Episode 172: Spatial Reasoning

Andy Psarianos

Hi, I'm Andy Psarianos.

Robin Potter

Hi, I'm Robin Potter.

Adam Gifford

Hi, I'm Adam Gifford.

Andy Psarianos

This is the School of School Podcast. Welcome to the School of School Podcast.

Welcome back, everyone, to another exciting episode of the School of School Podcast. And we've got the regulars here. Of course, we've got Robin Potter, and we've got Adam Gifford. Say hi, guys.

Adam Gifford

Hello.

Robin Potter

Hi.

Andy Psarianos

Very exciting guest today, Alison Borthwick. Alison, just so excited about having you here. And I'm so excited about what we're going to talk about, which is this paper put together by the primary and early years expert panel. It's a report and it's on spatial reasoning. I love talking about spatial reasoning, and I'm so excited you're here to talk to us about it. But before we jump in, can you just tell our audience a little bit about yourself so they know who you are and where you come from?

Dr Alison Borthwick:

Yeah, absolutely. So thank you very much for inviting me. So I've been in education for over 25 years. I started as a teacher, taught in an amazing school in London and then another amazing school in Norfolk. Once a reluctant mathematician, totally believed I couldn't do maths at primary and secondary. I then had a change of events, became a teacher, and I now love math, and I kind of badge myself as an ambassador for math.

I have been an education and a mathematics adviser for over 25 years now, and I've had the privilege of working across lots of the UK with UK schools, with multi-academy trusts, with lots of organisations, and also I've had the privilege of working in 26 countries with multiple different organisations. So yeah, that's me.

Andy Psarianos

That's quite the background. I'm always interested in talking to people who didn't connect with mathematics early on and then ended up working in education and in particular educating people on mathematics. So listen, Alison, I want to jump in on this spatial reasoning. I read this paper. I love it. I agree with everything in there. I'm so excited actually that you guys are bringing this up to the forefront. But I think before we dive in, can you explain to our audience when you talk about spatial reasoning, what are we talking about? Because I think some people will know, some people will have an idea, but it sounds pretty technical. What is spatial reasoning and why is it important?

Dr Alison Borthwick:

Oh, so two really, really big questions there. So I think the closest we probably currently think about spatial reasoning is we might think about it in terms of geometry. So when I'm thinking about our national curriculums, we would see geometry appearing in the primary curriculum and also in the secondary curriculum. In a previous iteration of the curriculums, we would call it shape and space. So I guess that's the beginning, that's the hook for our frame of reference for spatial reasoning.

But actually, what we realised, because we've read a lot of the research, we've looked at a lot of the international curriculums and the research that's out there, is that we know that spatial reasoning is much more than what we currently think. So spatial reasoning involves understanding and visualising spatial relations and spatial properties. So that would include quantities as well, whereas before we might have located geometry within geometry. Actually what we now know is that spatial reasoning can go and transcend across the whole of the mathematics curriculum.

Why is it important? Well, we can come back to that in a second, but I think that kind of importance, we're now starting to use this phrase spatial reasoning. And the reason, as I've said, it's within the literature, but we've also got some really interesting predictive research coming out from ACME, which is the Royal Society, which the paper is commissioned and written for, but also The Academy for the Mathematical Sciences, which is a protoacademy at the moment.

And we know that when we're looking at the data and we're looking at what is it that our students, our learners need in the next 10, 15, 20 years? Education is changing. We're living in the world of AI. We know that our computers can do quite a lot of the procedural stuff, but the spatial reasoning, that thinking about, "Where am I in space and how do I connect to it?" Is really important.

So if we just kind of think about, "Are we all involved in spatial reasoning?" We might want to think about, let's think about a few everyday examples just to kind of frame us into what it means. So if you're listening, do you drive? Do you get in a car with anybody that drives? Because I'm hoping if you are either a driver yourself or you've got into a car, that that person had spatial reasoning. Because otherwise, how do you keep to your side of the road? How do you kind of know that when you're driving down the road, you're not going to crash into the wall or you're not going to crash into the car in front? Or how do you reverse into a space if you don't have spatial reasoning?

So already we're starting to see that we all use spatial reasoning every day. Those of us that perhaps have a dishwasher. Now, if you talk to my husband, I don't have spatial reasoning when it comes to loading the dishwasher. Apparently I just throw things in and he then unpacks it and resorts it and kind of says, "No, no, no, no. If you stack the plates in this particular way, we can get more in." We're both using spatial reasoning. We're both looking at, "Well, how do I put things in a particular space to make it work?"

