Episode 205: Go slow to go fast. The importance of a varied toolkit in learning maths

Welcome back. I just had a practice of that intro and then I missed the mark but we're back we are back and sort of just about hitting the mark and we've got the usual suspects we've got Andy and Robin how are you both in the other side of the world where it's a bit chilly I think both of you suffering heat problems.

Yeah, Robin doesn't have any heat in her shed. Yes, she actually has a heated shed and I have no heat in my house. But other than that, we're doing fine. This would kind of crazy over here. Actually, there's been snow on the ground for like two weeks, which is quite rare for Vancouver. So, yeah, it's proper winter.

I'm hoping, I wanted to say we're very fortunate to have Ross Deans from Musclier Primary. Ross, I think the three of us have known you for quite some time now. First of all, I hope that you've got heating down south where you are. A quick heating status report if you don't mind.

Heading status is that I'm in a pretty chilly room, but I don't think it's as bad as Canada. In fact, we just had some friends from Canada come over and visit and they're speaking about how you guys have to get the ploughs out and clear the roads and we don't have any of that. So we're okay.

Exactly, first time in school-to-school history that the tropical northwest seems to be winning in the heating stakes, but we're not here to talk about heating. We're here to listen to you and to hear a bit more about your journey with Maths No Problem. And as I said, we've known you for a number of years, we've seen each other face to face many times, but for our listeners, can you just tell us a bit about you? Tell us a bit about your school and sort of where you're up to with Maths No Problem, the sort of origin story, all that sort of stuff. We're just going to sit back and listen for a while.

Okay, no problem. Well, our school has been working using Maths — No Problem! since about 2017, so quite a while now. And I should say that actually my predecessor first worked with you guys to bring it on board. And I was at the school at the time. I've been working at the school for about 13 years now. But yeah, so before Maths — No Problem!, I was quite involved in the development of Master of time in a way. And I think it'd be fair to say to describe our practice.

This is pretty everybody talking about mass mastery and that being a very common topic for a lot of schools. You pretty would have seen a pretty common three way differentiation split some firmly established ceilings for different learners at different levels. Planning progression that might not have been completely consistent across school and tied up nicely in terms of representations and the way that things are taught.

And I think it'd be fair to say a fairly dry mass diet. So a focus on teaching procedure. And what I know now is really only focusing on one approach or one method at a given time. And that's often the methods or the approach that the teacher has in their head. So a bit like this, this is what you need to do. This is how you do it. Practice it. Practice it again and do a bit more.

until you feel confident. And I think my predecessor, when they started bringing in mass masteries to the school and working with mass in a problem, we had a real journey to go on like a lot of schools to really understand what teaching for mastery even meant and about the way that we use resources, representations and...

all of those tools to develop children's understanding and love of maths. And I think we've come a really long way as a school, both in terms of how our data looks, but also the level of enjoyment for both staff and for children across school. A big shift, I still remember actually when we first started talking about things like bar models and using manipulatives, concrete pictorial abstract approaches. We had a lot of work to do there and we had to spend a lot of time with

different representations, trying to understand how to use them effectively and how to prepare children to adapt to those representations. I think a big part of Maths — No Problem! is that it's not a fixed approach. When you're looking at different problems, it's very much encouraged to explore different methods, different ways to tackle that problem. So that you're providing a varied toolkit so that children understand there's not just one fixed approach.

look at things in different ways. You can represent it in different ways and that gives you a much deeper understanding.

Sorry, I'm just curious. You mentioned toolkit. Can you think of things immediately that are in that toolkit for you?

Yeah, I think it's like I said, rather than fixing onto a procedure, it's, you know, we're doing some multiplication, I'll get the column method out. That would be a very limited toolkit. You know, I've got an algorithm, I know what I need to do, it's multiplication, that's what I'll do. And that can work up to a point, but it's not giving you very flexible understanding of your maths. So that very toolkit might be that you've got different ways to look at

look at number, different ways to understand what you can do with that. You can explore patterns and see them. You can use whether it's a bar model or a different representation to try and make sense of something that's more complex rather than just, you know, go down that familiar route every time. And I think about actually my own learning. So I've become teaching for 13 years now. I didn't go into teaching straight out of university. You know, I had a different career before and I came around to this and it did seem like quite an unlikely career for me, I think.

way back then, because it just wasn't where I was. And maths certainly wasn't a subject when I was at school that I felt particularly confident about. seeing a different way of teaching maths that really empowers children and helps me to love maths really changed my view of that. And I think back to it when I was probably in secondary school and in this situation where I've been taught lots of procedures, but with little conceptual understanding, and you can find yourself in a situation where you...

