lead you anywhere. It doesn't solve any huge problems. But you need to say, "Okay, well yeah, that's a prerequisite." It's just like if you want to write a book, you need to know how to structure a sentence, you need to know how to spell words. But largely, that's not the problem that we're trying to solve. That's just vocabulary things which you need to learn. And we become obsessed about those things in primary school mathematics.
But actually, what we want people to do is write a book that shares an idea, that communicates to somebody else another concept or another idea that they may not have thought about or to record their thoughts, or whatever it is. It's not about the vocabulary, it's not about the spelling, it's not about the grammar, although you need to know those things.
But in primary school mathematics, we seem to be obsessed with the grammar and the spelling and the vocabulary, and we forget about what the story is that we're trying to tell. And it's a bit of a problem. And geometry is the one for me I think, that opens up so many possibilities and it's just being able to think about certain things in a different way. I don't know, let me just give you an example of what I'm talking about.
So, if I said to you, "Can you draw three points on a piece of paper that are equally distant from each other?" You probably say, "Yeah, I think I can do that. I can draw three points on a piece of paper and each one is equal distance from each other." By the way, if you line those up, that's called an equilateral triangle. So, you can think about how you might be able to do that. Now, if I asked you the question, can you draw four points on a piece of paper that are equally distant from each other? You can try, but at some point you'll realise, well actually it's not possible for me to do that. It's not possible to draw four points on a piece of paper that are all equally distant from each other. You can only do it with three.
But if you add another dimension, if you make it a three-dimensional shape, you can, it's called the prism, triangular prism. An equilateral triangular prism. All the points are equally distant from each other. So, now here's an interesting concept. By introducing another dimension, I can now solve a problem that I couldn't solve before. That's an interesting idea. So, why do you think mathematicians do maths in like 11 dimensions sometimes? Because some of the problems can only be solved in 11 dimensions, even though we can't even imagine what 11 dimensions means, mathematically we can do it and then we can solve a problem in that geometrical space, that you can't solve in the real world. But now all of a sudden, because you've opened up what your definition of geometry is, you can now solve problems that were unimaginable to solve before. Well, that's a crazy idea.
Well, that's how artificial intelligence works, is because we don't have these physical limitations. We can do things like this, so we can link things in ways that we can't link in the real world by using this kind of stuff. Now, okay, I'm going on a real stretch here of imagination of trying to imagine what this looks like, but that's a geometrical problem. We're solving really complex problems that we can't solve in the real world by altering the geometry. So, simply by altering our geometry that we decide to work in, we can do things that we couldn't do before.
This is the kind of mathematics that really advance stuff is going on in. And are we equipping children when we fixate on, let's say calculation, are we opening up their minds to these kinds of possibilities? So, that's what we need to think about. What's the future world look like? It's going to look different than what it looks like right now. So anyway, I don't know if that's even imaginable what I just mentioned to you guys, but it's an interesting idea, right?
I mean, I just would like to draw on that really, because I recently took a group of children were invited to John Moores University. It was an engineering day empowering women engineers, and I took year four, five, and six, and it was just amazing. And we had a robot and we went to all these different workshops and it was all STEM. It was all about encouraging girls into engineering. And we did, we built things. It was just incredible. It was such an amazing day. But it made me start to think about the jobs that not just girls want to do, the jobs that any children would want to do in the future, kitchen fitter, bathroom designer, engineer, all of these things use maths, but they're all problem-solving maths. So, I just think the spatial awareness of it, somebody can plan a bathroom. Some children would see that they could fit it in that way, other children would have the bath sticking out and wouldn't be able to work out that actually that wasn't the best use with squared paper.
I mean, that's a low-level example, but you guys are hypothesising on them, "Ooh, right up there." And I'm just thinking about children and what they're going to be when they grow up and how exciting it was to be invited to John Moores University and see that maths was so huge and why they're so keen to get the children into science. But maths is a big part of it and it is not about number, a lot of it. It is about these other strands.
Yeah, that's great.
So yes, thank you for bringing it back. Debbie. Just to be clear, I'm not hypothesising with Andy and Adam on this, so I greatly appreciate the real world example, and I'm sure some of our listeners do too.
