The 3-ness of 3, mandarins, and more. In this episode, Andy and Adam are joined by Assistant Headteacher and Literacy Consultant, Katy Reeve, to discuss the connections between reading and maths. Do we need to emphasise more that maths word problems are just a reading exercise? Are quadratic equations useful at all in real life? Plus, Adam makes a maths sentence out of Andy's breakfast.
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Hi, I'm Andy Psarianos.
Hello, I'm Emily Guille-Marrett.
I'm Adam Gifford.
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Welcome to another website of the school of school podcast. And we're fortunate to have another amazing guest with us, Katy Reeve.
Katy, welcome to this episode and I just wonder maybe you could start us off just introducing yourself a little bit telling the list that I've seen next to your name, you've done loads of things. So can you just give us, or we run through some of the things that really interest you and keep you going day by day.
Yeah. Thank you. Thank you very much for having me on your podcast, it is really exciting to be here. I'm an assistant head teacher over at a primary school in Brighton Hove for a three four mansion, quite a big primary school.
And I'm a literacy consultant as well. I work part-time at the primary school and part-time as a literacy consultant where I train teachers and work in schools and alongside that I support parents to help their readers, their struggling readers at home. So pretty busy.
Cool. Yeah, that sounds fascinating. One of the things that I know we're discussing topics for the programme the episode that came up was reading comprehension and maths.
And I guess you've talked about your literacy connections, so really interested to know how that corresponds and relates to Mathematics and just wondering. What do you make of that? Is there a connection or are we dreaming when it comes to the connection between literacy and Maths?
Yeah, I think it's foundational. You can't do one without the other. I think to make progress with maths and to be a good mathematician. The language of maths is really different.
It's different to how we read and we write, you have to learn that as a language within itself. So there are children who are very capable mathematicians who really fall down when it comes to showing what they can do, because their reading of maths really struggles.
So, I think you can't really have one without the other, and we spend quite a bit of time looking at vocabulary and language and making sure that children have access to that understanding. So I think definitely problem solving is where it always comes out where children find that really difficult.
Can I just jump in and just ask something just very quickly? You are in a privileged position and I'm really fortunate because I've had this and Andy's also experienced this, being allowed to go into other people's schools.
And I always think it's such a treat and such a privilege to go into different schools and see what's on there. A phrase that I don't come across as often as maybe we should or could is reading mathematics.
I read mathematics. What's that about? Just picking up on what you said there, it sounds like we do need to read mathematics and mathematics is readable.
Absolutely. And using all those comprehension skills that we look at and expect in every other subject, we really need to make sure that that applies to mathematics as well.
And children need to really dig into the language to make... And as teachers, we need to make sure their understanding is there.
So for example, the meaning of a word can change, even if it's more than, less than depending on the problem that you're trying to solve. And that's where children, if it's just its face value where they're going through the procedure for more than always means it's going to be more. Well, actually sometimes in a question, it doesn't.
When you're writing word problems you're always trying to put twists and things like that because that's really... There's all these techniques that people have developed over the years and to say, circle the keyword and underline the...
And all this kind of stuff. And those things really don't work very well. They do on a very basic level for a very basic question, but it's so easy as an author of a word problem to just twist things around, like you say, so that all you have to do is ask.
John had whatever so many more than such and such, how much did such and such have. And then all of a sudden it's a subtraction question. It's not an addition question, right? Which is what you're implying. It's just all about logic and logic's all about language.
You can't have logic if you can't construct a sentence. If you think about it, when we write mathematics, we use these symbols and we think, well, then it's not a language. It's something else. It's like a dark art or something.
But really those are just shorthand, right? Because when you read it, like what Adam is implying, John has three more than Sally is a sentence, right? There's not is no other way to explain it. We just happen to have this real shorthand to write it. Which people they think that that's the thing, but it isn't the thing. Right? The thing is the logic, it's the sentence. It's always a sentence in mathematics.
Yeah. I like to think of it as stories as well that children can tell.
I love when they're just starting off and they use objects and colours to tell their mathematical stories. And I suppose that's where it starts. Isn't it?
Can I throw something out there? Right? Can I throw something out there? We've got this thing called the alphabet. Right? And we expect children to be able to put these symbols together in various combinations and then they code them to read them, yeah?
Are we doing exactly the same thing with the symbols in mathematics? Like if I write the digit seven and the addition sign and then three and then an equals sign and 10, are we not reading that? When we say seven, add three equals 10 or seven and three make 10 or however we decode those symbols.
Are we not talking about the same thing? It's just that one's called the alphabet and the other one's called the symbols of mathematics. Or am I going mad? I don't know. I'm just asking.
