Episode 232: Communication — Peer interaction is vital for learning

Ep.232.txt

Andy Psarianos

Hey, here we are having a load of fun again. Robin can't stop talking and laughing and Adam's always smiling, but here we are. Why is everybody so happy? Because it's time for another episode of the school of school podcast. And today we're talking about some of our favorite topics, which is, know, this, this idea of, of, competencies and what are competencies and mathematics and why are they important? And,

You know, this like mini series of competencies, like, um, you know, intense short podcasts, uh, is, I, I'm lost. I don't know what I'm saying, but you know what we're talking about communication, which I am failing at miserably right now. And that's what we're going to talk about and how important it is in teaching mathematics, but also how it is important in teaching anything really. Right. So, Hey, you know, you guys talk, I'm just, I'm just like, this is like a word salad here coming out of me.

Robin Potter

Yeah, it's so funny of all the time that you're stumbling. It's about communication. Andy, what's gotten into you? So unlike you.

Andy Psarianos

usually so clear, concise, and succinct in my thinking, right?

Robin Potter

Yeah, okay.

Adam Gifford

So you mentioned a really important word, and I think we're doing a little series on these about competencies in the first instance. You what are they, how do they work, and what do they got to do with maths or learning more generally? And often when we're talking about competencies, we tend to focus on five communication as one of them. But maybe thinking about competencies in a way that mathematics is a sort of vehicle to learn the competencies as opposed to that mathematics is the key, these competencies

are the key and they're called competencies for a good reason because we want children to be competent in them to be competent learners to be to them go on so it's not just about learning it's about the harder problem solving it's about the heart of being a really functional member of society which sounds quite high for learning but you've got to have these things and one of them is communication and that might seem really obvious on the surface it might just seem like yeah of course we've got to be able to communicate with each other because humans are so

beings. So end of story, that's it. Just learn to communicate, that's it. But I think that... Yeah, go, go, go. No, no, jump in. Go, go, go, because I'll come back.

Andy Psarianos

But you know, sorry, go ahead Adam. I just want, I'm so excited. You go, you go, No, no. Well, what I was going to say, you said it's, it's, it's obvious, but in some ways it's the least obvious for mathematics, right? Because you don't, it just, you know, like what a communication, what's that got to do with math? Like math's got to do with like numbers and you know, writing and examples on paper and whatever. How's that, what's that got to do with communicating? That's all I wanted to say. You carry on your idea.

Robin Potter

Yeah.

Adam Gifford

No, no, no, no, 100 % because I think there's parts of communication that just don't get talked about. When do we ever talk about reading mathematically?

Andy Psarianos

Exactly.

Adam Gifford

You know, that honestly gets lost so much. that act of reading and even and we know because we could probably go back to our childhoods and unfortunately in some schools this is still the case where mathematics is a largely silent subject apart from when your hand is the first one to shoot up and then you can share something momentarily. But I always think that that first thing in that communication is the idea that when we can communicate an idea, a thought, a

Robin Potter

Mm-hmm.

Adam Gifford

well, concisely and clearly, it's a really good reflection of how well we understand what we're talking about. And I think that in classrooms when we see it and someone says, well, I just knew it, it was in my head and I'm really struggling to explain something, that to me says, you're not at a level yet where you understand that concept so well, you've synchronized it with the language associated with it. And we need to provide those opportunities to either develop that language, practice that language, embed it against an idea or a concept

Robin Potter

Mm-hmm.

Adam Gifford

because that's part of the learning process. So it's not just about talking to each other or communicating ideas. To me, it's also about that connection between language and an idea. so almost, can't think of better word than synchronizing those two things together to deepen our understanding. I think that's really important.

Andy Psarianos

Mm-hmm.

Andy Psarianos

Yeah. Yeah.

Robin Potter

And I think you've touched on the fact that it's really important not just that the teacher be able to express mathematical ideas clearly to the students, but for the students to be able to express them to each other, to the entire classroom, to their teacher. So it goes both ways.

And it's critical for the students to be able to do that. And it's so nice when we go into some of our classrooms and we're able to just watch them in action. And that's exactly what they're doing.

They're the ones that are sharing their ideas, they're expressing, you know, maybe a certain concept to their friend next, you know, beside them. But it's really obvious that it's not just the teacher sitting there explaining it in a clear way. It's the students be able to do that themselves.

Andy Psarianos

Yeah, beep.

Yeah. So, you know, I'm going to pick up on all these points. so the first one that I want to pick up on is what Adam was saying about a student who just knows the answer, but doesn't know why they know the answer. Right. That's, know, those often those students that we perceive as being advanced have that problem. Right. So they just know the answer.

but they don't even know why they know the answer or they can't explain how they got the answer. Right. So that's not an advanced pupil. That's a pupil that has particular either great ability to remember things.

but doesn't, hasn't made the connections, hasn't generalized the ideas, right? Or it's very instrumental. So they know how to do addition, but they don't know what it means. Right? So, you know that, and that happens a lot, right? And, and, and certainly you can teach people so that they merely have an instrumental understanding. It's easy. It's hard for us because addition is like we're grownups and we've been doing this for a long time. It's hard for us to understand that someone might not know what addition means, but

If you choose a more complex topic like let's say fractions like if you ask people why you know What are you doing when you're dividing a fraction by a fraction? And when would you ever do that in the real world? You know that baffles most people right, but that's like they know how to do it. They remember that yeah, you do something like you flip of one of them over and you multiply or something and then that gives you the right answer they can tell you the instrumental the the relational bit, but they don't understand what it

Andy Psarianos

why they're doing it and why produces a the right answer or you say to somebody why is it when you divide something by a half

the number is larger. That's kind of like a crazy idea. Divide fractions are pieces and dividing means finding pieces. So how can finding pieces and then putting pieces surely should be like less than small, not bigger, right? It's kind of a crazy idea, but you know, that just means they don't have the relational understanding, you know, so that's something about half.

