Jo Boaler: How to Learn Math | Lex Fridman Podcast #226

00:00:00.000 | The following is a conversation with Jo Bowler,

00:00:02.740 | a mathematics educator at Stanford

00:00:04.840 | and co-founder of ucubed.org

00:00:08.080 | that seeks to inspire young minds

00:00:10.080 | with the beauty of mathematics.

00:00:12.520 | To support this podcast,

00:00:14.040 | please check out our sponsors in the description.

00:00:17.120 | This is the Lex Friedman Podcast,

00:00:19.320 | and here is my conversation with Jo Bowler.

00:00:22.400 | What to you is beautiful about mathematics?

00:00:27.200 | - I love a mathematics that some people

00:00:30.400 | don't even think of as mathematics,

00:00:32.760 | which is beautiful, creative mathematics,

00:00:37.640 | where we look at maths in different ways,

00:00:39.560 | we visualize it,

00:00:41.280 | we think about different solutions to problems.

00:00:44.720 | A lot of people think of maths as

00:00:47.000 | you have one method and one answer.

00:00:49.600 | And what I love about maths

00:00:51.200 | is the multiple different ways you can see things,

00:00:54.040 | different methods, different ways of seeing, different...

00:00:56.800 | In some cases, different solutions.

00:00:59.200 | So that is what is beautiful to me about mathematics,

00:01:02.160 | that you can see and solve it in many different ways.

00:01:05.840 | And also the sad part that many people think

00:01:10.040 | that maths is just one answer and one method.

00:01:13.880 | - So to you, the beauty emerges

00:01:16.360 | when you have a problem with a solution

00:01:18.600 | and you start adding other solutions,

00:01:21.120 | simpler solutions, weirder solutions, more interesting,

00:01:25.480 | some that are visual, some of their algebraic,

00:01:28.200 | geometry, all that kind of stuff.

00:01:30.120 | - Yeah, I mean, I always say that you can take any maths area

00:01:34.080 | and make it visual.

00:01:35.400 | And we say to teachers,

00:01:36.400 | give us your most dry, boring maths

00:01:39.920 | and we'll make it a visual, interesting, creative problem.

00:01:43.240 | And it turns out you can do that with any area of maths.

00:01:46.920 | And I think we've given...

00:01:49.640 | It's been a great disservice to kids and others

00:01:51.720 | that it's always been numbers,

00:01:54.440 | lots and lots of numbers.

00:01:56.160 | Numbers can be great,

00:01:57.080 | but you can think about maths in other ways besides numbers.

00:02:01.040 | - Do you find that most people are better visual learners

00:02:05.120 | or is this just something that's complimentary?

00:02:07.560 | What's the kind of the full spectrum of students

00:02:11.040 | and the way they like to explore math, would you say?

00:02:13.400 | - There's definitely people who come into the classes I do

00:02:17.480 | who are more interested in visual thinking

00:02:19.760 | and like visual approaches.

00:02:21.960 | But it turns out what the neuroscience is telling us

00:02:24.680 | is that when we think about maths,

00:02:26.680 | there are two visual pathways in the brain

00:02:29.160 | and we should all be thinking about it visually.

00:02:32.760 | Some approaches have been to say,

00:02:34.440 | well, you're a visual learner, so we'll give you visuals

00:02:37.400 | and you're not a visual learner.

00:02:40.640 | But actually, if you think you're not a visual learner,

00:02:45.120 | it's probably more important that you have a visual approach

00:02:48.880 | so you can develop that part of your brain.

00:02:51.560 | - So you were saying that there's some kind

00:02:52.880 | of interconnected aspect to it,

00:02:54.520 | so the visual connects with the non-visual.

00:02:56.680 | - Yeah, so this is what the neuroscience has shown us,

00:02:59.840 | that when you work on a maths problem,

00:03:01.160 | there are five different brain pathways

00:03:03.480 | and that the most high-achieving people in the world

00:03:06.720 | are people who have more connections

00:03:08.420 | between these pathways.

00:03:10.440 | So if you see a maths problem with numbers,

00:03:13.840 | but you also see it visually,

00:03:15.880 | that will cause a connection to happen in your brain

00:03:17.960 | between these pathways.

00:03:19.840 | And if you maybe write about it with words,

00:03:22.080 | that would cause another connection,

00:03:23.360 | or maybe you build it with something physical,

00:03:26.460 | that would cause a different connection.

00:03:28.360 | And what we want for kids is,

00:03:31.040 | we call it a multidimensional experience of maths,

00:03:33.640 | seeing it in different ways,

00:03:35.480 | experiencing it in different ways,

00:03:37.860 | that will cause that great connected brain.

00:03:40.600 | - You know, there's these stories

00:03:42.000 | of physicists doing the same.

00:03:43.280 | I find physicists are often better

00:03:45.000 | at building that part of their brain

00:03:47.160 | of using visualization for intuition building,

00:03:50.620 | 'cause you ultimately want to understand

00:03:53.020 | the deepest secret underneath this problem.

00:03:57.080 | And for that, you have to intuit your way there.

00:03:59.800 | And you mentioned offline that one of the ways

00:04:02.720 | you might approach a problem

00:04:03.560 | is to try to tell a story about it.

00:04:05.880 | And some of it is like legend,

00:04:07.800 | but I'm sure it's not always.

00:04:10.520 | Is you have Einstein thinking about a train

00:04:14.480 | and the speed of light,

00:04:16.680 | and that kind of intuition is useful.

00:04:20.000 | You start to imagine a physical world,

00:04:22.920 | like how does this idea manifest itself

00:04:25.480 | in the physical world,

00:04:26.320 | and then start playing in your mind

00:04:27.560 | with that physical world,

00:04:28.840 | and think, is this going to be true?

00:04:30.200 | Is this going to be true?

00:04:31.480 | - Right, right.

00:04:32.320 | Einstein is well known for thinking visually.

00:04:35.800 | And people talk about how he really

00:04:39.080 | didn't want to go anywhere with problems

00:04:41.520 | without thinking about them visually.

00:04:43.240 | But the other thing you mentioned

00:04:44.800 | that sparked something for me

00:04:46.400 | is thinking with intuition,

00:04:48.800 | like having intuition about math problems.

00:04:51.440 | That's another thing that's often absent in math class,

00:04:54.120 | the idea that you might think about a problem

00:04:55.840 | and use your intuition,

00:04:58.020 | but so important.

00:05:00.800 | And when mathematicians are interviewed,

00:05:02.860 | they will very frequently talk about

00:05:04.200 | the role of intuition in solving problems,

00:05:07.240 | but not commonly acknowledged

00:05:10.480 | or brought into education.

00:05:13.000 | - Yeah, I mean, that's what it is.

00:05:16.000 | If you task yourself with building

00:05:18.720 | an intuition about a problem,

00:05:21.320 | that's where you start to pull in,

00:05:23.720 | like what is the pattern I'm seeing?

00:05:27.200 | In order to understand the pattern,

00:05:28.600 | you might want to then start utilizing visualization.

00:05:31.760 | But ultimately, that's all in service

00:05:34.080 | of like solving the puzzle,

00:05:37.520 | like cracking it open

00:05:38.840 | to get the simple explanation

00:05:40.400 | of why things are the way they are,

00:05:43.760 | as opposed to, like you said,

00:05:46.160 | having a particular algorithm

00:05:47.640 | that you can then execute to solve the problem.

00:05:50.160 | Yeah, but it's hard.

00:05:51.160 | It's hard.

00:05:52.000 | - Yeah. - Like reasoning

00:05:52.840 | is really hard.

00:05:53.660 | - Yeah, it's hard.

00:05:55.160 | I mean, I love to value what's hard in maths

00:05:58.860 | instead of being afraid of it.

00:06:00.640 | We know that when you struggle,

00:06:02.520 | that's actually a really good time for your brain.

00:06:04.560 | You want to be struggling

00:06:06.160 | when you're thinking about things.

00:06:07.280 | So if it's hard to think intuitively about something,

00:06:10.120 | that's probably a really good time for your brain.

00:06:13.640 | I used to work with somebody called Sebastian Thrun,

00:06:16.760 | who is a great sort of mathematician,

00:06:19.600 | you might think of him, an AI person.

00:06:21.280 | And I remember in one interview I did with him,

00:06:23.780 | he talked about how they'd built robots,

00:06:25.840 | I think for the Smithsonian,

00:06:27.640 | and how they were having this trouble

00:06:29.400 | with them picking up white noise.

00:06:32.360 | And he said they had to solve it.

00:06:34.600 | They had to work out what was going on,

00:06:36.480 | and how he intuitively worked out what the problem was.

00:06:41.360 | But then it took him three weeks to show it mathematically.

00:06:45.640 | I thought that was really interesting,

00:06:47.080 | that how you can have this intuition

00:06:49.680 | and know something works.

00:06:51.840 | It's kind of different from going through

00:06:53.440 | that long mathematical process of proving it.

00:06:57.060 | But so important.

00:06:58.320 | - Yeah, I think probably our brains are evolved

00:07:01.680 | as like intuition machines.

00:07:04.000 | And the math of like showing it like formally

00:07:08.960 | is probably an extra thing that we're not designed for.

00:07:12.160 | You see that with Feynman and his,

00:07:14.160 | all of these physicists definitely you see

00:07:18.040 | starting with intuition,

00:07:21.180 | sometimes starting with an experiment,

00:07:23.520 | and then the experiment inspires intuition.

00:07:27.960 | But you can think of an experiment

00:07:29.360 | as a kind of visualization.

00:07:31.120 | Just like let's take whatever the heck we're looking at

00:07:34.320 | and draw it, and draw like the pattern as it evolves

00:07:38.700 | as the thing grows for N equals one,

00:07:41.120 | for N equals two, N equals three,

00:07:42.800 | and you start to play with it.

00:07:44.840 | And then in the modern day, which I loved doing,

00:07:48.720 | is you can write a program that then visualizes it for you.

00:07:52.480 | And then you can start exploring it programmatically.

00:07:55.520 | And then you can do so interactively too.

00:08:00.160 | I tend to not like interactive

00:08:03.600 | because it takes way too much work.

00:08:05.680 | 'Cause you have to click and move and stuff.

00:08:07.160 | I love to interact through writing programs.

00:08:09.880 | But that's my particular brain, software engineer.

00:08:12.480 | So you can do all these kinds of visualizations.

00:08:17.200 | And then there's the tools of visualization like color,

00:08:21.080 | all of those kinds of things.

00:08:22.640 | That you're absolutely right,

00:08:24.240 | they're actually not taught very much.

00:08:27.200 | Like the art of visualization.

00:08:28.800 | - Not taught.

00:08:30.040 | And we love as well color coding.

00:08:33.720 | Like when you represent something mathematically,

00:08:36.480 | you can show color to show the growth.

00:08:39.640 | And kind of code that.

00:08:41.000 | So if I have an algebraic expression for a pattern,

00:08:44.280 | maybe I show the X with a certain color,

00:08:46.680 | but also write in that color

00:08:47.960 | so you can see the relationship.

00:08:51.360 | Very cool.

00:08:52.280 | And yeah, particularly in our work with elementary teachers,

00:08:56.800 | many of them come to our workshops

00:08:58.720 | and they're literally in tears

00:09:00.720 | when they see things making sense visually.

00:09:03.840 | Because they've spent their whole lives

00:09:06.320 | not realizing you can really understand things

00:09:09.240 | with these visuals.

00:09:10.920 | It's quite powerful.

00:09:12.720 | - You say that there's something valuable to learning

00:09:17.720 | when the thing that you're doing is challenging,

00:09:20.480 | is difficult.

00:09:21.640 | So a lot of people say math is hard,

00:09:24.000 | or math is too hard, or too hard for me.

00:09:28.040 | Do you think math should be easy or should it be hard?

00:09:33.460 | - I think it's great when things are challenging,

00:09:36.940 | but there's something that's really key

00:09:39.180 | to being able to deal with challenging maths,

00:09:42.900 | and that is knowing that you can do it.

00:09:46.820 | And I think the problem in education

00:09:48.700 | is a lot of people have got this idea

00:09:51.200 | that you're either born with a maths brain or you're not.

00:09:54.020 | So when they start to struggle,

00:09:55.740 | they think, oh, I don't have that maths brain.

00:09:58.440 | And then they will literally sort of switch off

00:10:00.980 | in their brain and things will go downhill

00:10:02.860 | from that point.

00:10:04.060 | So struggle becomes a lot easier,

00:10:06.240 | and you're able to struggle if you don't have that idea.

00:10:10.940 | But you know that you can do it.

00:10:13.420 | You have to go through this struggle to get there,

00:10:16.000 | but you're able to do that.

00:10:18.720 | And so we're hampered in being able to struggle

00:10:21.780 | with these ideas we've been given about what we can do.

00:10:25.260 | - Can I ask a difficult question here?

00:10:26.940 | - Yeah.

00:10:27.780 | - So there's kind of, I don't know what the right term is,

00:10:31.980 | but some people struggle with learning in different ways.

00:10:36.980 | Like their brain is constructed in different ways.

00:10:42.420 | And how much should, as educators,

00:10:47.020 | should we make room for that?

00:10:49.260 | So how do you know the difference between this is hard,

00:10:52.380 | and I don't like doing hard things,

00:10:54.460 | versus my brain is wired in a way

00:10:57.060 | where I need to learn in very different ways.

00:10:59.040 | I can't learn it this way.

00:11:00.620 | How do you find that line?

