The following is a conversation with Joe bawler, mathematics, educators, Stanford and co, founder of you, cubed dot. Work that seeks to inspire young minds with beauty of mathematics to support this by gas. We check on our sponsors in the description. as usual. I do a few minutes of as now. No in the middle. I try to make these interesting. So, hopefully you know skip, but if you do please to check out the sponsor links in the description, it really is the best way to support this package I use their stuff, I enjoy it, I love it. Maybe you will too. This show is brought to you by true bill, a new app that helps you identify and stop paying for subscriptions. You don't need want, or simply forgot about Average people save up to seven hundred twenty dollars a year or two bill. I started using trouble and his kind of amazing how me subscriptions at all he forgot about those on both financially and just psychologically. Instead

Actually, it was good to let go of those subscriptions as you may know, I'm a big fan of minimalism and physical space. It allows me to focus on the people in my life and there's something about subscriptions that just kind of hanging on to the past and getting rid of those subscriptions they don't use any more is, is liberating it just. For me, it feels really good, but obviously there's big financial savings We probably don't have time for me to rant on how difficult it is to cancel things, but you should definitely use the battle for the job and true bill as a great one. You can start canceling subscriptions today,

Bill dot com, slash legs, like I said in terms of savings, you can save thousands of dollars a year, a true bill, dot, com, slash lex, that's true, bill, dot, com, slash lex: this episode is also brought to you by fund rise, spelled f, u n d r. I s e as a platform that allows to invest in private real estate. If you're looking to diversify your investment portfolio, this is a great choice, is better lotta conversations about cook the currency. Been a lot of conversations about investment I recommend that you diversify whatever that means to you and to me personally, it happen.

is that a fund rise and private real estate is, is a really great idea for diversification. I'm not a professional investor, but it just seems a common sense. A hundred fifty thousand invested use it. It takes just a few minutes to get started at fund rise, dot com, slash lex again spelled, is a few and de rise, not just fun, but fund fund arise, dot, com, slash lex, that fund rise, dot com, slash lex, The show is also brought you by express vp and I use them to protect my privacy on the internet and abuse. for many years. However, for me reasons. Obviously, on the privacy side eyes, bees collection, data, even when you're using incognito mode on chrome. So I think it's really good to use a vpn and expressive. Pn is my favorite. Also in terms of things like netflix or hulu. Express vpn allows you to change your location.

from the perspective of the website, the browsing or the update, your browsing. So there, allow me to watch shows that are only available in certain geographical locations. Finally, the big reason I love expressly pen and I've used it for many years- is that the connection is just fast. it works, falsely an aid device. Any operating system, including my favorite operating system linux anyway, go to express vpn that comes lifelike spot to get an extra three months free, let's express vp under com, slash legs Added did I mention that the design they have is simple, with a beautiful big button that just works. This episode is also brought to you by indeed a hiring website. I've used them as part of many hiring. Efforts have done for the teams have led in the past,

They have tools like indeed in the match, giving you quality candidates whose resumes are indeed fit. Your job description immediately, this first step of getting a great set of candidates, I think, is essential for an effective hiring process. I think it's one of the hardest to be honest and to me, one of the biggest joys in life is to work on a team of people. They make you excited to wake up in the morning and get some awesome stuff done and hiring obviously is the biggest part of it. So not just for financial reasons, but just for happiness reasons. You have to take hiring really. Firstly and use the best tool for the job anyway. Right now get up three. Seventy five dollars sponsor job credit, to encourage our posts and indeed their costs. Us, let's get it, and indeed the car slash lacks offers vow to september thirtieth terms and conditions apply,

wait three million businesses that use indeed, by going to indeed the calm, slash lex there. It is also brought to you by stamps dot, com, mail and ship anytime, anywhere right from your computer, without needing to take a trip to the post office, some letters she packages and pay less with discount rates. From? U s p s, and now you ps, it's a bit surreal and kind of an incredible feeling for meat to be doing a stance that calm, add read because I've been santa podcast for many years and stamps dot com has been supporting those podcasts, and so I almost the associate a stamps dot com read with a podcast that has truly made it. So I feel like I have made it. I know it's a silly feeling, but it is a what I feel

So he could save time and money was stance that come, there's no risk and with my promo code lux, you get a special offer that includes for weak trial, plus free postage and digital scale. no long term commitments or contracts just go to stamp, that calm click on a microphone at the top of the homepage and type in lex? That's stamps that come from a lux stance that come never go to the post office. Again. This is the legs friedman. Podcast in here my conversation with Joe bawler. What do you

beautiful about mathematics. I love a mathematics that somebody would don't think of as mathematics, which is beautiful, creative mathematics, where we look at mass in different ways, we visualize it. We think about different solutions to problems. A lot of people, think of math says 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 indifferent 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, and us the sad per that many people think that maths is just one answer one method say to you that beautiful The beauty emerges when you have a problem, the solution and you start adding other solutions. Simpler solutions,

weird or solutions more interesting, some their visual or some other elder brag geometry of that kind of stuff yeah I mean I, I always say that you can take any man, syria make it visual and we said it just give us your most dry boring maths and will make it a visual, interesting created problems. Does it. You can do that with any area mats and I think we ve given pete. It's been a great disservice to kids and others that it's always been numbers lots and lots. Both numbers can be great, but you can think about maths in other ways. Besides numbers defined at most, boy, better, visual learners, or is this just something? That's complimentary did what what's the kind of the force from a loose in the way they like to explore. Math would use this definitely people who come in to the club

as I do her more interested in visual thinking and like visual approaches, but it turns out. Will the neuroscience is telling us is that when we think about maths threat to visual pathways in the brain, and we should all be thinking about visually, Some approaches have been say. Well you, a visual lan ass, who will give you visuals and you're. not a visual learner, but actually view. Thank you not a visual learner. It's probably more important that you have a visual approach, so you can develop that part of your brain. You're, saying that there is some kind of interconnected aspect to us or the visual connects with the non visual yeah. So this is what the neuroscience shown us that when you work in a mass problem, there are five different brain pathways,

the most high achieving people in the world, a people have more connections between these pop phase. So if you see him ass problem with numbers, but you also see visually that will cause a connection to happen in your brain between these pathways and a few, maybe right about it with words that would cause and other connection or maybe 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 math, seeing it in different ways experiencing it, and in ways that will cause that great connected brain it? You know, there's the stories of physicists. Doing the same. I find physicists are often better at building that part their brain of using visualization for intuition building, because you ultimately want to understand the lake, the deepest secret underneath this problem for them.

