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Episode 98: What is Maths Mastery and the Singapore Maths Methodology?

Didactics, Singaporean similarities, and more. In this episode, Andy, Robin and Adam discuss what Maths Mastery actually is, as well as Singapore’s history. What is the core definition of Maths Mastery? Has anyone heard of the Cockcroft Report? Plus, hear why the term ‘Singapore Maths’ doesn’t really exist.

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Profile of Andy Psarianos expert educational podcaster.

Andy Psarianos


Andy was one of the first to bring maths mastery to the UK as the founder and CEO of the independent publisher: Maths — No Problem! Since then, he’s continued to create innovative education products as Chairman of Fig Leaf Group. He’s won more than a few awards, helped schools all over the world raise attainment levels, and continues to build an inclusive, supportive education community.
Profile of Adam Gifford expert educational podcaster.

Adam Gifford

In a past life, Adam was a headteacher, and the first Primary Maths Specialist Leader in Education in the UK. He led the NW1 Maths Hub’s delivery of NCETM’s Professional Development Lead Support Programme before taking on his current role of Maths Subject Specialist at Maths — No Problem!
Profile of Robin Potter expert educational podcaster.

Robin Potter

Robin comes to the podcast with a global perspective on parenting and children’s education. She’s lived in ten different countries and her children attended school in six of them. She has been a guest speaker at international conferences, sharing her graduate research on the community benefits of using forests for wellness. Currently, you’ll find Robin collaborating with colleagues and customers in her role as Head of Community Engagement at Fig Leaf Group, parent company of Maths — No Problem!

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Podcast Transcription

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.

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Robin Potter

Welcome back everyone to another episode of The School of School Podcast. I'm Robin, and I am here with our usual suspects, Adam. Hello Adam.

Adam Gifford

Hi Robin.

Robin Potter

And Andy.

Andy Psarianos


Robin Potter

I get questions all the time about when they ask... People ask me, "What's the company that you work for?" And, "Maths — No Problem! What is Maths — No Problem!?" And sometimes I get asked further questions about, "Well, I don't understand. What's maths mastery? What does that even mean? And what is Singapore maths? What's the methodology? Can you explain that to me?" So I thought I'd go to the experts here. I'm going to the source. Andy, Adam, who would like to start this off?

Adam Gifford

I don't mind starting in terms of maths mastery, I think maybe dispel a few myths as well. So just to start with, the mastery approach is not new. It's not in the last 10 years that all of a sudden mastery's become a catchphrase or keyword. It started, I don't know, '50s, '60s, there's a few big players. But without going into that, just give you a couple of headlines. Mastery effectively expects that, or we need to believe that everyone can learn given the right amount of time, the right conditions. So that's something that's really fundamental and underpins the mastery approach. And there's a few more technical aspects to it, so I don't know, knowing where your children are at to start with. That's a really important part of mastery. Really good instruction to a whole group at the beginning. That's part of mastery.

Formative assessment, keeping on top of listening to your students or your learners and being able to respond immediately and being able to support them if they've already learned something or they need more support. And being ready for taking that learning deeper. So I've covered quite a lot in a short space of time, but I think that right at the outset, it's having an expectation that everyone can learn. And that seems like, "Well, of course. Every educator has that, right?" But the problem is they don't. You could go into schools all over the world and you will have the triangle group and the square group and the yellow group, and believe me, if you went to them and said, "Right, who are the flash maths kids?" "Oh, that's the triangle group." "Oh, who are the kids that don't get maths?" "Oh, that's the circle group."

Research shows us that as soon as you do that, as an educator, as an adult, your expectations of those groups are different. And almost without fail, each of those groups will meet your expectations, but they very rarely exceed them. So if we start doing this and our starting place is these children are never going to be at the same place as someone else. You're absolutely right. That's where they'll stay. And stats have shown us that. We've had groups of children going through because the expectation's lower for them. It's as simple as that. So I think that's starting place of understanding that everyone is capable learning given the right conditions and the right amount of time, I just think that that has to be believed, not just understood, but it has to be believed by educators, otherwise we're in trouble. That's right at the outset.

Andy Psarianos

Yeah, I think that's the fundamental thing, is how you choose to teach so that you can teach what is seemingly a group of children who are at different levels of attainment. How can you teach them together? That's really the most fundamental point. So that everyone benefits, so that you're not doing it at anyone's detriment. Obviously if you make it too challenging, you're going to leave some kids behind, if you make it too easy... This is the common thinking. If you make it too easy, then the more challenged... The more seemingly advanced students will fall behind or lose interest or whatever the case may be. So how do you teach a whole class with all the varying different stages of comprehension and seemingly different abilities and/or attainment levels? How do you do that? And that's what mastery is supposed to be, I think.