00:11:02.340 | How do you operate in that gray area?

00:11:04.020 | - So this is why being a teacher is so hard.

00:11:07.380 | And people really don't appreciate

00:11:09.380 | how difficult teaching is when you're faced with,

00:11:12.300 | I don't know, 30 students who think in different ways.

00:11:14.940 | But this is also why I believe it's so important

00:11:19.500 | to have this multidimensional approach to maths.

00:11:21.940 | We've really offered it in one way,

00:11:24.700 | which is here's some numbers and a method.

00:11:27.380 | You follow me, do what I just did, and then reproduce it.

00:11:31.260 | And so there are some kids who like doing that,

00:11:33.900 | and they do well.

00:11:34.900 | And a lot of kids who don't like doing it,

00:11:37.700 | and don't do well.

00:11:39.140 | But when you open up maths,

00:11:40.820 | and you let kids experience it in different ways,

00:11:44.700 | maybe visually, with numbers, with words,

00:11:47.700 | what happens is there are many more kids who can access it.

00:11:52.500 | So those different brain wirings you're talking about,

00:11:56.220 | where some people are just more able to do something

00:11:58.900 | in a particular way, that's why we want to,

00:12:01.900 | that's one of the reasons we want to open it up,

00:12:04.740 | so that there are different ways of accessing it.

00:12:07.580 | And then that's not really a problem.

00:12:11.180 | - So I grew up in the Soviet Union,

00:12:14.460 | and fell in love with math early.

00:12:17.420 | I was forced into math early,

00:12:19.860 | and fell in love through force.

00:12:22.380 | - That's good.

00:12:23.220 | Well, good that you fell in love.

00:12:24.540 | (laughing)

00:12:25.820 | But something we talked about a little bit,

00:12:28.380 | is there's such a value for excellence.

00:12:33.300 | It's competitive, and it's also everybody kind of looks up,

00:12:37.900 | the definition of success is being,

00:12:42.900 | in a particular class, is being really good at it.

00:12:46.300 | And it's not improving, it's being really good.

00:12:50.900 | I mean, we are much more like that with sports,

00:12:53.220 | for example, we're not,

00:12:54.940 | it's like it's understood,

00:12:56.860 | you're going to star on the basketball team,

00:12:59.780 | if you're gonna start on the basketball team,

00:13:02.420 | if you're going to be better than the other guys,

00:13:05.140 | the other girls on the team.

00:13:06.540 | So that coupled with the belief,

00:13:12.220 | this could be partially a communist belief, I don't know,

00:13:14.700 | but the belief that everybody is capable of being great.

00:13:19.220 | But if you're not great, that's your fault,

00:13:22.220 | and you need to work harder.

00:13:23.460 | And I remember I had a sense that, probably delusional,

00:13:27.940 | but I could win a Nobel Prize,

00:13:29.660 | I don't even know what that entails.

00:13:31.460 | But I thought, like my dad early on told me,

00:13:38.100 | just offhand, and it always stuck with me,

00:13:40.540 | that if you can figure out how to build a time machine,

00:13:44.500 | how to travel back in time,

00:13:46.140 | it will probably give you a Nobel Prize.

00:13:48.380 | And I remember early in my life thinking,

00:13:50.420 | I'm going to invent the time machine.

00:13:52.620 | And the tools of mathematics were in service of that dream

00:13:57.620 | of winning the Nobel Prize.

00:13:59.460 | And it's silly, I didn't really think

00:14:02.300 | in those concrete terms,

00:14:03.500 | but I just thought I could be great, that feeling.

00:14:06.780 | And then when you struggle,

00:14:08.660 | the belief that you could be great,

00:14:10.460 | struggle is good.

00:14:13.140 | - Right, pushes you on, yeah.

00:14:14.580 | - And so the other thing about the Soviet system

00:14:17.500 | that I'd love to hear your comments about,

00:14:20.580 | is just the sheer hours of math.

00:14:23.860 | Like the number of courses,

00:14:25.660 | you're talking about a lot of geometry, a lot more geometry.

00:14:29.300 | I think in the American system,

00:14:30.700 | you take maybe one year of geometry.

00:14:33.100 | - In high school, yeah.

00:14:34.020 | - In high school, first of all,

00:14:35.740 | geometry is beautiful, it's visual.

00:14:37.500 | And then you get to reason through proofs

00:14:39.140 | and stuff like that.

00:14:40.180 | In Russia, I remember just being nailed over and over,

00:14:43.860 | it was just nonstop.

00:14:45.620 | And then of course,

00:14:46.700 | there's different perspectives on calculus

00:14:49.020 | and just the whole, the sense was that math is like,

00:14:54.020 | fundamental to the development of the human mind.

00:14:58.660 | So math, but also science and literature, by the way,

00:15:02.420 | was also hit very hard.

00:15:04.660 | Like we read a lot of serious adult stuff.

00:15:08.220 | America does that a little bit too.

00:15:09.940 | They challenge young adults with good literature,

00:15:12.620 | but they don't challenge adults very much with math.

00:15:16.180 | So those two things, valuing excellence

00:15:20.860 | and just a lot of math in the curriculum.

00:15:23.740 | Do you think, do you find that interesting?

00:15:26.900 | 'Cause it seems to have been successful.

00:15:28.580 | - Yeah, I think that's very interesting.

00:15:30.180 | And there is a lot of success,

00:15:32.740 | people coming through the Soviet system.

00:15:34.140 | I think something that's very different to the US

00:15:37.340 | and other countries in the world

00:15:39.500 | is this idea that excellence is important

00:15:41.940 | and you can get there if you work hard.

00:15:44.980 | In the US, there's an idea that excellence is important,

00:15:48.740 | but then kids are given the idea in many ways

00:15:52.180 | that you can either do it

00:15:53.780 | or you're one of the people who can't.

00:15:56.180 | So many students in the school system

00:15:58.500 | think they're one of the kids who can't.

00:15:59.740 | So there's no point in trying hard

00:16:02.300 | because you're never going to get there.

00:16:04.740 | So if you can switch that idea, it would be huge.

00:16:09.660 | And it seems from what you've said,

00:16:11.180 | that in the US, in the Soviet Union,

00:16:14.580 | that idea is really different.

00:16:16.380 | Now, the downside of that idea,

00:16:18.060 | that anybody can get there if you work hard,

00:16:21.740 | is that thought that if you're not getting there,

00:16:25.100 | it's your fault.

00:16:26.580 | And I would add something into that.

00:16:28.740 | I would say that anybody can get there,

00:16:30.740 | but they need to work hard

00:16:33.180 | and they also need good teaching

00:16:35.180 | because there are some people who really can't get there

00:16:38.020 | because they're not given access to that good teaching.

00:16:42.380 | But that would be huge, that change.

00:16:44.660 | As to doing lots of maths,

00:16:46.460 | if maths was interesting and open and creative

00:16:51.020 | and multidimensional, I would be all for it.

00:16:53.820 | We actually run summer camps at Stanford

00:16:56.100 | where we invite kids in

00:16:57.700 | and we give them this maths that I love.

00:17:00.740 | And in our camp classrooms, they were three hours long.

00:17:05.380 | And when we were planning,

00:17:07.740 | the teachers were like, "Three hours?

00:17:09.460 | Are we going to be able to keep the kids excited

00:17:11.500 | for three hours?"

00:17:12.500 | Turned out, they didn't want to go to break or lunch.

00:17:16.020 | They'd be so into these mathematical patterns.

00:17:19.460 | We couldn't stop them.

00:17:21.100 | It was amazing.

00:17:22.820 | So yeah, if maths was more like that,

00:17:25.220 | then I think having more of it would be a really good thing.

00:17:29.100 | - So what age are you talking about?

00:17:31.180 | Could you comment on what age is the most important

00:17:37.100 | when people quit math or give up on themselves

00:17:41.020 | or on math in general?

00:17:42.780 | And perhaps that age or something earlier

00:17:45.540 | is really an important moment for them to discover,

00:17:48.620 | to be inspired to discover the magic of math.

00:17:51.460 | - I think a lot of kids start to give up on themselves

00:17:54.420 | and maths around, from about fifth grade.

00:17:59.220 | And then those middle school years are really important.

00:18:02.380 | And fifth grade can be pivotal for kids

00:18:04.540 | just because they're allowed to explore

00:18:07.940 | and think in good ways in the early grades

00:18:11.460 | of elementary school.

00:18:12.300 | But fifth grade teachers are often like,

00:18:13.460 | "Okay, we're going to prepare you now for middle school.

00:18:15.460 | And we're going to give you grades and lots of tests."

00:18:18.180 | And that's when kids start to feel really badly

00:18:21.740 | about themselves.

00:18:22.580 | And so middle school years,

00:18:24.780 | our camps are middle school students.

00:18:27.020 | We think of those years as really pivotal.

00:18:29.180 | Many kids in those years are deciding,

00:18:31.580 | "Yes, I'm going to keep going with STEM subjects."

00:18:35.660 | Or, "No, I'm not, this isn't for me."

00:18:38.340 | So, I mean, all years are important.

00:18:40.780 | And in all years, you can kind of switch kids

00:18:43.100 | and get them on a different pathway.

00:18:45.620 | But I think those middle school years are really important.

00:18:48.420 | - So what's the role of the teacher in this?

00:18:50.820 | So one is the explanation of the subject,

00:18:53.060 | but do you think teachers should almost do like one-on-one,

00:18:58.060 | you know, little Johnny, I believe in you kind of thing?

00:19:01.780 | Like that energy of like--

00:19:03.820 | - Turns out it's really important.

00:19:05.340 | There's a study that was done,

00:19:07.460 | it was actually done in high school English classrooms,

00:19:10.380 | where all kids wrote an essay for their teacher.

00:19:14.060 | And this was done as an experiment.

00:19:16.060 | Half of the kids got feedback from their teacher,

00:19:18.860 | diagnostic feedback, which is great.

00:19:21.060 | But for half of the kids,

00:19:22.020 | it said an extra sentence at the bottom

00:19:23.940 | that the researchers had put on.

00:19:26.260 | And the kids who read that extra sentence

00:19:30.020 | did significantly better in English a whole year later.

00:19:33.500 | The only change was this one sentence.

00:19:36.740 | - What did the sentence say?

00:19:37.660 | - So what did the sentence say?

00:19:39.740 | The sentence said, I'm giving you this feedback

00:19:42.900 | because I believe in you.

00:19:44.140 | And the kids who read that did better a year later.

00:19:48.660 | - Yeah.

00:19:49.500 | - So when I share this with teachers, I say, you know,

00:19:52.940 | I'm not suggesting you put on the bottom of all kids' work,

00:19:56.020 | I'm giving this feedback because I believe in you.

00:19:58.420 | One of the teachers said to me, we don't put it on a stamp?

00:20:00.740 | I said, no, don't put it on a stamp.

00:20:03.380 | But your words are really important.

00:20:08.020 | And kids are sitting in classrooms all the time thinking,

00:20:12.540 | what does my teacher think of me?

00:20:13.900 | Does my teacher think I can do this?

00:20:15.700 | So it turns out it is really important to be saying to kids,

00:20:20.500 | I know you can do this.

00:20:22.620 | And those messages are not given enough by teachers.

00:20:27.620 | - And really believe it.

00:20:29.020 | - And believe it, yeah.

00:20:30.020 | - It's like--

00:20:30.860 | - You can't just say it, you have to believe it.

00:20:32.500 | - I sometimes, 'cause it's like,

00:20:34.380 | it's such a funny dance,

00:20:38.060 | 'cause I'm such a perfectionist,

00:20:39.580 | I'm extremely self-critical,

00:20:41.340 | and I have, when I have students come up to me,

00:20:43.660 | and it's clear to me that they're not even close to good.

00:20:48.660 | And it's tempting for me to be like,

00:20:52.340 | to sort of give up on them mentally.

00:20:54.340 | But the reality is, like,

00:20:55.860 | if you look at many great people throughout history,

00:20:58.980 | they sucked at some point.

00:21:00.380 | - Yeah, exactly.

00:21:01.220 | - And some of the greatest took non-linear paths

00:21:04.220 | to where they sucked for long into later life.

00:21:08.780 | And so always kind of believing

00:21:10.420 | that this person can be great.

00:21:13.300 | - Exactly.

00:21:14.500 | - You have to communicate that,

00:21:15.860 | plus the fact that they have to work hard.

00:21:17.620 | - That's it, yeah.

00:21:19.060 | Yeah, and you're right.

00:21:19.940 | Silicon Valley, where I live,

00:21:21.500 | is filled with people who were dropouts at school,

00:21:24.580 | or who had special needs, who didn't succeed.

00:21:28.820 | It's very interesting that have gone on

00:21:30.740 | to do amazing work in creative ways.

00:21:34.260 | I mean, I do think our school system is set up

00:21:36.660 | to value good memorizers,

00:21:41.460 | who can reproduce what a teacher is showing them,

00:21:44.740 | and push away those creative, deep thinkers,

00:21:49.220 | often slower thinkers, they think slowly and deeply.

00:21:53.620 | And they often get the idea early on

00:21:55.380 | that they can't be good at maths or other subjects.

00:21:59.060 | So yeah, I think many of those people

00:22:02.340 | are the ones who go on and do amazing things.

00:22:05.180 | - So there's a guy named Eric Weinstein.

00:22:08.300 | I know many mathematicians like this,

00:22:09.820 | but he talks a lot about having

00:22:14.740 | a non-standard way of learning.

