Transcript for #226 – Jo Boaler: How to Learn Math

I love a mathematics that some people don't even think of as mathematics, which is beautiful creative. mathematics, where we look at maths in different ways, we visualize it, we think about different solutions to problems, a lot of people think of maths as you have one method and one answer. And what I love about maths is the multiple different ways you can see things, different methods, different ways of seeing different, in some cases different solutions. So that is what is beautiful to me about mathematics, that you can see and solve it in many different ways. Also, the sad part that many people think that math is just one answer and one method.

Yeah, I mean, I always say that you can take any maths area and make it visual. And we say to teachers, give us your most dry boring maths and we'll make it a visual interesting creative problem. And tons of you can do that with any area of maths. And I think we've given it's been a great disservice to kids and others that it's always been numbers, lots and lots of numbers. Numbers can be great, but you can think about maths in other ways, besides numbers.

There's definitely people who come into the classes I do who are more interested in visual thinking and like visual approaches, but it turns out what the neuroscience is telling us is that when we think about maths there are two visual pathways in the brain and We should all be thinking about it visually. Some approaches have been say, well, you're a visual learner, so we'll give you visuals and you're not a visual learner. But actually, if you think you're not a visual learner, it's probably more important that you have a visual approach. So you can develop that part of your brain.

Yeah, so this is what the neuroscience has shown us that when you work on a maths problem, there are five different brain pathways, and that the most high achieving people in the world are people who have more connections between these pathways. So if you see a maths problem with numbers, but you also see it visually, that will cause a connection to happening your brain between these pathways. And if you maybe write about it with words, that would cause another connection or maybe you build it with something physical that would cause a different connection. And what we want for kids is we call it a multi-dimensional experience of maths, seeing it in different ways, experiencing it in different ways. That will cause that great connected brain.

Right. Einstein is well known for thinking visually. And people talk about how he really didn't want to go anywhere with problems without thinking about them visually. But the other thing you mentioned that sparked something for me is thinking with intuition, like having intuition about math problems. That's another thing that's often absent in math class. The idea that you might think about a problem in usual intuition. But so important. And when mathematicians are interviewed, they will very frequently talk about the role of intuition in solving problems, but not commonly acknowledged or brought into education.

Yeah, it's hard. I mean, I love to value what's hard in maths. Instead of being afraid of it, we know that when you struggle, that's actually a really good time for your brain. You want to be struggling when you're thinking about things. So if it's hard to think intuitively about something, that's probably a really good. time for your brain. I used to work with somebody called Sebastian Thrun, who is a great mathematician who might think of him as an AI person. I remember in one interview I did with him, he talked about how they'd built robots, I think for the Smithsonian, and how they were having this trouble with them picking up white noise, and he said they had to solve it, they had to work out what's going on, and how he intuitively worked out what the problem was. But then it took him three weeks to show it mathematically. I thought that was really interesting that how you can have this intuition and know something works. It's kind of different from going through that long mathematical process of proving it, but so important.

Not taught. And we love as well color coding. Like when you represent something mathematically, you can show color to show the growth. Yeah. And kind of code that. So if I have an algebraic expression for a pattern, maybe I show the X with a certain color, but I also write in that color so you can see the relationship very cool and um yeah we particularly in our work with elementary teachers many of them come to our workshops and they're literally in tears when they see things making sense visually because they've spent their whole lives and not realizing you can really understand things with these visuals it's quite powerful

I think it's great when things are challenging, but there's something that's really key to being able to deal with challenging maths and that is knowing that you can do it. And I think the problem in education is a lot of people have got this idea that you either born with a maths brain or you're not. So when they start to struggle, they think, oh, I don't have that maths brain and then they will literally sort of switch off in their brain and things will go downhill from that point. So struggle becomes a lot easier and you're able to struggle if you don't have that idea, but you know that you can do it, you have to go through this struggle to get there, but you're able to do that. And so we're hampered in being able to struggle with these ideas we've been given about what we can do.

So this is why being a teacher is so hard and people really don't appreciate how difficult teaching is when you're faced with, I know, 30 students who think in different ways. But this is also why I believe it's so important to have this multidimensional approach to maths. We've really offered it in one way, which is Here's some numbers in a method, you follow me, do what I just did and then reproduce it. And so there are some kids who like doing that and they do well and a lot of kids who don't like doing it and don't do well. But when you open up maths and you give, you let kids experience it in different ways, maybe visually with numbers with words, What happens is kids, there are many more kids who can access it. So those different brain wiring, you're talking about, where some people are just more able to do something in particular way, that's why we want to, that's one of the reasons we want to open it up, so that there are different ways of accessing it. And then that's not really a problem.