I think they are all the same thing. And I think you can also know the alphabet by rote and think that your child knows how to read and you can know your numbers to a hundred by rote and think you know how to count and what the meaning of number is as well.
So I think they're a really good parallel. It's about knowing what's the sevenness of seven. What does it mean? What's the threeness of three so that when I look at them I know what seven is and the same with the alphabets.
I think that's one of the biggest barriers is that children can learn the alphabet, it's just rote. It doesn't mean that you can speak English or that you understand it.
Yeah. A parrot can learn the alphabet. Right?
But I wonder if that message is understood by the children in our schools. Right? So something, and this being a podcast, obviously what I'm about to say, doesn't make for great listening.
But Andy, while we are sitting here is sort of just sneaking in his breakfast. I think it's breakfast time in Vancouver. Now, I don't know how many things, how many little bits he's got on his plate. Right?
But if I could use the alphabet and I could write like Andy is sat down at his desk and he's got his breakfast in front of him. And he's just sort of getting in mouthfuls as we go. Or if I had have known how many he had on his plate, I could write that same recount. I guess we would call it a recount if we were talking about English, but I might write it down as 10 subtract.
I don't know. I've seen him put at least four in his mouth. I think so far. So let's stick with that. 10 subtract four equals six. Yeah. And I've told that story. And instead of using the alphabet to tell a story, all I've used is different symbols, but it is still a story nevertheless.
It's not just 10 subtract four equals six. It's Andy had 10... What are you eating, Andy?
What am I eating? I'm eating little slices of Mandarin.
Right. Okay. So you had 10 slices of Mandarin. Yeah?
I just ate another one.
So we're going to have to change the equation, but this is what I'm saying. I just wonder like when we see that it gives the meaning to those numbers. It allows us to read mathematics in a way and how lovely and efficient, just to be able to do that, than writing a big recount about... Which might be appropriate in some cases.
Andy peeled the Mandarin and he, ta ta ta ta but actually my 10 subtract, well, five now, I guess. And he might have five left on his plate. That to me is still a recount that's readable.
And I just wonder if you've seen that Katy, and whether that message, is it something that's accepted? Is it discussed? Do we make enough of it? Should we even make enough of it? Maybe it's pointless. I don't know.
I think again, yeah. It's a really good point, that concrete understanding, isn't it? Taking everything back to real life, how we use it, how we apply it and for children, that is the game changer. If we keep jumping straight into the abstract symbols and we don't do the concrete into the pictorial, into the abstract, lots of children just really struggle.
Yeah. You have to be able to pin it to something, right. Otherwise it's just abstract nonsense. It's just remembering random facts that may or may not have any significance whatsoever to anything that you understand.
And it gets more and more difficult the further along you get. And if you don't build those disciplines early on... If you introduce mathematics, just remember all this stuff, because you'll have a test on Wednesday or whatever, then at some stage it just becomes overwhelming. Right?
There's just too many things to remember. Usually around the time you get to fractions especially because fractions are sort of bizarre, right?
Because you can generalise all these concepts as you go through your early sort of understanding of mathematics. You can generalise a lot of ideas and they sort of make sense.
Even, if you don't dig deep into them. You can have a surface knowledge, but they still kind of make sense. But by the time you get to fractions, if you don't understand what's going on, you'll never remember it. There's just too many things to remember.
And they're very counterintuitive. What do you mean when I multiply the number gets smaller, right? How does that make any sense? Right.
So, at that stage, if you don't have a solid, concrete underpinning, everything's just abstract nonsense. And you have to go through those stages. And I don't think it's a surprise. I don't think anyone should be surprised about concrete, pictorial, abstract.
Just think about human development over the centuries, over the millennia. We're so focused on what we.... Our visual cortex is so massive, right?
Seeing is such a big part of our existence. And so is using our hands. Right? When you think about the things that you do, you're constantly using your hands and experiencing the world through either your hands or your eyes. So wouldn't it just make sense if that's how you learn. Right?
I think those things, like what I find really interesting and interesting, that's probably a very diplomatic way of saying it. Is that say if I had done an English lesson in the morning.
From the very first time you start training as a teacher, I'm just going to keep going back to a recount. So for those who don't know what a recount is it literally does what it says in the 10 we're recounting something's happened, an event that's happened.
And the perfect lesson, if you like and I don't think that this would be too a question is loosely based around if I wanted to do a recount or I want to write a fictional story about a big house or something like that.
It would be to visit the big house. It would to be experiencing that and experiencing actually being there then maybe coming back and discussing that and having pictures around the room of this.
And then finally we get to the stage where we put the recount down or we write a story using the words in the alphabet and then we can switch to mathematics after the break, for example. And then if I go straight into that memorization, how does that marry up when we've got really good practise on one hand, if we did it the other way, round where we did maths based on memorization, it would be akin to...
