Episode 183: Expert practitioner shares findings from MBA dissertation on Maths Mastery

Andy Psarinaos:

Hi. I'm Andy Psarinaos.

Robin Potter

Hi. I'm Robin Potter.

Adam Gifford

Hi. I'm Adam Gifford.

Andy Psarinaos:

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

Adam Gifford

It's time for another School of School podcast episode. Robin, Andy, we've finally made it. What people don't know behind the scenes is it's been a bit of a mission, putting this one together, but we're here. And how are you both today?

Andy Psarinaos:

Yeah. I'm doing well.

Robin Potter

Yeah. Feeling great actually. Thanks for asking.

Adam Gifford

Good. Well, we're very fortunate today because we've got Wendy Liu here, director of studies, Math subject specialist, researcher, teacher at Old Vicarage School in London. I actually had the pleasure of speaking with Wendy yesterday too, which was lovely. Wendy, for people who don't know you, do you want to just introduce yourself and just tell us a little bit about yourself and things that you do?

Wendy Liu

Yeah. Sure. So I'm Wendy with over 25 years experience in the primary sector, and I branched out perhaps about 15 years ago specialising in Maths. It was actually during one of your first five-day course, the Maths — No Problem! courses that I went on with Dr. Yeap Ban Har, that propelled me onto this route, actually. I was so inspired by him at that meeting that I went on to pursue Maths Mastery and look at Singapore Maths more deeply.

So for the last 15 years or so, I've been an independent Mathematics consultant, working with schools, working with publishers, working with EdTech companies, and just developing Maths and sending out this message about Maths and being really passionate about Maths and how children learn as well. So it's been a really interesting road. And a couple of years ago that led me to pursue an MBA and during my final dissertation. I decided to write about my passion, which is the Mastery Maths route.

Andy Psarinaos:

Fantastic. So do you remember what year that five day course was?

Wendy Liu

Oh, I think it was 2013, something like that.

Andy Psarinaos:

Okay.

Wendy Liu

Yeah.

Andy Psarinaos:

So one of the really early ones. Yeah.

Robin Potter

Wow.

Wendy Liu

Really early ones. I think the other day you actually posted one of the pictures of that five-day, original five-day course, and I was there along with Simon Norton, so I remember that day.

Andy Psarinaos:

Were you there? Was that in...

Robin Potter

Oh, wow.

Wendy Liu

Yeah. One of the first days. It was a five day course. So it was one of the first ones you did. It was recorded.

Andy Psarinaos:

January, 2014.

Wendy Liu

Was it 2014?

Andy Psarinaos:

I didn't realise you were there, Wendy. I'm sorry. Because I was there.

Wendy Liu

You might see me in those old footage.

Andy Psarinaos:

Well, I'm going to go look at those photos now. Yeah. For sure. I'm sure you're in the footage. Yeah. It's funny because I passed that photo around.

Robin Potter

Yes. You sent it out to everybody asking how many people do you recognise here?

Andy Psarinaos:

Can you name in this photo, right? In our notebook, can't believe I missed you in there.

Wendy Liu

Yeah. Yeah. I think I'm there somewhere.

Andy Psarinaos:

Yeah. Yeah. Wow.

Adam Gifford

You are windy because I thought you look exactly the same today. I was quite jealous. I was thinking, oh, wow. What's Wendy's secret? What's the story?

Andy Psarinaos:

You know what, Wendy, I did make the connection now that I... Because I remember everyone from that. That was a transformational event for a lot of people, and I remember when we organised it and I organised it with... At the time the head of Math for Merton, I was really like, "Do you think people are going to come to a five day course?" This is a big investment and it's a big ask for a teacher to come out of class for five days to go to a training course. And I was surprised that we sold it out actually, and we ran it twice. We ran it twice. We ran five days. The five days that you came, and then immediately after we ran it again and we sold out both. So it was 10 days of full on training.

Wendy Liu

Training. Yeah. Yeah.

Andy Psarinaos:

Insane.

Wendy Liu

Really inspiring though that I remember. It did change my trajectory.

Andy Psarinaos:

Yeah. So how many people could you name in that?

Wendy Liu

Oh, maybe a handful. I remember Justina was there. I met Justina for the first time there.

Andy Psarinaos:

That's right.

Wendy Liu

And Simon and a few others.

Andy Psarinaos:

Ban Har, of course.

Wendy Liu

Yeah. Ban Har. Yeah. Brilliant. So no, it was a great, great day's worth of training. Yeah.

Andy Psarinaos:

Yeah.

