Jo Boaler: How to Learn Math
心理与人性音乐与艺术技术与编程生物与进化数学
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🎙️ 完整对话（1989 条）
Lex Fridman (00:00.000)
The following is a conversation with Jo Bowler,
以下是与乔·鲍勒的对话，
Lex Fridman (00:02.720)
a mathematics educator at Stanford
斯坦福大学数学教育家
Lex Fridman (00:04.840)
and co founder of ucubed.org
和 ucubed.org 联合创始人
Lex Fridman (00:08.080)
that seeks to inspire young minds
旨在激发年轻人的思想
Lex Fridman (00:10.080)
with the beauty of mathematics.
与数学之美。
Jo Boaler (00:12.520)
To support this podcast,
为了支持这个播客，
Lex Fridman (00:14.040)
please check out our sponsors in the description.
请在说明中查看我们的赞助商。
Jo Boaler (00:17.140)
This is the Lex Friedman podcast
这是莱克斯·弗里德曼的播客
Lex Fridman (00:19.340)
and here is my conversation with Jo Bowler.
这是我和乔·鲍勒的对话。
Lex Fridman (00:23.640)
What to you is beautiful about mathematics?
对你来说，数学有什么美妙之处？
Lex Fridman (00:27.200)
I love a mathematics that some people
我喜欢一些人认为的数学
Jo Boaler (00:30.400)
don't even think of as mathematics,
甚至不认为是数学，
Lex Fridman (00:32.720)
which is beautiful, creative mathematics,
这是美丽的、创造性的数学，
Jo Boaler (00:37.640)
where we look at maths in different ways,
我们以不同的方式看待数学，
Lex Fridman (00:39.520)
we visualize it,
我们将其形象化，
Jo Boaler (00:41.240)
we think about different solutions to problems.
我们思考不同的问题解决方案。
Lex Fridman (00:44.680)
A lot of people think of maths
很多人都会想到数学
Jo Boaler (00:46.120)
as you have one method and one answer.
因为你有一种方法和一个答案。
Lex Fridman (00:49.560)
And what I love about maths
我对数学的热爱
Jo Boaler (00:51.160)
is the multiple different ways you can see things,
是你看待事物的多种不同方式，
Lex Fridman (00:54.000)
different methods, different ways of seeing different.
Jo Boaler (00:56.760)
In some cases, different solutions.
Lex Fridman (00:59.160)
So that is what is beautiful to me about mathematics,
Jo Boaler (01:02.140)
that you can see and solve it in many different ways.
Lex Fridman (01:05.800)
And also the sad part that many people think
Jo Boaler (01:10.000)
that maths is just one answer and one method.
Lex Fridman (01:13.820)
So to you, the beauty emerges
Jo Boaler (01:16.340)
when you have a problem with a solution
Lex Fridman (01:18.560)
and you start adding other solutions,
Jo Boaler (01:21.080)
simpler solutions, weirder solutions, more interesting,
Lex Fridman (01:25.440)
some of their visual, some of their algebraic,
Jo Boaler (01:28.180)
geometry, all that kind of stuff.
Lex Fridman (01:30.080)
Yeah, I mean, I always say
Jo Boaler (01:32.280)
that you can take any maths area and make it visual.
Lex Fridman (01:35.360)
And we say to teachers,
Jo Boaler (01:36.400)
give us your most dry, boring maths
Lex Fridman (01:39.880)
and we'll make it a visual, interesting, creative problem.
Lex Fridman (01:43.200)
And it turns out you can do that with any area of maths.
Lex Fridman (01:46.900)
And I think we've given,
Jo Boaler (01:49.600)
it's been a great disservice to kids and others
Lex Fridman (01:51.680)
that it's always been numbers, lots and lots of numbers.
Jo Boaler (01:56.120)
Numbers can be great,
Lex Fridman (01:57.040)
but you can think about maths in other ways besides numbers.
Lex Fridman (02:01.000)
Do you find that most people are better visual learners
Lex Fridman (02:05.040)
or is this just something that's complimentary?