Well, after break guys, we're going to go through pages one to 10 of the dictionary and you're going to memorise all of the words. And then tomorrow we're going to do pages 11 to 20 and you going to memorise them.
And once you've memorise the dictionary, you're going to be amazing at English. It doesn't add up. This contradiction and what we know is really good practise, but I don't know why and Katy, I'm really keen to hear your opinion on this.
Why does that not make the link when we are the same teachers with the same children watching the same process? Why does it not make the link to mathematics as readily or as intuitively? I don't know.
Yeah. I think that teachers who take that leap and do embark on that. So one of the most powerful phrases that I've heard is can you imagine, and so many children who struggled with fractions, can you imagine a pizza? Can you imagine two equal halves? And you can see that's the game changer. That's the thing that really helps for them to understand fractions.
So it's great to do practical work as well, but if you can't and you don't have the resources available to hand, just that phrase, can you imagine? And it changes everything because that picture in their heads gives them that concrete experience in the moment.
So I think more and more people are seeing how powerful that is because more and more people are talking about it as well, that, this is what happened today in class, there's stuff and charts.
And that really changes the culture of the school as well, where you get to a point where it just becomes commonplace. You hear it, as you're walking down the corridor without having to even look for it. It's part of that everyday conversation.
And we want children to do that naturally. Don't we? That when they get stuck, we want them to journal to write it down, to put their own pictures to a problem, even if it's doing the part, whole or whatever. That Image is really the game changer for lots and lots of children.
Yes. The bridge, isn't it? It's the bridge between just utter confusion and some attachment to a real experience. And I think that we all too often forget to tie in those real experiences with whatever it is that we're doing.
And then that's when it becomes all too confusing for a lot of children. Right? And just remembering as a teacher, that you always have that skill, that opportunity to bring it back to some example.
Adam, to go back to your question, why is that? I think we're still wrestling in education with this old notion of calculation and arithmetic as a necessary skill or not even a necessary skill, but just like a very valuable skill, because it really wasn't that long ago, certainly in my lifetime, anyway, there were no calculators, right?
All calculation was done by hand and then there were people in rooms that, that's what they did. It's kind of a crazy idea, but that was a good job. Like all accounting, imagine all the stuff that you do in spreadsheets and databases now, at one point was being done by hand. Economists would sit in a room with a pencil and a piece of paper and scribble all day long.
Yeah. That's crazy.
None of this using Excel for all these, high level math. There's none of that. Right. Just like writing it down.
Just off the back of that point, Andy, I was thinking that its going to take a bit of time to work its way out of the system, because that's how I learned math.
And so when I come in to be a primary school teacher, I'm not coming in as a specialist, I didn't come in with say a maths degree, which doesn't necessarily mean that you're going to think in that way, but will give you a greater advantage of being exposed to a range of mathematics.
But, I think that we rely.... You think, well, how did I learn maths if I could do it okay. Surely my teachers back when I was starting to learn math, 70s and 80s, they must have done something half decent, because I can add and I can subtract then I can work out the change when I pay at the till and all that sort of stuff.
And so I think we take the lead from there and we got to remember that the people who were training me chances are a generation ago before me.
And so those ideas were even more ingrained. And what I hope is that when these changes take place, that it just becomes more of the system, not just at the core face, if you like of teaching children, but actually before teachers even set foot in the classroom.
As you were saying that I was thinking, well, who do I know from that generation? That generation that would've taught us. Right?
And I'm older than everybody here, but I... So I was thinking about my father who has unfortunately passed. But, I was thinking about my father and I was trying to remember if I ever saw my father use a calculator and you know what? I didn't think my father ever used a calculator.
I don't think his whole life he ever... They were around for the last third of his life, but I don't think he ever used one. I always saw him doing calculations on little bits of paper, usually on the side of the newspaper, he'd be writing stuff down.
Well, I've got a gorgeous little memento from my grandfather who died quite some time ago, but he was not just a keen gardener, but his garden was be beautiful. Just amazing, really cool, fruit everywhere, all that sort of stuff.
And one of the wee he treasures that, my mum gave me the last time I was in New Zealand was a little book. He used to make his own fertilisers out of natural stuff. Like he collects seaweed and all this sort of stuff.
And he'd write down all the calculations and then change the ratios and all the calculations are in this little book. There's certainly no calculator going on there.
There's nothing like that. This is lovely, we had a record that I get nostalgic about. The results on the orchids or this sort of thing and then he'll just mess with the ratio a little bit and the dilution and all this sort of stuff. But yeah, there's no way he was using a calculator. I wouldn't even know if he even owned one, to be honest.