When you get a pair of shoes or a pair of trainers and they come in a box, when you open the box, you think, "Well, when I take them out, how do they ever go back in?" Because they go in a certain way. Now I know that I'm using spatial reasoning. Even now, I'm kind thinking, "Okay, so I know that the trainer goes like that, and I know I have to, oh, turn it, flip it. No, I need to rotate. Oh, there we go. I've got it." So I'm really aware now of using spatial reasoning. So we actually use spatial reasoning in absolutely everything we do, including mathematics. So hopefully that's kind of given you a clue into, "Well, are we using spatial reasoning?" Yes.

So let's get back to that question about why is it important. So I think if we think about our very youngest learners, so the learners that are starting to come into school, so maybe our two-year olds, our three-year olds. They're starting to access pre-nursery education. And when we look at the mathematics in particular that they're doing, we are still placing, I would say, too much emphasis on their number ability. Can they count? Can they write numerals? Can they spot them?

And of course, having number sense is really important. But what we now know is that having pattern awareness and having spatial reasoning is equally important. And I think we now need to reframe what we consider to be important, and we need to say, "Of course numbers are important, but so are the other things." And pattern and pattern awareness is part of spatial reasoning.

We've now got two significant pieces of research that actually talk to us about spatial reasoning is predicting mathematics performance. At the early years, we can look at children, we can look at their number and we can say, "Well, yeah, these children can count to 20, or they have composition or composition to five, or they can subitize up to four." But we now need to look at how they are with their spatial reasoning. So have they got spatial awareness? Young children run into the classroom. Are they crashing into the furniture because they can't quite navigate round? Are they going up and through and under the various mazes?

So we now have research that shows us that when we teach children to think and work spatially, their performance in maths improves. And that has got to be lifelong benefits because we've tracked this to the end of primary. So we now have a correlation between those children who are good at spatial reasoning. We can now see what their performance will be at the end of year six. But we've also linked that end-of-year-six performance to secondary and beyond. So we now know that spatial reasoning connects to what we would call those STEM subjects, in particular STEAM as well, but definitely those STEM subjects. And what is it we need for the future? We need the STEM subjects.

Adam Gifford

Can I just jump in and ask something? I know we should look at the future, right? There's no question about that. I was looking at lots of the research, some of which is included in your paper. It predates the changes to the framework, right? So the latest early years framework, a lot of research predates it. The emphasis was taken away from space and shape. Yes, it was talked about in development matters. But I suppose, like I said, the importance in probably, I don't know how far back we should go, but I still don't understand the decision why? Because whenever we place an emphasis on the framework, the emphasis is on number. Then it stands to reason that that's where the emphasis in teaching can lie.

And I think that spatial reasoning, you can develop it so much through questioning, just through the continuous provision and the children just being in that environment and prompts to develop that. I just wonder if the framework concentrates so much on number, is that development of a question skill set to support spatial reasoning within their environment, A) is that a focus? And again, I'm going to ask based on your experience. And I suppose, like I said, I don't want to go back into the reasons why and how people feel about that, the importance is about going forward. But just simply, did it strike you as interesting, for lack of a better word, that the emphasis went back on number?

Dr Alison Borthwick:

So I think we have to kind of just clarify which frameworks in which curriculum we're talking about. So when we're talking about England, we don't have a national curriculum for early years in England. What we have is a statutory framework. And within the statutory framework, there's a small paragraph that talks about kind of the statutory things that we should be doing for early years for mathematics and all of the other areas as well.

Now, actually, that paragraph is a real winner, because it mentions the phrase spatial reasoning. I'd have to check, but that's a fairly recent, kind of we're talking '20, '21, '22 when that statutory framework was published. The national curriculum was written in 2013, published in 2014, and that has no mention of spatial reasoning at all. And so, our primary and secondary, but our primary curriculum is completely dominated by a focus on number.

And I have to say actually, even now with a lot of the training, the national training that we see, it's very much focused on number, the multiplication tables check, we've got a mastering number programme that comes out for early years in Key Stage 1. I think we are now starting to get the memo, particularly in Key Stage 1, that spatial reasoning is important. But until we have a curriculum change for primary, we won't really see very much movement on that.

In early years, the issue is that although we have the statutory framework, the majority of early years teachers that I talk to don't really know about it. So they will be using a published scheme of work to drive their early years curriculum. And it is really dependent on that published scheme of work that people use as to whether spatial reasoning is mentioned.