You have to sit into it your way there yeah and you you mentioned offline, that one of the ways you might approach your problems to try to tell a story about it, and some of it is like legend, but I'm sure it's not always is Oh, you have einstein thinking about a train it all and the and white, and in that kind of tuition is useful, yeah starting Like imagine a physical work like how does this idea manifests itself in the physical world and then start playing in your mind with that physical world and think is this going to be true? Is this going to be 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 mention that Something for me- is thinking with intuition coming intuition about mats problems. That's another thing that often absent in math ass- the idea that you might think about a problem,

use your intuition, but so important, and when mathematicians are interviewed. They were very frequently took about the role of intuition in solving problems, but knots commonly acknowledge store, bought into education. Yeah, I mean that's what it is like if, if you task yourself or building and intuition about a problem, that's when you start to plan like what is the pattern I'm seeing? in order to understand the pattern you might want to then start utilizing visualization, but ultimately it that's all in service of like. Solving the puzzle Craig. I opened the gate. The simple explanation of why? Why why These are the way they are to arm. said having a particular algorithm that can the next guy solve the problem. It was hard

the reason is really hard. Yeah, it's it's hard. I mean I love to Allie what's hard in maths, instead of being afraid of it. Oh that when you struggle that she really could times your brain, you want, be struggling when you think about things. So if it's hard thinking too to be about something, that's probably a really good time for your brain. I I used to work for somebody called sebastian thrun, who said I said, a mathematician, you might think them a person, and I remember him and you I did with him. He talked about how that built, robots liking for the smithsonian and how they were having this trouble with them pick a white noise and he said they had to soul that they had to work hollow. What's going on and how he intuitively wiped out while the problem was, but then it took him three weeks to show it mathematically. I thought I was really interesting. That's how you can have

intuition, and knows something works. It's kind of different from through that long, mathematical process of proving it, but so important is I think, probably our brains are involved as like into it machines and the other, the math of like showing it like formally is probably an extra thing that one design. For you see that firemen and his aid adjusts all these physicist. Definitely you see. I'm. Starting with intuition, sometimes starting with an experiment, and then the experiment inspires intuition But you can think of an experiment as a kind of visualization zation magnesite. Let's, let's take what the heck, we're looking at and draw it an android the pattern. Is it evolves? Is the thing grows for an equals? One for any cause to any was three starter

lay within an in the modern day, which I loved doing is in I write a program that then visualizes before before you think you could start exploring it and that that, and they now you can. So interactively too I I tend to not like interactive because away it takes to which which work, because you have to click, move and stuff. I love to interact writing programmes. That's my particular brain software engineer so like me, you can you can A dog these causes visualization and then there's the tool the visualization eye collar august as a thing m that europe say right, there. She not taught very much right the art visualization not taught, and we love as well color holding eye. When you represent someday mathematically, you can show colored, show the growth and can occur

that. So, if I have an algebraic expression for pattern, maybe I show the ex with a certain color, but I was right in that color. So you can see the relationship very cool and yeah. We particularly in our parliamentary teachers, many of them, come to our shops and their literally in tears when they see things making sense visually because they have spent their whole lives sing, not realised you can really understand things. Were these visuals, it's quite powerful. You say that there is something there's something valuable to learning when the thing you're doing is challenging is difficult so loud will say: math is hard or matters too hard or too hard. For me. Do you think math should be easy, or should it be hard? I think it's great when

is a challenging, but there's something that that's really key to being able to do. With challenging maths- and that is knowing that you can do it- and I think that lemon education- is a lot of people- have got this idea that, we, the born in the mats, brain or you're, not so when they start to struggle, they think. Oh, I don't have that mass brain and then they were literally said a switch off in their brain and things will go down from that point, so struggle becomes a lot easier and you are able to struggle if you don't have idea, but you know that you, you can do it. You have to go through this struggle to get there, but you you're, able to that, and so we are hampered in being able to struggle with these ideas we ve been given about what we can do. Ask a difficult question here, yes of theirs, I know I don't know what the right term is, but some people, Ah,

I'll- go with learning indifferent ways like their brain is constructed, indifferent way, and how much should as educators should we make room for that, so How do you know the difference between this is hard, and I don't doing hard things verses, my rain is wired and away. Why need to learn in very different ways? I can't learn it this way. How do you find them line in a grey area, so this why being a teacher so hard and You ve already done appreciate how difficult teaching is when you are faced with a thirty students think in different ways and This is also why I believe it so important to have this multi dimensional approached him ass. We ve really offered it in one way. We, his his numbers in the method you follow me do what I just did and then reproduce it

So there are some kid to light doing that and they do well and a lot of kids. You don't like doing it and don't do well but when you open up math sinew, give you let kids experience it into ways, maybe visually with numbers with words what happen says: kids. There are many more kids who can access it, so those different brain wiring. She you're talking about where some people addressed more able to do something in a particular way. That's why we want her as one of the reasons we want to open it up, so that there are different ways of accessing it and then that's not ready a problem, so I grew up in the soviet union and I fell in love with math early, was forced into math early and fell in love through force,

that's good well, I fell in love with her was, but there is also do it. Who talked about a little bit? Is there such a value for excellence, eyes competitive in its also everybody kind of look? up that the definition of success is being in a particular classes. in our being really good at it and like is not improving it really good? I we are much more like that with sports, for example, or not it's, I guess understood, you know you going to star in the basque lahti, if you're gonna, start on a basketball team, if you're going to be better than the other guys, the other girls on the team, so that cop with the belief as could be partially communist belief. I don't know but the boy. that everybody is capable of being great, but if you're not great, that's your fault,

to work harder? And I remember I had a sense that probably delusional, but could when a nobel prize or even though that entails, but I thought dom like my dad early on, told me just of handing over stuck with me that if you, if you can figure out how to build a time machine, had a travel ban. In time. It'll probably give you what price I remember early in my life thinking, I'm going to invent a time machine and like that, tools and mathematics, work in service of that dream, of weighing than about price in their it's silly at dinner, really. Think in those concrete terms, but I just thought I could be using and then than when you, struggle. The belief that you could be great is like struggle is good right, pushes yard and so the other thing about the soviet system- that my love to hear your comments about

It's just the sheer like hours of math like the number of forces. It is all about a lot of geometry, a lot more job, I think in the matter the three take, maybe one year of geometry and high school in high school, foresaw geologists. beautiful as visual and then get a reason for proof and stuff like that in russia, membership he nailed over and over would ya. It was just nonstop and then off of course, there's different perspectives on calculus and just the whole. The sense was that math is like f, like fundamental to the development of the human mind. So math, but also science and literature by the way, was also have hit very hard. Like we read a lot of serious adult stuff america a little bit too: they they challenge young adults with good literature, but they dont challenge adults very much with mad mad that those two things

valuing excellence and and just a lot of mass in the curriculum. Do you think you thinks diviner interesting because it seemed I have been successful 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: u s and other countries in the world is that idea that excellence is important and you can get there if you work hard, in the. U s, there's an idea that excellence is important, but then kids, given the idea in many ways that you can either do it or you one of the people who can't so many students in the school system thing that 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 in. It seems from what you said that in the euro and the Have union that ideas really different now the down

side of the idea that anybody can get there if you work hard. Is that thought that if you're not getting hurt your fault and I would add something into that. I would say that anybody can get there, but that they need to work hard and they also need good teaching. Is there are some people who really can't get? I because they're not given access to that good teaching so, but I would be huge that change as the doing of maps if, if rafts, was interesting and open and creative and multi dimensional? I would be all for it. We we actually run some camps stamford, where we invite, sudan them be given this matter that I love and the in our country. It seems that, with three hours long and boy 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 her 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 so what I age urge you talk about? Is there on? Could you comment on what age is like the most important when people quit math give up on themselves or a math in general, and perhaps that aid there's. Something earlier is really important moment. Discovered to be inspired to discover a magical math. I think a lot of kids start to give up on themselves and mats around. from about fifth grade and then those middle school years really important and fifth grade can be pivotal for kids, just because they're allowed to explore in thinking good ways in the early grades about it?