So now you just imagined the rate of change that's happening in the world. Right? Is school keeping up with that? Because the stuff that Katy is talking about here, it's so important we know that, and we know that the world is changing rapidly and we know that we need children to be able to go beyond just mere procedural calculation as a task ask, right?
Like, yeah. Of course we want them to know their number facts. Right? Of course, we want them to know all their number facts up to 20. We want them to know their multiplication tables well enough that they can do basic calculations without having to resort to a calculator.
But that's just not enough. Right? And that link between language and thinking and problem solving and mathematics is so much more important now than it ever was. The world is so much more complicated now than it ever was. Right?
I think it's really broad as well. I think it is really important for mathematics, but I think classrooms are changing children's knowledge of the world. How are we reflecting that in the topics that we're covering at school and how are we immersing children in that language, which environments that gives them a chance to do the real life mathematics that they can use and apply?
A saying you hear often is, when do you ever use quadratic equations in real life? Or when am I going to use this? And I think we want children to really have a sense that matches their world.
It's every day you're coming across it all the time. So it's not just a useful skill, it's actually an essential skill. It's not an option. You have to have these skills to be able to function, have options in life and be able to achieve what you want to.
So algebra, quadratic equations, or simultaneous equations, or any of these bizarre number wrangling exercises that you do when you enter secondary school, which seem incredibly abstract are actually things that you naturally do in your life all the time, without even really thinking about it.
And the shame of that, is that we don't spend enough time sometimes tying that logical storytelling to something that's seemingly really abstract, like a quadratic equation, for example.
You do that stuff. You do it naturally. Algebra is everywhere. When you start talking about, he had three apples and she had two apples, basically you're doing algebra. Right?
And having those interests as well. Yeah. Like the story about your grand dad, Adam and where it was obviously something that he was so passionate about and it was his world that he wanted to sit down and do those mathematical workings out because they meant something to him.
Yeah, totally. I also think when people write, just as you've said, Katy, about, what's quadratic equation's got to do with me effectively.? I think that's what they're saying when they say...
I think part of the problem is part of its marketing. So often you... I was watching a movie just the other night and there was a white board that was full of a huge equation.
If people saw that as, that was just another way to write the story. So if instead of that, they presented a lovely picture book and said, this is what I've just seen. Everyone would be far more accommodating. Right? They'd be like, oh yeah, tell me about that story.
Wow, that's amazing. So you could work out that that style was doing this or this comment was doing that or whatever it might have been, but because it's presented like that, for a lot of people that's readable, that tells a real life story.
They're not just symbols for symbol sake. This is something that each of these symbols represent something. And it's telling a story and it's telling us... And all those good things that we love, for example, about a good book, we make predictions about who done it, I'm halfway through and I reckon it's this person.
That's effectively what's happening here, except it's being recorded in symbols that may not be as familiar to other people, but if we looked at it and we thought that's telling a story, I wonder what that story was.
Probably when it was explained, yeah there might be some things that may be just a way bit too far removed in terms of understanding of...
I don't know, I'm thinking of graphing now, like a reasonably recent discovery. But I think that if we approached it with that's readable and it tells a story and that story may even be accessible to me. And not only that it might help me.
And it might be something I'm desperately interested in. I think that then maybe would be a little less quick to dismiss as that doesn't affect me in real life. I just don't think that's true.
All right, Katy, come on. We got to wrap this one up. What do you say to parents? I think most teachers probably have a good sense of this.
And most of the people listening, I imagine are teachers, but what do you say to parents when you try to get... Because, so many parents will come into school so focused on times tables or whatever it is, what they see mathematics as. How do you tie this language thing with the parents? What do you say to them?
Well, I think the children are really powerful in getting that message across because I think lots of parents are scared that we do it differently today to how they used to do it.
So I think that's quite a good way in is looking at that the language that your child uses, we need to keep some consistency at home and at school.
And we have the videos that Ban Har made as well. They are fantastic where he has 10 short videos that parents watch. And in that he models the language so beautifully that parents have said, they've found those really, really useful for making sure that what we're doing at school is what we're doing at home.
But I think really the biggest factor is that parents get real pleasure when they can talk to their children about maths at home when they're completing tasks and homework.
So in that I think, the children are so confident, I suppose, of the language that we want them to use, that they're really supporting their parents with that as well.
Absolutely. We need to put a link. Robin, we need to remember to put a link to those videos in the episode. Sorry, for those of you who don't know Robin, he's hovering around in the background, she's the producer of the podcast.
She does all the heavy lifting, Adam and I just show up and ask really clever people like Katy to join us. That's great, Katy, thanks so much for joining us. That was really, really fascinating.
Oh, it's been a pleasure. Thank you very much for having me. That was absolutely fantastic.
Thank you for joining us on the school of school podcast.
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