You will find elements of shape and space or elements of geometry, whichever terminology we want to call it, but the spatial reasoning is not really appearing as predominantly as it should. Go to some of the international platforms, and it's already there. We are starting to kind of lag behind internationally, which is why the three of us who wrote the paper on behalf of the Royal Society, but we really want to put this right in the middle of any new curriculum reform that we might have potentially.

Robin Potter

So Alison, obviously we need to improve, end of story. We need to improve children's ability for spatial reasoning. So how are we going to do that in the classroom and how difficult of a process would that be?

Dr Alison Borthwick:

So I think any kind of change in the classroom, you've kind of got two routes, but your main route is the national curriculum. So that's what drives everything. So if the national curriculum was to reform, was to kind of be revised, which is what we would hope, then we would be able to draw down the latest research and be able to say, "Okay, we're not saying that number isn't important, but what we're saying is that actually it's not the most important thing. We must make sure that we've got the spatial reasoning and also the data science alongside it." Because again, as we've kind of acknowledged, education has changed. If you think about education 20 years ago, we are not doing the same curriculum as we were 20 years ago, and we shouldn't. So we definitely need a change.

So in terms of impacting in the classroom, we definitely need a curriculum change, because usually what happens then is that people who are writing schemes of work or other kind of materials, they will write to the national curriculum. So people are then assured that if they use a particular scheme of work, for example, that's then reflecting the curriculum. Curriculum reflects the assessment, and then we can work on the pedagogy.

So the pedagogy, you asked how easy is it to change? Really easy. So I've been doing some research and I've been running some training with teachers for the past four years on spatial reasoning, and their excitement about it is just tangible. It's just so lovely. And actually, there's nothing particularly new there. It's things like thinking about tangrams, thinking about pentominoes. It's thinking about kind of that rotation and that reflection and that perspective-taking and position and direction. So there's lots of things that are there that are currently in the curriculum, but they're a little bit more kind of dampened down. They're a little bit more implicit. So what we really want to do is to raise the profile of spatial reasoning.

First of all, we want to educate people about the importance. People say to me, "Have you got a silver bullet? Can you tell me what I need to do to improve children's performance?" And I say, "Yeah." They're like, "Oh, oh, wow. What is it?" "Spatial reasoning." "Have you got another one? Have you got one to do with number?" "No." Because what we're doing with the number is we're doing number okay; less times tables, more kind of number sense, but we're doing okay with that.

What we're not doing so well at is thinking about the spatial reasoning. And I think we've got the geometry side of the spatial reasoning and those things that I've mentioned like position and direction, scaling, perspective-taking, composition, decomposition properties. We would probably recognise them all, but when I kind of show teachers the list and I say, "Which ones are you doing?" They go, "Oh, that one, that one, and that one." "What about these ones?" "Not so much."

So we know that there is a lack of understanding and a lack of curriculum time to doing these things. So that actually wouldn't be a big change. But then we need to bring back in the skills. So you heard me mention visualisation, really, really important. And we used to do this back in the day. "I'm thinking of a shape, put it in your head, turn it round, rotate it, etc, etc. What shape is it?" type of thing. Those kind of skills, bringing back those, we might call them some of those mental skills, really, really important.

But then, let me just go to a number line. So hopefully, we all know and love a number line. But when we're thinking about a number line, if I said to you, "Let's just imagine a number line from zero to 20. What number is halfway?" So already you are using your spatial reasoning to figure out what halfway is or what three-quarters of the way along, or what's kind of nearer to the left side than the right side? Or "What if I... Do you know what? Is your number line horizontal? I'm just going to rotate it." Can you now think about a number line that's vertical? Can you now think of a number line that's circular? So all we're doing is we're just thinking about spatial reason using spatial reasoning tools and skills to help us essentially mathematize the curriculum.

Andy Psarianos

So a lot of the things you talk about, Alison, are already in the curriculum. So do you think... Where is it going wrong? Is it there's not enough emphasis in the curriculum about it? Or is it being sabotaged somehow by content creators and influencers and trying to push people into this obsession with number and particular number facts? But where's it going wrong? Because all the sort of rotation, scaling, all the geometry, it's already in the curriculum, right? Is there not enough emphasis on it? Is that effectively what we're saying?

Dr Alison Borthwick:

I think there's a couple of things. And I might need to clarify you're talking early years curriculum or primary curriculum? But particularly if we're talking-

Andy Psarianos

I'm talking primary, one to six.