Did you school, but fifth grade. Teachers are often like okay, we're going to prepare you now for middle school and we're going to he grades and also tests, and that's when kid start too, I really badly about themselves and so middle school years we are camps, a middle school students. We think those years is really pivotal many kids in in those years deciding yes, I'm gonna keep going with stem subjects. Oh no! I'm not that this isn't for me So I mean oh yes, important and in all years, you can kind of switch kids and get them on a different pathway, but I think those middle school is a really important. So was the role rule the teacher and this one is the explanation of the subject, but giving too years should almost like one on one. You know little johnny, I believe in you,

a thing like tat that energy of like turns out. It's really important as them a study that was done every such hidden in high school english classrooms, where all kids wrote an essay the teacher, and this was done as an experiment. Half the kid scott feedback from their teacher diagnostic feedback, which is great but for her for the kids set an extra sentence, the bottom the researches had put on, and the kids who read that extra sentence did sir never get any better in english a whole year later, the oak the change was this one sentence. Sentence. So what does the sentence say? The sentence said I am 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 pull on the bottom of all kids work,

I'm giving this feedback. I believe in you one of the teacher said to me. We don't matter on a stamp. I said no, don't put it on a stamp its, but your words are very important and Kids, a city in classrooms, all the time thinking. What does my teacher think me? Does you think I can do this, so it turns out. It is really important be saying, because I know you can do this and those messages are not given enough by teachers and really believer unbelief, yeah, it's a kind of say you have to believe it. I I sometimes is such a funny desk zalm was such a perfection some- are extremely self critical enough where students come up to me and its clear to me, that they're not even close to good and its tempting. For me to be like serve, give up on them

the reality is that if you look at many great people throughout history, they sought at some point and in some of the greatest took nonlinear paths to where they sought for long into let into later life, and so always believing that this person can be great at exactly that. You have to communicate. That's plus the fact that they have to work hard. That's it yeah and you're right. Silicon valley, where I live, is filled with people who were dropouts school who had spent who needs who didn't succeed, it's for her interesting that have gone on to do amazing, work and creative ways. I mean I do think ass school system is set up to value, Good memorizes, who can reproduce what a teacher sharing 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 come. We good at math saw other subjects, so the I think, many of them if two people are the ones who go on and do amazing things there's a guy named Eric why's I know many mathematicians like this, but he he talks a lot. Not having us having a non standard way of learning I mean a lot of great mathematicians lot of great physicists like that, and he felt like he began. quickly. He got gonna species at harvard became quickly outcasts of the system like the the education especially early education system, didn't happen. Is there a ways for an education system to support people like that? Is it does

of multi dimensional, guarantee that eventually they absolutely I mean, I think our education system still uses an approach that was in classrooms. Hundreds of years ago, the text books have a lot to answer for and producing this very uninspiring mathematics but yeah. If you open up the subject and happy see and solved in different ways and value those different ways. Some. they I appreciate the lot is a mathematician could marry miss corny. Haven't you heard of her? She won the fields, shoes from IRAN. First, in the world, when the fields, meadow and mathematics is she died when she was forty issues at stanford, but her work was in tiny, 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 defence for one of my students and I went to the defence in the math department, and it was so interesting because this young woman spend night two hours sharing her work. All of it was visual if it has any numbers to himself I remember that day. Thinking wow, I could have brought her like thirteen year old into this phd defence. They would not recognise this is mats, but when Merriam is currently one the fields meadow. All these other mathematicians are saying that her work had connected, or these previously unconnected areas of mass and so, but when she was, she also shared that when she was in school, when she was about thirteen, she was told that she couldn't do maths. She was told that by her teacher, on issues regarding IRAN. So I love that in order to be told you can't

big it at mass and then go on in win the fields. Meadow is cool. I've been told by a lot of people. In my life tat, I cant do something I'm very definite nonsense, but politics. That is why people talk about the one teacher the changed everything that's all it takes is one teacher, that's right as as the power Then there is this or that that's like that should be inspiring teachers, I think it is yours, a single first and given the edge guy system, given the ascent, those you have the power to truly change laws, and like twenty years from now, that's how I feel little walk up to in and get things they have. You did that for me, yeah absolute, They and I share that, were teaches that even in this broken system of what they have to do for districts in textbooks,

a single seat you can change, kids, maths relationship or the subjects son forever was the role of the parents in this picture. Good turn up a different subject that is difficult subject and one study found that the amount of max anxiety parents had predicted the child's achievement in school, but only if they helped with homework so so when I there are some interesting implications of this. I mean you can see how it works do you have maths anxiety in your hoping you, kids, with homer you're, probably communicating things like. I was terrible at this school and an that's how it gets passed on to kids so one.

is, if you have a really bad relationship maths, you hate maths, you have my anxiety, just don't don't do math. So what will your kids? but we have on our website. We have a little sheet for parents of war. These two interact around maths with your kids and thus you cubed dot, org. That's, u cubed the or guess So one of the things I say to parents from I parent presentations is even if You hate max, you needed is fake it with your kids, you be always endlessly optimistic and happy about doing that. I am most curious about the so decide I hope you have kids. When did I kiss curly? parents so K would like sucking at math and then try to get their kid to be better than the essentially like that. Difficult thing for a lot appearance it is difficult to have like is asking

nothing like. I never got good at islam probably should have, and yet to me that you want to celebrate that, but I know a lot of people struggle would that, like coaches in sports, to to make an athlete. become better than them can be hard on the eager yeah. So I added and juice the same with parents too. I think I mean I haven't an experience. Parents worrying that their kids we best in them. I have experience. I have experience parents just having a really bad relationship with math gosh. You know 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 and school, their daughters. Achievement goes down so We know that kid's pick up on these messages and which is why I say, should fake it.

It also. I know that lots of people have just had a really bad relationship with maths. Even successful people I, the undergrads I teach 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 damn Parents believe that there's one methods that you memorize and then you reproduce it so two people have really had an experience of what I think of as the other mats, where until they 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 is therefore teacher before too long, systematize it is there something teachers can do to do more effectively, so you are ambitious emission. The textbook. Yes, why what are the additional thing,

You can add on top of this holy old school today, where teaching the and improve the process, so I do think as a way of teaching. Math changes, everything for kids, teachers. So I'm one of five writers of a new framework for the safe for any mass framework has come out next year. and we are recommending through this mouth framework the people teach in this way it's cold teeth two big ideas. So at the moment people have standards that have been written and then textbooks have taken. These standards made not very good dense, and if you look at the standards like I have some written down here, just read: the standards it makes it seem really boring and annoyance.