That's good. Well, could they fell in love?

Right, pushes you on, yeah.

Yeah, I think that's very interesting. And there is a lot of success people coming through the Soviet system. I think something that's very different to the US and other countries in the world is that idea that excellence is important and you can get there if you work hard. in the US there's an idea that excellence is important but then kids are given the idea in many ways that you can either do it or you're one of the people who can't. So many students in the school system think they're one of the kids who can't. So there's no point in trying hard because you're never going to get there. So if you can switch that idea, it would be huge and it seems from what you've said that in the Soviet Union, that idea is really different. Now, the downside of that idea that anybody can get there if you work hard, is that thought that if you're not getting out of your fault and I would add something into that I would say that anybody can get there but they need to work hard and they also need good teaching because there are some people who really can't get there because they're not given access to that good teaching so but there would be huge that change as to doing lots of maths if um If maths was interesting and open and creative and multidimensional, I would be all for it. We actually run some accounts at Stanford where we invite kids in and we give them this maths that I love and in our campus rooms there were three hours long and When we were planning the teachers like three hours, are we going to be able to keep the kids excited three hours? Turned out, they didn't want to go to break or lunch. They'd be so into these mathematical patterns. We couldn't stop them. It was amazing. So yeah, if maths was more like that, then I think having more of it would be a really good thing.

I think a lot of kids start to give up on themselves and maths around from about fifth grade and then those middle school years are really important and fifth grade can be pivotal for kids just because they're allowed to explore and thinking good ways in the early grades of elementary school, but fifth grade teachers are often like, okay, we're going to prepare you now for middle school and we're going to give you grades and lots of tests and that's when kids start to feel really badly about themselves. And so middle school years, we are camps and middle school students. We think of those years as really pivotal many kids in those years are deciding, yes, I'm going to keep going with STEM subjects or no, I'm not that this isn't for me. So I mean all years are important and in all years you can kind of switch kids and get them on a different pathway, but I think those middle school years are really important.

There's a study that was done and it's actually done in high school English classrooms. where all kids wrote an essay for their teacher. And this was done as an experiment. Half of the kids got feedback from their teacher, diagnostic feedback, which is great. But for half of the kids it said an extra sentence at the bottom that the researchers had put on. And the kids who read that extra sentence did significantly better in English a whole year later. The only change was this one sentence.

The sentence said, I'm giving you this feedback because I believe in you. And the kids who read that did better a year later. Yeah. So when I share this with teachers, I say, you know, I'm not suggesting you put on the bottom of all kids work and giving this feedback. So I believe in you. One of the teachers said to me, we don't put it on a stamp. I said no. Don't put it on a stamp. It's, um, but your words are really important. And kids are sitting in classrooms all the time thinking what does my teacher think of me does my teacher think I can do this um so it turns out it is really important to be saying to kids I know you can do this and those messages are not given enough by teachers and really believe it and believe it yeah it's a kind of say you have to believe it I sometimes because it's like

Yeah, and you're right. Silicon Valley where I live is filled with people who are dropouts at school or who had special needs who didn't succeed. It's very interesting that have gone on to do amazing work in creative ways. I mean, I do think our school system is set up to value good memorizers who can reproduce what a teacher is showing them and push away those creative deep thinkers often slower think as they think slowly and deeply and they often get the idea early on that they can't be good at math or other subjects. So yeah, I think many of those people are the ones who go on and do amazing things.

Absolutely. I mean, I think education system still uses an approach that was in classroom hundreds of years ago. The textbooks have a lot to answer for and producing this very uninspiring mathematics. But yeah, if you open up the subject and have people see and solve it in different ways in value, those different ways. Somebody I appreciated a lot is a mathematician called Mary Misakani. I don't know if you heard of her she. When the field's medals she was from Iran, first woman in the world, when the field's medal in mathematics, she died when she was 40, she was at Stanford. But her work was in a highly visual and she talked about how her daughter thought she was an artist because she was always visualizing and I attended, she asked me to chair the PhD defense for one of her students. And I went to the defense in the math department. And it was so interesting because this young woman spent like two hours sharing her work all of it was visual. In fact, there's nothing I saw any numbers at all. And I remember that day thinking, wow, I could have brought her like 13 year old into this PhD defense. They would not recognize this as math. But when Maryam is currently one of the fields medal, all these other mathematicians are saying that her work had connected all these previously unconnected areas of maths. But when she was, she also shared that when she was in school, when she was about 13, she was told that she couldn't do maths. She was told that by her teacher.

