Episode 182: The secrets to Singapore’s success

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. As per usual, we've got Robin Potter with us. Go on Robin, you know what I want you to say.

Robin Potter

Hello. Hi, hi, everybody.

Andy Psarianos

And we've got Adam Gifford with us as well.

Adam Gifford

I'm pleased to be here too, Andy.

Andy Psarianos

Yeah, sounds like it. Okay-

Adam Gifford

That were supposed to come across, I really am. I can't wait.

Andy Psarianos

We got a super exciting guest today. We got Wenxi Lee, who wrote this really amazing book, which I've got a copy of here, called The Secret to Singapore's World-Class Math Curriculum. Now, anyone who's ever listened to this podcast knows that we love to talk about Singapore's education system and the fact that they've skyrocketed in the '80s or in the '90s anyway, they became top of the world. They've been there ever since, a real outlier. Even Malcolm Gladwell wrote about it. It's definitely something that everybody should know, everybody in education should know more about, and that's why I'm really excited to have Wenxi here because Wenxi's written this book. And going through that book, I mean, everything just resonates. It's what we've been saying all along, and Wenxi's the experts here.

So before we jump in, Wenxi, can you tell us a little bit about yourself to the audience, so they know who we're talking to? And then we're going to jump right in. Yeah?

Wenxi Lee

Yeah, of course. Hi, everyone. I'm so thrilled to be here. Thank you for the invite. So I'm actually currently doing my PhD in math education at the University of Illinois at Chicago. And my current dissertation is actually heavily focused on teachers. So my research is based on a teacher training programme at a local school in the US. So, really excited to get into the data and write about that.

And I think what's really interesting or sets me apart in the math education field is my undergraduate background in mathematics and art history, so I've really got that interdisciplinary approach to teaching and to research. And because I'm born and bred in Singapore, I love the Singapore math system. I teach it right now, actually to this day. I've been teaching it for 10 years now, so.

Andy Psarianos

Wow.

Wenxi Lee

Right, I just feel like I can't escape it right now, right? I was born into it and then now I'm just continuing the legacy. Yeah, so that's kind of what I've been doing and for the past couple years of my life. And yeah, that's pretty much all about me.

Andy Psarianos

Fantastic.

Robin Potter

I feel like that only scratches the surface. So Andy, dig right in.

Andy Psarianos

Yeah. Well, I'm going to launch right in on your book. So, what is the secret to Singapore's world-class math curriculum?

Wenxi Lee

I mean, there's so many. You got to read the book to know.

Andy Psarianos

I know.

Wenxi Lee

You know?

Andy Psarianos

I know, I know.

Wenxi Lee

Yeah, but so what's funny is that my initial intention for the book wasn't to get it published. I actually was writing it as a guidebook for the parents of my students because I started out my career focusing on teaching home schoolers in Illinois. And I'm not sure if you guys are familiar, but Singapore math is a huge curriculum for the homeschool community here.

And so while I was working with a lot of the parents who came to me and was like, "Hey, you know what? We love Singapore math. We saw the curriculum and we wanted our kids to do it." But as I'm chatting with them more and as I'm teaching their kids, I realise that they don't really know what the curriculum is about. So I wanted to write this book to kind of let them know what it's about, what are the myths or misinformation that's going on that's been circulated in the media, especially about the curriculum. And what are some of the things that we can actually do to help children succeed who are using that curriculum? So that's pretty much what my book is about. A lot of debunking myths, a lot of takeaways as you guys know, because it sounds like you've read the book.

Yeah, and I just really hope that even though I'm an academic, I just really hope that my book isn't a theoretical approach to talking about Singapore math. I really wanted people to have some kind of hands-on or practical advice and takeaways that they can actually use in their classrooms or in their everyday lives.

Andy Psarianos

Yeah, no, I think it doesn't read as an academic book at all. I mean, what I mean by that is, obviously you've done your research and that's clear, and you've made references to where the research came from and everything, which is great. But it doesn't read, it's not reading a thesis or anything. I mean, it's very readable. Right? It's an easy book to read. It's actually a really pleasant book to read as well. And obviously it's a subject that's close to our hearts, so I was excited to go through it and see some of the points that you make and stuff.