Firing. What what it? What are the kind of can you give a few examples would so. This is an interesting set of plans. Third grade. There are three different standards about unit squares, okay, so this is one of them a square with side length. One unit put a unit square is said to have one square unit of area and can be used to measure area, there's something you are expected to learn. That is something that sort of standard the textbook authors, I wanna, make a question about that and they translate the standards into narrow questions. They measure success ability to deliver on these standards. So the standards themselves, I think, of math son. Many people think that in this way is a subjective like a few big ideas and really important connection.

between them? I'm so like an eager thinks it is like a network map of ideas and connections and what standards there as they take that beautiful map, and they chop it like this. And tell us a little pieces and they deliver the pieces, the schools and so teaches, don't see the connection. Between ideas, noted the kids, so try this bit of a long way of saying that what we ve done in this new initiative is, we have set out mats, is a set of big ideas, connections between them. So this is a great three. So, instead of there being sixty standards, we have said- or you can pull these different standards to get in with each other and also value the ways these are connected and by the way for people who are just listen, we're looking at a small number of, like big concepts, will mathematics score

measuring fractions shape in time, and then the house are interconnected The goal is for this is for great three, for example. Yet then, so we ve set out for the state Before any of the whole of mathematics K ten 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 a is a big idea. What rich deep activity can I use then teaches measuring tickets and ass kids work on these deep rich activities may be

a few days turns out a lot of mass comes into it, so we recommending that, let's not teach maths according to all these multiple multiple statements and lots and lots of short questions instead teach maths by thinking about what the big ideas and mortar really rich deep activities, the tea those big ideas through the sea like how you teach it maximize learning what about like from us school district perspective. Like measuring how are doing. You know the grades and tests like that. Do you throw those out or there is not a fan of grades and tests myself? I think grades are fine if they're used at the end of it was so at the end of my math schools. I might get a great because a great is meant to be a summit if measure it kind of

scribes your summit of achievement, but the problem we have in maths classrooms across the eu at the: u S is people use grades or the time every week or every day, even my own kids, when they went through high school technology, has not helped to this when they went through higher. They knew they have been granted for everything they did. Everything and so any where they been greatly for everything, but they could see it in the great book on line and it would also every class they went into. So this is the old some at what I covers a performance culture you're there to perform some measuring you, you see your score, so I think that's not conducive folk, deep learning and I have a great at the end of the year, but during the year you can assess kids in much better way site teachers can a great way of assessing kids is to give them a rubric

that kind of outlines what their learning over the course of a unit or a few weeks, so kids can actually, see the journey there their night. This is what we're doing mathematically sometimes they self assess on those units and and teachers. show what what they can, while the kids can do with a rubric and also right notes, light in in the next four weeks. You might like to learn to do that. So so, instead of kids thank you. I am an acre to be kid or I have this letter attached to me their eyes seeing mathematically what's important and they are involved. in the process of where they are mathematically at the end of the year should they can have a great during the year. They get these much more informative measures. I do think that this might be more for college, but maybe not at some

best classes have had is, when I got a special set aside, like the professor clearly saw, those interested in some aspect of a thing and then of a few in mind, one take her when he said that he carnage as mrs outside of grades and others that kind of stuff that basically reverse psychology. I don't. I don't think this can be done. And so I gave everything to do that, but it does things of this was that happened to be an artificial intelligence class, but I think that, like special treatment of taking students who are especially will like excellent at a particular little aspect, the issue their eyes light up. I I often think, like maybe something for teacher, think you ve already succeed, it there. But there actually signalling to you that I, like you,

really launch him on their way here and That's too much to expect from teachers. I thing to do to pay and all that is really difficult, but I sk. I remember who are the biggest and most important people in in the history of my life of education is those for those who really didn't just like inspire me with their awesomeness, which they did, but also just they pushed me little yet again, a little push and requires folks. and the quote unquote excellent. Yes in the class yeah, I think, what's important, though, is Teachers to have the perspective that they don't know who's gonna be excellent. That was something before they give out the activities that, with an end, ass camp classes that we ran sometimes- students would finish ahead of other students and we

say to them. Can you write a question that slight bisbee different oh and and over time we encourage them to like extend things further I remember we were doing one activity where kids were work at the borders of a square and how big this border would be indifferent case sizes One of the boys came up at the end of the cost, has said I've been thinking about how you do this are the pentagon. I say that her stick? How do what does it look like repented? The gulf in I find out saving discover so I didn't know he was gonna, come up and say that and I didn't I have 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 you re doing well in something have them extend that go further,

scrape, and then you also like this is a teacher and coach. You could say it in different ways soon sake for me, the right thing to say is almost to say: I think you could do is too hard like that I need to hear I know I know you did his immediate push, but with some people a little bit more is all has without bringing Gal your genetics is they might be much more than might break them. Yeah that might break them cause. They have to be also senses. To that I mean teaching is really really difficult. For this very reason, it is so what is the best way to teach math to learn, math, that it does Only a few days we capture them, I do thing as she does. A video of me doing this on our website that I love when I first meet students

This is what I do. I show a picture. This is the picture I show them and it's a picture of seven dots like this and I sure for just a few seconds and I saved to them. I'd like just tell me how many there are, but I don't need to count them. I went to group the dots and I, sure at them, and then I I I take way before them even had enough time to countenance, and then I asked them. So how did you see it? and I got on the room and amazingly enough, there's probably eighteen different ways of seeing these seven dots and so I ask people, tell me hey how you group too, and some people see it is like an outside hole with ascend to adopt some people see light stripes of lines. Some people see segments and I click

when I put them on the board and at the end I say this. We are a class of thirty kids and we saw these seven dots in eighteen. Different ways is actually a mathematical term, for this is called group, tithing group or tyson yeah, like it is kind of Oh so turns out, though, that how well you group it eyes predicts how are you doing mats as it is a raw towns as you just something they often gets through adopting new born group enticing. I think that some kids have developed that ability like an you, can learn it you can. So this to me is part of how wrong we have mats that we think to tell whether kids good at maths were going to give them a speed test on fact or multiples, but actually seeing how kids group dots could be a more important assessment of how well they're going to do maths any rate I divulge. What would I like to do that when I start over?

it's a show them. I'm gonna give you mass problems, I'm in a valley, the different ways. You see them and you can do this kind of problem asking people how they grouped ups with young child and with graduate students and its engaging for all of them, you talk about creativity. A little bit inflexibility in your book limitless. What was the role of that so it sounds like there's a bit of that a thing involved in group retiring yeah, yeah this term? So what's what words say Israel, creativity, inflexibility, thin and the learning of math. I think what we know now is that what we need for this twenty four century world we live in is a flexible mind.