So I love that you know to be told you can't be good at maths and then go on and win the field medal is cool

Yeah, absolutely. And I share that with teachers that even in this broken system of what they have to do for districts and textbooks a single teacher can change kids math, relationship or other subjects and forever.

Yeah, that is difficult subject. One study found that the amount of maths anxiety parents had predicted their childhood achievement in school, but only if they helped with homework. So

But there are some interesting implications for this. I mean, you can see how it works. If you have maths anxiety and you're helping your kids with homework, you're probably communicating things like, oh, I was terrible at this at school and that's how it gets passed on to kids. So one implication is if you have a really bad relationship maths, you hate maths, you have maths anxiety, just don't do maths, don't want with your kids. But we have a on our website, we have a little cheat for parents of ways to interact around maths with your kids.

That's ucube.org. So one of the things I say to parents when I get parent presentations is even if you hate maths, you need to just fake it with your kids. You should be always endlessly optimistic and happy about doing maths.

Yeah. So I said, and do you experience the same with parents too? I think, I mean, I have an experience parents worrying that their kids will be better than them. I have experience, I have experience parents. just having a really bad relationship with maths and not wanting to help, not knowing how to help, saying things. Like another study showed that when mothers say to their daughters, I was bad at maths in school, their daughters' achievement goes down. So we know that kids pick up on these messages and which is why I say you should fake it. But also, I know that lots of people have just had a really bad relationship with maths, even successful people. The undergrad scientists at Stanford have pretty much always done well in maths. But they come to Stanford thinking maths is a set of methods to memorize. And so, so many parents believe that there's one method that you memorize and then you reproduce it. So until people have really had an experience of what I think covers the other maths, where until they've really seen that it's a really different subject, it's hard for them to be able to shift their kids to see it differently.

So I do think there's a way of teaching maths that changes everything for kids and teachers. So I'm one of five writers of a new framework for the stage of California and new maths framework. It's coming out next year. And we are recommending through this maths framework that people teach in this way. It's called teaching to big ideas. So at the moment, people have standards that have been written and then textbooks have taken these standards and made not very good questions. And if you look at the standards like I have some written down here, just reading a standard, it makes it maths seem really boring and uninspiring.

So this is an interesting example. In third grade, there are three different standards about unit squares. Okay. So this is one of them. A square with side length one unit, called a unit square, is said to have one square unit of area and can be used to measure area.

That is something that's sort of standard. The textbook authors say, well, I'm going to make a question about that and they translate the standards into narrow questions.

So the standards themselves, I think of maths and many people think maths in this way is a subject of like a few big ideas and really important connections between them. So like you could think of it as like a network map of ideas and connections. and what standards do is they take that beautiful map and they chop it up like this into lots of little pieces and they deliver the pieces to schools and so teachers don't see the connections between ideas, nor do the kids. So you know this is a bit of a long way of saying that what we've done in this new initiative is we have set out maths as a set of big ideas and connections between them so this is grade three. So instead of they're being 60 standards, we've said, well, you can pull these different standards to get in with each other and also value the ways these are connected.

And so we've set out for the state of California, the whole of mathematics, K, 10, as a set of big ideas and connections. So we know that teachers, it works really well if they say, okay, so a big idea in my grade is measuring. And instead of reading five procedural statements that involve measuring, They think, okay, measuring is a big idea, what rich deep activity can I use than teaches measuring to kids? And as kids work on these deep, rich activities, maybe over a few days, turns out a lot of maths comes into it. So we're recommending that let's not teach maths according to all these multiple statements and lots and lots of short questions. Instead, let's teach maths by thinking about what are the big ideas and what are really rich, deep activities that teach those big ideas.