00:22:16.860 | I mean, a lot of great mathematicians,

00:22:19.700 | a lot of great physicists are like that.

00:22:22.100 | And he felt like he became quickly,

00:22:24.660 | he got his PhD at Harvard,

00:22:26.420 | became quickly an outcast of the system.

00:22:28.580 | Like the education, especially early education system

00:22:32.260 | didn't help him.

00:22:33.180 | Is there ways for an education system

00:22:37.900 | to support people like that?

00:22:40.340 | Is it this kind of multi-dimensional learning

00:22:42.420 | that you're mentioning? - Yeah, absolutely.

00:22:44.300 | I mean, I think our education system

00:22:46.620 | still uses an approach that was in classrooms

00:22:48.860 | hundreds of years ago.

00:22:50.340 | The textbooks have a lot to answer for,

00:22:53.740 | and producing is very uninspiring mathematics.

00:22:57.460 | But yeah, if you open up the subject

00:23:00.700 | and have people see and solve it in different ways

00:23:02.940 | and value those different ways.

00:23:05.300 | Somebody I appreciated a lot

00:23:07.260 | is a mathematician called Mary Mizzikani.

00:23:09.660 | I don't know if you've heard of her.

00:23:10.540 | She won the Fields Medal.

00:23:12.460 | She was from Iran.

00:23:14.460 | First woman in the world

00:23:15.580 | to win the Fields Medal in mathematics.

00:23:17.780 | She died when she was 40.

00:23:19.460 | She was at Stanford.

00:23:21.220 | But her work was entirely visual.

00:23:24.820 | And she talked about how her daughter

00:23:27.580 | thought she was an artist

00:23:28.740 | because she was always visualizing.

00:23:30.660 | And I attended, she asked me to chair the PhD defense

00:23:35.660 | for one of her students.

00:23:37.420 | And I went to the defense in the math department.

00:23:40.260 | And it was so interesting

00:23:41.420 | because this young woman spent like two hours

00:23:45.260 | sharing her work.

00:23:46.780 | All of it was visual.

00:23:47.780 | In fact, I don't think I saw any numbers at all.

00:23:50.460 | - That's awesome.

00:23:51.300 | - And I remember that day thinking,

00:23:53.460 | wow, I could have brought her like 13 year old

00:23:55.940 | into this PhD defense.

00:23:56.980 | They would not recognize this as maths.

00:24:00.300 | But when Mary Mizzikani won the Fields Medal,

00:24:03.740 | all these other mathematicians were saying

00:24:05.660 | that her work had connected

00:24:07.940 | all these previously unconnected areas of maths.

00:24:11.220 | And so, but when she was,

00:24:14.260 | she also shared that when she was in school,

00:24:16.140 | when she was about 13,

00:24:17.700 | she was told that she couldn't do maths.

00:24:21.100 | She was told that by her teacher.

00:24:22.740 | - This is Iran?

00:24:24.020 | - Mm-hmm, in Iran.

00:24:25.260 | Yeah.

00:24:26.100 | So I love that, you know,

00:24:27.380 | to be told you can't be good at maths

00:24:29.380 | and then go on and win the Fields Medal is cool.

00:24:33.900 | - I've been told by a lot of people in my life

00:24:37.180 | that I can't do something.

00:24:38.220 | I'm very definitely non-standard.

00:24:39.860 | But all it takes, that's why people talk about

00:24:44.420 | like the one teacher that changed everything.

00:24:46.700 | All it takes is one teacher.

00:24:48.060 | - That's right.

00:24:48.900 | - That's the power of that.

00:24:50.420 | So that should be inspiring to teachers.

00:24:55.860 | - I think it is.

00:24:57.580 | - You as a single person,

00:24:58.820 | given the education system, given the incentives,

00:25:01.020 | you have the power to truly change lives.

00:25:03.300 | And like 20 years from now,

00:25:05.060 | a Fields Medalist will walk up to you and say thank you.

00:25:08.020 | - You did that for me.

00:25:09.380 | Yeah, absolutely.

00:25:10.380 | And I share that with teachers

00:25:12.180 | that even in this broken system

00:25:15.580 | of what they have to do for districts and textbooks,

00:25:19.820 | a single teacher can change kids' maths relationship

00:25:22.940 | or other subjects and forever.

00:25:26.500 | - What's the role of the parents in this picture?

00:25:29.620 | Let's go to another difficult subject.

00:25:31.660 | - Yeah, that is a difficult subject.

00:25:34.140 | One study found that

00:25:36.140 | the amount of maths anxiety parents had

00:25:42.780 | predicted their child's achievement in school,

00:25:45.420 | but only if they helped with homework.

00:25:50.420 | (both laughing)

00:25:55.140 | - That's so funny.

00:25:55.980 | - Yeah, there are some interesting implications for this.

00:25:59.820 | I mean, you can see how it works.

00:26:01.300 | If you have maths anxiety

00:26:02.540 | and you're helping your kids with homework,

00:26:03.900 | you're probably communicating things like,

00:26:06.300 | oh, I was terrible at this at school,

00:26:08.180 | and that's how it gets passed on to kids.

00:26:12.440 | So one implication is

00:26:14.620 | if you have a really bad relationship with maths,

00:26:16.980 | you hate maths, you have maths anxiety,

00:26:19.100 | just don't do maths homework with your kids.

00:26:22.400 | But on our website, we have a little sheet for parents

00:26:28.540 | of ways to interact around maths with your kids.

00:26:32.240 | - That's ucubed.org?

00:26:36.620 | - That's ucubed.org, yes.

00:26:39.360 | So one of the things I say to parents

00:26:41.020 | when I give parent presentations is,

00:26:43.000 | even if you hate maths,

00:26:44.700 | you need to just fake it with your kids.

00:26:46.780 | You should be always endlessly optimistic

00:26:50.000 | and happy about doing maths.

00:26:51.740 | - I'm always curious about this.

00:26:55.460 | So I hope to have kids one day,

00:26:57.900 | I don't have kids currently.

00:26:59.300 | Are parents okay with sucking at math

00:27:04.120 | and then trying to get their kid

00:27:06.460 | to be better than them, essentially?

00:27:08.180 | Is that a difficult thing for a lot of parents?

00:27:10.020 | - It is difficult.

00:27:10.940 | To have like, it's almost like an ego thing.

00:27:12.860 | Like I never got good at this

00:27:15.140 | and I probably should have.

00:27:16.540 | Yeah, I mean, to me, you wanna celebrate that,

00:27:20.860 | but I know a lot of people struggle with that.

00:27:23.860 | Like coaches in sports,

00:27:26.220 | to make an athlete become better than them,

00:27:29.700 | it can be hard on the ego.

00:27:31.780 | - Yeah.

00:27:32.620 | - Do you experience the same with parents?

00:27:34.660 | - Parents too.

00:27:35.500 | I haven't experienced parents worrying

00:27:38.540 | that their kids will be better than them.

00:27:40.820 | I have experienced parents

00:27:44.740 | just having a really bad relationship with maths

00:27:47.980 | and not wanting to help,

00:27:50.300 | not knowing how to help, saying things.

00:27:54.020 | Like another study showed

00:27:55.660 | that when mothers say to their daughters,

00:27:58.100 | "I was bad at maths in school,"

00:28:00.100 | their daughter's achievement goes down.

00:28:02.460 | So we know that kids pick up on these messages,

00:28:05.020 | which is why I say you should fake it.

00:28:08.420 | But also I know that lots of people

00:28:10.180 | have just had a really bad relationship with maths,

00:28:12.340 | even successful people.

00:28:15.140 | The undergrads I teach at Stanford

00:28:17.540 | have pretty much always done well in maths,

00:28:20.100 | but they come to Stanford thinking maths

00:28:24.060 | is a set of methods to memorize.

00:28:27.020 | And so do many parents believe that.

00:28:31.460 | There's one method that you memorize

00:28:34.340 | and then you reproduce it.

00:28:36.900 | So until people have really had an experience

00:28:40.100 | of what I think of as the other maths,

00:28:42.300 | where until they've really seen

00:28:43.740 | that it's a really different subject,

00:28:45.580 | it's hard for them to be able to shift their kids

00:28:51.300 | to see it differently.

00:28:52.620 | - Is there for a teacher,

00:28:55.060 | if we're to like systematize it,

00:28:57.100 | is there something teachers can do

00:28:59.820 | to do this more effectively?

00:29:01.420 | So you mentioned the textbook.

00:29:04.060 | - Yeah.

00:29:04.900 | - So what are the additional things

00:29:07.220 | you can add on top of this whole old school,

00:29:09.980 | traditional way of teaching that can improve the process?

00:29:14.700 | - So I do think there's a way of teaching maths

00:29:17.540 | that changes everything for kids and teachers.

00:29:21.660 | So I'm one of five writers of a new framework

00:29:25.460 | for the state of California, a new maths framework.

00:29:27.580 | It's coming out next year.

00:29:29.220 | And we are recommending through this maths framework

00:29:32.220 | that people teach in this way.

00:29:33.900 | It's called teaching to big ideas.

00:29:37.540 | So at the moment, people have standards

00:29:42.540 | that have been written,

00:29:43.500 | and then textbooks have taken these standards

00:29:45.820 | and made not very good questions.

00:29:48.900 | And if you look at the standards,

00:29:50.500 | like I have some written down here,

00:29:53.060 | just reading the standards,

00:29:54.580 | it makes maths seem really boring and uninspiring.

00:29:57.780 | - What are the kind of, can you give a few examples?

00:30:00.980 | - So this is an interesting example.

00:30:03.220 | In third grade, there are three different standards

00:30:06.180 | about unit squares.

00:30:07.680 | - Okay.

00:30:11.660 | - So this is one of them.

00:30:12.660 | A square with side length one unit, called a unit square,

00:30:16.180 | is said to have one square unit of area

00:30:18.820 | and can be used to measure area.

00:30:20.580 | - And that's something you're expected to learn.

00:30:23.420 | - That is something, so that's a standard.

00:30:25.620 | The textbook authors say,

00:30:26.940 | oh, I'm gonna make a question about that.

00:30:28.460 | And they translate the standards into narrow questions.

00:30:32.180 | - And then you measure success

00:30:33.340 | by your ability to deliver on these standards.

00:30:36.940 | - So the standards themselves,

00:30:39.100 | I think of maths, and many people think of maths in this way,

00:30:41.820 | as a subject of a few big ideas

00:30:44.780 | and really important connections between them.

00:30:47.140 | So you could think of it as a network map

00:30:50.420 | of ideas and connections.

00:30:52.660 | And what standards do is they take that beautiful map

00:30:55.820 | and they chop it up like this into lots of little pieces,

00:30:58.780 | and they deliver the pieces to schools.

00:31:01.060 | And so teachers don't see the connections between ideas,

00:31:05.300 | nor do the kids.

00:31:06.500 | So anyway, this is a bit of a long way of saying

00:31:08.460 | that what we've done in this new initiative

00:31:11.900 | is we have set out maths as a set of big ideas

00:31:16.140 | and connections between them.

00:31:17.580 | So this is grade three.

00:31:20.900 | So instead of there being 60 standards,

00:31:25.180 | we've said, well, you can pull these different standards

00:31:29.700 | to get in with each other,

00:31:32.220 | and also value the ways these are connected.

00:31:37.220 | - And by the way, for people who are just listening,

00:31:39.860 | we're looking at a small number of big concepts

00:31:44.020 | within mathematics, square tiles,

00:31:46.420 | measuring fraction, shape, and time,

00:31:49.060 | and then how they're interconnected.

00:31:50.900 | And so the goal is for,

00:31:52.940 | this is for grade three, for example.

00:31:55.060 | - Yeah.

00:31:55.900 | And so we've set out for the state of California,

00:31:58.980 | the whole of mathematics K10

00:32:02.500 | as a set of big ideas and connections.

00:32:05.100 | So we know that teachers, it works really well

00:32:08.460 | if they say, okay, so a big idea in my grade is measuring.

00:32:13.460 | And instead of reading five procedural statements

00:32:19.140 | that involve measuring, they think,

00:32:21.460 | okay, measuring is a big idea.

00:32:22.540 | What rich, deep activity can I use

00:32:25.340 | that teaches measuring to kids?

00:32:27.860 | And as kids work on these deep, rich activities,

00:32:30.420 | maybe over a few days,

00:32:32.580 | turns out a lot of maths comes into it.

00:32:34.940 | So we're recommending that let's not teach maths

00:32:40.100 | according to all these multiple, multiple statements

00:32:43.380 | and lots and lots of short questions.

00:32:45.580 | Instead, let's teach maths by thinking about

00:32:48.060 | what are the big ideas and what are really rich,

00:32:51.020 | deep activities that teach those big ideas.

00:32:53.700 | - So that's the, like how you teach it

00:32:55.900 | and maximize learning.

00:32:57.580 | What about like from a school district perspective,

00:33:01.420 | like measuring how well you're doing,

00:33:04.620 | grades and tests and stuff like that?

00:33:06.980 | Do you throw those out or is it possible?

00:33:08.900 | - I'm not a fan of grades and tests myself.

00:33:13.460 | I think grades are fine

00:33:15.940 | if they're used at the end of a course.

00:33:18.980 | So at the end of my maths course,

00:33:21.020 | I might get a grade because a grade

00:33:22.820 | is meant to be a summative measure.

00:33:24.340 | It kind of describes your summative achievement.