its scope 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 I that's what I love about. Math is the key, two different ways you can see it and so helping our kids there's a book. I like a lot by and bye physicists. You probably know this book could elastic, we might know it I and it's about how we want elastic, mind, 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 memory, zation member,

as a nation during procedures, a lot of things that we spend a lot of time in school on in the world. When kids leave school, a computer will do that and better. Then they will, but that creative, flexible thinking, we're kind of at ground zero at computers being able to engage in that thinking, maybe we're a little above ground zero, but the human brain is perfectly suited for that creative, flexible thinking. That's what humans are so great that so I would like the balance the shift in schools. Maybe you still need to do some procedural kind of thinking, but this should be a lot more of that create a flexible thinking. and though, was the role of other humans in this picture? So, collaborative yeah learning so brainstorming together. The creativity as it emerges from the collect

intelligence of multiple yeah soup important in no that also helps develop your brain, that social side of thinking and I love mathematics, collaboration where people builds on each other's ideas and they come up with me. Using things ass. She took a hundred students calculus stamford recently underground. and we taught them to cooperate, So these students came in Stamford and most of them were against collaboration in math. This is before covert in person yeah. It was just before cove it hit. It was to that nineteen The sunday you said there against is really interesting, so that only experience maths individually is in a kind of competitive. your way and if they had experienced it as group work, it has been a bad experience Maybe they were the one who did it all in the others? Didn't do much so there,

kind of against collaboration. They didn't see any role for it in maths and we told them to collaborate, It was hard work because, as well as the fact that they were kind gains collaboration. They came in with a lot of light social comparison thinking sought I'm in this room and other stamford undergrad and that better than me or so we seven to a kind of mass prevalence gather the first one was kind of a disaster because they, but we're like their best in may that foster the me they came up with something I didn't come up with, so we told them to let go of that thinking and to work well together and one of the things we did. We decided we want to do a pre and post test at the end of this teaching was only four weeks long. but we knew we don't want to give them like a time test of individual work, so we gave them and applied problems do at the beginning and we gave them to pass to

over and we gave each of them had different colored pen and said work on this activity together and keep using up so then we have of these pieces as to work and what we saw was they just? What on separate parts of the paper This isn't like red pen section on agreeing penetration, and I didn't do that. Well on it even though it was a problem. middle or high school kids could do, but it was like a problem solving common problem and then gave him the same ones. Do at the end gave him the same colours and actually they had learned to cooperate and not only with a cavalry thing, the second time round, but that boost to their achievement and the one who collaborated did better on the problem collaboration important having people and what was sir, I opening for these undergrad and they talked about it in lovely ways was, I learn to value other people's thinking on a problem, and I learned

The value that other people saw it in different ways, and it was quite a big experience for me They came out thinking you know like I can do mass with other people. People can see it differently, We can build on each other's way. Ways of thinking. I get a chance to iraqi no day, oconnors that in chess interact. I do and I think the first cause he had a few, but one famous collaboration throughout his life with diversity and adjust like you know. He has met me before in person, but just a number of questions. He was asking just a curiosity. They think one of the skills that collaboration itself as a skill, an admirable at my expense. With him was like. Ok, I get why you are so good collaboration, because he was just extremely good

listening and genuine curiosity about how the other person, about the world sees the world and then together, he's here hold me in that particular case. He doesn't know in particular like much about autonomous vehicles, but he kept like asking all these questions and then like ten minutes in work, together, trying to solve the problem of autonomous driving. Unlike in that I mean, that's really fulfilling. That's really reaching, but also in their movement made me realize it's kind of a skill. You can put your ego side here put your view of the other side and try to learn how the other programmes and the other thing you have to put aside as this social comparison when can I give you a sitting there thinking wow? That was amazing idea, he's so much better than I am that's really going to stop you taking on value. If that idea

So there's a lot of that going on between the stamp of students when they came and yeah but try to help them. Let go of that one of the things I discovered just because being a little bit more in the public eye, How rewarding it is to celebrate others yeah. How much going to actually pay off in the long term for this kind of sale. Thinking of like I want approved a small people around me that I'm really smart and do so by basically not celebrating huh, the other people are yes, actually, maybe short term. It seems its strategy, but long term? It's not, I think, if you pranks at the student level and then at the career law at every single stage. I think that's, ultimately I I agree with you. I think that's really good way of thinking about it. You mentioned textbooks, use it

You said there may be. Textbooks is in the perfect way to teach mathematics, but I love textbooks. There's three pretty pictures and they smell nice. They open, I metabolic physical. Some of them the greatest experiences have been just like. Oh, I guess really well done when we're talking about basic, like high school calculus biology, chemistry, those like those are incredible: it's working yeah. But what color and the nice that you must have seen some good textbooks if they had pretty pictures in color? yeah we're a member. I guess who is very, very standard. Like a peek, a be calculated, ably biology became a story. I thought those rights from the happy days of my life in terms of learning was highschool causes It's very easy. Honestly, it fell part at the time, but you

simply doing a worldwide tour of all of science yeah yeah with without having to like you, do literature, shakespeare, calvin, ecology, physics, chemistry what else anatomy physiology, gee. Computer science without nobody's telling you what to do with your life is doing all those things. That's a good thing, your aim, but I remember the textbooks what I mean I'm romanticizing the passage, but I'm over. They they weren't there they're pretty good, but so you think what role do you think they play still unlike in this more modern, digital age. What was the best materials with which to do these kinds of yours?

a war or intrigue that you have such a good experience with textbooks. I mean I can remember, loving some textbooks I had when I was learning and I love books. I love to pick up books and look through them, but a lot of mass textbooks and not good expense, it says for kids, they do. 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. The textbook is kind of like the bible. You have to follow it and every day it slightly differently. On monday, you do two point three. Point two and on tuesday. Eighty two point three point three and on wednesday, and do you never go off? That's that's like every single day and that's not inspiring fur

the kids, so one of the things they loved, my account was just that were no books, even though we gave them sheets of paper. Instead, they still felt more free because they were, just like trotting through exercises excited so like what would a textbook allows? You is like you're, the the everything you said they might not like the two point: yeah right, Do you feel like you, making progress and like you is the little celebrations gives you do the problem, this is really hard not to do it, and then you try it and try and then eventually see me make that little step and yet further progress, and then you get to the end of a chapter. and you get a like its closure yeah right. I got that figured on and then you go onto the next chapter. I can see that I mean, I think it could be it. Export q and have a good experience of the textbook, but if it

no what's important is what is what is in that textbook? What are you doing inside it again I mean I grew up in england. in england we learn math. Sweden have this separation, algebra and geometry, and I don't think the country, apart from the? U S, has that, but I look kids in algebra classes, whether doing algebra four year, and I think I would have been pretty good doing that, but like you, we can we analyze your bringing real quick. Why do british folks call mathematics maths Why is it then plural? Is it? Is it because the very thing you're saying was a bunch of sub discipline? Yeah I mean mathematics. Issue is supposed to be the the map, the different maps, the you look at do, whether you think of that.

as topics, geometry and probability. Oh, oh. I think this is masses, smoke damage so lots of ways, but that's why it was called mathematics and then it was shown to maths and then for some reason it was just math in the us, but to me man has not more singular, feel threatened them there's an expression here which is do the math, which basically means a calculation, that's what people made by do the math. So I don't like that expression, gas mask, be anything. Does the calculation and say I like it's because it has more of that broad feel to it. Gotta love that maths kind of emphasize the multi dimensional, like variety of different, the different disciplines, different approaches, yeah, okay, oh it would so but outside of the textbook. What do you see?

like broadly be used. Emissions Sebastian thrown in books, online education do things, that's an effective, so amby, I mean online having great teaches on, And of his late extend as those too, just to many more people? And that's a wonderful thing? I have quite a few online courses myself. I got the bug working, especially in when he was it released. His first move- and I thought Maybe I could do one in maths, education and I didn't know if anybody would take it. I remember release to get that first, summon as a free online class and thirty thousand maths teachers took it that summer and they were all talking about it with each other and sharing it and it was like took off. In fact, it was that mooc that cool got me to create you cubed with Kathy williams, who's, the co founder and because people took the mooc and then they said. Ok,.