I know, a fan of grades and tests myself. I think, grades are fine if they're used at the end of a course. So at the end of my math course, I might get a grade because a grade is meant to be a summative measure. It kind of describes your summative achievement. But the problem we have in math classrooms across the US is people who use grades all the time every week or every day even. My own kids, when they went through high school, technology has not helped with this. When they went through high school, they knew they'd been graded for everything they did. Everything. And not only were they been graded for everything, but they could see it in the grade book online, and it would alter every class they went into. So this is the ultimate, what I think of as a performance culture. You're there to perform, somebody's measuring you, you see your score. So I think that's not conducive for deep learning. And yes, have a great at the end of the year, but during the year, you can assess kids in much better ways. Like, teachers can a great way of assessing kids is to give them a rubric that kind of outlines what they're learning over the course of a unit or a few weeks. So kids can actually see the journey they're on. This is what we're doing mathematically. Sometimes they self assess on those units. And then teachers will show what the kids can do with a rubric and also write notes. In the next few weeks you might like to learn to do this. So instead of kids just thinking I'm an A kid or a B kid or I have this letter attached to me, they're actually seeing mathematically what's important and they're involved in the process of knowing where they are mathematically. At the end of the year, sure, they can have a grade, but during the year they get these much more informative measures.

Yeah. I think what's important though is teachers to have the perspective that they don't know who's going to be excellent at something before they give out the activity. Exactly. And in ass camp classes that we ran Sometimes students would finish ahead of other students. And we would say to them, can you write a question that's like this but different? And over time, we encourage them to like extend things further. I remember we were doing one activity where kids work out the borders of a square and how big this border would be in different case sizes. And one of the boys came up at the end of the class and said, I've been thinking about how you do this with a pentagon. And I say that's fantastic. How do you have what does it look like? We're going to go find out, see if you can discover. So I didn't know he was going to come up and say that and I didn't have it in my head like this is the kid who could have this extension task. But you can still do that as a teacher when kids get excited about something or they're doing well in something, have them extend it, go further. That's great.

Yeah, that might brighten them.

I do something actually. There's a video of me doing this on our website that I love when I first meet students. And this is what I do. I show them a picture. This is the picture. I show them. And it's a picture of seven dots like this. And I show it for just a few seconds, and I say to them, I'd like just tell me how many dots there are, but I don't need to count them. I went to group the dots, and I show it them, and then I take it away before they've even had enough time to count them. And then I asked them, so how did you see it? And I go around the room and Amazingly enough, there's probably 18 different ways of seeing these $7. And so I asked people to tell me how you grouped it. And some people see it as like an outside hole with a center dot. Some people see like stripes of lines. Some people see segments. And I collect them all and I put them on the board. And at the end, I say, look at this. We are a class of 30 kids and we saw these $7.18 different ways. There's actually a mathematical term for this. It's called groupitizing.

It's kind of cool. So turns out though that how well you groupatize predicts how well you do in maths.

I think it's real. I don't think you're born groupatizing. I think but some kids have developed that. ability if you like and you can learn it so this to me is part of how wrong we have maths that we think to tell whether a kid's good at maths we're going to give them a speed test on the fact on multiples but actually seeing how kids group dots could be a more important assessment of how well they're going to do a math. Anyway, I do what I like to do so when I stop with kids is show them. I'm going to give you math problems. I'm going to value the different ways you see them and turns out you can do this kind of problem asking people how they group dots with young children or with graduate students and it's engaging for all of them.

is a flexible mind. It's school should not really be about teaching kids, particular methods, but teaching them to approach problems with flexibility, being creative thinking creatively is really important. So people don't think the words, maths and creativity come together, but that's what I love about maths is the creative different ways you can see it. And so helping our kids There's a book I like a lot by been by physicists. You probably know this book could are elastic. You might know it. And it's about how we want elastic minds. Same kind of thing. Flexible creative minds. And schools do very little on developing that kind of mind. They do a lot of developing the kind of mind that a computer now does for us. memorization, memorization, doing procedures, a lot of things that we spend a lot of time in school on in the world when kids leave school are computable do that. And better than they will, but that creative flexible thinking we're kind of a ground zero at computers being able to engage in that thinking. Maybe we're a little above Granger, but the human brain is perfectly suited for that creative flexible thinking. That's what humans are so great about. So I would like the balance of shift in schools. Maybe you still need to do some procedural kind of thinking, but there should be a lot more of that creative flexible thinking.

Yeah, super important. And we know that also helps develop your brain, that's social side of thinking. And I love mathematics collaboration where people build on each other's ideas. And they come up with amazing things. I actually taught a hundred students calculus that Stanford recently, undergrad's, and we taught them to collaborate. So these students came in Stanford, and most of them were against collaboration in math.

