Episode 230: Exploring the 5 Core Competencies - Visualisation

Adam Gifford

Welcome back. Time for another episode of the School of School podcast joined by Robin and Andy. How are you both today?

Andy Psarianos

Yeah, let's do it.

Andy Psarianos

I'm good. You sound very enthusiastic, Adam.

Robin Potter

Yeah, very well. Thanks for asking.

Adam Gifford

I'm always enthusiastic. When has there been a podcast episode where I've not started thinking, can't wait for this. So I'm going to keep going with this.

Robin Potter

Yeah.

Andy Psarianos

I can't recall.

Adam Gifford

With our approach, we often talk about the competencies. What are the competencies? What are the key set of skills that we want learners to acquire and for us to be able to support with? And one of them on the list is visualization. Really important skill, really important competency. And so we're just going to talk about that. It's just going to be a brief hit on visualization. Why bother? What do we do? How do we go about our business? What does it mean? Those sorts of things. Andy, do you want to want to kick us off on this one?

Andy Psarianos

Yeah. So let's talk about what we mean by these competencies, right? So, so, you know, the, big idea with the competencies is, that competencies is what you're actually teaching. It's not, it's not, you're not teaching math. Well, you are, you're teaching math through the competencies. You're not teaching the competencies through the math. Okay.

Okay, does that make sense? Like the math is like what you use to teach competencies. Okay, so it's the most important thing.

And visualizing is one of them or visualization, whatever you want to call it. So the question is like, what is visualizing or what is visual, you know, what is it? What does it mean? Like, well, what it, what it means, obviously it's got something to do with seeing stuff visual, right? But the core idea, it's not necessarily seeing things as like, I can see a picture, but it's being able to see in your mind's eye, you know, when you say stuff like, I see what you mean.

Right? What is that? Why do you use that word? See. You don't see inside the person's brain. Right? It's because we think visually. We think visually. We even, it comes out in our language when we talk about things. I see what you mean. Yeah? I see how to do that.

Robin Potter

Mm-hmm. Yeah.

Adam Gifford

Mmm.

Andy Psarianos

Okay, so it's visualizing. I see the process. Okay, so we know that we need to develop this visualizing because in order to do mathematics, but just also just to think logically, you need to be able to visualize. So it's the ability to represent mathematical ideas in our context, concretely, pictorially, abstractly in your mind. Okay, and that's what it is.

Adam Gifford

Mm-hmm.

Andy Psarianos

So you're going to say, why does that matter? Well, go on, Adam. You tell everybody why it matters.

Adam Gifford

Well, if you're lacking all of those, there's a few things that happen straight away. So the first example is you're going to make a really poor decision if you can't visualize something. So I often use an example where there's something that happens in New Zealand. It's a Maori cultural thing where I say, would you like to come to a hangi? You know, quickly make up your mind and decide. If you don't know what that is and you can't visualize that, all of your decision making around that all of a sudden becomes flawed because it's not based on the hangi because you can't see it. You don't know what to do.

Andy Psarianos

Yeah.

Adam Gifford

bring the appropriate thing when you come as well. So not only are going to come to it, make sure you bring the right thing. You can't make those decisions. It manifests itself in the classroom where if we say to a child if they can't see five in a number of different ways and we ask them a question like, can you see the two and the five?

Andy Psarianos

Yeah.

Andy Psarianos

Mm-hmm.

Adam Gifford

Like if you can only visualize the abstract representation of that symbolic representation of 5, that written digit 5, you could be looking all day long, there's no 2 in there. You'll say, I can't see the symbol in there, what's going on? But if you saw it as 5 counters...

Andy Psarianos

Yeah.

Adam Gifford

then you'd be able to identify two counters in amongst that. So you know you could start to move those, manipulate those and do those sorts of things. So it is essential and I'm sure that we can all come up with other examples where it feeds into that. And we've got to develop that skill set otherwise we're at a significant disadvantage in our decision making, our ability to manipulate and make something work, generalize all those other things.

Andy Psarianos

Yeah.

Andy Psarianos

Yeah, that's right.