Jo Boaler (02:08.360)
What's the kind of the full spectrum of students
Lex Fridman (02:11.000)
in the way they like to explore maths, would you say?
Jo Boaler (02:13.360)
There's definitely people who come into the classes I do
Lex Fridman (02:17.440)
who are more interested in visual thinking
Lex Fridman (02:19.720)
and like visual approaches.
Lex Fridman (02:21.920)
But it turns out what the neuroscience is telling us
Jo Boaler (02:24.640)
is that when we think about maths,
Lex Fridman (02:26.680)
there are two visual pathways in the brain
Lex Fridman (02:29.120)
and we should all be thinking about it visually.
Lex Fridman (02:32.720)
Some approaches have been to say,
Jo Boaler (02:34.400)
well, you're a visual learner, so we'll give you visuals
Lex Fridman (02:37.360)
and you're not a visual learner.
Lex Fridman (02:40.580)
But actually, if you think you're not a visual learner,
Lex Fridman (02:45.080)
it's probably more important that you have a visual approach.
Lex Fridman (02:48.840)
So you can develop that part of your brain.
Lex Fridman (02:51.560)
So you were saying that there's some kind
Jo Boaler (02:52.920)
of interconnected aspect to it.
Lex Fridman (02:54.520)
So the visual connects with the non visual.
Jo Boaler (02:56.680)
Yeah, so this is what the neuroscience has shown us
Lex Fridman (02:59.840)
that when you work on a maths problem,
Jo Boaler (03:01.160)
there are five different brain pathways
Lex Fridman (03:03.480)
and that the most high achieving people in the world
Jo Boaler (03:06.720)
are people who have more connections between these pathways.
Lex Fridman (03:10.440)
So if you see a maths problem with numbers,
Lex Fridman (03:13.840)
but you also see it visually,
Lex Fridman (03:15.880)
that will cause a connection to happen in your brain
Jo Boaler (03:17.980)
between these pathways.
Lex Fridman (03:19.840)
And if you maybe write about it with words,
Jo Boaler (03:22.080)
that would cause another connection
Lex Fridman (03:23.380)
or maybe you build it with something physical
Jo Boaler (03:26.460)
that would cause a different connection.
Lex Fridman (03:28.360)
And what we want for kids is we call it
Jo Boaler (03:31.480)
a multi dimensional experience of maths,
Lex Fridman (03:33.640)
seeing it in different ways,
Jo Boaler (03:35.480)
experiencing it in different ways,
Lex Fridman (03:37.860)
that will cause that great connected brain.
Jo Boaler (03:40.600)
You know, there's these stories of physicists doing the same.
Lex Fridman (03:43.300)
I find physicists are often better
Jo Boaler (03:45.000)
at building that part of their brain
Lex Fridman (03:47.160)
of using visualization for intuition building,
Jo Boaler (03:50.600)
because you ultimately want to understand
Lex Fridman (03:53.920)
the like the deepest secret underneath this problem.
Lex Fridman (03:57.040)
And for that, you have to intuit your way there.
Lex Fridman (03:59.760)
And you mentioned offline that one of the ways
Jo Boaler (04:02.720)
you might approach a problem
Lex Fridman (04:03.680)
is to try to tell a story about it.
Lex Fridman (04:05.840)
And some of it is like legend,
Lex Fridman (04:07.760)
but I'm sure it's not always is, you know,
Jo Boaler (04:10.880)
you have Einstein thinking about a train,
Lex Fridman (04:14.880)
you know, and the speed of light
Lex Fridman (04:16.680)
and you know, that kind of intuition is useful.
Lex Fridman (04:20.000)
You start to like imagine a physical world,
Jo Boaler (04:22.960)
like how does this idea manifest itself
Lex Fridman (04:25.480)
in the physical world?
Lex Fridman (04:26.320)
And then start playing in your mind
Lex Fridman (04:27.560)
with that physical world and think,
Lex Fridman (04:29.240)
is this going to be true?
Lex Fridman (04:30.200)
Is this going to be true?
Jo Boaler (04:31.480)
Right.