So if we dig right in, what are some of the myths? In the book you talk about spiral curriculum, for example, and you talk about vertical, horizontal and all this kind of stuff. I mean, maybe let's just get right into it. So a lot of this stuff comes from Jerome Bruner, obviously originally. Let's just jump right in. I mean, most of our audience is teachers anyway, so they should be familiar with some of the underpinnings, I guess, of this. What is it? What is Singapore's math curriculum all about?

Wenxi Lee

Yeah, for sure. So I would say Singapore's math curriculum has four major aspects to it. So I think a few has really been the selling point of Singapore math outside of Singapore. I think the first thing is the concrete pictorial approach, I think that's something that everyone talks about. Right? So it's pretty much three stages that children and actually adults too, have to go through when they're learning a new concept or a new topic. And I think what Singapore does really well is bringing in the manipulatives and the pictorial stage where we use our bar modelling as a strategy to kind of solve word problems. And speaking of bar modelling, that's like the crown jewel of Singapore's curriculum whenever we hear about it, whenever we talk about it, and even when we teach it. And I think what's so special about the bar modelling is that it's really a skill to be learned, but a lot of people think of bar modelling as a skill that you are born with, much like mathematics.

Speaker 5:

Oh, interesting.

Wenxi Lee

Right, so that's something that I found really interesting when I started teaching children in the US, bar modelling is that they're just kind of like, "Oh, I don't know how to do it." Not because nobody taught them how to do it, but just because, "Oh, I'm not good at math, and so I can't draw my bar models." And that's absolutely not true. So I think that kind of thinking and philosophy really seeps into the entire math education system. Yeah, but I think for bar modelling in Singapore's context, it's really to prolong that pictorial stage so that children can kind of learn and internalise the abstract concepts of mathematics using rectangular models, using the unit thinking and things like that.

And so then the third one is what you just said, Andy, it's about the spiral curriculum. Right? So a lot of people in the US don't think of Singapore as a spiral curriculum because in the US when we say the word spiral curriculum, and this is of course about vocabulary in different contexts, it is when a curriculum actually just alternates bite-sized topics throughout the year. So they could do time today and then they can do fractions tomorrow, and then they'll do whole numbers again on Wednesday, and so on and so forth. Right? But for Singapore, it is still a spiral curriculum, but we have to look at it in terms of the whole package, in terms of the entire primary or elementary school curriculum.

So what it does is, as a kid, I vividly remember this because I'm just like, every single year for math, I step into the classroom, I know exactly what to expect. We always start the year with whole numbers, especially with place values, and then we go on to review or to learn new things about the four operations, right? And then maybe that goes on for a couple of months and then I know what's coming next. Maybe it's fractions or maybe it's a new topic, for every grade level. So what I was saying in the book is that for Singapore math, the spiralling, it's really occurring across the grade levels instead of within. But that being said, they are actually introducing some of the spiralling within the grade level too, in Singapore's local curriculum now. So I think Singapore is really taking into account a lot of the different research that is coming up, or a lot of the different evidence-based strategies that are working.

And the one last aspect for a Singapore method that I think doesn't really get talked about is the entire framework. I think sometimes people forget that it's a whole system. Right? People just kind of look at the textbook and the workbook and say, "Oh, you know what? We can do this. We can teach this." But it's really not just that. It's a whole system of teachers, it's a whole system of the assessment. I don't think the US has implemented any kind of Singapore-based assessment yet if they're using the curriculum. So that's a huge kind of challenge for teachers implementing the curriculum in the US, because the assessment is so different from what they're learning. Yeah, and so it's a whole system that we have to be mindful of. It's not just like a copy and paste. Right? I wish it was, because then it'll be so easy to replicate its success, but it's really not. It's a whole thing, it's a whole package and it's very comprehensive.

Yeah, and it really ties into every other aspect of Singapore's education system as a whole as well. So that's something that we don't really think about when we are implementing Singapore math here.

Robin Potter

Can I just ask one quick question, Wenxi? Because you're asking or you're explaining how it's this whole system. And you do, I know one of your takeaways in the book was creating a math mindset.

Wenxi Lee

Right.

Robin Potter

Instilling that in your pupils. And I'm curious, is that what you mean by a math mindset, or could you explain that to listeners what you mean by that?