00:33:27.660 | But the problem we have in maths classrooms across the US

00:33:31.260 | is people use grades all the time,

00:33:33.420 | every week or every day even.

00:33:36.340 | My own kids, when they went through high school,

00:33:38.540 | technology has not helped with this.

00:33:40.540 | When they went through high school,

00:33:41.780 | they knew they were being graded

00:33:42.820 | for everything they did, everything.

00:33:45.860 | And not only were they being graded for everything,

00:33:48.100 | but they could see it in the grade book online

00:33:50.380 | and it would alter every class they went into.

00:33:52.860 | So this is the ultimate,

00:33:54.900 | what I think of as a performance culture.

00:33:57.460 | You're there to perform, somebody's measuring you,

00:34:00.060 | you see your score.

00:34:01.820 | So I think that's not conducive for deep learning.

00:34:08.580 | And yes, have a grade at the end of the year,

00:34:10.940 | but during the year,

00:34:12.380 | you can assess kids in much better ways.

00:34:14.580 | Like teachers can, a great way of assessing kids

00:34:18.700 | is to give them a rubric that kind of outlines

00:34:22.060 | what they're learning over the course of a unit

00:34:23.980 | or a few weeks.

00:34:25.740 | So kids can actually see the journey they're on,

00:34:28.740 | like this is what we're doing mathematically.

00:34:31.100 | Sometimes they self-assess on those units.

00:34:34.340 | And then teachers will show what the kids can do

00:34:39.340 | with a rubric and also write notes.

00:34:42.140 | Like, in the next few weeks,

00:34:43.540 | you might like to learn to do this.

00:34:45.980 | So instead of kids just thinking about,

00:34:49.820 | I'm an A kid or a B kid,

00:34:51.140 | or I have this letter attached to me,

00:34:53.220 | they're actually seeing mathematically what's important.

00:34:56.940 | And they're involved in the process

00:34:58.620 | of knowing where they are mathematically.

00:35:02.340 | At the end of the year, sure, they can have a grade,

00:35:04.820 | but during the year,

00:35:06.260 | they get these much more informative measures.

00:35:09.220 | - I do think this might be more for college,

00:35:14.780 | but maybe not.

00:35:16.340 | Some of the best classes I've had

00:35:18.700 | is when I got a special set aside.

00:35:23.100 | The professor clearly saw that I was interested

00:35:27.900 | in some aspect of a thing.

00:35:29.900 | And then I have a few in mind,

00:35:33.260 | and one in particular,

00:35:34.900 | he said that he challenged me.

00:35:38.140 | So this is outside of grades and all that kind of stuff.

00:35:41.380 | That basically it's like reverse psychology.

00:35:44.940 | I don't think this can be done.

00:35:47.260 | And so I gave everything to do that particular thing.

00:35:50.980 | So this happened to be in an artificial intelligence class.

00:35:54.380 | But I think that special treatment of taking students

00:35:59.380 | who are especially excellent at a particular little aspect,

00:36:03.540 | that you see their eyes light up.

00:36:06.180 | I often think maybe it's tempting for a teacher

00:36:09.500 | to think you've already succeeded there,

00:36:11.740 | but they're actually signaling to you

00:36:13.460 | that you could really launch them on their way.

00:36:17.300 | And I don't know, that's too much to expect from teachers,

00:36:21.660 | I think, to pay attention to all of that,

00:36:24.940 | 'cause it's really difficult.

00:36:25.980 | But I just kind of remember who are the biggest,

00:36:30.040 | the most important people in the history

00:36:32.380 | of my life of education.

00:36:34.860 | And it's those people who really didn't just inspire me

00:36:38.900 | with their awesomeness, which they did,

00:36:40.420 | but also just, they pushed me a little.

00:36:43.180 | They gave me a little push.

00:36:45.220 | And that requires focusing on the quote unquote excellent

00:36:48.420 | students in the class.

00:36:51.060 | - I think what's important though,

00:36:52.540 | is teachers to have the perspective that they don't know

00:36:56.060 | who's gonna be excellent at something

00:36:58.460 | before they give out the activity.

00:37:00.340 | - Exactly.

00:37:01.180 | - And in our camp classes that we ran,

00:37:04.740 | sometimes students would finish ahead of other students.

00:37:10.420 | And we would say to them,

00:37:12.500 | "Can you write a question that's like this, but different?"

00:37:16.940 | Oh, and over time, we encouraged them

00:37:21.460 | to like extend things further.

00:37:24.780 | I remember we were doing one activity

00:37:26.820 | where kids were working out the borders of a square

00:37:30.180 | and how big this border would be in different case sizes.

00:37:33.540 | And one of the boys came up at the end of the class

00:37:36.300 | and said, "I've been thinking about how you do this

00:37:38.860 | "with the Pentagon."

00:37:40.460 | And I said, "That's fantastic.

00:37:42.140 | "How do you, what does it look like with Pentagon?

00:37:44.380 | "Go find out, see if you can discover."

00:37:47.220 | So I didn't know he was gonna come up and say that.

00:37:49.740 | And I didn't have in my head,

00:37:52.740 | like this is the kid who could have this extension task.

00:37:55.620 | But you can still do that as a teacher.

00:37:58.820 | When kids get excited about something

00:38:01.380 | or they're doing well in something,

00:38:03.220 | have them extend it, go further.

00:38:05.420 | It's great.

00:38:07.100 | - And then you also, like this is like teacher and coach,

00:38:10.500 | you could say it in different ways to different students.

00:38:13.940 | Like for me, the right thing to say is almost to say,

00:38:18.940 | I don't think you could do this, this is too hard.

00:38:21.340 | Like that's what I need to hear.

00:38:23.020 | 'Cause it's like, no, there's an immediate push.

00:38:26.340 | But with some people, if they're a little bit more,

00:38:29.220 | I mean, it all has to do with upbringing,

00:38:30.940 | just how your genetics is.

00:38:33.220 | They might be much more, that might break them.

00:38:35.380 | - Yeah, that might break them.

00:38:36.220 | - And so you have to be also sensitive to that.

00:38:38.380 | I mean, teaching is really difficult.

00:38:39.700 | - It is really difficult.

00:38:41.180 | - For this very reason.

00:38:42.220 | - It is.

00:38:43.260 | - So what is the best way to teach math,

00:38:47.780 | to learn math at those early few days

00:38:50.780 | when you just wanna capture them?

00:38:52.420 | - I do something, actually there's a video of me

00:38:56.340 | doing this on our website that I love

00:38:58.860 | when I first meet students.

00:39:03.180 | And this is what I do.

00:39:04.300 | I show them a picture, this is the picture I show them.

00:39:08.260 | And it's a picture of seven dots like this.

00:39:10.980 | And I show it for just a few seconds.

00:39:15.100 | And I say to them, I'd like you to tell me

00:39:16.740 | how many dots there are, but I don't need to count them.

00:39:19.140 | I want you to group the dots.

00:39:20.820 | And I show it them and then I take it away

00:39:24.140 | before they've even had enough time to count them.

00:39:27.060 | And then I ask them, so how did you see it?

00:39:29.780 | And I go around the room and amazingly enough,

00:39:34.780 | there's probably 18 different ways

00:39:36.980 | of seeing these seven dots.

00:39:38.340 | And so I ask people, tell me how you grouped it.

00:39:42.260 | And some people see it as like an outside hole

00:39:44.340 | with a center dot.

00:39:45.700 | Some people see like stripes of lines.

00:39:49.260 | Some people see segments.

00:39:51.780 | And I collect them all and I put them on the board.

00:39:53.780 | And at the end I say, look at this,

00:39:55.460 | we are a class of 30 kids and we saw these seven dots

00:39:58.460 | in 18 different ways.

00:40:00.300 | There's actually a mathematical term for this.

00:40:01.940 | It's called groupitizing.

00:40:03.780 | - Groupitizing?

00:40:04.780 | - Yeah.

00:40:05.620 | (laughing)

00:40:06.440 | - I like it.

00:40:07.280 | - It's kind of cool.

00:40:08.100 | So turns out though that how well you groupitize

00:40:11.900 | predicts how well you do in math.

00:40:14.660 | - Is it a raw talent or is it just something

00:40:18.980 | that you can develop?

00:40:19.820 | - I don't think you're born groupitizing, I think.

00:40:22.660 | But some kids have developed that ability if you like.

00:40:27.340 | And you can learn it.

00:40:28.260 | You can, so this to me is part of how wrong we have math.

00:40:33.260 | That we think to tell whether a kid's good at math,

00:40:36.660 | we're gonna give them a speed test on multiples.

00:40:40.660 | But actually, seeing how kids group dots

00:40:43.920 | could be a more important assessment

00:40:46.180 | of how well they're gonna do in math.

00:40:48.260 | Anyway, I diverge.

00:40:49.620 | What I like to do when I start off with kids is show them,

00:40:53.300 | I'm gonna give you math problems.

00:40:54.580 | I'm gonna value the different ways you see them.

00:40:57.100 | And turns out you can do this kind of problem

00:40:59.900 | asking people how they group dots with young children

00:41:03.100 | or with graduate students.

00:41:05.500 | And it's engaging for all of them.

00:41:08.220 | - You talk about creativity a little bit

00:41:12.180 | and flexibility in your book "Limitless".

00:41:15.180 | What's the role of that?

00:41:16.780 | So it sounds like there's a bit of that kind of thing

00:41:19.780 | involved in groupitizing.

00:41:22.700 | - Yeah, yeah.

00:41:24.620 | - I love this term.

00:41:25.700 | So what would you say is the role of creativity

00:41:28.580 | and flexibility in the learning of math?

00:41:31.340 | - I think what we know now is that what we need

00:41:34.820 | for this 21st century world we live in is a flexible mind.

00:41:39.820 | School should not really be about teaching kids

00:41:44.420 | particular methods, but teaching them to approach problems

00:41:47.980 | with flexibility.

00:41:49.500 | Being creative, thinking creatively is really important.

00:41:52.900 | So people don't think the words math and creativity

00:41:56.980 | come together, but that's what I love about math

00:42:00.260 | is the creative different ways you can see it.

00:42:02.900 | And so helping our kids, there's a book I like a lot

00:42:07.900 | by, I think by physicists.

00:42:10.980 | You probably know this book called "Elastic".

00:42:13.940 | You might know it.

00:42:14.860 | And it's about how we want elastic minds.

00:42:18.460 | Same kind of thing, flexible, creative minds.

00:42:21.500 | And schools do very little on developing that kind of mind.

00:42:26.500 | They do a lot of developing the kind of mind

00:42:31.780 | that a computer now does for us.

00:42:35.300 | - Memorization.

00:42:36.580 | - Memorization, doing procedures, a lot of things

00:42:41.580 | that we spend a lot of time in school on.

00:42:45.380 | In the world, when kids leave school,

00:42:47.540 | a computer will do that.

00:42:49.580 | And better than they will.

00:42:52.540 | But that creative, flexible thinking,

00:42:54.860 | we're kind of at ground zero at computers

00:42:57.140 | being able to engage in that thinking.

00:42:59.500 | Maybe we're a little above ground zero,

00:43:00.900 | but the human brain is perfectly suited

00:43:05.780 | for that creative, flexible thinking.

00:43:07.540 | That's what humans are so great at.

00:43:09.860 | So I would like the balance to shift in schools.

00:43:12.060 | Maybe you still need to do some procedural kind of thinking,

00:43:15.140 | but there should be a lot more

00:43:16.700 | of that creative, flexible thinking.

00:43:19.900 | - And what's the role of other humans in this picture?

00:43:23.940 | So collaborative learning, so brainstorming together.

00:43:28.940 | So creativity as it emerges

00:43:31.620 | from the collective intelligence of multiple humans.

00:43:34.500 | - Yeah, super important.

00:43:36.500 | And we know that also helps develop your brain,

00:43:40.580 | that social side of thinking.

00:43:42.300 | And I love mathematics collaboration

00:43:44.900 | where people build on each other's ideas

00:43:47.540 | and they come up with amazing things.

00:43:49.780 | I actually taught 100 students calculus

00:43:54.100 | at Stanford recently, undergrads.

00:43:56.900 | And we taught them to collaborate.

00:43:59.460 | So these students came in Stanford

00:44:01.300 | and most of them were against collaboration in math.

00:44:04.660 | - This is before COVID in person?

00:44:06.260 | - Yeah, it was just before COVID hit.

00:44:08.380 | It was 2019.

00:44:10.260 | And this summer--

00:44:12.100 | - Sorry, you said they're against?

00:44:13.780 | - Yeah, so it's really interesting.

00:44:16.780 | So they'd only experienced maths individually

00:44:20.220 | in a kind of competitive individual way.

00:44:22.140 | And if they had experienced it as group work,

00:44:24.700 | it had been a bad experience.

00:44:26.620 | Like maybe they were the one who did it all

00:44:28.860 | and the others didn't do much.

00:44:31.540 | So they were kind of against collaboration.

00:44:33.180 | They didn't see any role for it in maths.

00:44:35.140 | And we taught them to collaborate.

00:44:37.540 | And it was hard work because as well as the fact

00:44:42.180 | that they were kind of against collaboration,

00:44:43.580 | they came in with a lot of like social comparison thinking.

00:44:48.540 | So I'm in this room with other Stanford undergrads

00:44:51.500 | and they're better than me.

00:44:53.540 | So when we set them to work on a maths problem together,

00:44:55.820 | the first one was kind of a disaster

00:44:57.260 | because they were all like, they're better than me,

00:44:59.300 | they're faster than me.