What now I have finished? What what can I have next? So that was where we made our website, but so I think online education can be great. I do think along the moocs. Don't have great pedagogy they're, just a talking head and. You can actually engage people more active ways. Even an online learning so I learned from the university principle when I work at you dusty, never to talk more than five minutes and but there then to ask people to do something so that so the pedagogy of the online causes I have is a little bit of prison. something and then people do something in those of a bit more because I think you do you have a half hour video you just switch off and start doing. Other thing so the way you'd ass. He did so like five ten minute like a bit of teaching,

and then with some visual stuff, perhaps, and then there's like a quiz, and then you answer, question yeah yeah. Now that that's the yeah, that's really effective! You mentioned you cubed. So what's the mission was the goal you measure how it started, but one what were you out now, and would you what's your dream with it or whatever the kind of things that people should go in check out on that We started view cubed. I guess it was about five years ago now and we have had over fifty two million visitors, the site silo very happy about that. And our goal is to share good ideas the teaching with teachers, students, parents in maths and to help We have a set of sub goal of a raising maths anxiety, that's important. But also to sham axis this beautiful creative subject: and its we really great. We have lessons on the site.

But one of the faint one of the reasons I thought this was needed. Is this a lot of knowledge in the academy about how to teach maxwell, loads and loads of research? urgent journals and lots of things written up, but teaches don't read it they. They then have access to it. There often behind pay balls. They the written and ready inaccessible ways, so people would want to read them or understand them. So this I see the big blow me. You have this whole industry of people finding out each well, not sharing it with the people who are teaching. So that's what made you and instead of just putting articles up saying here, some things to read about how to teach? Well, we translate it. What was coming from research into things that teach you could use so lesson. Is there a videos to show kids and the tipps repair there are also things on the site and it's been amazing as we had. We took him,

frazier from the week of code, which got teaches turf. Some coding for weak, and we have this thing could do week of inspirational max and we say just try it for weak, just give us one week and try it and see what happens, and so it's been downloaded millions of times teaches use every year. They start the school year with it and what they tell us is It is amazing that kid's lights were on their excited. They loved it the weak finished and I opened my text books and the lights went out. They were not interested but getting that first inspiration is still powerful. I it is. I wish me my what I would is if we could have, They extend that for the whole year. We small team at Stanford and we're trying to keep up with great things to put on a site. We haven't the capacity to

produce these create a visual masters for every age group for every day, but I would love to do that difficult does it do I ask you to come up with the visual formulations of these are big. Important topic seemed to think about in a way that you know. the time the the you could teach having it. We can do it Actually, we went from the weak, inspirational maths and we made K eight maths books with exactly that. Big ideas, reach activities visuals, we just finished ass One- we ve been doing it for five years and it's been exhausting, and we just finish now, there's a whole k, eight set of books, their organised in that way. These the big ideas here, a rich, deep activities, not, though, what you can do

every day for year there, so some teachers use them as a kind of supplement to their boeing textbook, and some people I said: okay, this is the year. This book tells us what the areas and then will supplement. These bacteria is written. so there being used and teaches really like someone really happy about them. I just always want more and it s one of the things I would like for you cubed on my personal goals, is that every teacher of bats knows about youtube at the moment and lot of teachers come to us a really happy. They found it, but there's a lot of other teaches you don't know that I hope this helps yeah from a student perspective and not classroom, but at home, studying in new, is there some advice you can give and how to best study mathematics for was the role of the student outside the classroom, yeah,

I think one thing we know is a lot of people when they were you material, whether its mass or anything else, don't do it in the best way. I think- problem. Unless people have is they read through maybe a teaches explanation or way of doing mats, and it makes sense, Actually I've got an they move on, but and it's not until you come to try and work on. something into a problem. The? U s you realize you didn't really understand. It just seemed to make sense I would say this is also something that neuroscientist took about two key, giving yourself questions is a really good way to study rather then looking through lots material. It was like giving us have lots of tests, is a good way to actually deeply understand things and know what you do any don't understand so the questions be in the form of

The material. Your reviewing is the answer to that question, or is it almost like beyond? Is the polygon thing? Imagine where is almost like, I wonder what is the bigger picture was asking like causes, extended insomnia that that that would be great it's a similar. I mean a question. I get us losses about homework. What is a good thing if it gets you for homework and one of the recommended since I give is to not have kids just do lots of questions for homework but to actually asking to reflect on what we have learned that what was the big idea? where'd you learn today. Oh, what did you find if go? What to do? struggle with what was something that was exciting there. and kids go home and they have to kind of reflect in a deeper way a lot of times. I don't if you have this expense as a math student, lots of people do. It's going through half's questions that successful they get them right,

but they only really know what thereabout and let's go through many years of mass like that. Do not sir questions, but that really knowing what even the topic so what it's about? What is important for so having students go back and think at the end of the day? What was the big idea from this matchless and wise important, where would I find that in real life, those a really good questions for kids to be thinking about sprawly? For everybody be thinking, about. I think most of us go through life. Never asking like the bigger question almost like You know those like layers of. Why questions that kid's ask when their very young yeah. We need to keep doing that. We know like what one of the term, is he coughed first principles, thinking some people call that which is like. Why are we doing it this way

but what one nice thing is to do that usually good outside the reason we did this way is because it works for this reason, but then, if you want to do- something totally novel. Is you say? Well, we ve been. doing it? This way? Because historical reasons, but really it is not best way to do it? There might be other ways and that's all, mention happens right and then you get through use one. Every aspect of life like choosing your career choosing your arm. I do not wait where you live, yeah, we're romantic partner as again everything everything yeah and I think you're, probably stars with that doing that in math yeah, I guess started doing I want. I mean, I wonder How we didn't do very much of that for most of my education asking why

except for leal much later in the subjects on my grad school, when you're doing research on them, when your first task could do something novel using This or solving a problem really outside the classroom they have to publish on is the first time you think weight. Why are these things sure thing useful, which other things very useful and the I guess, those though that would be nice. Who did them much earlier that down the quest of invention, yeah yeah I mean one of the sad pieces of research data. I think about. Is the questions kids ask in school- goes down like in a linear progression. From an they early years. You can't stop kids asking these questions, but they learned not to us the questions. I think you told someone