Wenxi Lee

So I think the mathematical mindset is one of the things that is really focused on in the math education's framework in Singapore. So if we really dive into the curriculum and what it's set out to achieve, one of the core or fundamentals of Singapore's math curriculum is to develop that mathematical mindset. And what I mean by that is, really just having the persistent to solve problems and to kind of treat mathematics as a positive subject, even though it may be really hard at times. I think with that, we're talking about Dr. Carol Dweck's book, right? Mindset in general too, and Joe Bowler's research on mathematical mindsets. And it's that growth mindset where you don't think that you're born with that ability, which is something that I spoke about initially, but instead, it's a skill that you can learn.

So I think with that, what's interesting about that is that I think a lot of it is also cultural in a sense. In Singapore, I think everyone is expected to learn math and learn math well, and even parents too. It's not acceptable to just be like, "I can't do math." It's just not, it's culturally unacceptable. But I think in the US sometimes even parents will tell me like, "Hey, I didn't do well in math. I'm not a math person, so I'm not really expecting my kids to also be math people." And I try to tell them like, "Hey, you shouldn't say that in front of your kids," because that's how it gets ingrained in their mind, right? So I think that's that cultural shift there too, that I'm trying to work on as well, is just that sometimes math is hard. Right? I acknowledge that to my students, but it's something that we can do together and it's something that can be learned.

Adam Gifford

I think one thing that I find, Wenxi, I just want to pick up on that point, that expectation that everyone learns maths. I think sometimes when that gets talked about, we often think that it's just referring to the students, the pupils in the school. And I know that because the system's different, I'm assuming it's the same in America, but certainly in the UK, there's so many different options to getting into teaching. So we don't have that uniformity, like the uniformity of the teachers who are trained in Singapore, for example. And I'm not convinced that there is an attitude that everyone needs to learn math within the teaching community, in terms of ongoing learning.

So I know when I was first trained, there was a real attitude of, if you can do primary school maths, you can teach it. Right? There was no real differentiation between teaching it and you just showed them how you did it and expect them to replicate it. Do you find that your experience outside of Singapore would suggest that people feel like, ah, if it's primary school maths, it's not that hard to teach? It's only primary school maths, whereas actually the complexity of supporting someone to learn mathematics is vast, and I don't think you ever stop learning about it. But is that your experience, that that attitude is very different outside of Singapore?

Wenxi Lee

Yes, it definitely is. It's one of the things that really shocked me when I first got into math education in the US. I learned that high school math teachers are expected to have that specialised math content knowledge. Usually they would need to have a math major or a math minor in order to be a high school math teacher here. Yeah, but like you said, Adam, for primary or elementary school teachers and preschool teachers too, they don't really need that specialised math knowledge, or it's not expected of them with their teaching certification or through their teaching training programmes in school.

So teachers and parents, I think in the US, I found that generally they do consider primary or elementary math much simpler. I think in the homeschool community, parents are kind of like, "Oh, you know what? I can teach my kids how to add and that's what I'm going to do," right? And which is totally fine, but when they're teaching them how to add, they're not necessarily also strengthening that concept of place values, which is so important in order for them to advance in math. And so they're just like, I think there are details and a lot of specific pedagogical knowledge that doesn't really get talked about when we're talking about early math or elementary math. And yeah, that's definitely the attitude that I've seen in the US as well.

Andy Psarianos

Yeah, and that's so important because is, and we've talked about this on the podcast before, but it's kind of hard to imagine what it's like to not understand some of the basic concepts in mathematics. Right? But for young children, obviously we take it for granted that, something like you've mentioned, place value. Place value is not an obvious thing really, right? If you think about it. It took how many years for humans to develop the concept of place value? And even the zero as a placeholder is like, that's not an obvious thing, it's really not an obvious thing. Right? Like counting 1, 2, 3, 4, 5, just keep going all the way past 10 to every... Just rote counting is obvious, but writing it down in this place value format is a really difficult concept. And things like, and I'm talking about for very young children here, the notion of the different types of numbers. Right?

So you've got counting numbers, you've got this idea of sets, so cardinality. So when you say, okay, if you ask a very small child to say, "Okay, I want you to count these objects," let's say a bunch of pens, and they count them and they go, "1, 2, 3, 4, 5, 6, 7, 8." Okay, fine. If you say, "Show me seven," they're likely to show you the seventh one and not show you a group of seven pens. And what that means is for them, counting is a nominal thing. You're naming every single one, just like you would name this is bus 25. And that is a concept of number, but it's a different concept than cardinality, like this is a set of things that together is seven. Right? It's a different concept. And then there's... So there's all these different types of numbers, nominal numbers, ordinal numbers, cardinal numbers, whatever they are. As an adult, we can easily jump back and forth between them, but for a small child that's not obvious. Right? And then throw place value on top of that, that's even more complicated.