Lex Fridman (04:32.320)
Einstein is well known for thinking visually.
Lex Fridman (04:35.800)
And people talk about how he really didn't want
Lex Fridman (04:39.480)
to go anywhere with problems
Jo Boaler (04:41.520)
without thinking about them visually.
Lex Fridman (04:43.240)
But the other thing you mentioned
Jo Boaler (04:44.780)
that sparked something for me is thinking with intuition,
Lex Fridman (04:48.760)
like having intuition about math problems.
Jo Boaler (04:51.400)
That's another thing that's often absent in math class,
Lex Fridman (04:54.080)
the idea that you might think about a problem
Lex Fridman (04:55.800)
and use your intuition, but so important.
Lex Fridman (05:00.760)
And when mathematicians are interviewed,
Jo Boaler (05:02.820)
they will very frequently talk about the role
Lex Fridman (05:04.400)
of intuition in solving problems,
Lex Fridman (05:07.200)
but not commonly acknowledged or brought into education.
Lex Fridman (05:12.200)
Yeah, I mean, that's what it is.
Jo Boaler (05:14.200)
Like if you task yourself with building an intuition
Lex Fridman (05:18.960)
about a problem, that's where you start to pull in,
Lex Fridman (05:23.280)
like what is the pattern I'm seeing?
Lex Fridman (05:26.680)
In order to understand the pattern,
Jo Boaler (05:28.080)
you might want to then start utilizing visualization.
Lex Fridman (05:31.240)
But ultimately, that's all in service
Jo Boaler (05:33.600)
of like solving the puzzle, like cracking it open
Lex Fridman (05:38.280)
to get the simple explanation of why things are wrong.
Lex Fridman (05:42.160)
Why things are the way they are,
Lex Fridman (05:43.680)
as opposed to, like you said, having a particular algorithm
Jo Boaler (05:47.560)
that you can then execute to solve the problem.
Lex Fridman (05:50.080)
Yeah, but it's hard.
Jo Boaler (05:51.080)
It's hard, like reasoning is really hard.
Lex Fridman (05:53.480)
Yeah, it's hard.
Jo Boaler (05:55.080)
I mean, I love to value what's hard in maths
Lex Fridman (05:58.780)
instead of being afraid of it.
Jo Boaler (06:00.560)
We know that when you struggle,
Lex Fridman (06:02.440)
that's actually a really good time for your brain.
Jo Boaler (06:04.480)
You want to be struggling when you're thinking about things.
Lex Fridman (06:07.200)
So if it's hard to think intuitively about something,
Jo Boaler (06:10.000)
that's probably a really good time for your brain.
Lex Fridman (06:13.560)
I used to work with somebody called Sebastian Thrun,
Jo Boaler (06:16.680)
who is a great sort of mathematician,
Lex Fridman (06:19.520)
you might think of him, AI person.
Lex Fridman (06:21.200)
And I remember in one interview I did with him,
Lex Fridman (06:23.720)
he talked about how they'd built robots,
Jo Boaler (06:25.760)
I think for the Smithsonian,
Lex Fridman (06:27.560)
and how they were having this trouble
Jo Boaler (06:29.320)
with them picking up white noise.
Lex Fridman (06:32.300)
And he said they had to solve it.
Jo Boaler (06:34.540)
They had to work out what's going on
Lex Fridman (06:36.400)
and how he intuitively worked out what the problem was.
Lex Fridman (06:41.280)
But then it took him three weeks to show it mathematically.
Lex Fridman (06:45.560)
I thought that was really interesting
Jo Boaler (06:47.000)
that how you can have this intuition
Lex Fridman (06:49.600)
and know something works.
Jo Boaler (06:51.760)
It's kind of different from going through
Lex Fridman (06:53.380)
that long mathematical process of proving it,
Lex Fridman (06:56.980)
but so important.
Lex Fridman (06:58.240)
Yeah, I think probably our brains are evolved
Jo Boaler (07:01.600)
as like intuition machines
Lex Fridman (07:03.920)
and the math of like showing it like formally
Jo Boaler (07:08.920)
is probably an extra thing that we're not designed for.