a bottom early memory you had in your own education, where you asked the question Maybe those an example you gave way was shut down. Oh yeah, you listen to something I said But beware of asked was something of a caught me yeah. I remember very vividly lacking you tell the memory yeah I was it's funny I can remember. It must have really impacted me in that moment, because you know have is lots of hours of school. We don't remember at all, but I I I I remember. sitting in everything I was in high school, a high school maths class, although their cooler in england and the teacher said and it was like the first class of this teaches class and he said Ask if you have any questions, so I won't and I put my hand up, and I said I have a question and he sits in the night that your question and as I

okay, I'm not asking any more questions hard in a way where you didn't want to use the lesson you learn from that. I'm not gonna ask yeah! That was absolutely that's nice! That's the last question asking and I was here he was the chair. The mats depart with a really well so Maybe because of that experience, one of the things we encourage or may teach kids is asking questions and we value when they are. Questions me, but my walls and celebrate ten. It's funny cause, I was sure, assures a feedback signal because he probably put deposits banana. He probably didn't realize the negative impact he's had a moment right. If you only knew seated probably william, more mature and grad school, at an amazing professor, named Ali shook a fine day in computer science and he would get pew incursion

oceans, but then he would tell her we had done their questions are way was it was thought I guess if you show, if you see it would love and respect behind it. Then it's more like a friendly, humorous encouragement for more question. Yes, an art raby added to that issue to right- and this is where I hardly after time at re, because this problem- a humorous, probably better for one year, in grad school version you're in the early education, I found, I guess, kids or young people get whether somebody's. doing it to be funny or has it this I mean this is why teacher so hard? Even your tone can be impact for is so sad because, like for it for that particular human, the teacher is just had a day and one statement can have profound negative impact. I know, sadly, the mast disallowed him ass teachers, who

that kind of approach and nay, I think those suffering from the fact that they think If the Msp found out math people and that comes across in their teaching, but on the flip side, one positive statement, yeah keep him gone, that's right. That is the flip side of that, and I myself have They won t church, who is really amazing for me in maths, and she kept me in the subject I was then who is she She was an aim, as mrs Marshall She was my a level. Maths teacher so I was it I mean in england. You do lots of subjects your sixteen and then you choose like three, or for subjects are chosen mats and you go to high levels probably equivalent more to a masters degree in the. U s cause you more specialised but anyways. She was my teacher and

the first time in my whole career in maths. She would give us problems and tell us to talk about them. Other, and so here I was sitting that seventeen talking with friends about how to sober mouth problem, and that was it. That was the change that she made, 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 were taught together on. Come up with solutions- and I was like that was it that changed maths. For me what it was in some kind of personal interaction with her. It was more like she, she the catalyst for that collaborative experience I mean The many ways teaches can inspire kid swimming. Sometimes it's a personal message. it can be or teaching approach that changes mass for kids cal newport here you're a book called deep work.

And he's a mathematician theoretical computer scientists and he talks about the come. The focus required to do that kind of work deserves something eating comment on. Your will in a world full of distractions that that seems like one of the elements studying, and especially the studying of subjects to require thinking like math does difficult, is there something from a student perspective from a teacher perspective that encourages deep work they can come. 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 act,

Please realize I do I. I give a problem out often when I'm working with teachers- and I say to them: alright, I'm going to check him with you often hour and they're like an hour. They think it's shocking and then they work on this problem and after an hour, sir kay how we doing that now has come by. How is this possible? And so everybody needs those rich, deep problems most kids go through their whole maths. Experience of, however, many years, never once working on a problem in that kind of diet way. So I the the undergrad class I teach at Stanford. We do that. We work on these deep plums every session and the students come away going. Ok, I never want to go back to that mouth's relationship had where I was just about quick answers. I I just don't want to go back to that and so

We can all old teachers can incorporate those problems and that classrooms- maybe they don't do that today, but they at least, kids, some experience of being out too. slowly and deeply and to go to deeper places and not be told they ve got five minutes to finish twenty questions. but a part of it is also just the young, the action the sitting there maintaining focus aplomb praised the time. That's not often I know that the skill yeah there's a skill that that also could be discouraging, like if you dont practices at this sitting, down for ten ministry emitting. Deep focus could be exceptionally challenging, like if you really thinking about a problem and to re, I think it's really important to realize that that's a skill that you can just like a must

Well, you can bill. You can start with five minutes and goes to ten minutes of thirty into an hour and and to be successful. Thing is certain subjects like mathematics. You want to be able to develop their skill, otherwise you're not going to get to They did the really rewarding experience. Yes, all these problems definite there is this a done of kids in school where they were asked. How long were you gonna maths problem before you give up and decide? It's not possible so that nation and they result on average across the kids with two minutes. That's a bad sign that was the powerful sign that that they need to learn to not give up so quickly we mention are fine, because we ve been talking so much above visualization grandson, and threw one brown so.

He's inspired millions of people with a kind of exactly the kind of way of thinking that you ve been talking about. We I love his work, convert. sort of mathematical concepts into visual? like visually, representing them, exploring them in ways that the help you illuminate, like the concepts whoop. we think is the role of ass a he uses, mostly programmatic visualization visualization thing I met, you were There's like animations, created by writing computer programs like what would you think, husk noble is that approached by, but in general, what thought is it's amazing? I should work with him yeah I I can share some of our visuals and he can make them in that amazing way and so part of his storytelling

get out of his like is creating the visuals and then weaving a story with those visuals that kind of bills like there's, also a mean this also drama in it. He said with a smaller sample, and then you pay it's all of a sudden, there's a surprise yeah it really. I mean it makes you fall in love with the that's right with the concept he does talk about, that his senses like some of the stuff he he he doesn't feel like he's teaching like the core curriculum, which is something you know he he sees himself as an inspirational figure but because I think is too difficult to colonel covered, all the curriculum into the elements and papa you don't need to. I mean you if people get to experience by radical ideas in the way that he shares them

and that will change them and it would change the way they they think. Maybe they could go on to take. Some other mathematical idea make that beautiful or he deserve all this he created a library called madam he open source. In that library is, the people should check it out. It's written python and use that some of those same elements like it allows it. Many equations and animate little shapes like people that he's, a very distinct style, his videos and whatever salted and even though, from a software engineer perspective, the code you This is not like super well documented perfect. Him, releasing that now there's, all of the other little to edge again and that the court to me personally the course thing is the sea, like people they're not No, don't have like a million subscribers, or something is the day there

the few views in the video, but it seems like the process of them creating a video were they teach is like transforming them. Yeah students, We had old, fine man thing the best way to learn to teach right and I m releasing than to the wild yeah. It shows that that bacteria, absolutely, I think, just giving people that I, If you can do that with maths and other subjects them to be people all around too can create more, which is cool here. They deafening So I recommend people. Do a javascript escaped her python, you get. You can build visuals nations of most concepts in high school yeah can do a lot of cancer visuals patients and doing that yourself, plus. If you do that yourself, of people really love it. You actually people love visualization of man.