Maybe you're in a test and you've got to guess, what is it? I've got a times the numerators or I've got a, do I need to do? What did they tell us to do? But without the understanding, it's kind of guesswork and following instructions rather than, you know, making connections and bringing it all together. So trying to give children a much deeper understanding to make connections and to have that very toolkit. So they've got a range of ways to approach problems, makes it a much more powerful subject for them.

gives everybody a way in as well. It's not just about being quick with automatic facts, you've got a way to approach problems.

Ross, that's really interesting. I'm one of the things I want to pick up on one of the things you said, which was that you never envisioned yourself as either an educator and in particular being, putting so much emphasis on mathematics education with young children. That's quite a common thing, I think, for a lot of people who are on this journey. Why do think that is? Why do you think so many people don't see math? Mathematics is something that they want to pursue in their career, whether it's teaching or just mathematics in general, when they're going through school.

Not necessarily the children that you're teaching because I would probably imagine it's different for them, but you know as part of your own journey what what put you off mathematics?

Going back to what I said earlier about that idea of learning these abstracts algorithms with little understanding, I think it was that not fully understanding what you're doing, they're very much right or wrong culture being put on the spot, not having any other options.

I very much, I remember not being secure with timetables in secondary school and just being scared I was going to be put on the spot and be embarrassed because I wouldn't be able to say the correct answer.

Whereas what we're trying to do nowadays is actually, a lot of the time a real mantra I have with the classes when I teach is that I know the answer, I don't need you to tell me the answer. That's not the point here. The point is that we're talking about what we notice, what our understanding is, what patterns we see and making those connections.

When you can open up the subject like that, so everybody's got something to offer, it becomes much more accessible and fun. And I definitely think when I was in school, unless you were really able with maths, a lot of people didn't really enjoy it as a subject. And that's really not what I feel now. I feel certainly in our school, children really love maths, even children that you can tell it's really difficult for them, but they can still see it as a lesson in which you can be creative and you can explore and you can use manipulatives and you can feel successful.

I think that creativity is a really important word because I believe quite strongly that what you're describing is your experience. It's probably not all that dissimilar from many of our listeners. And certainly I know for a fact that Adam and Robin probably that resonates with them as well. It's kind of like, success in mathematics meant being able to remember a lot of things and being able to recall them quickly, right?

but it didn't really have much to do with creativity at all. And now, you know, the emphasis on, you know, the way that you're teaching is, hey, let's look at this. Let's think about this creatively. Like, sure, we know we can do the algorithm. That's great. We all learned it. We all know how to use it. And that's really good. And it's useful because sometimes that's the best way. But what other ways are there? Can we see something here? How is this the same as the thing we did yesterday?

Even though seeming, you know, on the, on the exterior, they really seem to have very little in common, but now we're picking up, maybe we're finding underlying structures that, that ties it in with other things that we've done before. And that becomes a creative process. And that's interesting. And, know, children are curious, right? And they, once you point out that there's things to find, it becomes like a, little, a game almost, right? A challenge, you know, see, Hey, maybe this is similar to that other thing we did. Can we apply what we learned last year or last week or?

you know, whatever the case may be, or can we come up with an entirely new way that ties different things that we know together? And I think that's a lot more fun, isn't it, than just saying, you know, this is what the internal angles of this shape always add up to this, just remember it, because that's the question on the next test, you know, some random fact that meaningless fact, right?

Yeah, and a way, if you think about a master problem worksheet and the structure of a lesson, you're not just going to learn a column methods, now practice it endlessly until you get the column. You know, it's in any lesson, really, you're exploring a real life context, which is really powerful. Adam, when I joined you for one of your trainings and you were talking a lot about framing master stories and.