Wendy Liu

Lovely. Yeah.

Robin Potter

So you're clearly an original. We'll call you an OG and just to stay current and-

Wendy Liu

I think I've just been sold ever since Andy told us his story about his daughter. So that was it. You had me hooked from that moment.

Andy Psarinaos:

Yeah. Oh, right. Okay. Good to know.

Robin Potter

And so it sounds like you've had a lot of time and a lot of inspiration when it came to writing your thesis and about Math Mastery. Can you share some of what you looked at and some of the discoveries you might've made that you didn't expect to make or you did expect to make?

Wendy Liu

Yeah. Sure. Actually, it was a real life consultancy project that I was preparing for our school. We're looking to change our Math scheme for years, been using the original Oxford Inspire Maths publication, but that ceased publication and we were looking for a new scheme and obviously my first thought was Math - no problem! but also equally there was power Maths on the market at the same time. And so I thought it would be good to do a comparison. I particularly looked at the development of soft skills through Mathematics teaching because I feel that Maths is no longer about computation. You can get a computer to do that, a calculator will do it for you, but it's actually the development of the soft skills, which are the most important elements of Mathematics teaching.

And so I looked at how the Math scheme really promoted the development of these soft skills, and I looked at the educationalists and theorists behind the publications, especially the likes of Piaget and Bruner and Dean's and Vygotsky, and I researched what they were saying and how that then fit into how each scheme were using this piece of it or these pieces of information and instilling that within their education.

So essentially, I obviously couldn't look at everybody. So I took some key ones, which turned out to be a few of the key ones that Maths — No Problem! really are affiliated with and a few others. And then I broke it down to look at how the soft skills would be developed through that Mathematical teaching. It's really interesting because you ask people now... Especially, I think they did some research recently on Gen Z, and they were saying they wish that they had been taught these soft skills at school because that is what employees are looking for. They're looking for people who are able to communicate really well or have critical thinking skills or can work as a team, articulate and all of those things. Which Maths is that perfect vehicle from which to do it.

Adam Gifford

The research is quite powerful and is well established and is still cited and work as of today and stands up to that rigour. Did you consider why it is that in classrooms and countries that have access to all of this research and people who are well versed in it, who make decisions, why is it we still have classrooms? And when you get into the talking of teaching and teaching Mathematics particularly, why is it we still have practise? Do you think that still flies in the face of so much of what we know is really good practise that helps children learn?

Wendy Liu

Well, I think primarily it's the lack of teacher training themselves. They were taught the chalk and talk or sage on the stage. They were taught in that way, and that's all they know. If I go back to when I first started teaching, I remember having to teach... I think it was multiplying fractions. Could I remember how to teach it? Could I remember what to do? I had to Google it. I had to work out how to do it. And then I taught the children by rote. I just said, "Oh, you just do this to the numbers and multiply here and do that, and then you'll get your answer." No idea why I was doing it. Where it came from, and don't talk about dividing fractions. And I always remember I was sitting around a room full of Maths specialists when I was part of the Ealing Research Group.

We were all Maths specialists sitting around this table. And I posed this question, I said, "Well, why is it when we divide by a fraction, we do this whole keep flip change thing?" And nobody could answer me. Nobody knew. And we are all Maths specialists. We're all Maths teachers, Maths education. We had a hundred years worth of experience between us, but nobody could tell me. And so we all sat down with bits of paper. I remember Dr. Yeap Ban Har would say, "If in doubt, draw it out or use bits of paper." So we all sat there with bits of paper and we suddenly figured it out. We suddenly said, "Oh, it's because we tried to think about the story. If you've got three quarters divided by a half, essentially, well, what does that mean in the story?" And we couldn't figure it out in terms of sharing, but we could figure it out in terms of grouping.

Oh, that's how many halves fit into three quarters. And then from that perspective, everything changed and we realised, we can see... If we see it this way, then it works and we can create a story around it. And it's never so powerful. And now we'll always remember why we do keep flipping change because we understand it conceptually. But if as a teacher you've never been taught in that way, you don't know what you don't know. So you just keep going back to the old ways because that's safe and it worked for you, so you keep doing it for the next generation.