Andy Psarianos

That's right. And where does it, where, can you see evidence when it hasn't happened? Well, when people remember things by rote, right? So you remember your times table by rote, you just know you're, you're repeating like a, you know, like a, like a bird, you know, like a pigeon, you're saying, you know, you know, six times three equals 18, right? Six times three equals 18. You're just saying that as a bunch of words. have no visual idea of what that means. Then you can't make the connection.

between that let's say and something else that you need to be able to work out like maybe you know instead of six times three what's what's seven times three right because you don't know what six times three means you can't visualize it in your mind you don't know that all you need to do is add three right because that's a that's a visual model

Robin Potter

And then you can't show somebody what you mean. So it's like a domino effect.

Andy Psarianos

Exactly. Yeah.

Exactly. That's exactly it. And then as a teacher, how do you build that? Well, it's like, can you show me that? Can you show me that with materials? Right.

Can you draw what's happening in this problem? Can you make a model? Can you draw a diagram? And that's how you build visualization. So that's, you know, it's so important, right? It's one of the most, well, it's one of five things, and we're gonna cover all five in these short little bursts, right? It's one of the five things that you need to teach to. need to, you need to teach, so when you're teaching multiplication, you're teaching visualization, yeah?

You're teaching visualization through multiplication. That's the goal, right? That's what teaching to competencies means.

Adam Gifford

I think one other thing to add to this as well, and you linked it Andy, we talked about starting with the concrete and being able to visualize it and then moving to the abstract. You know, the other thing too is we want our children to move on from using those cubes as well. you don't want, know, like imagine being a child, they have pockets full of cubes as you walk around. So every time you're to add something, you've got to pull out these concrete materials. No, you want to be able to take them with you every time you go in your head. So it frees up, it frees up that aspect of it. we just, like you're saying,

Andy Psarianos

Mm.

Andy Psarianos

That's right.

Adam Gifford

We must be mindful of this as a competency that needs to be looked at and developed because it may not happen naturally. You know, and you just have to look at the number of children that just have to use their fingers, concrete materials that haven't moved on to that visualization. And they're at a significant disadvantage because we've not concentrated on yet. We've got to move them to that point. We can't leave it to chance. And yeah, too important.

Andy Psarianos

Yeah.

Andy Psarianos

Yeah, that's right

Andy Psarianos

Yeah. Exactly.

Robin Potter

Sorry, one comment. And I think maybe we all were doing it, but when Andy was talking about grouping or, you know, what's six times three and using counters. Like immediately I start visualizing that in my head. You know, it's pretty much impossible for me not to do that as I'm sure for the two of you. So it's...

Andy Psarianos

Yeah.

Andy Psarianos

Yeah. Well that, so that's the point. You're doing it in your head. So you're doing it in your mind's eye. So the thing is, that

So, and this is the, so if we get into what's the theoretical underpinning behind all of this, right? It's Jerome Bruner. It's the CPA approach, you know, or inactive iconic symbolic as he called it, right? Which we are often referred to as the CPA concrete pictorial abstract approach, right? And it is the basis. It's the basis. It's the whole idea behind what Jerome Bruner called the spiral curriculum. Okay. And the idea is, that you start off with very

concrete experiences and then you revisit the idea

in a more advanced, more sophisticated way with pictorial representations so that you're no longer counting apples, right? But now maybe the next step would be to represent the apples with something else like a counter and then moving on to drawing a diagram, right? So you're moving away from abstract into more pictorial representations. You're drawing a little diagram, but still the one-to-one representation. Later, you move from that one-to-one representation to like maybe a bar or

or a circle or something that represents a group or a number, right? So it's no longer one-to-one representation up until the point where you can actually just do it with symbols and you can visualize it in your head, which is what you describe. Immediately when you're talking about it, my mind saw this. Well, that's what we're talking about. That's what visualization is. And if you can't do that, you can't do mathematics. It's as simple as that.

Adam Gifford

I'm not here.

Andy Psarianos

And that is mathematics, but it's not just mathematics. It's thinking, it's logic, it's doing. And that's the point. So going back to Jerome Brunner, CPA.

Adam Gifford

Mm-hmm.

Andy Psarianos

is how you do it to teach. You teach through CPA and the point is that it's spiral so that you reintroduce ideas. You're not going to teach everything about fractions in one go. You need to introduce those ideas and they reappear over and over and over again each time a little bit more complex, a little bit more sophisticated. So visualization, who told us what's the theoretical underpinnings? It's all Jerome Bruner and that's what it is and you got to do it.