Lex Fridman (07:12.120)
You see that with Feynman and his,
Jo Boaler (07:14.960)
I mean, it just, all of these physicists,
Lex Fridman (07:16.960)
definitely you see starting with intuition,
Jo Boaler (07:21.140)
sometimes starting with an experiment
Lex Fridman (07:24.520)
and then the experiment inspires intuition.
Lex Fridman (07:27.920)
But you can think of an experiment
Lex Fridman (07:29.320)
as a kind of visualization.
Jo Boaler (07:31.080)
Just like let's take whatever the heck we're looking at
Lex Fridman (07:34.320)
and draw it and draw like the pattern as it evolves,
Jo Boaler (07:38.680)
as the thing grows for N equals one,
Lex Fridman (07:41.120)
for N equals two, N equals three,
Jo Boaler (07:42.880)
you start to play with it.
Lex Fridman (07:44.800)
And then in the modern day, which I loved doing is,
Jo Boaler (07:49.440)
you can write a program that then visualizes it for you.
Lex Fridman (07:52.480)
And then you can start exploring it programmatically.
Lex Fridman (07:55.520)
And then you can do so interactively too.
Lex Fridman (08:00.160)
I tend to not like interactive
Jo Boaler (08:03.600)
because it takes way too much work
Lex Fridman (08:05.680)
because you have to click and move and stuff.
Jo Boaler (08:07.160)
I love to interact through writing programs,
Lex Fridman (08:09.880)
but that's my particular brain, software engineer.
Lex Fridman (08:12.480)
So like you can do all these kinds of visualizations
Lex Fridman (08:16.960)
and then there's the tools of visualization,
Jo Boaler (08:19.320)
like color, all of those kinds of things
Lex Fridman (08:22.640)
that you're absolutely right.
Jo Boaler (08:24.240)
They're actually not taught very much.
Lex Fridman (08:27.200)
Like the art of visualization.
Jo Boaler (08:28.800)
Not taught.
Lex Fridman (08:30.040)
And we love as well color coding.
Jo Boaler (08:33.720)
Like when you represent something mathematically,
Lex Fridman (08:36.480)
you can show color to show the growth and kind of code that.
Lex Fridman (08:41.040)
So if I have an algebraic expression for a pattern,
Lex Fridman (08:44.280)
maybe I show the X with a certain color,
Lex Fridman (08:46.720)
but also write in that color
Lex Fridman (08:48.000)
so you can see the relationship.
Jo Boaler (08:51.360)
Very cool.
Lex Fridman (08:52.320)
And yeah, particularly in our work
Jo Boaler (08:54.920)
with elementary teachers,
Lex Fridman (08:56.800)
many of them come to our workshops
Lex Fridman (08:58.720)
and they're literally in tears
Lex Fridman (09:00.720)
when they see things making sense visually
Jo Boaler (09:03.840)
because they've spent their whole lives
Lex Fridman (09:06.280)
not realizing you can really understand things
Jo Boaler (09:09.200)
with these visuals.
Lex Fridman (09:10.920)
It's quite powerful.
Jo Boaler (09:12.680)
You say that there's something valuable to learning
Lex Fridman (09:17.800)
when the thing that you're doing is challenging,
Jo Boaler (09:20.480)
is difficult.
Lex Fridman (09:21.600)
So a lot of people say math is hard
Jo Boaler (09:24.000)
or math is too hard or too hard for me.
Lex Fridman (09:28.040)
Do you think math should be easy or should it be hard?
Jo Boaler (09:33.440)
I think it's great when things are challenging,
Lex Fridman (09:36.920)
but there's something that's really key
Jo Boaler (09:39.160)
to being able to deal with challenging maths
Lex Fridman (09:42.880)
and that is knowing that you can do it.
Lex Fridman (09:46.800)
And I think the problem in education
Lex Fridman (09:48.680)
is a lot of people have got this idea
Jo Boaler (09:51.200)
that you're either born with a maths brain or you're not.