Andy Psarinaos:

So there's a really interesting... So I'm glad to use that example. So three quarters divided by one half... Most people... First of all, for most people, it makes absolutely no sense because the answer of a division of two fractions is larger than either of the two fractions, right. So the answer is one and a half. Now, why? It's just absolute... At this point, it's so abstract and complete absolute nonsense to most people that it's almost impossible for them to understand what a real world scenario of divided to fractions would actually be, right. And you nailed it. You said it's all about grouping. Now here's the bit that people don't understand often because they think it's all about teaching that one lesson. So, okay, if you teach that one lesson well, then people are going to come to the right answer and they may even understand it. But what they don't realise actually is this, and you nailed it, the notion of grouping. Because when you teach division, especially when you teach division in the early years, when you first start with division, everyone's so fixated on sharing as a concept.

Wendy Liu

That's it.

Andy Psarinaos:

So it's like, I've got 12 cookies and I want to share them equally amongst four children, how many... Which is exactly the problem that most people come up with, right. But what they don't realise is that if children don't have the notion of grouping, which is the flip side of that, right, is how many groups of three cookies can I make from 12? Which is a different question. It's an entirely different question, right. Although on paper it looks the same.

Wendy Liu

It's the same. Yeah.

Andy Psarinaos:

It's an entirely different question.

Wendy Liu

Yes. It's a different story.

Andy Psarinaos:

It's a completely different story. You need to teach that in year two because the three quarters, and you need to teach it in year two, and you need to reinforce it in year three, in year four, in year five. And then when you tackle it, either in year six or year seven, which is normally when a question that would come up, if you look at all the various curriculums around the world, it certainly wouldn't come up before year six, probably not before year seven. In most countries, the kids are ready for it and they go, "Oh yeah, of course. Yeah. It's just one of these." So you wonder why? The whole point is the kids that can do the magic seemingly, wow, these kids are really clever in year six and beyond is because what their year two teacher did.

Wendy Liu

Yeah. Absolutely.

Andy Psarinaos:

And their year two teacher could only do it because what the reception teacher did.

Wendy Liu

Yeah, that's it.

Andy Psarinaos:

And it's that continuity. That continuity all the way through is so critical. They call it coherence. A lot of people call it coherence, but they don't actually really know what it means. So I'm glad you picked that example because it's so important, right.

Wendy Liu

Yeah. I've been on training where I've been to schools to train the teachers and the support staff. And I actually went to train them about the grouping and the sharing concept, the two different concepts, and they turned around and said, "Well, why do they need to know about grouping? So surely division is just sharing." So even at this stage where you are trying to teach the teachers, a lot of them are not accepting it because they don't have that understanding themselves. They haven't got that concept and they don't feel it's important to teach the children.

And a lot of the times when we're talking about teaching variation as well, surely if they know how get the right answer, that's okay, then. That's all that matters. Well, no, because it's not about getting the right answers because you give them a non-routine problem. They don't have anything to pin their learning their concepts on, so they can't actually figure things out. They only know one way, so they don't really understand it. There's not that true conceptual understanding. So I think the hardest uphill struggle that we have actually is teaching the teachers and teaching the people that are in charge how to teach Maths properly.

Adam Gifford

Well, I think that's the worry, right. So you guys have just talked about the early days 10 years ago. Where you had a huge number of people that were really interested in learning and really quite profoundly changed in their practise. And this was time after time after time. So it wasn't just those two, it was that kept on going, kept on going. The curriculum, was written in such a way and talked about in such a way that that approach should be adopted by and large. And yet here we are 10 years down the track and Wendy, we caught up yesterday with some other trainers and talking about this perception of understanding Mathematics. But these things are still coming up. And I think it's a real concern and it's a real worry because some of those messages that I think that probably we moved away from, I say we, like the people that perhaps learned a little bit more and invested time in learning more and understood a bit more about what good teaching and learning looks like.

The worry is that 10 years down the track, we're still running into the same things. I actually think that there's a slightly bigger problem as well at the moment because there's a lot of people that would perceive that they know things very well, and that's even more dangerous because it's like, "Well, I don't need to learn anymore about this because I already know it. You don't talk to me about mastery, don't talk to me about this or these other things." But actually I think you're absolutely right is that if the teacher training doesn't allow for that, or the flip side of that is you are ready to teach at the end of your teacher training and it's like, "Yeah, you'll learn bits about the craft but not necessarily about the content." Then something's got to be done.

People have got to realise that no, there is a lot more to it than that. And it's a continuation of professional development and learning and understanding that actually there's a fair amount to be done and that don't be confused that if you come out of your teacher training that you ready... That you know it all or enough. I just don't think that that's the case.