You know, what's one divided by half? It's two. That doesn't make any sense, right? Like you surely it should be like a quarter or something, right? Is you're dividing twice, you know, do you know what I'm saying? So this is like, that's what we're talking about. So, so can you explain it? If you can't explain it, it's a sign that you don't actually have the other things, right? So that's really important. The other thing is that,

Adam Gifford

Yeah.

Robin Potter

Yeah.

Andy Psarianos

You you talked a little bit about like the teacher being the, you know, the, the, sort of really smart person in the room who knows all the information is just going to deliver that information to the rest of the room.

Well, the research tells us basically that's not true, right? Like actually kids learn more from each other usually than they do from the teacher and they need to be able to communicate, you know, so they need to be able to communicate together. And the other thing you want to think about too is, like sometimes people even might be able to do things and they might be able to understand the relational bits of it, but they can't communicate it to other people, right? And what use are they to society?

Like who cares if you're so smart in your head, but you can't communicate any of your ideas with the rest of the world. We don't need you, right? You're of no use, you know, to society and think about it, right? Like what good is that person? Yeah. So, you know, that those are just things to think about, you know, but, that's what we're talking about communication, right? There has to be that to and fro in that communication, written communication, but more, maybe more importantly, verbal communication and that, that tussle between

Adam Gifford

think that.

Andy Psarianos

pupils, right?

Adam Gifford

I read something too, it was actually a coder, computer coder at MIT and they were talking about how, and I don't profess to know about coding, but what was written down in the flow of it made absolute sense to me, is that you code something then you have to run it because the encoding, the understanding of what you've taken in needs to be tested to find out whether or not what you've taken in is correct, so you've got to run it, right? And that's the thing with

Andy Psarianos

It's not that interesting.

Andy Psarianos

Mm.

Adam Gifford

children is that they may have believed that they've taken in whatever they're looking at, an idea has been communicated to them, but if they can't have an opportunity to communicate it back in the way that they understood it.

then how can we pick up on their understanding of what's being communicated? We can't just assume that everything gets taken in verbatim, understood at the level that we might want it to. So there has to be an opportunity for them to say, well, this is my take on it. Right. This is what I understood you to say. And how many times is that process not happened where you go away and say, what are you doing? Well, Robin, Andy, what are you doing over there? And they say, well, I thought you meant this when you said that. And you're going, no, no, no, no,

Andy Psarianos

Yeah. Yeah.

Adam Gifford

Completely misunderstood what I've said, you know, it's this this and this so again that that process of testing is the Communicate is is the initial input if you like or follow-up input How's that been if you like encoded? How's that been taken on board as a child? Because that's what's gonna last that's what they're gonna take out the door with them And so we need to have these opportunities to communicate to say did they understand it as it was intended close or close enough, you know, they've got the core

Andy Psarianos

Mm.

Robin Potter

Hmm.

Andy Psarianos

Yeah.

Andy Psarianos

Yeah.

Andy Psarianos

Yeah.

Adam Gifford

idea there or thereabouts you know and if we don't do that then again we're leaving things to chance and that's a phrase I use all the time but but I'll keep coming back to it we can't allow that to happen

Andy Psarianos

Yeah.

Andy Psarianos

No, absolutely. So let's just think about a little bit about what are the theoretical underpinnings behind this in education. This is Vygotsky. It's got Vygotsky written all over it, right? So Vygotsky is mostly known for, you know, what he called, some people called the zone of proximal development, which is, you know, is this kind of like.

An idea that's connected to this well actually the underpinnings for that idea are really this this idea of communication So what are we talking about with saying communication? It's basically the ability to express mathematical ideas clearly

using words, using symbols, using diagrams and other representations. But also equally and maybe possibly more important is to understand others mathematical thinking. To take somebody else's perspective. And that's really hard for what we sometimes misdiagnose as advanced pupils. They only have one way of thinking about it and they don't want to look at somebody else's. If you say draw me a diagram, they're like I don't want to

diagram. I don't want to have to think that way because I just know the answer right. So communication is clear and and communication is the best way to create turbulence in the Piaget sense of disequilibrium

in a child, know, so we're getting into heavy into learning theories here, but you know, that's a great way to, to, sort of, force a child to move away from merely assimilating ideas and accommodating them. That's Piaget. We'll talk about that some other time, but

Andy Psarianos

What's important about all this? Why does it all matter? It's the vehicle. It's the way Vygotsky called social learning. It's called the social. It's like when students explain their thinking to peers, they clarify their own understanding. They expose gaps in their reasoning when they do that, right? So they are forced to go further because they have to explain it. So it's really important for people's own personal development to have to explain things. And also when they listen

others they encounter new strategies and new perspectives you know and and and that's that's obviously super important so you know for a teacher you have to make sure that you're making you're not only making these opportunities for communication to happen but that you're actually that is just how the mathematics classroom works so that talks about that's getting into how do you group children how do you prepare activities and questions and stuff how do children's

interact with each other because the idea is so in the ZPD, the Zone of Proximal Development for Vygotsky, the idea is that you want to bring people just to that learning threshold, that bit where they can do it on their own but this bit they can't do on their own. They need to be with a more knowledgeable other. That's the term that he used. Sometimes that's the teacher. Most of the time it's their peers.

Okay, it's in a conversation with their peers. I don't think you're right. My idea is better than yours. Whatever. That's when they're experiencing that more knowledgeable other. That's when the learning happens. When the zone of proximal development is extended is when they're taking in new ideas through communication. Math is all about language.

It's all about logic. There's no logic without language. Language is about communication. Communication is one of the five core competencies that they have to crush in order to progress in mathematics.