Lex Fridman (09:54.000)
So when they start to struggle,
Jo Boaler (09:55.720)
they think, oh, I don't have that maths brain.
Lex Fridman (09:58.440)
And then they will literally sort of switch off
Jo Boaler (10:00.960)
in their brain and things will go downhill from that point.
Lex Fridman (10:04.080)
So struggle becomes a lot easier
Lex Fridman (10:06.240)
and you're able to struggle if you don't have that idea,
Lex Fridman (10:10.960)
but you know that you can do it.
Jo Boaler (10:13.400)
You have to go through this struggle to get there,
Lex Fridman (10:16.000)
but you're able to do that.
Lex Fridman (10:18.720)
And so we're hampered in being able to struggle
Lex Fridman (10:21.760)
with these ideas we've been given about what we can do.
Lex Fridman (10:25.240)
Can I ask a difficult question here?
Lex Fridman (10:26.920)
Yeah.
Lex Fridman (10:27.760)
So there's kind of, I don't know what the right term is,
Lex Fridman (10:31.960)
but some people struggle with learning in different ways,
Jo Boaler (10:38.640)
like their brain is constructed in different ways.
Lex Fridman (10:42.400)
And how much should, as educators,
Lex Fridman (10:47.000)
should we make room for that?
Lex Fridman (10:49.280)
So how do you know the difference between this is hard
Lex Fridman (10:52.360)
and I don't like doing hard things
Lex Fridman (10:54.440)
versus my brain is wired in a way
Jo Boaler (10:57.040)
where I need to learn in very different ways.
Lex Fridman (10:59.040)
I can't learn it this way.
Lex Fridman (11:00.640)
How do you find that line?
Lex Fridman (11:02.320)
How do you operate in that gray area?
Lex Fridman (11:04.040)
So this is why being a teacher is so hard
Lex Fridman (11:07.360)
and people really don't appreciate
Lex Fridman (11:09.360)
how difficult teaching is when you're faced with,
Lex Fridman (11:12.280)
I don't know, 30 students who think in different ways.
Jo Boaler (11:14.920)
So, but this is also why I believe it's so important
Lex Fridman (11:19.480)
to have this multi dimensional approach to maths.
Jo Boaler (11:21.960)
We've really offered it in one way,
Lex Fridman (11:24.680)
which is here's some numbers in a method.
Jo Boaler (11:27.360)
You follow me, do what I just did and then reproduce it.
Lex Fridman (11:31.200)
And so there are some kids who like doing that
Lex Fridman (11:33.840)
and they do well.
Lex Fridman (11:34.880)
And a lot of kids who don't like doing it
Lex Fridman (11:37.680)
and don't do well.
Lex Fridman (11:39.120)
But when you open up maths and you give,
Jo Boaler (11:42.760)
you let kids experience it in different ways,
Lex Fridman (11:44.640)
maybe visually with numbers, with words.
Lex Fridman (11:47.640)
What happens is kids,
Lex Fridman (11:49.960)
there are many more kids who can access it.
Lex Fridman (11:52.440)
So those different brain wirings you're talking about,
Lex Fridman (11:56.160)
where some people are just more able to do something
Jo Boaler (11:58.840)
in a particular way.
Lex Fridman (12:00.240)
That's why we want to,
Jo Boaler (12:01.840)
that's one of the reasons we want to open it up
Lex Fridman (12:04.680)
so that there are different ways of accessing it.
Lex Fridman (12:08.360)
And then that's not really a problem.
Lex Fridman (12:11.160)
So I grew up in the Soviet Union and fell in love
Jo Boaler (12:15.960)
with math early.
Lex Fridman (12:17.400)
I was forced into math early
Lex Fridman (12:19.800)
and fell in love through force.
Lex Fridman (12:22.320)
That's good.
Jo Boaler (12:23.160)
Well, good that you fell in love about the force.
Lex Fridman (12:25.400)
Well, but something we talked about a little bit
Jo Boaler (12:28.360)
is there is such a value for excellence.