Yeah, it was just before COVID hit. It was 2019. And this time you said they're against, yeah. It's really interesting. So there are only experienced maths individually in a kind of competitive individual way. And if they had experienced it as group work, it had been a bad experience. Maybe they were the one who did it all and the others didn't do much. So they were kind of against collaboration. They didn't see any role for it in maths. And we taught them to collaborate. and it was hard work because as well as the fact that they were kind of against collaboration, they came in with a lot of like social comparison thinking. So I mean this room with other Stanford undergrad and they're better than me or so when we set them to a kind of math problem together, the first one was kind of a disaster because they put all like they're better than me, they're faster than me, they came up with something I didn't come up with. So we taught them to let go of that thinking and to work well together and one of the things we did we decided we wanted to do a pre-imposed test at the end of this teaching it was only four weeks long but we knew we didn't want to give them like a time test of individual work so we gave them and applied problems to do at the beginning and we gave them to do the pairs together and we gave each of them a different colored pen and said work on this activity together and keep using that pen. So then we had all these pieces of student work and what we saw was they just worked on separate parts of the paper and this is like red pen section and a green pen section. And they didn't do that well on it. Even though it was a problem that middle or high school kids could do, but it was like a problem solving kind of problem. And then we gave them the same one to do at the end, gave them the same colors, and it actually they had learned to collaborate. And not only were they collaborating the second time round, but that boosted their achievement. And the ones who collaborated did better on the problem. Calaberation is important having people and what was so eye-opening for these undergrad and they talked about it in lovely ways was I learned to value other people's thinking on a problem and I learned to value that other people saw it in different ways. And it was quite a big experience for them that they came out thinking, you know, I can do maths for other people. People can see it differently. We can build on each other's way, ways of thinking.

And the other thing you have to put aside is this social comparison, thinking. If you are sitting there thinking, wow, that was an amazing idea. He's so much better than I am. That's really going to stop you taking on the value of that idea. And so there's a lot of that going on between these Stanford students when they came. And... Yeah, but trying to help them let go of that.

I agree with you. I think that's really good way to think about it.

You must have seen some good textbooks. If they had pretty pictures in color.

Yeah. Well, I mean, I'm intrigued that you had such a good experience with textbooks. I mean, I can remember loving some textbooks. I had when I was learning and I left books. I loved to pick up books and look through them. But A lot of math textbooks are not good experiences for kids. We have a video on our website of the kids who came to our camp and one of the students says, In maths, you have to follow the textbook. It's kind of like the Bible. You have to follow it. And every day, it's slightly different. Like on Monday, you do 2.3.2. And on Tuesday, you do 2.3.3 and on Wednesday. And you never go off that. That's like every single day. And that's not inspiring for a lot of the kids. So one of the things they loved about a canvas just that they're no books, even though we gave them sheets of paper instead, they still felt more free. because they weren't just like tossing through exercises exercises.

I can see that. I mean, I think it could be in a textbook you can have a good experience with a textbook. But what's really important is what is in that textbook? What are you doing inside it? I mean, I grew up in England and in England we learn maths. We don't have this separation of algebra and geometry. And I don't think any other country, apart from the US, has that. But I look at kids in algebra classes, whether they're doing algebra for year. And I think I would have been pretty bored doing that.

Yeah, I mean mathematics is supposed to be the the different maths that you look at whether you think of that as topics like geometry and probability or I think it is maths is just multidimensional lots of ways but that's why it was called mathematics and then it was short to maths and then for some reason it was just math in the US but to me math has that more singular feel to it than there's an expression here which is do the math which basically means do a calculation that's what people mean by do the math so I don't like that expression because no math could be anything doesn't have to be a calculation and So yeah, I like maths because it has more of that broad field to it.

Can be. I mean online. having great teachers online obviously extends those teachers to many more people and that's a wonderful thing. I have quite a few online courses myself. I got the bug working with Sebastian when he was hit released his first MOOC and I thought maybe I could do one in math education and I didn't know if anybody would take it. I remember releasing it that first summer and it was a free online class and 30,000 math teachers took it that first summer and they were talking about it with each other and sharing it and it was like took off. In fact, it was that MOOC that called got me to create you cubed with Kathy Williams who's the co-founder because people took the MOOC and then they said okay what now I finished what what can I have next and so that was where we made our website but so yeah I think online education can be great I do think a lot of the MOOCs don't have great pedagogy they're just a talking head and You can actually engage people in more active ways, even in online learning. So I learned from the Udacity principle when I was working at Udacity, never to talk more than like five minutes. And then to ask people to do something. So that's the sort of pedagogy of the online classes I have. There's a little bit of presenting something and then people do something and there's a little bit more. Because I think if you have a half hour video, you just switch off and start doing other things.