So between the ages of let's say three to seven or eight, you got to assimilate all these different concepts and be able to categorise them properly, so that you know that you don't multiply bus number 23 with bus number 17, that that's nonsense. Right? That's not just really obvious to a very small child. As an adult you've already covered that so many years ago, you forget what it's like not to know that. Right? So you jump right in and you say, "Just do as I do and everything will be fine," but somehow you need to cover those things and we forget that. It's actually really hard. It's actually really, really hard.

Wenxi Lee

It is, and so I'm glad you brought that up because that's actually one of my biggest challenge working in this field and specialising in Singapore math. So one of the things that I do do outside of school is I train teachers as well.

And for me, just for example, the bar modelling strategy, right? It's so innate in me. Whenever I see a word problem, my go-to immediately is bar model, and I don't even have to think, I just draw it out. But when I'm training teachers who don't have a base knowledge of what bar models are, sometimes it's really hard for me to, I think, relate to them and to figure out what kind of knowledge I need to scaffold for them in order to get them to that stage. So that's definitely a learning process for me. I mean, I'm still learning it to this day because for different groups of teachers, you have to scaffold it differently. And then there are suddenly things that I thought was really common sense to me, but it's really not common at all, it's really just for me because I grew up in this. And I have to constantly tweak what I do in my trainings in order to get them up to speed or to get them to that base knowledge that I was talking about.

Andy Psarianos

Well, you touch on this in your book, actually. When you talk about process versus procedure, right? And the idea that if someone is taught procedurally and solving word problems or anything that's like algebraic in nature, let's say, just to narrow it down a bit. Because you've come through this strong foundation of concrete, pictorial abstract, and your immediate go-to is to go through that process of understanding the problem first, being able to visualise it. Visualisation in the sense is being able to, in your mind or the way you're describing it for these particular problems is being able to show it visually with bar models. Right? And having that real kind of underpinning where immediately, your visualisation skills are so strong that you can see the problem and you can show the problem, draw the problem in a visual way, in order for you to solve it. It's so ingrained in you because you've come through this way of learning.

For these other people, they didn't have that benefit, so they immediately jumped into procedures. It's like, oh, if you have this type of problem, then you write it this way and then you go through these sets of steps to... But in a meaningless way. They really don't have any visual concept of what's going on. They just do these steps and the right answer comes out the other side, and that, that's exactly what you're talking about. And for you, it's almost impossible to understand why they can't visualise it, right?

Wenxi Lee

Yes, right. So that's part of my learning process, is to figure out how to map certain things. So I think we talk about mapping for children, in terms of manipulatives too, right? It's sometimes while we're going from the concrete to pictorial stage, it's not always obvious for kids to instantly map your blocks or your 10 frame to what we're talking about in math. And I think that's what happens to training teachers too, is just figuring out how to map certain things onto their current knowledge base. Right? So it's kind of like, I don't want them to unlearn anything that they have because whatever knowledge that they have is also very valuable. Right? But it's kind of like, how do we build on that and how do we kind of strengthen that so that they can then talk to their kids about it?

Adam Gifford

You have such a... it's not, it won't be unique take on it, but it'll be something that most educators outside of Singapore won't have, is that you've been a child through the system. So you've seen it, you can reflect on it as an adult, and not just as an adult, but an adult that is reflecting on something in a really analytical, academic considered way, that you're putting time aside to consider these things.

So I suppose my question for you is, is that you've got your educator's hat on and that you're working with children and parents. You've got your academic hat on, so you're looking at the practise and pedagogy that's involved in this approach. You've got your lived experience of actually being in the classroom and listening to your teachers and the takeaways that entails.

So my question is this. What's the... I know you've got a chapter on takeaways, but what's that sort of first step? When you go to work with people, if you're going to work with a group of people, whether it's teachers, children or anything else, and you've got all of that combined experience, you've got all those different perspectives. What's your starting point? What's the first thing that you think, right, in order to make this work, these are the first two, three things that we really need to get across right at the very beginning, if you want to have that big impact?