Andy Psarinaos:

Yeah. That's right. And I think because I want to bring it back to one of the things you started talking about it Wendy is, so you said, and Adam, you've just reinforced this idea, the importance of training. When you really look at it, what's the one thing? It's about training teachers, right. Because if you create... You create whatever tool you want, if people can't interpret it and see which bits of it are... Then it's not going to have the impact. You might do better with a good tool than you did without a good tool, but you're not going to have the impact you could have if the people using the tool don't know how to use it, right, don't really understand what it's all about. Just think about it from another... The problem with teaching is people always... Everybody thinks they can teach, right.

Because it's like, "Well, I went to school so therefore I can teach because I spent a lot of time in school." Which is of course complete nonsense because it's like saying, "I spent a lot of time in a hospital so I could be a doctor." It's just a ridiculous concept, but they think teaching is easy. But what I wanted to pick up on was you said that you looked at these various different programmes that were out there, but we didn't get beyond that. So what happened when you looked at all these different programmes?

Wendy Liu

So I did like-for-like comparison, because obviously at this point in time, we've only got two DFE approved schemes in the UK, which is the massive problem in the power mass. And just compared them in terms of... They're much to much in many ways. There's slight differences in terms of the teacher training, but I think both schemes use a lot of the research, the background from the theorists that I looked into. So it's very similar in terms of the programme, but for me, I don't know, massive problem always seemed to have that edge. It just seems to be a bit more user-friendly for me as well. So I like that. And the characters within it as well, because they are mostly real life characters. The children in there also brings it to life a bit more as well. But in terms of, a Math scheme is only as good as its user.

So it doesn't matter how good your scheme is, if the people behind it are not using it properly, that's where it all falls down. So I have seen in the past where schemes like Maths — No Problem!... People chosen to withdraw from that scheme because they haven't had that adequate training. And so everything just boils back down to making sure that teachers are trained up properly. And also for teachers to change their mindset to begin to understand that Maths is not about getting a page full of right answers, which is... Whenever I speak to colleagues, that's all they're interested in. They always say to me, "Oh, Maths is easy because it's just easy to assess because it's about right or wrong, whether they get it right or wrong." And I say to them, "Well, it is not really because it's multifaceted in the sense that there's so many different ways to get to that right answer or be a wrong answer. You need to figure out where that misconception is."

And so the assessment is so, so important and it's a massive journey. And that's why things like journaling is really, really important for us as teachers in terms of formative assessment. But whenever I talk to colleagues, it's always the same. Maths is right or wrong, and even children, they're unhappy when they make a mistake. So alongside teaching them in this way, I do a lot of growth mindset and that comes hand in hand. And my year two children, they know about metacognition, they know about growth and fixed mindset. In fact, they use that language.

Because it's so important. So alongside any teaching of the Maths, I think teachers also need to become au fait with this whole idea of teaching for a growth mindset. And not just... You ask teachers, oh, I know what teaching for a growth mindset is. It means that they're not afraid of making mistakes. But if you actually teach for a growth mindset, you are constantly talking about it with your children. I'm constantly telling my children at school that I'm fascinated by their brains and how they learn.

And when they come across things that are tricky, we celebrate, we say, "Yay." I say, "Are you struggling?" "Oh yes, I'm struggling." "That's brilliant because I've pitched it. Right. That means you're learning something." Or somebody's made a mistake. We do a little cheer. "Oh yeah. Somebody's made a mistake. That means we've got something to learn." Something new to learn. And so it is really nice and you build that in and you see the resilience and the perseverance that the children gain from that. And that has to come hand in hand with any teaching, not just Maths teaching, but any teaching is for them to build up that grit. And again, a much sought after soft skill for the 21st century.

Adam Gifford

That point about having that attitude towards Maths as if it's right and wrong. It's so limited and so flawed. And I think of all of these incredible things. Not that long ago, a few months ago, it was somewhere where it was really dark. So there was not a lot of natural light around. And all Elon Musk's Starlink, it was like something out of star Wars, came over the sky and I didn't know what it was, right. People around me did this. "Oh, that's starlink." But you could see it was free. Now that only happened because of Mathematics. There's other things if someone has to have the idea and those things. But that link between Mathematics, I remember playing a video game as a kid, it was like an Olympic games zone. You did 10 different things. It was an arcade game, right, and the javelin throw, you had to hold the button long enough for the angle to change and the perfect angle, you'd think it was 45 degrees, it was 47.

Wendy Liu

All right.

Adam Gifford

But the point that I'm trying to make is that that was totally different way. And when we started to think about it, well if you held it too long and it was 80 degrees, it shot straight up in the air and went off the screen didn't work. That was a far better way about learning about angles than when I went to school. It was simply, "Can you use the protractor? Can you do this? Can you do that?" And I think that this association with Mathematics and the vast majority of the greatest discoveries ever historically over thousands of years have had Mathematics at the heart of it.