Dr Alison Borthwick:

Yeah. Yeah. So if we talk-

Andy Psarianos

Yeah. Primary, one to six, 2014 national curriculum.

Dr Alison Borthwick:

So first of all, the actual phrase-

Andy Psarianos

For England

Dr Alison Borthwick:

... spatial reasoning isn't in the curriculum. So we have geometry, and geometry is split into two subsections. We have position and direction and properties of shape. If you look at even just the amount of objectives that are in kind of each year group compared to the number, it's number absolutely huge, geometry, tiny.

Andy Psarianos

Yes. Okay, I see what you mean.

Dr Alison Borthwick:

So first of all, we definitely haven't got the right emphasis. Secondly, there are some things that are missing. So you won't find things like composition and decomposition of shape in the curriculum. Now that doesn't mean that people aren't doing it, but just kind of understanding, "Well, what do we mean by composition of shape?" "Well, actually we mean let's take a square and let's put a right angle triangle on it. Now, can you imagine, can you visualise the outline of the two shapes together?" So it's that kind of understanding. And then, decomposing the shapes, breaking them apart, seeing shapes within shapes. We do those kind of things for number. We don't necessarily do them for shape. And of course, data. I could transpose all of that that I've just been saying to data as well. So there's definitely not enough curriculum objectives, time, emphasis in the primary curriculum.

There are things that are missing. Perspective-taking does not appear at all in any of the curriculum. So we kind of have a bit of a light touch, and we don't necessarily have the right things even within the geometry curriculum. "We kind of do a bit on position and direction." "Well, okay, but what about transformation?" "Well, we do a little bit when we talk about quadrants." "What about composing and decomposing?" "Well, we get them to name shapes and we get them to do a bit, but maybe not enough."

And then, there's the whole trench of pedagogy. So actually, and I've done this over the last four years, I've said to teachers, "Right, we're going to talk about spatial reasoning. Can you just write me a definition? Anybody know what spatial reasoning is?" "Well, we think we might know, but we're not really sure." So there's definitely some work to do around, well, what does it mean? Where is it in the curriculum? And therefore if I think it's that important, could I then do more with the curriculum? And then, let's have a look at the skills. Let's look at some of the ways that we can kind of use some of the spatial reasoning within the curriculum. Yes to begin with within what we might class as the geometry part. But then, let's go broad. Let's look at spatial reasoning within number. Let's look at spatial reasoning within statistics.

And then we start to see the power of it, and we start to see that and it is malleable. That's the other thing, that this is not a fixed mindset. Everybody can improve with their spatial reasoning. And then, we put on the layer that actually this is one of, and the research is saying the biggest predictor of how well children will do in maths. Why aren't we doing it?

In fact, the Ontario curriculum has a huge thing about spatial reasoning. And some of the researchers actually, one of their most famous lines is, "We're still talking about spatial reasoning?" Like, "Why are we still talking about it? Surely we're all just doing it. It doesn't make sense not to talk about spatial reasoning." And I think we've got a bit of a catch-up to do at the moment in this country. But we're getting there, hopefully, paper published.

Andy Psarianos

I won't tell you what's happening in Ontario as far as education goes, it'll break your heart. But anyway. And this brings me to another interesting point, which is this sort of politicisation of curriculums and that sort of, I guess influential people, sometimes politicians, sometimes not politicians who have their own ideas and interests in particular things having too much influence, doing really damaging things.

And the other problem that I see in what you're talking about is people who create content for teachers to use who really shouldn't be doing that because they just don't know what they don't know. It is always that horrible thing of knowing enough to think you know everything, but not knowing enough to know that you actually don't know very much. Right? And it's that dangerous place where people think they know more than they actually do. So then they start trying to be helpful and are actually being very damaging.

And I could pull out a lot of examples of this happening, very popular materials being used within schools that don't take into account any of the things that you've talked about and anything else other than just really covering the surface of it, just ticking the box. "Curriculum says we need to do this, click, and we did it." But not really exploring it or thinking about actually how far do you need to go?

And being obsessed with numbers. It's like this obsession with numbers. It's almost kind like the invention of place value destroyed mathematics, is one way you could kind of put it down. Because look, if you go before place value, most mathematics was done with geometry and spatial reasoning. Right? So if you wanted to multiply two numbers before place value, you would use an area model because there's no place value. Can you imagine trying to multiply two Roman numerals together? Right? Good luck with that.