Yeah, we started you cubed. I guess it was about five years ago now. And we've had over 52 million visitors to the site. So I know. Very happy about that. And our goal is to share good ideas for teaching with teachers, students, parents, in maths, and to help. We have a sort of sub goal of a raising maths anxiety. That's important to us, but also to share maths as this beautiful creative subject. And it's been really great. We have lessons on the site. But one of the reasons I thought this was needed is there's a lot of knowledge in the academy about how to teach maths well. Loads and loads of research and journals and lots of things written up. But teachers don't read it. They don't have access to it. They're often behind pay walls. They're written in really inaccessible ways so people wouldn't want to read them or understand them. So this I see is a big problem. You have this whole industry of people finding out how to teach well, not sharing it with the people who are teaching. So that's why we made you cubed. And instead of just putting articles up, saying here's some things to read about how to teach well, we translated what was coming from research into things that teach you could use. So lessons, there were videos to show kids. And there were tips for parents, there were all sorts of things on the site. And it's been amazing. As we took inspiration from the week of code, which got teachers to focus on coding for a week and we have this thing called the week of inspirational maths and we say just try it for a week, just just give us one week and try it and see what happens and so it's been downloaded millions of times teachers use it every year they start the school year with it and what they tell us is it was amazing the kids liked were on they were excited they loved it And then the week finished and I opened my textbooks and that light went out and they were not interested.

It is. I wish, I mean, what I would love is if we could actually extend that for the whole year. We were small team at Stanford and we're trying to keep up with great things to put on the site. We haven't the capacity to produce these creative visual masters for every year group for every day, but I would love to do that.

I mean, we can do it. We actually, we went from the week of inspirational maths and we made K8 maths books with exactly that big ideas, rich activities, visuals. We just finished the last one. We've been doing it for five years and it's been exhausting and we just finished. So now there's a whole K8 set of books. and they're organized in that way. These are the big ideas here are rich deep activities. They're not though what you can do every day for a year. So some teachers use them as a supplement to their boring textbook and some people have said, okay, this is the year. This book tells us what the year is and then we'll supplement these big activities with So they're being used and teachers really like them and they're really happy about them. I just always want more. And I guess one of the things I would like for you cubed, one of my personal goals is that every teacher of maths knows about you cubed. The moment a lot of teachers who come to us are really happy they found it, but there's a lot of other teachers who don't know that it is.

Yeah, I think one thing we know is a lot of people when they review material, whether it's math or anything else, don't do it in the best way. I think a problem a lot of people have is they read through maybe a teacher's explanation or way of doing maths and it makes sense and they think we have got that and they move on. But then it's not until you come to try and work on something and do a problem that you actually really shouldn't really understand it just seem to make sense. So I would say this is also something that Neuroscientists talk about to keep giving yourself questions is a really good way to study rather than looking through lots of material. It's always like giving yourself lots of tests is a good way to actually deeply understand things and know what you do and you don't understand.

That would be great. And it's a similar, I mean, a question I get asked a lot is about homework. What this is a good thing for kids to do for homework. And one of the recommendations I give is to not have kids just do lots of questions for homework, but to actually ask them to reflect on what they've learned. Like, what was the big idea you learned today? Well, what did you find difficult? What did you struggle with? What was something that was exciting? Then kids go home and they have to kind of reflect in a deep away. A lot of times I don't know if you have this experience as a math student, lots of people do. Kids are going through maths questions, they're successful, they get them right, but they only really know what they're about. And a lot of kids go through many years of maths like that, doing lots of questions, but they're really knowing what even The topic is, or what it's about, what it's important for, so having students go back and think at the end of a day, what was the big idea for this math lesson? Why is it important? Where would I find that in real life? Those are really good questions for kids to be thinking about.

That would be good if we start doing it.

Yeah, yeah. I mean, one of the sad pieces of research data I think about is the questions kids ask. In school, it goes down, like in a linear progression. In the early years, you can't stop kids asking there's questions, but they learn not to ask the questions.

Oh yeah. You listened to something I said. Yeah.