And that's really, really powerful that every lesson is tying to something that's relatable and practical. And using stories is really powerful for learning. We all know that as teachers, it's such a powerful way to connect to information. But throughout a lesson, you're really going to just be doing an algorithm and repeating it. It's going to be exploring relationships, exploring different ways of doing things. There's this kind of what if moments, what if I change this aspect?

and the misconceptions, the things that can go wrong. So it really is like an exploration. You learn a concept, you graph with the concepts and you explore it in depth rather than just robotic more of the same stuff.

Did you find Ross, when it was first introduced, I think what you've described, and like Andy said, we've had experience with this with lots of other people, I went through it myself, it's that sense of learning which is incredibly empowering because you see maths in a different way for yourself and that allows you to kind of teach differently.

Did your colleagues also find it of like A, confronting and that there was this different way of teaching mathematics that wasn't as, and let's be honest, easy, as saying to a child, right, just remember this.

That's maths. Just remember that. Because if that's all you have to do, that's quite straightforward, isn't it? You just give them something, they memorise it, you move on to the next, memorise it. But so one, did your colleagues find it sort of confronting? But did they too sort of feel that empowerment that allowed them to say kind of what you're saying, which is I learned something new, you know, like this is something that I realised that this was another way of teaching that was different to what I've been doing.

Were those conversations happening in the school at all or over time?

Yeah, there's a few things that the link to that actually. mean, firstly, I'd say I know lot of schools that have spoken to you that it was a long process to adapt as well teaching and it didn't happen overnight and it was a slow evolution. My colleague who also works on maths for me in the school, will, you know, to share that in the early days she's like, what is this? And had a quite negative reaction to it because it didn't feel comfortable, but then grew to understand just like the children needed to, they need to adapt to a different way of learning.

Just think about something you said about it's easier to teach in a standard way. It is easier in the moment. It's easier to say, look, this is what I want you to do. Do it exactly like me. Get it on your whiteboard. Do the same. Do it 10 times. That is easier in the moment, but it's not developing very secure schema. And it's also easier to forget, right? So, and that's probably my head.

Yeah, there's definitely just so everyone's clear. There's no link between me saying it's easier and this is a great way to do it and buy yourself a few hours. Not in the least, but it is in terms of the teaching practice. You know, if someone said to me, right, how do you teach maths?

You know, here's the series of facts. Like this is your year group series of facts. They just need to memorise that by the end of the year. You think this is great. This is this piece of cake. I'll just give them one a week. I'm just going to have a cup of tea and relax.

And in aspects of the curriculum it can seem like that kind of it's not that much stuff But obviously when you break it down, it's yeah, it's very complex. But Yeah, so you kind of think about that that quite go slow to go fast, you know you you need to really lay the groundwork and develop understanding and and then Again going back to I mentioned about the toolkit earlier Robin But when you've got different approaches different ways to understand something and different angles to look at it from

then you've got an understanding you can take forward with you. If you're just learning, this is how it's done, you've got no real reason to remember that next week, next month. We all know, every house forgets in curve. It's a part of learning, isn't it? We forget straight away and also over time. So we need to really foster a way to make it memorable, to make those connections stronger.

I love that line, got to go slow to go fast. That's brilliant and so true. And yet I don't think people think about that enough or, you know, teachers think about that enough. It's like you were saying, okay, you know, follow me, do it 10 times, let's move on. And really that's not what learning is about. And, you you talk about being creative and being curious and, you know, creating a story, you know, or a game out of

what you're learning and really letting it sink in too, just not moving on so quickly from a lesson, being able to come back to that lesson and let's do it again but in a different way. I mean, those things are just so important for the pupils and for the teacher.

Yeah, and particularly, think if you think about those learners that struggle to have those automatic facts quickly, that's, it's really going to turn them off, isn't it? If it's all about quickly learning procedures and moving on, they won't be able to keep up. Whereas if you've got time to explore, then everybody can do that. Everybody can feel successful.

Was it Confucius or Sun Tzu or something? I'm just looking it up right there. That said slow, slow, fast, fast.

It's definitely not my quote. And if I think we had one of the the conference that your conferences where my colleague Catherine and I were talking about it afterwards.

Who's going to take credit for it?

There's a song, there's a song, a children's song, so slow fast. Anyway. Sorry, I didn't mean to distract everyone.

It's probably a strong suggestion that these types of things that get said have been around for a long time because they're And that is something that is worth knowing that your experience will tell you too, right? Is that, know, and I think that's the thing is that the other thing that I think sometimes gets missed in amongst conversations like this is the relatability of whatever you've learned. then it's so, you know, and that's, I think that's part of what you're probably saying is that, is that makes learning the next bit so much easier.