So geometry and spatial reasoning has always been a big part, but then we kind of got away from it. And then, you have these really damaging... I think, and people hate me for saying this but I've said it publicly before, this Ready To Progress document that was created by the NCETM is one of the worst things that's ever happened in primary education in the UK, in England, in my opinion. Because it basically said, "You don't need to worry about anything else other than number." And what a kind of stupid idea was that? How did that happen?

Dr Alison Borthwick:

Well, yeah, and I think that's a really interesting kind of take. We are absolutely too obsessed with number. And again, I don't want people listening to say, "Well, we've said that number isn't important," because of course it is. But it's not the be all and end all that we think it is.

The Ready To Progress document is an interesting one, because it was actually written by the NCETM for the Covid period. So when schools were really, really struggling and we'd had children off school for weeks and for months, and we hadn't really got the online learning sorted, teachers were really panicking about how to get through the curriculum. So what NCETM did was they said, "Well, hang on a minute. We'll look at the curriculum and we'll strip it out and we'll maybe just kind give you the bare bones of what you need to teach." And that's why they called it the Ready To Progress. Now, whether they got the right stuff there or not is kind of another minefield, but actually what it seems to have become is that, for me, it was always that's what we were doing in Covid.

Andy Psarianos

That' the new curriculum.

Dr Alison Borthwick:

And it kind of has now become the new curriculum, and it was never intended for that. So one of the things that I talk about and I share with teachers is, "Could you go back to the national curriculum, which is not the Ready To Progress?" Absolutely. That is your Covid curriculum. We are now no longer in Covid, but we still haven't caught up with... If we're looking at accountability and we're looking at our year six national curriculum tests data, we are still not where we were back in 2017. So I would kind of, I'd like to hypothesise that we might be getting there. But if we were having better results back in 2017, and that was up to 2023, maybe it's time for a change. And I am absolutely, the more I read and the more I engage with teachers and children about spatial reasoning, the more I am convinced. Because we're not ditching number. What we're doing is we're actually kind of giving number a purpose. We're actually saying, "Let's think about the spatial element within number as well." And that's got to be a good thing.

Andy Psarianos

And I think the national curriculum is the place to start. And I think you're right. But we all know that there needs to be more, there needs to be a way of getting this message out to the teachers so that they can understand what that means in their day-to-day practise in the classroom.

And there's the other very important factor, which I think a lot of people don't really want to talk about because it's commercial and it's like it's money involved and companies; but the content creators, those people, those companies that are putting materials into the classroom that are giving so-called solutions to teachers on how to teach things need to come on board. Because there's still this horrible, horrible stuff that's being created in England that's being put into classrooms. I know people are trying to do the right thing, but it's not working. Some of this stuff is atrocious, especially when it comes to spatial reasoning.

And there needs to be a dialogue with content creators as well, because if people are going to put stuff out in the market and they're going to present it as a solution, they need to do their homework. Because the mere mortal teachers that are in the classroom every day, they just don't have the time or the expertise to really figure out, "What's the best lesson to teach this particular thing?" Right? And if the content creators are doing a bad job, it isn't going to work. It doesn't matter what the curriculum says, because the teachers just don't have the time to figure it out themselves.

Dr Alison Borthwick:

No, you're absolutely right. And I've kind of got two trains of thought on that. I think we are in a situation at the moment, and I think it probably was exasperated by Covid, but we're in a situation now where we are de-skilling so many teachers across the country because they are literally just picking up a scheme of work and following it kind of almost blindly. And I know that workload is an issue. And I do understand why they're doing it, but it's not the right approach.

If we really want to get back to really solid mathematics teaching and learning, we've got to get back to planning mathematics. It's absolutely fine to have a whole load of resources, and there's some brilliant stuff out there, absolutely. One of the reasons I'm talking to you guys, to Math, No Problem, is that I love your resources and I love the effort and the energy that goes into it. But actually, we've got to get back to not just giving every single line of every single lesson on a sheet of paper that teachers follow. Because if we provide it, then teachers will follow it because there's so much going on in the classroom.

But back to your thing about the content creators and also back to the national curriculum, one of my bug bears, and one of the things that I would want for the future, either with an iteration, a new iteration of a national curriculum or with any of the content creators going forward, is do your research. Actually, if your materials, whether it's a national curriculum or materials for schools in the classroom, if it's research-based and it's good research, so international and forward-thinking, not forward kind of going backwards, then actually we will get some really good things out there.

But what happens is that unfortunately, we sometimes have situations where our national curriculums are not written by experts. It's not drawn down from international research. And the same goes with some of the schemes of work that are out there as well. So let's get back to what we know works.