00:45:00.540 | They came up with something I didn't come up with.

00:45:02.660 | So we taught them to let go of that thinking

00:45:05.980 | and to work well together.

00:45:08.620 | And one of the things we did,

00:45:10.020 | we decided we wanted to do a pre and post test

00:45:12.580 | at the end of this teaching.

00:45:13.540 | It was only four weeks long,

00:45:15.780 | but we knew we didn't want to give them

00:45:17.220 | like a time test of individual work.

00:45:19.340 | So we gave them an applied problem to do at the beginning

00:45:23.740 | and we gave them to do in pairs together.

00:45:26.220 | And we gave each of them a different colored pen

00:45:28.620 | and said, work on this activity together

00:45:31.060 | and keep using that pen.

00:45:33.060 | So then we had all these pieces of student work.

00:45:35.180 | And what we saw was they just worked

00:45:37.580 | on separate parts of the paper.

00:45:39.220 | So there's a little like red pen section

00:45:42.060 | and a green pen section.

00:45:43.740 | And they didn't do that well on it,

00:45:45.940 | even though it was a problem

00:45:48.100 | that middle or high school kids could do,

00:45:49.820 | but it was like a problem solving kind of problem.

00:45:52.740 | And then we gave them the same one to do at the end,

00:45:55.060 | gave them the same colors

00:45:56.220 | and actually they had learned to collaborate.

00:45:59.220 | And not only were they collaborating the second time around,

00:46:02.140 | but that boosted their achievement.

00:46:04.060 | And the ones who collaborated did better on the problem.

00:46:07.900 | Collaboration is important, having people,

00:46:10.260 | and what was so eye opening for these undergrads

00:46:12.540 | and they talked about it in lovely ways

00:46:15.380 | was I learned to value other people's thinking on a problem.

00:46:19.980 | And I learned to value

00:46:21.540 | that other people saw it in different ways.

00:46:24.340 | And it was quite a big experience for them

00:46:29.340 | that they came out thinking,

00:46:31.700 | I can do maths with other people,

00:46:33.660 | people can see it differently,

00:46:34.860 | we can build on each other's ways of thinking.

00:46:38.340 | - I got a chance to,

00:46:39.540 | I don't know if you know who Daniel Kahneman is,

00:46:42.020 | got a chance to interact with him.

00:46:44.100 | And like the first, 'cause he had a few,

00:46:46.900 | but one famous collaboration throughout his life

00:46:50.500 | with Tversky and just like,

00:46:55.940 | he hasn't met me before in person,

00:46:58.540 | but just the number of questions he was asking,

00:47:01.300 | just the curiosity.

00:47:03.140 | So I think one of the skills,

00:47:05.420 | the collaboration itself is a skill.

00:47:07.980 | And I remember my experience with him was like,

00:47:10.780 | okay, I get why you're so good at collaboration

00:47:14.020 | because he was just extremely good at listening

00:47:17.460 | and genuine curiosity about how the other person

00:47:21.420 | thinks about the world, sees the world.

00:47:23.380 | And then together, he pulled me in,

00:47:25.940 | in that particular case,

00:47:27.460 | he doesn't know in particular

00:47:29.340 | like that much about autonomous vehicles,

00:47:31.180 | but he kept like asking all of these questions.

00:47:34.540 | And then like 10 minutes in,

00:47:36.380 | we're together trying to solve the problem

00:47:38.100 | of autonomous driving.

00:47:39.900 | And like, and that, I mean, that's really fulfilling,

00:47:43.100 | that's really enriching,

00:47:43.940 | but it also in that moment made me realize

00:47:46.700 | it's kind of a skill

00:47:48.180 | is you have to kind of put your ego aside,

00:47:50.740 | put your view of the world aside

00:47:52.500 | and try to learn how the other person sees it.

00:47:55.780 | - And the other thing you have to put aside

00:47:57.580 | is this social comparison thinking.

00:48:00.660 | Like if you are sitting there thinking,

00:48:03.300 | wow, that was an amazing idea,

00:48:04.860 | he's so much better than I am,

00:48:06.660 | that's really gonna stop you

00:48:09.180 | taking on the value of that idea.

00:48:11.500 | So there's a lot of that going on

00:48:14.300 | between these Stanford students when they came.

00:48:16.660 | And trying to help them let go of that.

00:48:21.980 | - One of the things I've discovered

00:48:24.300 | just because being a little bit more in the public eye,

00:48:27.380 | how rewarding it is to celebrate others.

00:48:31.300 | And how much is going to actually pay off in the long term.

00:48:35.820 | So this kind of silo thinking of like,

00:48:38.220 | I want to prove to a small set of people around me

00:48:41.260 | that I'm really smart

00:48:43.220 | and do so by basically not celebrating

00:48:47.500 | how smart the other people are,

00:48:48.820 | that's actually maybe short term,

00:48:51.580 | it seems like a good strategy, but longterm it's not.

00:48:54.580 | And I think if you practice at the student level

00:48:56.500 | and then at the career level, at every single stage,

00:48:58.900 | I think that's ultimately--

00:49:00.540 | - I agree with you,

00:49:01.380 | I think that's a really good way of thinking about it.

00:49:04.460 | - You mentioned textbooks.

00:49:06.020 | And you didn't say it,

00:49:08.300 | maybe textbooks isn't the perfect way to teach mathematics.

00:49:15.460 | But I love textbooks.

00:49:17.340 | They're like pretty pictures and they smell nice.

00:49:19.940 | I mean, I talk about like physical,

00:49:21.700 | some of my greatest experiences have been just like,

00:49:24.340 | 'cause they're really well done.

00:49:27.340 | When we're talking about basic,

00:49:28.580 | like high school, calculus, biology, chemistry,

00:49:33.580 | those are incredible.

00:49:36.900 | It's like Wikipedia, but with color and nice little--

00:49:40.340 | - You must have seen some good textbooks

00:49:42.020 | if they had pretty pictures and color.

00:49:44.580 | - Yeah, I mean, I remember,

00:49:46.260 | I guess it was very, very standard,

00:49:49.260 | like AP calculus, AP biology, AP chemistry.

00:49:53.540 | I felt those are like some of the happiest days of my life

00:49:56.140 | in terms of learning was high school.

00:49:58.100 | 'Cause it was very easy, honestly.

00:50:00.780 | It felt hard at the time,

00:50:03.300 | but you're basically doing a whirlwind tour

00:50:07.140 | of all the science.

00:50:08.540 | Without having to pick, you do literature,

00:50:12.220 | you do like Shakespeare, calculus, biology, physics,

00:50:16.740 | chemistry, what else?

00:50:19.100 | Anatomy, physiology, computer science,

00:50:23.580 | without like nobody's telling you what to do with your life.

00:50:26.780 | You're just doing all of those things.

00:50:28.060 | - That's a good thing, you're right.

00:50:29.700 | - But I remember the textbooks weren't,

00:50:32.460 | I mean, maybe I'm romanticizing the past,

00:50:35.420 | but I remember they weren't, they're pretty good.

00:50:38.660 | But so you think, what role do you think they play still?

00:50:42.020 | And like in this more modern digital age,

00:50:45.500 | what's the best materials

00:50:47.740 | with which to do these kinds of educations?

00:50:50.100 | - Well, I'm intrigued that you had such a good experience

00:50:52.860 | with textbooks.

00:50:53.700 | I mean, I can remember loving some textbooks

00:50:56.820 | I had when I was learning and I love books.

00:50:59.540 | I love to pick up books and look through them.

00:51:03.140 | But a lot of math textbooks

00:51:06.580 | are not good experiences for kids.

00:51:08.940 | We have a video on our website

00:51:12.940 | of the kids who came to our camp

00:51:14.140 | and one of the students says,

00:51:15.660 | "In maths, you have to follow the textbook.

00:51:18.780 | "The textbook's kind of like the Bible.

00:51:20.500 | "You have to follow it."

00:51:22.460 | And every day, it's slightly different.

00:51:25.940 | Like on Monday, you do 2.3.2

00:51:28.820 | and on Tuesday, you do 2.3.3 and on Wednesday.

00:51:32.500 | And you never go off that.

00:51:35.100 | That's like every single day.

00:51:37.860 | And that's not inspiring for a lot of the kids.

00:51:42.540 | So one of the things they loved about our camp

00:51:45.420 | was just that there were no books.

00:51:46.860 | Even though we gave them sheets of paper instead,

00:51:50.700 | they still felt more free

00:51:53.020 | because they weren't just like trotting through exercises.

00:51:57.580 | - Like what a textbook allows you is like,

00:52:02.060 | the very thing you said they might not like,

00:52:06.660 | the 2.3, 2.3, it feels like you're making progress

00:52:11.100 | and like it's a little celebration

00:52:12.740 | 'cause you do the problem and it seems really hard

00:52:16.180 | and you don't know how to do it.

00:52:17.300 | And then you try and try and then eventually succeed.

00:52:20.940 | And then you make that little step and further progress.

00:52:23.620 | And then you get to the end of a chapter

00:52:26.180 | and you get to like, it's closure.

00:52:28.020 | You're like, "All right, I got that figured out."

00:52:29.860 | And then you go on to the next chapter.

00:52:31.340 | - I can see that.

00:52:32.260 | I mean, I think it could be in a textbook.

00:52:34.900 | You can have a good experience with a textbook,

00:52:38.980 | but what's really important is what is in that textbook?

00:52:43.180 | What are you doing inside it?

00:52:45.300 | And I mean, I grew up in England and in England,

00:52:49.300 | we learn maths.

00:52:50.460 | We don't have this separation of algebra and geometry.

00:52:54.380 | And I don't think any other country

00:52:56.140 | apart from the US has that.

00:52:58.220 | But I look at kids in algebra classes

00:53:01.220 | where they're doing algebra for a year.

00:53:02.740 | And I think I would have been pretty bored doing that.

00:53:05.860 | (laughing)

00:53:08.420 | - By the way, can we analyze your upbringing real quick?

00:53:13.060 | Why do British folks call mathematics maths?

00:53:18.060 | Why is it the plural?

00:53:21.580 | Is it because of everything you're saying

00:53:23.100 | or is it a bunch of sub-disciplines?

00:53:25.180 | - Yeah, I mean, mathematics is supposed to be

00:53:29.820 | the different maths that you look at,

00:53:34.820 | whether you think of that as topics

00:53:38.020 | like geometry and probability,

00:53:39.940 | or I think of it as maths is just multi-dimensional,

00:53:44.940 | lots of ways, but that's why it was called mathematics.

00:53:48.700 | And then it was shortened to maths.

00:53:50.500 | And then for some reason, it was just math in the US,

00:53:53.340 | but to me, math has that more singular feel to it.

00:53:58.340 | And there's an expression here, which is do the math,

00:54:02.860 | which basically means do a calculation.

00:54:05.220 | That's what people mean by do the math.

00:54:07.500 | So I don't like that expression

00:54:09.380 | 'cause math could be anything.

00:54:11.260 | It doesn't have to be calculation.

00:54:13.540 | So yeah, I like maths

00:54:14.620 | 'cause it has more of that broad feel to it.

00:54:17.340 | - Yeah, I love that.

00:54:18.180 | Maths kind of emphasizes the multi-dimensional,

00:54:20.020 | like a variety of different sub-disciplines,

00:54:22.900 | different approaches, yeah.

00:54:24.340 | Okay, but outside of the textbook,

00:54:28.700 | what do you see broadly being used?

00:54:33.700 | You mentioned Sebastian Thrun and MOOCs, online education.

00:54:37.940 | Do you think that's an effective set of-

00:54:39.460 | - Can be.

00:54:40.980 | I mean, online, having great teachers online

00:54:45.100 | obviously extends those teachers to many more people,

00:54:48.140 | and that's a wonderful thing.

00:54:49.820 | I have quite a few online courses myself.

00:54:54.300 | I got the bug working with Sebastian

00:54:56.300 | when he had released his first MOOC.

00:54:59.820 | And I thought, hmm, maybe I could do one in maths education.

00:55:03.500 | And I didn't know if anybody would take it.

00:55:06.460 | And I remember releasing it that first summer,

00:55:08.460 | and it was a free online class,

00:55:09.940 | and 30,000 maths teachers took it that first summer.

00:55:13.820 | And they were all talking about it with each other

00:55:16.060 | and sharing it, and it was like, took off.

00:55:18.060 | In fact, it was that MOOC that got me to create Ucubed

00:55:23.060 | with Kathy Williams, who's the co-founder,

00:55:27.060 | because people took the MOOC,

00:55:29.580 | and then they said, "Okay, what now?

00:55:32.500 | "I finished, what can I have next?"

00:55:35.380 | So that was where we made our website.

00:55:36.860 | But so yeah, I think online education can be great.

00:55:40.620 | I do think a lot of the MOOCs don't have great pedagogy.

00:55:45.460 | They're just a talking head.

00:55:47.540 | And you can actually engage people in more active ways,

00:55:52.540 | even in online learning.

00:55:54.860 | So I learned from the Udacity principle

00:55:57.740 | when I was working at Udacity

00:55:59.140 | never to talk more than like five minutes,

00:56:01.580 | and then to ask people to do something.

00:56:05.740 | So that's the sort of pedagogy of the online classes I have,

00:56:09.740 | is a little bit of presenting something,

00:56:12.420 | and then people do something,

00:56:13.540 | and then there's a little bit more.