Yeah, I remember it really vividly.

Yeah, it's funny. I can remember it must have really impacted me in that moment because you know how there's lots of hours of school. You don't remember at all, but anyway, I can remember where I was sitting in everything. I was in high school maths class, although they didn't call it an England. The teacher said, and it was like the first class of this teacher's class. And he said, ask if you have any questions. So at one point, I put my hand up and I said, I have a question. And he said something like that to a question. And I was like, OK, I'm not asking any more questions.

Yeah, that was absolutely this. And I asked that's the last question I was asking. That was, yeah, he was the chair of the maths department. I remember that really well. So maybe because of that experience, one of the things we encourage when we teach kids is asking questions and we value it when they ask questions and we put them up on walls and celebrate and it's funny because

Right. Well, and I guess kids, or young people, get whether somebody is doing it to be funny, or has it? I mean, this is why I teach you so hard, even your tone can be impactful.

But I know sadly that maths there's a lot of math teachers who have that kind of approach and they I think they're suffering from the fact that they think people are math people not math people and that comes across in their teaching

That's right. That is the flip side of that. And I myself had one teacher who was really amazing for me in maths and she kept me in the subject. She was, um, her name is Mrs. Marshall. She was my A-level maths teacher. So I was in England. You do lots of subjects. So you're 16 and then you choose like three or four subjects. So I chosen maths and you go to high levels. Probably equivalent to a master's degree in the US because you're more specialized, but anyways, she was my teacher and for the first time in my whole career in maths, she would give us problems and tell us to talk about them with each other. And so here I was sitting there like 17 talking with friends about how to solve a math problem. And that was it. That was the change that she made. But it was profound for me. I, because like those calculus students, I started to hear other people's ways of thinking and seeing it. We would talk together and come up with solutions. And I was like, that was it. That changed math for me.

I mean, yeah, the many ways teachers can inspire kids. I mean, sometimes it's a personal message, but it can be your teaching approach that changes math for kids.

Yeah, I think. Giving kids really inspiring deep problems, and we have some on our website, is a really important experience for them. Even if they only do it occasionally, but it's really important. They actually realize, I give a problem out, often when I'm working with teachers, and I say to them, all right, I'm going to check in with you after an hour. And they were like, and how are? They think it's shocking. And then they work on this problem. And after an hour or so, okay, how are we doing? And then like, an hour has gone by. How is this possible? And so everybody needs those like rich, deep problems. Most kids go through their whole math experience of however many years never once working on a problem in that kind of deep way. So I, the, the undergrad class, I just Stanford, we do that. We work on these deep problems every session. And the students come away going, okay, I never want to go back to that. Maths relationship I had, where it was just all about quick answers. I, I just don't want to go back to that. And so, We can all all teachers can incorporate those problems in their classrooms. Maybe they don't do them every day, but they at least give kids some experience of being able to work slowly and deeply and to go to deeper places and not be told they've got five minutes to finish 20 questions.

definitely there was a survey done of kids in school where they were asked how long were you working on a maths problem before you give up and decide it's not possible to solve it and the result on average across the kids was two minutes yeah that's a bad sign but that's that was a powerful sign that they need to learn to not give up so quickly yeah

I think it's amazing. I should work with him. I can share some of our visuals and he can make them in that amazing way.

And probably you don't need to. I mean, if people get to experience pathological ideas in the way that he shares them, That will change them and it will change the way they think and maybe they could go on to take some other mathematical idea and make it that beautiful.

Yeah, absolutely. I think just giving people that idea that you can do that with maths and other subjects, they're bound to be people all around to create more, which is cool.

Have you ever noticed that hotels always filled with patterns? I was just noticing at the hotel, I mean, now all of their carpets are pattern carpets and then they have patterns on the walls.

I mean, that's one of the perspectives that I love students to take is to be at Patton Seeker. And in everything. Yeah, certainly in all of maths. I mean, you can think of all of maths as a kind of subject of patterns and not just visual patterns, but when you think about multiplying by five and the fact you can, you know, if you're multiplying 18 times five, you can instead think of nine times 10. That's a pattern that always works in mathematics. You can have a number and double them at number. And so yeah, I just think there are patterns everywhere. And if kids are thinking their role is to see patterns and find patterns, it's really exciting.

I think it's good. I think it's good. I think that is what started the Mook, I did, was using that platform.