Lex Fridman (12:33.320)
It's competitive and it's also everybody kind of looks up
Jo Boaler (12:37.920)
the definition of success is being in a particular class
Lex Fridman (12:44.440)
is being really good at it.
Lex Fridman (12:47.640)
And like, it's not improving.
Lex Fridman (12:49.680)
It's like being really good.
Jo Boaler (12:50.920)
I mean, we are much more like that with sports, for example.
Lex Fridman (12:53.800)
We're not, it's like, it's understood,
Jo Boaler (12:56.880)
you're going to star on the basketball team
Lex Fridman (12:59.760)
if you're gonna start on the basketball team
Jo Boaler (13:02.400)
if you're going to be better than the other guys,
Lex Fridman (13:05.120)
the other girls on the team.
Lex Fridman (13:06.520)
So that coupled with the belief,
Lex Fridman (13:12.160)
this could be partially a communist belief, I don't know,
Lex Fridman (13:14.640)
but the belief that everybody is capable of being great.
Lex Fridman (13:19.120)
But if you're not great, that's your fault
Lex Fridman (13:22.160)
and you need to work harder.
Lex Fridman (13:23.400)
And I remember I had a sense that probably delusional,
Lex Fridman (13:27.880)
but I could win a Nobel prize.
Lex Fridman (13:29.600)
I don't even know what that entails.
Lex Fridman (13:31.360)
But I thought, like my dad early on told me just offhand
Lex Fridman (13:39.560)
and it always stuck with me that if you can figure out
Lex Fridman (13:42.520)
how to build a time machine, how to travel back in time,
Lex Fridman (13:46.120)
it will probably give you a Nobel prize.
Lex Fridman (13:48.360)
And I remember early in my life thinking
Lex Fridman (13:50.400)
I'm going to invent the time machine.
Lex Fridman (13:52.440)
And like the tools of mathematics were in service
Lex Fridman (13:56.720)
of that dream of winning the Nobel prize.
Jo Boaler (14:00.000)
It's silly. I didn't really think in those concrete terms,
Lex Fridman (14:03.480)
but I just thought I could be great at feeling.
Lex Fridman (14:06.760)
And then when you struggle,
Lex Fridman (14:08.640)
the belief that you could be great is like,
Jo Boaler (14:11.920)
struggle is good.
Lex Fridman (14:12.960)
Right, pushes you on, yeah.
Lex Fridman (14:14.520)
And so the other thing about the Soviet system
Lex Fridman (14:17.240)
that I'd love to hear your comments about
Jo Boaler (14:20.520)
is just the sheer like hours of math.
Lex Fridman (14:23.840)
Like the number of courses,
Jo Boaler (14:25.600)
you're talking about a lot of geometry, a lot more geometry.
Lex Fridman (14:29.280)
I think in the American system,
Jo Boaler (14:30.640)
you take maybe one year of geometry.
Lex Fridman (14:33.080)
In high school, yeah.
Jo Boaler (14:33.920)
In high school.
Lex Fridman (14:35.240)
First of all, geometry is beautiful, it's visual.
Lex Fridman (14:37.480)
And then you get to reason through proofs
Lex Fridman (14:39.120)
and stuff like that.
Jo Boaler (14:40.160)
In Russia, I remember just being nailed
Lex Fridman (14:42.600)
over and over with geometry.
Jo Boaler (14:43.840)
It was just nonstop.
Lex Fridman (14:45.600)
And then of course there's different perspectives
Jo Boaler (14:48.160)
on calculus and just the whole,
Lex Fridman (14:50.320)
the sense was that math is like fundamental
Jo Boaler (14:56.000)
to the development of the human mind.
Lex Fridman (14:58.600)
So math, but also science and literature, by the way,
Jo Boaler (15:02.400)
was also hit very hard.
Lex Fridman (15:04.600)
Like we read a lot of serious adult stuff.
Jo Boaler (15:08.200)
America does that a little bit too.
Lex Fridman (15:09.920)
They challenge young adults with good literature,
Lex Fridman (15:12.600)
but they don't challenge adults very much with math.