The problem with it is that it's become jargon that everybody wants to say, "Well, we do mastery," and then they have their own interpretation of it. So it's hard to... Obviously when you get into the details, people have different ideas about what it should look like. Beware of the jargon, I would say. But I think the intention is, as Adam stated, and this idea of the whole class teaching. So how do you do that? I mean, we could debate that for days. And we have. At Maths — No Problem! we have a pretty rigid idea of what that should look like. And that's not based on any of our own in individual opinions, but largely based on how mathematics has been taught in Singapore since the 1980s, and the advancements and things that Singapore has done in education since the 1980s.

Which brings us to this idea of what is the Singapore maths methodology? I mean, the important thing to understand about Singapore maths is that there really isn't such a thing. In Singapore they wouldn't call it Singapore maths. Clearly they would just call it mathematics, and they're mystified that other people in the world call it Singapore maths because none of the ideas come from Singapore. What Singapore did, which no one else seems to have done as well as they have, is they've really, really cracked down and said, "Okay, what does the research say? What do the grand learning theories say? How can we put those things together in develop a programme?" And that's what Singapore did, and they did it really, really well. And then they, since the 1980s, have been crafting it and trying to get it better every year and working towards this ideal goal, which they haven't reached, no one has, but they're probably the closest.

And I think the thing is that it's really put your egos aside and just really look at... Let's be empirical about it, let's look at what the facts say. Let's do something and let's see how well it works and let's measure it, and let's continuously do that over decades. And eventually you end up with this amazing way of teaching, which is what they've developed, which is what we follow along that same path, we've borrowed that from them. Why? Because let's face it, they have the world's most successful education system by far. Not just in mathematics, but for sure in mathematics. And why would we think that we can do better than that? It took them decades to get there. They're very, very generous with it. They share it with the world. They tell everybody what they've done. We just pay attention to them, that's all.

So that's what Singapore maths is. There's other places that do really, really well, and they do really, really well in slightly different ways or sometimes very different ways. Singapore just... They're the most similar to countries like the UK or out of all the countries that do remarkably well. If you look at a place like Shanghai, Shanghai is not really a country, it's a city, but you could argue that it's a city state like Singapore. They do remarkably well. They do it differently, but culturally it's very different. You've got one place that's very heterogeneous and they've got another one that's very homogeneous, and they're not similar, and culturally there's a lot of big differences between Shanghai and Singapore. Singapore culture's more similar to places like, let's say, England or Canada or the United States, in the sense that there's lots of different people from different cultures all mixed up together, different socioeconomic groups and stuff.

Robin Potter

Would you say then that even though Singapore maths, they're sharing it with the world, it's not like everyone can't learn this way? Or is it because you're saying culturally there may be some differences, so what works in Singapore may not work in Shanghai, for example?

Adam Gifford

I'm going to flip it over if you don't mind, and just jump on that, and say Singapore to the UK. I think one of the big challenges is that the starting place here is very different, and the conversations that we'd have with colleagues would be very different to Singapore because the approach is so clear. There's an expectation that everyone follows that approach. And I think that the hard part in the UK is that we've got this amazing system, an amazing structure, but there's still, I think, in part a reluctance or a reservation about taking the time to understand it and to implement it, and the time it takes to train teachers. Because if you're trained in Singapore, you're going to know a lot more about it than you are in the UK. So by default, it means that when you become a teacher in the UK, you're going to have to do more training while you're teaching in order to understand it.

But I think that one thing that I just think can't be highlighted enough is that Singapore, I think, is in such a unique position and that they've been sculpting this, as Andy said, for decades. I can't think of too many countries, and sometimes politics becomes involved in this, that have had a ministry of education... Look, I'm being diplomatic here, but have had an education system that has made incremental changes, not great sweeping changes. And I don't mean necessarily to the curriculum, but the way that it's delivered and the basis for the training of the teachers. And what an absolute treat to be able to see that and to look at the outcomes from it, and for us to be able to take that approach on in our products. But I think that it's still one of those that in the UK, I think that starting place is we can go in any direction, or not just we can go in any direction, we can maintain the direction that we're on regardless of whether there's certain things in research telling us that this will support our students better.

As a school leader I can say, "Well, I'm not taking that on board. I'm afraid it's just too big of a change," or it's whatever it is, even though it flies in the face of the research. And I think that that's the hard part, is that you've got a system, you've got the understanding of how mathematics is learned. I think you used the word crafted, Andy, but I think that makes such a difference. It makes such a huge difference to someone who... I don't know, I know when I was... I hadn't been teaching long when I came to the UK, but it doesn't matter whether in the UK or New Zealand, I was struggling to teach mathematics in hindsight. I found it really difficult.