I think there's definitely you can bring in good pedagogy into online learning and I think the idea of putting things online so that people all over the world can access them. It's great. I don't think the initial excitement around Mook's sort of democratizing education and making it more equal. came about because they found that the people taking MOOCs tended to be the more privileged people. So that was I think this still something to be found in that. There's still more to be done to help that online learning reach those principles. But definitely I think it's a good invention. And I have an online class that's for kids that's little free class that gets to the topic. It's called How to Learn Maths. How to Learn Maths. It shows maths as this visual creative subject and it shares mindset and some brain science and Kids who take it do better maths class. We've studied it with randomised control trials and given it to middle school kids and other middle school kids who don't take it but are taught by the same teachers so their teachers are the same and the kids who take the online class end up 68% more engaged in their maths class and do better at the end of the year so that's a little 6 session 15 minute class and It changes kids math's relationship so it is true that we can do that with some words that aren't, you know, it's not a huge change to the education system.

I think if I were to give advice to people, especially young people, my advice would be to always it sounds really corny but always believing yourself and know that you can achieve because although that sounds like obvious of course we want kids to know that they can achieve things I know that millions of kids are in the school system have been given the message they cannot do things and adults too they have the idea oh I did okay in this I went into this job because those other things I could never have done okay in so actually when they hear hey maybe you could do those other things Even adults think, you know, maybe I can and they go back and they encounter this knowledge and they relearn things and they change careers and amazing things happen. So for me, I think that message is really important. You can learn anything. Scientists try and find a limit. They're always trying to find a limit. Like how much can you really learn? What's the limit to how much you can learn? And they always come away not being able to find it. People can just go further and further and further. And that is true of people born with brain, you know, areas of their brain that aren't functioning well that have what we call special needs. Some of those people also go on to develop and do amazing things. I think that really experiencing that, knowing that, not just saying it, but knowing it deeply, you can learn anything, is something I wish all people would have.

Yeah, and if people tell you you can't do things, you have to hear from other people who believe you know, I think you're absolutely right about that. So sad the number of people who have had those negative messages from parents. in my limitless mind book I interviewed quite a few people who had been told they couldn't do maths sometimes by parents sometimes by teachers and fortunately they had got other ideas at some point in their life and realized there was this whole world of mathematical thinking that was open to them so it's really important that people do connect with people who believe in them however hard that might be to find those people what do you hope their education system

Yeah, I definitely have hope. There is change can happen in the education system. In recent years, it's been microscopically slow. I do actually see change happening that we were talking earlier that data science is now, of course, you can take in high school instead of algebra two. And that's pretty amazing because that content was set out in 1892 and hasn't changed since then. And so now we're actually seeing a change in the content of high school. So I'm amazed that that's happening in very happy it's happening, but so change is very slow in education usually, but When you look ahead and think about all that we know and all that we can offer kids in terms of technology, you've got to think that 100 years from now education will be totally different to the way it is now. Maybe we won't have subject boundaries anymore because those don't really make much sense.

Yeah, you would think that all kids are growing up learning to program and create. So I just think I mean the system of schooling we have now people call it a factory model. It's not designed to inspire creativity and I feel like that will also change people might look back on these days and think they were hilarious but maybe we'll in the future kids will be doing their own programming and they'll be able to learn things and find out things and create things even as they're learning and Maybe the individual subjects boundaries will go, data science itself coming into the education system kind of illustrates that because people realize it doesn't really fit inside any of the subjects. So what do we do with it? Where does it go? And who teaches it? So it's already raising those kind of questions and questioning how we have these different subjects boundaries.

Yes, it's happening across the United States as we speak.

It does. I think so. I think so. It's been an interesting journey seeing data science take off actually. There was a course that was developed in 2014. by some people who thought data science was a good idea for high schoolers and then after some kids took the course and nothing bad happened to them. They went to college and people started to accept it more and then this was a big piece of the changing California the UC system communicated They sent out an email last year to 50,000 high school saying we now accept data science kids can take it instead of algebra 2. That's a perfectly legitimate college pathway. So that was like a big green light for a lot of schools who were like wondering about whether they could teach it. So I think it happens in small spaces and expands. So now it goes viral. Yeah. And it goes viral. California's a head. I think in creating courses and having kids go through it, but it's certainly when I last looked there were 12 states that were allowing data scientists at the high school course. And I think by next year that will have doubled or more. So change is happening.

Thank you. It's really good to talk to you.