00:56:15.100 | Because I think if you have a half hour video,

00:56:17.180 | you just switch off and start doing other things.

00:56:20.940 | - So the way Udacity did it is like five, 10 minute,

00:56:24.740 | like bit of teaching with some visual stuff, perhaps,

00:56:29.700 | and then there's like a quiz almost.

00:56:31.100 | - Then you answer a question, yeah.

00:56:32.380 | - Yeah, that's really effective.

00:56:35.980 | You mentioned Ucubed.

00:56:37.060 | So what's the mission, what's the goal?

00:56:38.780 | You mentioned how it started, but what's,

00:56:40.980 | yeah, where are you at now, and what's your dream with it?

00:56:46.580 | Or what are the kind of things

00:56:48.260 | that people should go and check out on there?

00:56:50.460 | - Yeah, we started Ucubed,

00:56:52.420 | I guess it was about five years ago now,

00:56:54.140 | and we've had over 52 million visitors to the site,

00:56:57.340 | so I'm very happy about that.

00:56:59.420 | And our goal is to share good ideas for teaching

00:57:03.860 | with teachers, students, parents in maths,

00:57:08.020 | and to help, we have a sort of sub-goal

00:57:10.660 | of a raising maths anxiety, that's important to us,

00:57:13.260 | but also to share maths as this beautiful creative subject.

00:57:17.900 | And it's been really great.

00:57:21.420 | We have lessons on the site,

00:57:23.860 | but one of the reasons I thought this was needed

00:57:26.980 | is there's a lot of knowledge in the academy

00:57:29.620 | about how to teach maths well.

00:57:31.180 | Loads and loads of research and journals

00:57:34.460 | and lots of things written up, but teachers don't read it.

00:57:38.380 | They don't have access to it.

00:57:41.140 | They're often behind pay walls.

00:57:43.260 | They're written in really inaccessible ways,

00:57:46.500 | so people wouldn't want to read them or understand them.

00:57:49.300 | So this I see as a big problem.

00:57:51.180 | You have this whole industry of people

00:57:53.780 | finding out how to teach well,

00:57:55.740 | not sharing it with the people who are teaching.

00:57:58.780 | So that's why we made U-Cubed.

00:58:01.420 | And instead of just putting articles up saying,

00:58:03.660 | here's some things to read about how to teach well,

00:58:05.780 | we translated what was coming from research

00:58:08.220 | into things that teacher could use.

00:58:10.500 | So lessons, there were videos to show kids,

00:58:13.580 | and there were tips for parents.

00:58:16.420 | There were all sorts of things on the site.

00:58:17.980 | And it's been amazing.

00:58:20.260 | We took inspiration from the Week of Code,

00:58:24.860 | which got teachers to focus on coding for a week.

00:58:29.540 | And we have this thing called

00:58:31.380 | the Week of Inspirational Maths.

00:58:33.900 | And we say, just try it for a week.

00:58:35.820 | Just give us one week and try it and see what happens.

00:58:39.380 | And so it's been downloaded millions of times.

00:58:42.660 | Teachers use it every year.

00:58:44.580 | They start the school year with it.

00:58:46.540 | And what they tell us is, it was amazing.

00:58:49.660 | The kids' lights were on.

00:58:50.740 | They were excited.

00:58:51.780 | They loved it.

00:58:52.980 | And then the week finished, and I opened my textbooks,

00:58:56.020 | and the lights went out, and they were not interested.

00:59:00.020 | - Yeah, but getting that first inspiration

00:59:02.780 | is still powerful.

00:59:04.140 | - It is.

00:59:04.980 | I wish, I mean, what I would love

00:59:07.700 | is if we could actually extend that for the whole year.

00:59:11.620 | We're a small team at Stanford,

00:59:13.980 | and we're trying to keep up with great things

00:59:17.020 | to put on the site.

00:59:19.660 | We haven't the capacity to produce

00:59:22.500 | these creative visual math tasks

00:59:24.180 | for every year group for every day,

00:59:25.820 | but I would love to do that.

00:59:27.140 | - How difficult is it to do?

00:59:28.580 | I mean, to come up

00:59:30.420 | with visual formulations of these big, important topics

00:59:37.420 | you need to think about in a way that you could teach.

00:59:42.420 | - I mean, we can do it.

00:59:44.780 | We actually, we went from the Week of Inspirational Maths,

00:59:47.420 | and we made K-8 maths books with exactly that.

00:59:51.980 | Big ideas, rich activities, visuals.

00:59:54.940 | We just finished the last one.

00:59:56.580 | We've been doing it for five years,

00:59:58.980 | and it's been exhausting, and we just finished.

01:00:01.660 | So now there's a whole K-8 set of books,

01:00:05.580 | and they're organized in that way.

01:00:07.140 | These are the big ideas, here are rich, deep activities.

01:00:10.280 | They're not, though, what you can do every day for a year.

01:00:16.060 | So some teachers use them as a kind of supplement

01:00:19.060 | to their boring textbook, and some people have said,

01:00:22.940 | "Okay, this is the year.

01:00:24.340 | "This book tells us what the year is,

01:00:26.420 | "and then we'll supplement these big activities with."

01:00:29.260 | So they're being used, and teachers really like them

01:00:34.440 | and are really happy about them.

01:00:36.240 | I just always want more.

01:00:37.500 | And I guess one of the things I would like for U-Cubed,

01:00:40.280 | one of my personal goals, is that every teacher of maths

01:00:43.660 | knows about U-Cubed.

01:00:45.500 | At the moment, lots of teachers who come to us

01:00:48.500 | are really happy they found it,

01:00:49.800 | but there's a lot of other teachers

01:00:51.220 | who don't know that it exists.

01:00:53.700 | - I hope this helps.

01:00:54.940 | - Yeah.

01:00:55.980 | - From a student perspective, and not in the classroom,

01:00:59.460 | but at home, studying,

01:01:01.560 | is there some advice you can give

01:01:07.380 | on how to best study mathematics?

01:01:09.820 | So what's the role of the student outside the classroom?

01:01:13.760 | - Yeah, I think one thing we know is a lot of people,

01:01:17.560 | when they review material,

01:01:19.700 | whether it's maths or anything else,

01:01:21.340 | don't do it in the best way.

01:01:23.680 | I think a problem a lot of people have

01:01:25.840 | is they read through maybe a teacher's explanation

01:01:29.000 | or a way of doing maths, and it makes sense.

01:01:32.840 | And they think, "Oh yeah, I've got that," and they move on.

01:01:36.360 | But then it's not until you come to try and work on something

01:01:39.880 | and do a problem that you actually realize

01:01:41.320 | you didn't really understand it,

01:01:42.600 | it just seemed to make sense.

01:01:44.840 | So I would say this is also something

01:01:48.520 | that neuroscientists talk about,

01:01:50.680 | to keep giving yourself questions

01:01:53.500 | is a really good way to study,

01:01:56.640 | rather than looking through lots of material.

01:01:59.440 | It's almost like giving yourself lots of tests

01:02:02.560 | is a good way to actually deeply understand things

01:02:05.480 | and know what you do when you don't understand.

01:02:07.680 | - So would the questions be in the form of the material

01:02:12.240 | you're reviewing is the answer to that question,

01:02:14.520 | or is it almost like beyond,

01:02:16.080 | it's the polygon thing that you mentioned,

01:02:18.160 | or square, is it almost like,

01:02:19.960 | "I wonder what is the bigger picture?"

01:02:22.800 | Always kind of asking, "How is this extended?"

01:02:25.760 | And so on.

01:02:26.600 | - Yeah, that would be great.

01:02:28.720 | And it's a similar, I mean,

01:02:30.480 | a question I get asked a lot is about homework,

01:02:32.520 | what is a good thing for kids to do for homework.

01:02:35.000 | And one of the recommendations I give

01:02:37.000 | is to not have kids just do lots of questions for homework,

01:02:42.840 | but to actually ask them to reflect on what they've learned,

01:02:46.080 | like, "What was the big idea you learned today?"

01:02:49.720 | Or, "What did you find difficult?

01:02:51.880 | "What did you struggle with?

01:02:53.420 | "What was something that was exciting?"

01:02:56.580 | Then kids go home and they have to kind of reflect

01:03:01.120 | in a deeper way.

01:03:02.440 | A lot of times, I don't know if you have this experience

01:03:04.520 | as a math student, lots of people do,

01:03:06.640 | kids are going through math questions,

01:03:08.800 | they're successful, they get them right,

01:03:10.920 | but they don't even really know what they're about.

01:03:13.960 | And a lot of kids go through many years of math like that,

01:03:17.160 | doing lots of questions,

01:03:18.200 | but not really knowing what even the topic is

01:03:21.940 | or what it's about, what it's important for.

01:03:24.400 | So having students go back and think at the end of the day,

01:03:28.680 | "What was the big idea from this math lesson?

01:03:31.560 | "Why is it important?

01:03:33.260 | "Where would I find that in real life?"

01:03:36.040 | Those are really good questions

01:03:37.920 | for kids to be thinking about.

01:03:39.920 | - It's probably for everybody to be thinking about.

01:03:42.400 | I think most of us go through life

01:03:44.320 | never asking the bigger question.

01:03:48.160 | Almost like those layers of why questions

01:03:51.600 | that kids ask when they're very young.

01:03:53.920 | We need to keep doing that.

01:03:55.960 | - We do.

01:03:56.800 | - Like what, that's the, whatever the term is,

01:03:59.680 | you call first principles thinking,

01:04:01.400 | some people call it that,

01:04:03.320 | which is like, why are we doing it this way?

01:04:08.560 | - But one nice thing is to do that

01:04:11.760 | 'cause there's usually a good answer.

01:04:13.080 | Like the reason we did it this way

01:04:15.360 | is because it works for this reason.

01:04:17.760 | But then if you want to do something totally novel,

01:04:20.640 | is you'll say, "Well, we've been doing it this way

01:04:24.160 | "because of historical reasons,

01:04:28.520 | "but really this is not the best way to do it.

01:04:30.440 | "There might be other ways."

01:04:32.240 | And that's how invention happens.

01:04:34.440 | And then you get, that's really useful

01:04:36.480 | in every aspect of life.

01:04:38.320 | Like choosing your career, choosing your,

01:04:42.400 | I don't know, where you live,

01:04:44.840 | who your romantic partner is,

01:04:46.920 | like everything. - Everything, yeah.

01:04:48.960 | - And I think it probably starts doing that in math class.

01:04:53.200 | - That would be good if we started doing that.

01:04:55.840 | - I mean, I wonder,

01:04:57.440 | I probably didn't do very much of that

01:05:01.000 | for most of my education, asking why,

01:05:03.760 | except for later, much later,

01:05:07.240 | in the subjects on like grad school

01:05:09.600 | when you're doing research on them.

01:05:12.280 | When your first task of doing something novel using this

01:05:16.680 | or solving a problem really outside the classroom,

01:05:20.000 | they have to publish on it.

01:05:20.840 | It's the first time you think,

01:05:22.520 | "Wait, why are these things interesting, useful?

01:05:27.000 | "Which are the things that are useful?"

01:05:29.480 | And yeah, I guess that would be nice

01:05:31.680 | if we did that much earlier,

01:05:32.880 | that the quest of invention.

01:05:35.280 | - Yeah, yeah.

01:05:37.000 | I mean, one of the sad pieces of research data I think about

01:05:40.280 | is the questions kids ask in school goes down

01:05:45.280 | like in a linear progression from in the early years,

01:05:50.840 | you can't stop kids asking those questions,

01:05:53.840 | but they learn not to ask the questions.

01:05:56.760 | - I think you told somewhere about an early memory you had

01:06:00.520 | in your own education where you asked the question,

01:06:04.720 | or maybe that was an example you gave,

01:06:06.320 | but it was shut down.

01:06:07.480 | - Oh yeah.

01:06:08.920 | You've listened to something I said, yeah.

01:06:11.080 | (laughing)

01:06:12.160 | - I don't remember where it was, but it caught me.

01:06:15.240 | - Yeah, I remember it really vividly.

01:06:17.720 | - Well, can you tell the memory?

01:06:19.880 | - Yeah, it's funny, I can remember.

01:06:21.840 | It must have really impacted me in that moment

01:06:24.000 | because you know how there's lots of hours of school

01:06:26.360 | you don't remember at all.

01:06:27.280 | But anyway, I can remember where I was sitting

01:06:30.280 | and everything.

01:06:31.120 | I was in a high school maths class,

01:06:33.400 | although they don't call it that in England,

01:06:35.320 | and the teacher said, and it was like the first class

01:06:40.320 | of this teacher's class, and he said,

01:06:42.440 | "Ask if you have any questions."

01:06:44.440 | So at one point I put my hand up and I said,

01:06:46.800 | "I have a question."

01:06:48.260 | And he said something like, "That's your question?"

01:06:50.760 | (laughing)

01:06:53.880 | And I was like, "Okay, I'm not asking any more questions

01:06:56.840 | "in this class."

01:06:57.680 | - And that hit hard in a way where you didn't wanna,

01:07:00.000 | the lesson you learned from that is I'm not gonna ask

01:07:02.120 | that question. - Yeah, that was absolutely

01:07:03.360 | that's the last question I'm asking.

01:07:06.360 | And that was, yeah, he was the chair of the maths department

01:07:11.360 | and I remember that really well.