And what I've learned through this approach makes me just such a better teacher because I understood the maths better. Me. I understood primary school maths better. And that's as a result of a country that's been able to do that. I just can't think of an equivalent that's been able to do that. And the medium that Andy talks about, where Shanghai's different in that they have more specialist maths teachers, that they don't teach full time, they're given time each week to go and think about their mathematics. That's not true of teachers in a lot of countries. Singapore in front of a class of 40, different languages being spoken, different cultures. The challenges are already in place there, and they've found a way to deal with them. And I think that's really special. I think to find an example that is really rare and we should sit up and take notice.

Andy Psarianos

So there's different philosophical approaches to education that are taken by different countries, and some of them are because of their geography, the realities of their geography. A large expansive of a country like the United States with lots of people in the education system is not going to look like the education system in Singapore for very, very practical reasons. Singapore is a bit like a laboratory. But what you need to take into account is that what they've done works, and that you don't need to change the whole country. You can instil that in your school, or you can instil it in your district or your council, or you can instil it in your trust, your multi academy trust, or whatever your community is, you can apply those ideas in that community. You can't change an entire country. Because in the end countries have to just make very broad decisions about education.

And they may not even think about it this way, but it ends up being this, do you want to create an education system where you're going to create the best in any domain? That's what you're going to do. Is that your goal? Or is your goal to make sure that everybody learns enough? So those are two very, very, very different goals, and the money goes either in one direction or in another. Now the UK probably, I know that they wouldn't say this, but if you look at their education system, I know they're trying to change it in the UK, and have been trying for a very long time. Originally, historically, it was about the elite.

You go back and I'm talking about history now, that's a tremendous thing to try to change in a country. So there's still battling that. While Singapore made a very clear statement in 1982. "No, we're going to teach everybody, and everybody is going to become good." The problem is their idea of good is probably the equivalent of great for most countries. Singapore does so well, it's shocking. Their bottom 10%, just to give you an idea, their bottom 10% of the students in Singapore, the worst 10% in Singapore performs as well as the average student in Canada.

Robin Potter

That's an incredible fact. Shocking.

Andy Psarianos

Take the three worst kids in any classroom, three worst kids in any classroom, and they perform better than the average student in Canada. That's pretty damn good. So now one would then say, "Yeah, well what about the kids at the top?" Well, they do so much better than the kids at the top anywhere else, so clearly we need to pay attention to what they're doing because whatever it is, it seems to be serving everybody. So that's the remarkable thing about Singapore. So what is it? Take all the research, take everything that we know about how people learn, everything that we know about what they need to learn, what are the didactics of teaching mathematics? What order do you need to teach things in? And what do they need to know before they know the other thing and all those kinds of things?

Structure that. Don't leave any of it to chance. Structure it to the best of our knowledge, the best of our ability, and constantly challenge whether or not we got it right. And when we find that there's maybe a slightly better way, change it and then measure it and make sure it got better. Then if it didn't get better, change it again until it gets better and do that over decades and decades and decades, you're going to get somewhere. That's what they did. Most places, unfortunately politicians have too much of a say in the education system, and maybe because they want to come in and do good things and say, "We need to change. We're not doing well enough." But the thing is that they then start putting their opinions into it because nobody seems to be able to tell them what to do. So then they go with what their gut tells them. And then somebody else gets selected and he changes it again, right?

Adam Gifford

Here's an example of that, Robin. If you surveyed, I don't know, pick a number of teachers across the UK and you said, "Have you ever heard of the Cockcroft Report. I imagine 90%, maybe more, would say, "No, never heard of it." And this is one of the most important documents that Singaporeans come across, that they help them shape the idea of, "Oh, we're going to learn through problem solving." This was done and commissioned in the UK. This is the sort of thing, and again, this is where I think we should be thankful to the Singaporeans, is because no stone was left unturned. This was a real, genuine, not lip service, we want to discover what the best education system in the world looks like. So I think that some of these things that have happened around us, and they're literally at our fingertips, largely ignored. And for what?

And I think that last bit, and I think that we can take this as well into our own schools, is what Andy said, that cycle of change, but the most important part for me is the evaluation to see whether that change has made a difference. Is it better for the students? And I think that that's the part we sometimes miss, or school systems outside of Singapore miss, because we haven't got a chance. A political cycle finishes, the evaluation doesn't take place, and a new idea comes in. And I think that that cycle, even on a small level, a school level, needs to be in place, and we don't take the headline of make a change and then guess whether it works. We've got a system here that's so well evaluated, so well researched, that we're doing a disservice to the kids if we don't sit up and pay attention, I think.

Andy Psarianos

Well, there you have it, maths mastery and Singapore maths.

Thank you for joining us on The School of School Podcast