Lex Fridman (15:16.160)
So those two things, valuing excellence
Lex Fridman (15:20.840)
and just a lot of math in the curriculum.
Lex Fridman (15:23.680)
Do you think, do you find that interesting?
Jo Boaler (15:26.880)
Because it seems to have been successful.
Lex Fridman (15:28.680)
Yeah, I think that's very interesting.
Lex Fridman (15:30.160)
And there is a lot of success,
Lex Fridman (15:32.680)
people coming through the Soviet system.
Jo Boaler (15:34.080)
I think something that's very different to the US
Lex Fridman (15:37.320)
and other countries in the world
Jo Boaler (15:39.440)
is that idea that excellence is important
Lex Fridman (15:41.920)
and you can get there if you work hard.
Jo Boaler (15:44.920)
In the US, there's an idea that excellence is important,
Lex Fridman (15:48.680)
but then kids are given the idea in many ways
Jo Boaler (15:52.120)
that you can either do it
Lex Fridman (15:53.720)
or you're one of the people who can't.
Lex Fridman (15:56.120)
So many students in the school system
Lex Fridman (15:58.440)
think they're one of the kids who can't.
Lex Fridman (15:59.680)
So there's no point in trying hard
Lex Fridman (16:02.280)
because you're never going to get there.
Lex Fridman (16:04.680)
So if you can switch that idea, it would be huge.
Lex Fridman (16:09.600)
And it seems from what you've said
Jo Boaler (16:11.120)
that in the Soviet Union, that idea is really different.
Lex Fridman (16:16.280)
Now, the downside of that idea that anybody can get there
Jo Boaler (16:19.560)
if you work hard is that thought
Lex Fridman (16:24.000)
that if you're not getting there, it's your fault.
Lex Fridman (16:26.480)
And I would add something into that.
Lex Fridman (16:28.680)
I would say that anybody can get there,
Lex Fridman (16:31.800)
but they need to work hard and they also need good teaching
Lex Fridman (16:35.120)
because there are some people who really can't get there
Jo Boaler (16:37.960)
because they're not given access to that good teaching.
Lex Fridman (16:41.240)
So, but that would be huge, that change.
Jo Boaler (16:44.600)
As to doing lots of maths,
Lex Fridman (16:46.480)
if maths was interesting and open and creative
Lex Fridman (16:50.960)
and multi dimensional, I would be all for it.
Lex Fridman (16:53.760)
We actually run summer camps at Stanford
Jo Boaler (16:56.040)
where we invite kids in and we give them this maths
Lex Fridman (16:59.080)
that I love.
Lex Fridman (17:00.680)
And in our camp classrooms, they were three hours long.
Lex Fridman (17:05.320)
And when we were planning, the teachers were like three hours,
Jo Boaler (17:09.440)
are we going to be able to keep the kids excited
Lex Fridman (17:11.480)
for three hours?
Jo Boaler (17:12.480)
Turned out they didn't want to go to break or lunch.
Lex Fridman (17:15.960)
They'd be so into these mathematical patterns.
Jo Boaler (17:19.440)
We couldn't stop them.
Lex Fridman (17:21.080)
It was amazing.
Lex Fridman (17:22.800)
So yeah, if maths was more like that,
Lex Fridman (17:25.160)
then I think having more of it would be a really good thing.
Lex Fridman (17:29.040)
So what age are you talking about?
Lex Fridman (17:30.960)
Is there, could you comment on what age is like
Jo Boaler (17:35.480)
the most important when people quit math
Lex Fridman (17:39.120)
or give up on themselves or on math in general?
Lex Fridman (17:42.760)
And perhaps that age or something earlier
Lex Fridman (17:45.520)
is really an important moment for them to discover,
Jo Boaler (17:48.560)
to be inspired to discover the magic of math.
Lex Fridman (17:51.440)
I think a lot of kids start to give up on themselves
Lex Fridman (17:54.400)
and maths around from about fifth grade.
Lex Fridman (17:59.200)
And then those middle school years are really important.