Yeah, but, but, but, but, but hang on, because I don't think we're at odds here. Because I think that all of this stems from conversations and curiosity. So, I've got no doubt that a very young Albert Einstein, for example, wandered around the world just with wide eyes, curious, curious about stuff. And that's what I think. But mathematics can provide a language or something that can help explain something, but I just think it's the meeting up of it. So Debbie, when you show the children these things and some amazing ideas that have come to fruition, do they relate that to the language of mathematics or those sorts of things? Whereas I think we do a better job of that in English and say art or something, you take it to an art gallery and there's that physical relationship between the paint pots and that sort of thing, is that you go, "Oh wow, you could do this. And then we do that with English. "And you could write this," or with words. With maths, how often do we look at a beautiful piece of architecture and think about the mathematics that goes behind that?
Well, funnily enough, we have actually done some of this. One of the other things that I haven't yet talked about was these maths days, these inspiring, raising the priority of maths and the profile of maths and making sure an excited ... and this love maths thing that we talked about. And we have had some people come in with these great big, big doweling rods and we've made huge tetrahedrons and then we've built these tetrahedrons on top of each other and we've built these massive towers. And so, we've had lots of these maths days that are ... everybody loves them and half the children don't even realise they're doing maths, other than the fact we've told them it's a maths day.
Or we linked it to a story Bean Thirteen, how you can never actually share 13 beans out equally between these bugs, so that was ... So, every term we have these maths days, but we do try and have them so that they are these out of ... completely different and a lot of them are linked to geometry but this shape one is absolutely fantastic. And we took photographs as well, and it just was all the children working together, building these things and in the end they all did it. So yeah, it's just trying to get excitement, isn't it? Engagement?
Space, geometry in general, I think we underemphasize in primary school, personally. The other one is measures, the importance of measures, the importance of things, like just measures in general. I mean, whether it's mass or length time. Because just if you just think about living in the real world, when do you use mathematics? I mean, very rarely do you ever use mathematics where it has no ties to measuring something in some way, shape, or another. It's always linked to those things. And the other one I think that we don't think enough about is probability and statistics because a lot of disciplines in the world really come down to probability and statistics. And it's something that we very much leave for later on. And I know that that's a complex subject and we can't introduce it, but some of the principles need to be introduced a little bit earlier, I think, especially probability. And for some reason, we don't emphasise these things very much.
But picking up on what you said, Debbie, which is really important, some kids really excel in space, or measures, or probability even though they can't remember what seven times eight is. Should they be penalised for that? Should we be torturing them to remember random facts? Some people still don't know how to spell certain words, including me, and I still don't know how to spell a lot of words and that's-
But you're right with something like angles, so say you're doing angles, some children really get ... you're trying to make them ways of them recognising the types of angles, but then you take them outside of the field and say, "Make me a right angle. Two of you lay on the floor. Make me an obtuse, make me an acute." And so, sometimes you've got to do it in more fun ways, you've got to take it out of the classroom. You've got to put it in a real life situation. Not that you actually need to lay down and make a right angle, but for year four children, that works. But it is looking at an angle.
When you're putting shelves up, it's all about angles. It's all about measuring. In the future, we hope that these children will have their own homes and they're probably going to put some shelves up. But if you can't measure and you can't use the spirit level and you can't be accurate, then actually ... I sound like I put shelves up, I have to say I don't, but I'd like to think I could.
But even just looking around the room and saying, "Where are some right angles in your room? Where are some angles that are obtuse or acute? And what about this other angle on the other side? Is that ever relevant? Let's talk about the angle over here, the small one. What about the one on the other side? Is that important? When does that come into play?" It's just an interesting idea that we don't often think about. What are the external angles of a triangle add up to? Is it always the same? Why is it always the same? Or is it not always the same? It's just interesting questions.
I think this questioning that you're going here brings me to something that I really was on my list, that we're probably jumping the gun, but it's this challenge element, this finding things that challenge children and get them thinking out of the box and laterally thinking and connecting different things. And this is a really big area that I think we as a school need to work on and something that I think ... And obviously you have your maths teaser book, but compared to your other resources, it's not as engaging as colourful.