01:07:13.760 | So maybe because of that experience,

01:07:18.120 | one of the things we encourage when we teach kids

01:07:20.440 | is asking questions and we value it when they ask questions

01:07:23.040 | and we put them up on walls and celebrate.

01:07:25.720 | - It's funny 'cause I wish there was a feedback signal

01:07:31.400 | because he probably, to put a positive spin on it,

01:07:35.080 | he probably didn't realize the negative impact

01:07:37.480 | he's had in that moment, right?

01:07:38.760 | If he only knew.

01:07:40.280 | See, this is probably when you're more mature in grad school.

01:07:44.160 | Had an amazing professor named Alicia Kafande

01:07:47.000 | in computer science and he would get,

01:07:50.000 | he encouraged questions, but then he would tell everybody

01:07:52.480 | how dumb their questions are.

01:07:54.320 | But it was, I guess if you show,

01:07:57.400 | if you say it with love and respect behind it,

01:08:00.800 | then it's more like a friendly, humorous encouragement

01:08:03.720 | for more questions.

01:08:05.120 | It's an art, right?

01:08:06.360 | - Yeah, teaching is very hard.

01:08:09.080 | - You have to time it right because that kind of humor

01:08:12.360 | is probably better for when you're in grad school

01:08:15.480 | versus when you're in early education.

01:08:18.040 | - Right, well, and I guess kids or young people

01:08:21.880 | get whether somebody's doing it to be funny or has it.

01:08:29.360 | I mean, this is why teaching is so hard.

01:08:31.200 | Even your tone can be impactful.

01:08:35.160 | - It's so sad because like for that particular human,

01:08:39.720 | the teacher, you could have just had a bad day

01:08:42.840 | and one statement can have a profound negative impact.

01:08:45.960 | - I know, sadly, that maths, there's a lot of maths teachers

01:08:50.160 | who have that kind of approach and they,

01:08:52.880 | I think they're suffering from the fact

01:08:56.040 | that they think people are math people, not math people.

01:08:58.240 | And that comes across in their teaching.

01:09:01.080 | - But on the flip side, one positive statement

01:09:03.800 | to keep them going.

01:09:04.760 | - That's right, that is the flip side of that.

01:09:07.280 | And I myself had like one teacher

01:09:09.960 | who was really amazing for me in maths

01:09:12.640 | and she kept me in the subject.

01:09:14.320 | - Who was she?

01:09:17.200 | - She was, her name was Mrs. Marshall.

01:09:20.900 | She was my A-level maths teacher.

01:09:27.680 | So I was in England. - What's that mean?

01:09:30.120 | - You do lots of subjects until you're 16

01:09:32.080 | and then you choose like three or four subjects.

01:09:35.360 | So I had chosen maths and you go to--

01:09:39.680 | - Higher levels.

01:09:41.480 | - Probably equivalent more to a master's degree in the US

01:09:44.680 | 'cause you're more specialized.

01:09:46.200 | But anyways, she was my teacher.

01:09:48.760 | And for the first time in my whole career in maths,

01:09:52.720 | she would give us problems

01:09:54.360 | and then tell us to talk about them with each other.

01:09:58.040 | And so here I was sitting there at like 17

01:10:01.040 | talking with friends about how to solve a math problem.

01:10:04.040 | And that was it, that was the change that she made.

01:10:07.840 | But it was profound for me

01:10:10.040 | because like those calculus students,

01:10:13.400 | I started to hear other people's ways of thinking

01:10:16.220 | and seeing it and we would talk together

01:10:17.960 | and come up with solutions.

01:10:19.920 | And I was like, that was it, that changed maths for me.

01:10:22.560 | - And so it wasn't some kind of personal interaction

01:10:25.080 | with her, it was more like she was the catalyst

01:10:29.240 | for that collaborative experience.

01:10:32.040 | - I mean, yeah, the many ways teachers can inspire kids.

01:10:34.960 | I mean, sometimes it's a personal message

01:10:36.920 | but it can be your teaching approach

01:10:39.840 | that changes maths for kids.

01:10:42.440 | - You know, Cal Newport, he wrote a book called "Deep Work"

01:10:47.440 | and he's a mathematician,

01:10:50.000 | theoretical computer scientist.

01:10:51.480 | And he talks about the kind of the focus required

01:10:55.720 | to do that kind of work.

01:10:57.140 | Is there something you can comment on?

01:11:01.760 | You know, we live in a world full of distractions.

01:11:04.960 | That seems like one of the elements that makes studying

01:11:08.400 | and especially the studying of subjects

01:11:10.280 | that require thinking like math does difficult.

01:11:14.500 | Is there something from a student perspective,

01:11:17.440 | from a teacher perspective that encourages deep work

01:11:20.640 | that you can comment on?

01:11:21.480 | - Yeah, I think giving kids really inspiring deep problems

01:11:26.480 | and we have some on our website,

01:11:31.440 | is a really important experience for them.

01:11:33.920 | Even if they only do it occasionally,

01:11:38.180 | but it's really important.

01:11:40.080 | They actually realize, I give a problem out often

01:11:44.320 | when I'm working with teachers and I say to them,

01:11:47.040 | all right, I'm gonna check in with you after an hour.

01:11:49.760 | And they're like, an hour?

01:11:51.480 | They think it's shocking.

01:11:53.520 | And then they work on this problem and after an hour,

01:11:56.160 | I say, okay, how are we doing?

01:11:57.880 | They're like, an hour has gone by?

01:11:59.560 | How is this possible?

01:12:02.000 | And so everybody needs those like rich, deep problems.

01:12:07.000 | Most kids go through their whole maths experience

01:12:11.960 | of however many years never once working on a problem

01:12:16.080 | in that kind of deep way.

01:12:18.000 | So the undergrad class I teach at Stanford, we do that.

01:12:22.720 | We work on these deep problems every session

01:12:26.320 | and the students come away going,

01:12:28.040 | okay, I never wanna go back to that maths relationship

01:12:31.040 | I had where it was just all about quick answers.

01:12:32.920 | I just don't wanna go back to that.

01:12:35.640 | And so we can all, all teachers can incorporate

01:12:40.640 | those problems in their classrooms.

01:12:42.320 | Maybe they don't do them every day,

01:12:43.600 | but they at least give kids some experience

01:12:47.240 | of being able to work slowly and deeply

01:12:50.840 | and to go to deeper places and not be told

01:12:55.840 | they've got five minutes to finish 20 questions.

01:12:59.680 | - But part of it is also just the exercise

01:13:03.800 | of sitting there and maintaining focus

01:13:05.320 | for prolonged periods of time.

01:13:07.040 | That's not often, I mean, that's a skill.

01:13:11.960 | It's a skill that also could be discouraging.

01:13:16.000 | Like if you don't practice it,

01:13:18.120 | just sitting down for 10 minutes straight

01:13:20.520 | and maintaining deep focus could be exceptionally challenging

01:13:23.480 | like if you're really thinking about a problem.

01:13:26.600 | And I think it's really important to realize

01:13:29.240 | that that's a skill that you can just like a muscle,

01:13:31.920 | you can build, you can start with five minutes

01:13:33.560 | and it goes to 10 minutes to 30 and to an hour.

01:13:36.760 | And to be successful, I think in certain subjects

01:13:39.040 | like mathematics, you wanna be able to develop that skill.

01:13:42.560 | Otherwise, you're not going to get

01:13:46.680 | to the really rewarding experience

01:13:49.720 | of solving these problems.

01:13:51.360 | - Definitely.

01:13:53.600 | There was a survey done of kids in school

01:13:55.960 | where they were asked,

01:13:56.800 | how long will you work on a math problem

01:13:58.360 | before you give up and decide it's not possible to solve it?

01:14:02.520 | And the result on average across the kids was two minutes.

01:14:11.320 | - Yeah, that's a bad sign,

01:14:13.440 | but that was a powerful sign that they need to learn

01:14:17.520 | to not give up so quickly.

01:14:19.040 | We mentioned offline because we've been talking so much

01:14:24.360 | about visualization, Grant Sanderson, 3Luwan Brown.

01:14:29.240 | So he's inspired millions of people

01:14:32.080 | with exactly the kind of way of thinking

01:14:35.520 | that you've been talking about.

01:14:36.680 | - Yeah, I love his work.

01:14:39.000 | - Converting sort of mathematical concepts into visual,

01:14:44.000 | like visually representing them, exploring them in ways

01:14:49.520 | that help you illuminate like the concepts.

01:14:52.160 | What do you think is the role of that?

01:14:55.040 | So he uses mostly programmatic visualization.

01:14:58.000 | So it's the thing I mentioned where there's like animations

01:15:01.280 | created by writing computer programs.

01:15:04.500 | Like, what do you think, how scalable is that approach?

01:15:08.400 | But in general, what do you think about his approach?

01:15:10.440 | - I think it's amazing.

01:15:11.880 | I should work with him.

01:15:13.180 | I can share some of our visuals

01:15:17.000 | and he can make them in that amazing way.

01:15:19.580 | - So part of his storytelling,

01:15:23.040 | part of it is like, it's creating the visuals

01:15:26.360 | and then weaving a story with those visuals

01:15:29.400 | that kind of builds, like there's also,

01:15:32.080 | I mean, there's also drama in it.

01:15:34.960 | You start with a small example and then you kind of,

01:15:37.640 | all of a sudden there's a surprise.

01:15:39.640 | - Yeah, yeah, yeah.

01:15:41.080 | - And it really, I mean, it makes you fall in love

01:15:43.480 | with the concept.

01:15:45.600 | He does talk about that.

01:15:47.060 | His sense is like some of the stuff,

01:15:50.920 | he doesn't feel like he's teaching,

01:15:54.000 | like the core curriculum, which is something,

01:15:58.460 | he sees himself as an inspirational figure,

01:16:03.640 | but because I think it's too difficult

01:16:05.800 | to kind of convert all of the curriculum

01:16:08.120 | into those elements.

01:16:09.640 | - And probably you don't need to.

01:16:11.040 | I mean, if people get to experience mathematical ideas

01:16:15.960 | in the way that he shares them,

01:16:17.840 | that will change them and it will change the way they think

01:16:21.640 | and maybe they could go on to take

01:16:23.880 | some other mathematical idea and make it that beautiful.

01:16:26.360 | - Well, he does that.

01:16:27.400 | He created a library called Manum and he open sourced it.

01:16:33.000 | And that library is the, people should check it out.

01:16:36.440 | It's written in Python and uses some of those same elements.

01:16:41.440 | Like it allows you to animate equations

01:16:44.080 | and animate little shapes, like people that,

01:16:47.680 | he has a very distinct style in his videos

01:16:50.400 | and what that resulted in,

01:16:51.720 | even though from a software engineer perspective,

01:16:54.220 | the code you release is not like super well-documented

01:16:57.840 | or perfect, but him releasing that,

01:17:01.820 | now there's all of these people educating it.

01:17:05.260 | And the cool, to me personally,

01:17:06.860 | the coolest thing is to see like people,

01:17:10.280 | they're not, don't have like a million subscribers

01:17:13.820 | or something, they have just a few views in the video,

01:17:17.500 | but it just seems like the process of them creating a video

01:17:22.500 | where they teach is like transformative to them

01:17:26.220 | from a student perspective.

01:17:27.220 | It's the old Feynman thing,

01:17:28.380 | the best way to learn is to teach.

01:17:30.300 | And then him releasing that into the wild is,

01:17:32.660 | it shows that impact.

01:17:35.820 | - Yeah, absolutely.

01:17:37.500 | I think just giving people that idea

01:17:39.860 | that you can do that with maths and other subjects,

01:17:42.940 | there's bound to be people all around

01:17:45.700 | who can create more, which is cool.

01:17:48.780 | - Yeah, I definitely, so I recommend people do

01:17:51.180 | like JavaScript or Python.

01:17:52.620 | You can build like visualizations of most concepts

01:17:56.460 | in high school math,

01:17:58.060 | you can do a lot of kinds of visualizations

01:18:00.060 | and doing that yourself.

01:18:01.540 | Plus if you do that yourself, people will really love it.

01:18:04.420 | People actually, people love visualizations of math.

01:18:09.020 | - Yeah.

01:18:09.860 | - 'Cause they, I mean, it's something in us

01:18:11.180 | that loves patterns, loves figuring out difficult things

01:18:14.340 | and the patterns in there

01:18:16.820 | then are unexpected in some way.

01:18:19.060 | - Yeah, have you ever noticed that hotels

01:18:22.060 | are always filled with patterns?

01:18:24.260 | I was just noticing it at the hotel.

01:18:25.500 | I mean, now all of their carpets are pattern carpets

01:18:28.740 | and then they have patterns on the walls.

01:18:30.940 | - Yeah. - So, yeah.

01:18:33.100 | - We humans love the symmetry in patterns,

01:18:36.460 | the breaking of symmetry in patterns.

01:18:38.900 | - Yeah.

01:18:39.980 | - And it's funny that we don't see mathematics

01:18:42.900 | as somehow intricately connected to that, but it is, right?

01:18:45.980 | - I mean, that's one of the perspectives

01:18:47.380 | I love students to take is to be a pattern seeker.

01:18:50.820 | - In everything.

01:18:52.260 | - Yeah, certainly in all of maths.

01:18:53.860 | I mean, you can think of all of maths

01:18:55.340 | as a kind of subject of patterns

01:18:57.180 | and not just visual patterns,

01:19:00.100 | but when you think about multiplying by five

01:19:05.100 | and the fact you can, if you're multiplying 18 times five,

01:19:10.740 | you can instead think of nine times 10.