One of the reasons that the spatial reasoning paper that we're going to publish on the Royal Society is so powerful is that it is drawn down from the research. This isn't the three of us. I was lucky enough to write it with Dr. Sue Gifford and Dr. Emily Farron. But one of the reasons that it's a good paper is that we didn't just sit in a room and think, "What should we think up today?" We actually read everything that was out there on spatial reasoning. And then, we've synthesised it and then we've said, "Look. Actually guys, why don't we use this as the basis for a new maths curriculum going forward?"

Andy Psarianos

That's a good question. It makes a lot of sense to me. I've always agreed. I agree fully with what this paper says. I think, to me, it's obvious. But that's my intuition. Also, everything that I've ever read backs that up. I think it's kind of obvious. Even if you read between the lines between the big idea, sort of mathematics, if you look at Zoltan Dienes's work, or you look at Jerome Brugger's work, I'm talking about the real fundamental ideas that back most of the things that we work about, it's just all over the place. That's basically always what they're talking about.

The whole idea of concrete pictorial abstract is effectively saying, "Use spatial reasoning to teach everything." Right? "Start with concrete things." That's spatial reasoning, right? "Move it to a visual model in your mind." That's spatial reasoning. "And then, introduce the abstract. It doesn't matter what subject you teach, always do it that way." What does it say? "Teach everything through spatial reasoning." Right? What does Zoltan Dienes say? Zoltan Dienes, even his concepts around variation and everything are all based around the principles of spatial reasoning. It's littered all over the place, even if they don't use the terminology. It's so obvious, but we seem to have forgotten, right? It's like what you said about the number line.

But it's user beware. You also need to look at the research and say, "You're going to start introducing cardinal numbers with the number line? No, you're not, because that's a more advanced concept. So you've got to do the one-to-one representation first, knowing what that progression is." But it's all about spatial reasoning in the end, right? Even number.

Dr Alison Borthwick:

Yeah, absolutely.

Andy Psarianos

It's one of Dienes' blocks.

Dr Alison Borthwick:

Yeah. Yeah.

Andy Psarianos

The Base 10 blocks.

Dr Alison Borthwick:

Yeah.

Andy Psarianos

They're all spatial reasoning.

Dr Alison Borthwick:

Yeah. And it's lovely that you can kind of see that existing research coming through. And I think we have used that, but there's so much really, really up-to-date research. And I'm not just talking the research of one child in one country on one day. We are talking about some peer reference, some longitudinal, some really robust research. And everything that we've put in there has been fact-checked, research-checked so we know that it is solid.

So yeah, spatial reasoning is the future. We can all be better at it. And it will just, I think the reaction that I've had from my teachers when we've looked at the spatial reasoning, we've looked at the research, we've had a go at some of the activities, they've had a go with the activities with their children in the classroom, which is the whole Guskey model, absorb the information, go and try it out, figure out if it works, kind of that. They've just come back and they're so excited. So if nothing else, it will just revitalise and re-energise the curriculum, but actually going in the right way, and going in the way of the international market as well.

That's the other thing. I don't know if you saw we've included the latest PISA references in there. So the 2020 PISA results have just come out. And England, it's moving up the charts. What is the one thing that we are lacking at? It says it in black and white from the OECD, shape and space, spatial reasoning. So we might be doing well at number, we might be doing well at problem solving, but actually the rest of the world is doing better at spatial reasoning. And they're going to overtake us, so let's get on board.

Andy Psarianos

I'm so happy you guys are doing this work, Alison, I really am.

Robin Potter

You can have a whole other episode now. Andy's just started to...

Andy Psarianos

Oh, don't. Yeah, no.

Robin Potter

... scratch the surface with you. He can delve deep.

Andy Psarianos

This is my favourite subject, right?

Robin Potter

Yeah.

Andy Psarianos

So this is by far.

Dr Alison Borthwick:

Brilliant.

Andy Psarianos

I love talking about spatial reasoning. Alison, so excited about having you on.

Dr Alison Borthwick:

You're welcome.

Robin Potter

Yeah. It's been great.

Dr Alison Borthwick:

Well, it's lovely to talk to enthusiasts and maths enthusiasts and maths educators. And yeah, so it was lovely to meet two out of the three of you at the conference and to just kind of carry on and keep talking. Yeah, it's a pleasure. My pleasure.

Andy Psarianos

Thank you for joining us on the School of School Podcast.