So, challenge and making these really ... I mean I know you have it in the Mind Workout and it's in the books and everything, but challenge is a big thing. Pushing these children on, these children that are really high thinkers and the ones that will in the future hypotheses about maths. And the next level down, the more you get children to think out of the box and to connect things that they hadn't thought and bring in different strands to problem solve really quite complicated problems. And I do think that's an area for development that ... John Moores University really showed me that because we looked at space, we looked at building catapults, we looked at making robots. I mean, it was just an incredible day. And I think the children were very honoured to be part of it, and so was I, but it made me realise that actually how lovely, if more children could have that experience and then they would change their mind.
I just want to pick up on two things. So, there's two things. One, when Andy's talking about this, you're having a conversation. So, the examples that you've given, and every single time it's like a conversation. And Debbie, you've just said that you've gone somewhere that's out of the classroom and you're doing things that I suggest. It's just something where you've got no option but with your children just to have a conversation. And I wonder if, again, when we come into teaching, our experience as primary school teachers by and large is we think about the practise of what maths look like in our classrooms and those sorts of things, and whether or not we need to think about how comfortable we are just having a conversation about those sorts of things, so it becomes natural and normal. Because I think that leads to exploration. But if we're not having those, if we don't feel comfortable with exploring these ideas, it then becomes quite stilted and focused just simply on, right, here's the skill, you produce the skill. And then we'll say that that's success.
But actually, I think having that same conversation ... I'll go back to English because I think that when we're writing things, we're more inclined to just have a general conversation around it. I wonder what would happen if da, da, da, da, da. If you're describing that. Does that feel like ... Do we have those same conversations in mathematics? And I think sometimes, Debbie, you've explained a situation where we're out of the classroom, and I've seen this a lot with teachers, where there's almost a freedom just to have that conversation and to explore stuff. I see it a lot when we're doing training, when people are out and they can just talk about ideas. And you're thinking, that same conversation will be so rich with your group of children. Exactly what you're just talking about. Just talking and observing stuff and noticing. I think that's something that we just need to do.
And just noticing the mathematics around you, right?
Yeah, totally. Totally.
And this lines up very much with what the Labour Party is talking about a little bit too, about this real world example. So, we immediately gravitate towards things like financial literacy and the importance of it and whatever. But part of it is just kind of changing the mindset a little bit of where mathematics fits in the real world. And I'm just looking at you right now, Adam, in this video screen, and I see a brick wall behind you and I see that, okay, so the bricks are laid out in a particular fashion and then the next row that goes up, they're all offset, right? Well, why is that? We don't even need to answer that question.
I mean, we probably have some ... because there must be a reason, right? All the brick walls are put together, so why don't you ask the children that question? And it doesn't even matter if they can answer it or not.
We had the same thing. One of my other maths days was maths in nature, so looking for spirals, looking for straight lines, looking for tesselation. And it was fascinating. I brought all these vegetables in and we didn't have to, as you say, have to answer the questions, but we realised these things were around us just in concentric circles. There was spirals, it was just so interesting.
It is so interesting. And it's like, "Oh, look at this honeycomb. It's all hexagons. They're all equilateral. They're all exact, perfect hexagons where all the sides are the same length and the angles are the same. Why is that?" That's a good question, right? Why? How did all the bees all around the world agree that this is how they were going to build their honeycombs? And why the hexagons, why aren't they triangles or squares? Turns out there's a really good reason, but they don't even need to come up with the answer. Just get them to start thinking that way, right?
Yeah, and it was quite a challenge to find some honeycomb, I have to say. And in the end, Mark & Spencer's came up trumps, they had some in a jar.
I was like, yes.
So, we actually looked at some. Yes, and it was delicious. We ate it afterwards.
Well, that's even better.
Does anybody know why honeycombs are hexagons? It's the most efficient tessellation of all. It uses the least amount of wax. So, the bees worked this out through evolution, so that's a really fascinating thing, isn't it? So, there's no more efficient way to build a tessellated shape than to use hexagons, right?
Tessellation's fascinating isn't it?
It's clever, eh? It's clever, really clever.
Tessellation is fascinating.
Well that's a fun fact, but I'm afraid we're going to have to leave it there because this conversation-
... will go on. Well, it's not over, but we're going to have to wrap up this episode. So again, thank you, Debbie for joining us. We loved having you on and talking about content strands with Andy and his bees.
Oh, it's been great. Really enjoyed it.
Thank you for joining us on the School of School podcast.