Wenxi Lee

So I actually ask them. So whether it's working with a student or teachers or even parents, I start by asking them what their mathematical education experience was. Right? How they grew up learning math, because I think in the US, sure, we can kind of generalise and say that a lot of people learned math through the procedural way, but there are some people who learned it in a more conceptual and a more comprehensive way. So I like to meet them where they are, and I think that's something that I think do differently, perhaps with other Singapore math educators too, is that I don't force Singapore math down people's throats, if that makes sense. Even though I am doing my dissertation on Singapore math.

But I can use Singapore math strategies with any curriculum. Give me any curriculum, and I can kind of sneak Singapore math in there, here and there, without you even knowing. We don't have to call it that. You know what I mean? So I like to kind of follow where my audience is going. If they want to talk about a topic and they want to learn more about the concepts piece, then I'll go with the flow. So there's not really a starting point that I use, in terms of with Singapore's system, but I kind of just go off with my audience. I try to see where they're at, and then I try to meet them there. I don't know if that answers your question. I feel like that's kind of broad and vague, but it's hard.

Adam Gifford

No, no, no, it does make sense. I just wondered if there's sort of uniformity in that of course, you have to take on, I guess like any teaching, whether it's in the classroom or other people. You've got to assess and then decide what your response is based on that assessment, where they're at and those sorts of things. But I just wondered, in more sort general terms that whether it's, I don't know, you've talked about certain approaches, the concrete Victorian approach whether it's bar modelling. I don't mean to sort of single those out, but whether it's, I don't know, like an attitude thing or whether it's... I don't know, I just thought that you have a different perspective from the three of us because we weren't taught in Singapore, for example.

So we've all got our experiences that we've shared on other podcasts about our own educational experiences. And so all of us, when we're dealing with teachers children, I'm sure that's just part of us, right? So we can't get rid of it. That's just part of us and there'll be biases and all that sorts of things that we bring into any sort of education setting because of that. You are part of a system that you are now spending a lot of time looking at considering supporting people to learn. So it was really about that.

But I understand your point, that it's, I guess, if one takeaway from that is, is don't assume, right? Don't assume that the people in front of you are your standard cookie cutter, non-Singaporean, teacher, which doesn't exist. But, you know what I mean? So no, that is takeaway. I just wondered if there's anything else that sort of jumps out that you go, yeah, this is generally something that we need to address.

Wenxi Lee

So I think my methods would mirror the curriculum. So Singapore's curriculum is very, it's very systemic, it's very structural, and it's very logical and coherent. And so the way I explain certain things or the way I conduct a lesson or a training session is mirroring that. So I try to manifest or embody the curriculum in a way too, that really helps them understand where the curriculum is coming from. Yeah, and I try to be very intentional about the questions that I ask and the concepts that I'm trying to bring forth using Singapore math philosophy and vocabulary as well. I think those are the things that I really take note of whenever I'm planning a session or a lesson.

Robin Potter

So, we could go on and on because there's just so much here to unpack. But I do want to bring out the fact that you do have a book, that that's what we're talking about. Could you let us know, can you let the listeners know, there it is, Secrets to Singapore's World-Class Math Curriculum. Could you let us know-

Andy Psarianos

All teachers should buy this book and read it.

Robin Potter

There we go.

Andy Psarianos

And parents as well. Everybody should buy this book and read it. Okay?

Robin Potter

There you go.

Andy Psarianos

It's an excellent book.

Robin Potter

And where would we be able to get that? Can you tell our listeners?

Wenxi Lee

Yeah, for sure. So you can purchase it from Amazon, or if you have access to Singapore Math Inc's, like if you're part of their shipping destinations, then you can also purchase it from them.

Robin Potter

Okay, and what about you? If they want to find out more about Wenxi Lee, where do we find more about you?

Wenxi Lee

Yeah, of course. So you can. I do have a website it's, www.wenxilee.com, so it's just my full name, .com, and you can find ways to contact me there. Shoot me an email, I would love to chat.

Robin Potter

Fantastic. This has been-

Andy Psarianos

Wenxi, real pleasure. Real pleasure.

Robin Potter

Such a great experience. So thank you so much for coming on the podcast. And yeah, we feel so lucky that you've been here to share all of your knowledge with us.

Andy Psarianos

And send us your dissertation.

Wenxi Lee

No, thank you.

Andy Psarianos

Send us your dissertation when it's published, let us know.

Wenxi Lee

Yeah, for sure, I will. I will be sending it to the whole white world. Been working on this for years.

Andy Psarianos

Can't wait.

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