01:19:13.820 | That's a pattern that always works in mathematics.

01:19:17.260 | You can have a number and double the number.

01:19:19.100 | And so, yeah, I just think there are patterns everywhere.

01:19:21.340 | And if kids are thinking their role is to see patterns

01:19:24.820 | and find patterns, it's really exciting.

01:19:28.460 | - What do you think about like MIT OpenCourseWare

01:19:31.980 | and the release of lectures by universities?

01:19:36.300 | - I think it's good.

01:19:37.900 | I think it's good.

01:19:38.740 | I think that is what started the MOOC I did

01:19:43.740 | was using that platform.

01:19:46.100 | - So you ultimately think like the Udacity models

01:19:48.780 | is a little bit more effective

01:19:50.500 | than just a plain two-hour lecture?

01:19:52.500 | - I think there's definitely,

01:19:53.660 | you can bring in good pedagogy into online learning.

01:19:57.060 | And I think the idea of putting things online

01:19:59.620 | so that people all over the world can access them is great.

01:20:02.780 | I don't think the initial excitement around MOOCs

01:20:06.060 | sort of democratizing education and making it more equal

01:20:09.620 | came about because they found that the people taking MOOCs

01:20:14.140 | tended to be the more privileged people.

01:20:17.100 | So that was, I think there's still something

01:20:20.220 | to be found in that.

01:20:21.500 | There's still more to be done to help

01:20:24.660 | that online learning reach those principles.

01:20:27.740 | But definitely I think it's a good invention.

01:20:31.900 | And I have an online class that's for kids

01:20:35.180 | that's a little free class that gives them--

01:20:37.100 | - What's the topic?

01:20:38.060 | - It's called How to Learn Maths.

01:20:39.620 | - How to Learn Maths.

01:20:40.620 | - It shows maths as this visual creative subject

01:20:44.500 | and it shares mindset and some brain science.

01:20:47.220 | And kids who take it do better in maths class.

01:20:51.340 | We've studied it with like randomized controlled trials

01:20:54.300 | and given it to middle school kids

01:20:57.340 | and other middle school kids who don't take it

01:21:00.100 | but are taught by the same teachers.

01:21:01.420 | So their teachers are the same.

01:21:03.060 | And the kids who take the online class

01:21:04.980 | end up 68% more engaged in their maths class

01:21:08.820 | and do better at the end of the year.

01:21:10.620 | So that's a little six session, 15 minute class

01:21:15.220 | and it changes kids' maths relationships.

01:21:19.060 | So it is true that we can do that with some words

01:21:24.060 | that aren't, it's not a huge change to the education system.

01:21:29.580 | - Do you have advice for young people?

01:21:33.260 | We've been talking about mathematics quite a bit

01:21:36.060 | but in terms of their journey through education,

01:21:39.340 | through their career choices, through life,

01:21:41.940 | maybe middle school, high school, undergrad students

01:21:46.220 | of how to live a life they can be proud of.

01:21:48.860 | - I think if I were to give advice to people,

01:21:54.300 | especially young people, my advice would be to always,

01:21:59.300 | it sounds really corny, but always believe in yourself

01:22:03.540 | and know that you can achieve

01:22:05.420 | because although that sounds like obvious,

01:22:08.020 | of course we want kids to know that they can achieve things.

01:22:10.460 | I know that millions of kids who are in the school system

01:22:13.900 | have been given the message they cannot do things.

01:22:17.300 | And adults too, they have the idea,

01:22:20.660 | oh, I did okay in this, I went into this job

01:22:23.340 | because those other things I could never have done okay in.

01:22:26.980 | So actually when they hear,

01:22:28.620 | hey, maybe you could do those other things,

01:22:31.580 | even adults think, you know, maybe I can.

01:22:35.060 | And they go back and they encounter this knowledge

01:22:38.140 | and they relearn things and they change careers

01:22:40.820 | and amazing things happen.

01:22:42.660 | So for me, I think that message is really important.

01:22:45.980 | You can learn anything.

01:22:47.820 | Scientists try and find a limit.

01:22:50.180 | They're always trying to find a limit.

01:22:51.260 | Like how much can you really learn?

01:22:52.540 | What's the limit to how much you can learn?

01:22:54.300 | And they always come away not being able to find it.

01:22:56.540 | People can just go further and further and further.

01:22:59.540 | And that is true of people born with brain,

01:23:03.140 | you know, areas of their brain that aren't functioning well

01:23:06.420 | that have what we call special needs.

01:23:08.780 | Some of those people also go on to develop

01:23:10.980 | and do amazing things.

01:23:12.780 | So I think that really experiencing that,

01:23:17.380 | knowing that, not just saying it, but knowing it deeply,

01:23:22.380 | you can learn anything,

01:23:24.200 | is something I wish all people would have.

01:23:28.740 | - Actually also applies when you've achieved

01:23:30.700 | some level of success too.

01:23:32.500 | What I find, like in my life with people that love me,

01:23:36.380 | when you achieve success,

01:23:37.980 | they keep celebrating your success

01:23:40.420 | and they want you to keep doing the thing

01:23:42.780 | that you were successful at,

01:23:45.100 | as opposed to believing in that you can do something else,

01:23:49.220 | something big, whatever your heart says to do.

01:23:51.700 | And one of the things that I realized the value of this,

01:23:55.020 | you know, quite recently, which is sad to say,

01:24:00.540 | is how important it is to seek out,

01:24:03.300 | when you're younger, to seek out mentors,

01:24:05.060 | to seek out the people,

01:24:07.460 | like surround yourself with people that will believe in you.

01:24:10.340 | - Yeah.

01:24:11.180 | - It's like a little bit is on you.

01:24:13.300 | It's like, you don't get that,

01:24:16.940 | sometimes if you go to like grad school,

01:24:20.260 | you think you kind of land on a mentor,

01:24:22.420 | maybe you pick a mentor based on the topic

01:24:24.580 | they're interested in.

01:24:25.820 | But the reality is the people you surround yourself with,

01:24:29.100 | they're going to define your life trajectory.

01:24:32.540 | So select people that--

01:24:34.740 | - That's really true.

01:24:35.620 | And get away from people who don't believe in you.

01:24:38.780 | - Sometimes parents can be that.

01:24:40.220 | - Yeah.

01:24:41.060 | - They can love you deeply, but they set,

01:24:44.660 | it's the math thing we mentioned,

01:24:46.420 | they might set certain constraints

01:24:48.980 | on the beliefs that you have.

01:24:51.060 | And so in that, if you're interested in mathematics

01:24:55.180 | and your parents are not that interested in it,

01:24:56.900 | don't listen to your parents on that one dimension.

01:24:58.460 | - Right.

01:24:59.700 | Exactly.

01:25:00.900 | Yeah, and if people tell you you can't do things,

01:25:02.980 | you have to hear from other people who believe in you.

01:25:06.740 | I think you're absolutely right about that.

01:25:09.340 | It's so sad the number of people

01:25:10.900 | who've had those negative messages from parents.

01:25:14.140 | In my Limitless Mind book,

01:25:15.620 | I interviewed quite a few people

01:25:16.940 | who'd been told they couldn't do math,

01:25:18.620 | sometimes by parents, sometimes by teachers.

01:25:21.820 | And fortunately, they had got other ideas

01:25:24.980 | at some point in their life

01:25:26.140 | and realized there was this whole world

01:25:28.620 | of mathematical thinking that was open to them.

01:25:32.340 | So it's really important that people

01:25:35.820 | do connect with people who believe in them.

01:25:39.220 | However hard that might be to find those people.

01:25:42.020 | - What do you hope the education system,

01:25:44.940 | education in general, looks like 10, 20, 50,

01:25:48.100 | 100 years from now?

01:25:49.700 | Are you optimistic about this future?

01:25:51.780 | - Yeah, I definitely have hope.

01:25:53.140 | There is, change can happen in the education system.

01:25:56.660 | In recent years, it's been microscopically slow.

01:26:00.660 | But I do actually see change happening.

01:26:06.940 | Like we were talking earlier that data science

01:26:10.260 | is now a course you can take in high school

01:26:12.460 | instead of algebra two.

01:26:14.380 | And that's pretty amazing

01:26:15.620 | because that content was set out in 1892

01:26:19.980 | and hasn't changed since then.

01:26:22.180 | And so now we're actually seeing a change

01:26:25.220 | in the content of high school.

01:26:26.980 | So I'm amazed that that's happening

01:26:29.580 | and very happy it's happening.

01:26:31.380 | So change is very slow in education usually,

01:26:34.060 | but when you look ahead and think about all that we know

01:26:39.060 | and all that we can offer kids in terms of technology,

01:26:43.980 | you've got to think that 100 years from now,

01:26:48.660 | education will be totally different to the way it is now.

01:26:52.620 | Maybe we won't have subject boundaries anymore

01:26:56.100 | because those don't really make much sense.

01:26:59.060 | - And it's interesting to think how certain tools

01:27:02.500 | like programming, maybe they'll be deeply integrated

01:27:05.700 | in everything we do.

01:27:06.540 | - You would think, yeah.

01:27:07.380 | You would think that all kids are growing up

01:27:08.980 | learning to program and create.

01:27:12.780 | So I just think, I mean, the system of schooling

01:27:16.020 | we have now, people call it a factory model.

01:27:18.940 | It's not designed to inspire creativity.

01:27:23.740 | And I feel like that will also change.

01:27:27.340 | People might look back on these days

01:27:29.060 | and think they were hilarious,

01:27:30.620 | but maybe in the future,

01:27:33.980 | kids will be doing their own programming

01:27:35.300 | and they'll be able to learn things

01:27:36.740 | and find out things and create things

01:27:38.580 | even as they're learning.

01:27:39.580 | And maybe the individual subject boundaries will go.

01:27:44.580 | Data science itself coming into the education system

01:27:48.940 | kind of illustrates that because people realize

01:27:51.940 | it doesn't really fit inside any of the subjects.

01:27:56.540 | So what do we do with it?

01:27:57.860 | Where does it go?

01:27:58.860 | And who teaches it?

01:28:01.420 | So it's already raising those kind of questions

01:28:04.700 | and questioning how we have

01:28:06.660 | these different subject boundaries.

01:28:09.020 | - So you've seen data science be integrated

01:28:10.780 | into the curriculum?

01:28:12.220 | - Yes, it's happening across the United States as we speak.

01:28:15.620 | - I wonder how they got initiated.

01:28:16.940 | Like how does change happen in the education system?

01:28:19.820 | Is it just a few revolutionary leaders?

01:28:22.860 | - I think so, I think so.

01:28:24.380 | It's been an interesting journey

01:28:25.980 | seeing data science take off, actually.

01:28:28.980 | There was a course that was developed in 2014

01:28:33.980 | by some people who thought data science

01:28:37.100 | was a good idea for high schoolers.

01:28:39.460 | And then after some kids took the course

01:28:42.300 | and nothing bad happened to them,

01:28:44.380 | they went to college and people started to accept it more.

01:28:49.300 | And then this was a big piece of the change in California.

01:28:52.300 | The UC system communicated.

01:28:54.900 | They sent out an email last year

01:28:56.380 | to 50,000 high schools saying,

01:28:58.100 | "We now accept data science.

01:28:59.820 | Kids can take it instead of Algebra II.

01:29:01.900 | That's a perfectly legitimate college pathway."

01:29:04.740 | So that was like a big green light for a lot of schools

01:29:08.340 | who were like wondering about whether they could teach it.

01:29:11.220 | So I think it happens in small spaces and expands.

01:29:14.740 | So now-- - It goes viral.

01:29:16.220 | - Yeah. - In this modern age.

01:29:17.780 | - Then it goes viral.

01:29:18.660 | California's ahead, I think, in creating courses

01:29:23.660 | and having kids go through it.

01:29:25.460 | But it's, certainly when I last looked,

01:29:28.940 | there were 12 states that were allowing data science

01:29:31.700 | as a high school course.

01:29:32.540 | And I think by next year, that will have doubled or more.

01:29:37.540 | So change is happening.

01:29:41.100 | - Joe, as I said, I think mathematics

01:29:44.860 | is truly a beautiful subject.

01:29:47.940 | And you having an impact on millions of people's lives

01:29:52.220 | by educating them, by inspiring teachers

01:29:54.980 | to educate in the ways that you've talked about

01:29:57.980 | in multi-dimensional ways, in visual ways,

01:30:01.460 | I think is incredible.

01:30:02.460 | So you're spreading beauty-- - Thank you, I really

01:30:04.260 | appreciate that. - Into the world.

01:30:06.060 | So I really, really appreciate that you spent

01:30:08.060 | your valuable time with me today.

01:30:09.260 | Thank you for talking. - Thank you.

01:30:10.100 | It was really good to talk to you.

01:30:12.580 | - Thanks for listening to this conversation with Joe Bowler.

01:30:15.300 | To support this podcast, please check out our sponsors

01:30:18.020 | in the description.

01:30:19.540 | And now let me leave you with some words

01:30:21.420 | from Albert Einstein.

01:30:23.660 | Pure mathematics is the poetry of logical ideas.

01:30:27.980 | Thanks for listening and hope to see you next time.

01:30:31.540 | (upbeat music)

01:30:34.140 | (upbeat music)

01:30:36.740 | [BLANK_AUDIO]

Jo Boaler: How to Learn Math | Lex Fridman Podcast #226

Chapters