Wendy Liu

Yeah. Absolutely.

Adam Gifford

And do teachers even get the fact that that is the case, that these things can't happen without Mathematics and there's nothing more creative than that? Go on buildings. People might do studies of buildings. The Mathematics that involved in that is phenomenal. And yet we seem to, in education, reduce it down to this binary, is that box filled with the correct looking symbol? That's almost what it comes down to. It's absurd. But maybe people never associate these things that they take great pleasure in. The fact that we get our music whenever we want on demand that's based on a binary system. Do people know about that? All of these things. I don't know.

Andy Psarinaos:

Music's all around us right.

Adam Gifford

100 percent.

Wendy Liu

Yeah.

Adam Gifford

And I think-

Andy Psarinaos:

So why is it 47 Adam and not 45? Did you ever-

Adam Gifford

I don't know. I never did work it out. I think that it just needed a little bit more height because the drop off at the end, it went further on an upward trajectory, which went longer. It must have run out the momentum of it must have started to tail off at the end. So 47. But you could do a study on that.

Andy Psarinaos:

But as a kid I would've read discoveries of humankind have been based off pondering an obscure question like that. Why is it 47, not 45? And that leads people into all thought experiments. That's just what Einstein did. That's all he did. He says... It doesn't really add up. This doesn't really make sense. What if... And then boom, boom, boom, boom, boom. And then next thing you know, the entire universe changed. Math is the language of the universe. That's what it is, right.

Wendy Liu

Yeah. It should be steeped in real life because it is real life. So this is why I love things like the Maths — No Problem! explore questions because it steeped in real life that children can relate to and they take it and they run with it because it's something that they know.

Andy Psarinaos:

And we take great pride in the fact that they're accurate too. So if we say, I don't know, whatever watermelon weighs X, we actually went out and figured out how much a watermelon weighs, right. What the beans is.

Adam Gifford

The reality is that with so many things that weigh under about, I'm going to go so far as to say under two kilogrammes. We've weighed the... I've got various sets of scales in my house down to like grammes.

Wendy Liu

We realise.

Adam Gifford

And so it's like grapes... I put grapes on and I had different size grapes.

Andy Psarinaos:

But whatever it's... Population of countries or distance between one city and another, they're all correct. And that's another thing is there's a great opportunity to teach other things with Mathematics, like geography and all those things. Because it's an interesting thing, if you could get a sense... If you ask a child... This is a real crude measure. But if you ask a child, what's something that's a hundred kilometres away or a hundred miles away, if you live in England, ask them that question. And if they tell you it's Tokyo, right, most children really actually don't-

Wendy Liu

Can't relate to it.

Andy Psarinaos:

... necessarily understand. That's why it's important to make it accurate and real, right. Because if I can guarantee you, if you asked the child in mass problem, "How much do you think a watermelon weighs?" Let's just say they wouldn't be off by any orders of magnitude because they have seen it so many times, the fruit and the weights and all this stuff throughout the programme, that they have a sense. If they can't tell you whether it's like one kilogramme or a hundred kilogrammes, what have you really taught them?

Wendy Liu

Yeah. Absolutely.

Andy Psarinaos:

Right. Think about it. How much does three coins weigh?

Wendy Liu

And they actually love the fact that it is very real life because it's something that they have in common. They all understand it. And that's where the collaboration really comes into play because you just pose the question, you lead them to it, and they come up with all weird and wonderful ways of doing things. And it's so lovely to watch them talk and argue and articulate and persuade each other. And it so lovely to see that they can just do it. And as a teacher, you just go around to just go around facilitating questions, asking them, "What would happen if that you did this?" Or you know, ask them, pose the question. That might make them realise that actually they've got a misconception there without actually telling them that there's something wrong. It's so lovely to see that those light bulb moments. Call them light bulb moments or penny drop moments.

Adam Gifford

Let me just pick up on two things. Andy's reference to Einstein, your reference to questioning and Robin giving the wrap it up movement. So I'm just going to finish with this. I read somewhere that Einstein's mum, when he came home from school, didn't used to ask. Have you had a good day? Should ask, "Have you asked any good questions today?" So I'll leave you with that one just to finish. But thank you.

Wendy Liu

Thank you. Pleasure.

Adam Gifford

For coming on the podcast.

Andy Psarinaos:

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