I mean, there's something in us that loves patterns laws, figuring out difficult things in the patterns in their than are unaware. In some way. Yeah, have you ever is. The hotels are always filled with patents. Noticing at that time and now all of carpets a patent carpets and then they are patents on the walls. So we humans, love The symmetry and patterns rigging of symmetry pattern, yeah added its funding that we ask mathematics is somehow injure golly connected to that, but it is that's one of the prospectus. I love students to take is to be a passing seeker. Everything in it

and son in all of math, so many you can think of all of maths as a kind of subject of patterns and not just visual patterns. But you know when you think about multiplying by five and the fact you can you know if you, if you're multiplying eighteen times five, you can instead think of nine times ten. That's a pop that always works in mathematics. You can have a number and double in number and so yeah. I just think there are patterns everywhere and if kids are thinking that role is to see patterns and find patterns, it's really exciting. thing? What do you think about like mit open course? Where and the release of lecturers by universities. I ask it it's good. I think me, that is what started. The milk I did was using that platform: z autonomy.

Think like the. U dusty models is alive and more effective than just a plain to our lecture. I think this deaf and you can bring in good pedagogy, enter online learning and I think idea of putting things online so that people all over the world can access them is great. I don't the initial excitement around moose, so mokroe sizing education and make it more equal came about. Because they found that the people take him extended to be the more privileged people, so that work, I think there's still something to be found in that the still more to be done to help the online learning reach those principles but definite. I think it's it's a good invent then I have an online class thats for kids. That's little free! that goes to the topic. It's good, how taylor maths on earth it shows me.

since this visual creative subject in it shares mind certain some brain science son kid suited kit do better mats class with studied it with light, randomize control trials and given it to middle school, kids and other middle school kids, you don't take it, but I taught by the same teaches that teaches of the same and the kids who take the online class end up sixty eight percent more. aged in them ass clubs and do better at the end of the year. So that said, the full succession, fifteen minute, klaus and changes kids, maths relationship. So it is true that we can do that with some words that aren't you, no, no, it's not huge change to the education system. Do you have advice for young people? We've been talking about mathematics quite a bit, but in terms of their journey through education.

through their career choices through life, maybe middle school, high school undergrad students how to live a life that they can be proud of. I think, if I were to give advice, tat people, especially young people, my advice would be her. Always it sounds. Corny, but always believe in yourself and know that you can achieve because although that sounds like obvious. Of course, you want kids to know that they can achieve things. I know that millions of During the school system have been given the message. They cannot do things and adults too. They have the idea. Oh, I did ok and this I went into this job because those other things I could never have done. I can, so actually, when they hear hey, maybe you could do this other things, even adults. Thank you. No, I haven't,

but I can and they go back and they encounter this knowledge and they rely on things and they change careers. An amazing things happen. So for me, I think that message is really important. You can learn anything. scientists try and find a limit their ways? and 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, as is true of people born with brain in all areas of their brain, the functioning well have what we call a special needs. Some of those people also gone to developing, do amazing things, so I think that really experiencing that's knowing that feel not just saying it, but knowing it deeply. Learn. Anything is something I wish or people would have actually also applies when you achieved some of of success. To what I find,

I can my life. Would people love me you and you success? They they keep. Celebrating your success and they will you keep doing the thing that europe excess flat as opposed to believing in that you can do that. There's something else, something be whatever your hearts as the direct and one of the things I realise the value of this are quite recently, which you sad to say is how important is to seek out that, when you're younger, to seek out mentors to seek out the people like surround yourself with people that will believe in you yeah. It's a A little bit is on. You is like a young, get that sometimes, if you're gonna to grad school, if you think you kind of land on a match or maybe pick a match or based on the topic they are interested in, but the reality is that please round yourself with their goods,

define your life yet trajectory risa city select peoples. True, I'm get away from people who don't believe you don't hear. Sometimes parents can be that. May I love you deeply, but they be the oh they set It's? The math thing we mentioned: they might set certain constraints on the beliefs they you have and in that if Europe they mathematics, your parents are not vanished, don't listen to your prayers and that wonder agent exactly there, and if people tell you can't do things you have to hear from other people who believe me, I think, you're, absolutely right about that so sad the number of people have had those negative messages from parents in me. Limitless mind book kind for quite a few people had been told they couldn't do math, sometimes by parents, sometimes by teachers, and

Fortunately, they had got other ideas, some point in their life and realise that was this whole world of math, article 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 to find those people would he hoped education system education. General looks like ten twenty fifty hundred years from now. I hope optimistic about the future. Here I did, they have hope there is change can happen in the education system in some is its being microscopically slow and am. But I do actually see change happening like we were talking earlier that data. It is now a course you can take in high school instead of algebra, but- and that's pretty amazing, because that content was set out in eighteen. Ninety two and hasn't changed

then- and so now we actually seeing a change in the content of high school. So I'm amazed that that's happening and very happy it's happening, but So change is very slow in education, usually but you look ahead and think about, but we know and all that we and off kids in terms of technology. You ve got to think that a hundred years from now education will be totally different to the way now! Maybe you and have subject boundaries anymore, because those don't really make much sense is issued to think certain tools like programming, maybe they'll, be D. We intervene in everything we drank yeah. You would think that all kids a growing at learning programme and create. So I just I'm in the system of schooling, we have now become 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 their learning, and maybe the individual subjects boundaries we'll go data science itself come into the education system kind of illustrates that, because people realize 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 unquestioning how we have these different subject boundary. So. You seen data size be integrated into the curricula. Yes, it's happening across the united states. We speak. I wonder how they got initiating a cottage change happen in the education system, is a

if you revolutionary, like it does eaters, I think so I think so. It's been an interesting journey. Seeing data science take off actually it, and there was a course that was developed in two thousand and fourteen in by some people who thought data. Science was a good idea for high schoolers and then, after some kids to the course and nothing bad happened to them, but he went to college people started to accept it more and then this was a big piece of the change in California, the you see system communicated they said, Imagine email. Last year the fifty thousand high schools saying we now accept data science, kids can take it instead of algebra two and that's a perfectly legitimate college pathway. So that was like a big green light for a lot of schools are like wondering about whether they could

we chat. So I think it happens in small spaces and expands. So now goes viral yeah the lottery age. Then it goes viral california's a head and I think can creating courses and having kids go through it, but it's but suddenly, when I last looked, there were twelve states that were allowing data scientist, the high school girls and I think by next year that will have doubled or more so just happening job, as I said, I think mathematic. It is truly beautiful subjects and you having an impact on millions of people's lives by educating them by aspiring teachers to educate in the ways that you ve talked about in Malta, it's your ways in visual ways. I think is incredible, so

if you're spreading around the world? So I really really appreciate that you spend your valuable time with me today. Thank you for talk. Thank you. It was really good sooty, thanks for listening to his conversation with Joe bowler to support this podcast. Please check out our sponsors in the description and now. Let me leave you some words from albert einstein. Pure mathematics is the poetry of logical ideas, thanks for listening and hope to see you stop it