You know, like learning hundreds of facts if you don't know that they're based off say a single idea or a couple of ideas that's hard work that's really hard work but if you understand sort of what underpins it and you just change these bits but it still seems to keep working that's just better like learning two things well is better than trying to slug your way through a hundred plus things.

Yeah, it's coming back to exploratory approach, isn't it? That it's not just formulaic. It's about exploring and understanding and asking questions and as we said earlier, being creative. So I think it's journaling for us, it's still something we're developing. I think that's a really slow thing to develop actually, to do it really well. using journaling, getting children to be able to write down and be quite creative and actually going back to a creative point, if you look at our mass journals,

they definitely look like the most creative books that the children use. You they look more like art books at times. They've got bar models and different representations and drawings at times. And they're really fun books. And again, it's just coming down to that being explorers and trying to find connections. And that's what makes it really fun.

I think the last thing, just, not the last thing, but the last thing I was going say on this in relation to this is that it also demonstrates and allows the children and teachers to experience what mathematicians do. I wish as part of like, you know, we do kind of day trips and field trips and whatnot. I think almost a prerequisite of all teaching should be a day trip or a field trip to some mathematicians. And watching them struggle with biscuits and tea,

pondering a question for day upon days and you know all this sort of stuff because what we've described you know you don't have a series of sort of mathematicians working away thinking right I've got to memorize this list today and this list tomorrow and whatnot you know they're really giving a lot of time to think and consider and that creativity the artistic nature of finding a solution to something that doesn't yet exist how cool is that I mean that's that's really cool and I think that that giving that experience to it to our children and staff as well

realizing that actually this is what mathematicians do. This is what it feels like and looks like.

And I think also the important thing to understand is that sometimes people forget how important the really the precision aspect of mathematics is as well, right? But it's not all that mathematics is about and it's interesting because I was having this conversation just two days ago while was visiting visiting my son in Toronto who's who's at uni right now

And we're oddly enough talking about this. He's studying maths at university. There's a real correlation with language in the sense that if you look at language studies, which is varied, you've got people who make dictionaries, Whose whole passion and kind of devotion is to being precise and succinct, right?

is to find the essence of a word. It's very, very kind of precision work. Sort of like, I guess what you would look calculation could be in some people's minds. It's all about precision, right? How can you capture in a very precise way the meaning of a word? And then on the flip side, you got poets who completely break all the rules and use words in the wrong context, but in a very colourful way. So metaphors and similes as an example, right?

They're trying to find the wrong word to describe something that gives an essence that builds a relationship. And mathematics is just as varied as that, you know? And if you think about like brilliant breakthroughs in mathematics or science in general, whether it's physics, mathematics, chemistry, it doesn't matter. It's always those people who are on the fringe who are looking at, you know, well, how can all this be changed? How can you reinvent the universe, know, in Einstein's case, right? Yeah.

Newton was kind of right, but actually he was wrong. Right? And you could change all the rules, all of them, just with this simple idea, you know, and that's kind of, that's kind of really quite fascinating, right? There is a tremendous amount of interesting stuff to be done within mathematics and, and it's opening people's minds to that. And I think for some reason we got so fixated on one side of it. It'd be like saying to children, you know, okay, we're going to learn English, but we're only going to look at the dictionary.

and we're only gonna talk about dictionary. And that could be a point of view of learning English, But it would be pretty sad, it?

I think as well actually maybe not quite as ambitious as that but I was thinking when when when you were speaking earlier Adam children often question you know why do we need to do this we've got an iPhone in our pocket or you know or whatever and it's well that's not really the point with learning all of this maths is you could go forward in life and be a slave to needing a device to solve your problems for you but you're never going to think creatively you're never going to be able to figure things out for yourself and I often try and relate it to quite

simple things like you're doing a bit of DIY and pop into the hardware shop and just being able to think creatively about what you could do and how you could solve a problem in a different context.

And learning maths helps to give you that problem solving brain. And I think that's really powerful as well. And yes, you could go on to be a mathematician that solves an era-defining problem, but also just having that ability to to be able to think flexibly and creatively is really powerful in so many careers as well.