Lex Fridman (18:02.360)
And fifth grade can be pivotal for kids
Lex Fridman (18:04.520)
just because they're allowed to explore
Lex Fridman (18:07.920)
and think in good ways
Lex Fridman (18:10.560)
in the early grades of elementary school.
Lex Fridman (18:12.240)
But fifth grade teachers are often like,
Lex Fridman (18:13.520)
okay, we're going to prepare you now for middle school
Lex Fridman (18:15.440)
and we're going to give you grades and lots of tests.
Lex Fridman (18:18.160)
And that's when kids start to feel really badly
Jo Boaler (18:21.720)
about themselves.
Lex Fridman (18:22.560)
And so middle school years,
Jo Boaler (18:24.760)
our camps are middle school students.
Lex Fridman (18:27.000)
We think of those years as really pivotal.
Jo Boaler (18:29.160)
Many kids in those years are deciding,
Lex Fridman (18:31.640)
yes, I'm going to keep going with STEM subjects
Jo Boaler (18:35.640)
or no, I'm not, that this isn't for me.
Lex Fridman (18:38.280)
So, I mean, all years are important
Lex Fridman (18:40.760)
and in all years you can kind of switch kids
Lex Fridman (18:43.080)
and get them on a different pathway.
Lex Fridman (18:45.600)
But I think those middle school years are really important.
Lex Fridman (18:48.400)
So what's the role of the teacher in this?
Lex Fridman (18:50.800)
So one is the explanation of the subject,
Lex Fridman (18:53.040)
but do you think teachers should almost do like one on one,
Lex Fridman (18:58.320)
you know, little Johnny, I believe in you kind of thing?
Lex Fridman (19:01.760)
Like that energy of like.
Jo Boaler (19:03.800)
Turns out it's really important.
Lex Fridman (19:05.320)
There's a study that was done,
Jo Boaler (19:07.440)
it was actually done in high school English classrooms
Lex Fridman (19:10.360)
where all kids wrote an essay for their teacher.
Lex Fridman (19:14.040)
And this was done as an experiment.
Lex Fridman (19:16.000)
Half of the kids got feedback from their teacher,
Jo Boaler (19:18.840)
diagnostic feedback, which is great.
Lex Fridman (19:21.040)
But for half of the kids,
Jo Boaler (19:22.000)
it said an extra sentence at the bottom
Lex Fridman (19:23.920)
that the researchers had put on.
Lex Fridman (19:26.240)
And the kids who read that extra sentence
Lex Fridman (19:30.000)
did significantly better in English a whole year later.
Jo Boaler (19:33.480)
The only change was this one sentence.
Lex Fridman (19:36.720)
What did the sentence say?
Lex Fridman (19:37.640)
So what did the sentence say?
Lex Fridman (19:39.720)
The sentence said, I'm giving you this feedback
Jo Boaler (19:42.880)
because I believe in you.
Lex Fridman (19:45.200)
And the kids who read that did better a year later.
Jo Boaler (19:48.640)
Yeah.
Lex Fridman (19:49.480)
So when I share this with teachers,
Jo Boaler (19:52.320)
I say, you know, I'm not suggesting
Lex Fridman (19:53.840)
you put on the bottom of all kids work.
Jo Boaler (19:56.000)
I'm giving this feedback because I believe in you.
Lex Fridman (19:58.400)
One of the teachers said to me, we don't put it on a stamp.
Lex Fridman (1:00:01.600)
So now there's a whole K8 set of books
Lex Fridman (1:00:05.560)
and they're organized in that way.
Jo Boaler (1:00:07.120)
These are the big ideas.
Lex Fridman (1:00:08.320)
Here are rich, deep activities.
Jo Boaler (1:00:11.960)
They're not though what you can do every day for a year.
Lex Fridman (1:00:16.040)
So some teachers use them as a kind of supplement
Jo Boaler (1:00:19.040)
to their boring textbook.
Lex Fridman (1:00:21.000)
And some people have said, okay, this is the year.
Jo Boaler (1:00:24.360)
This book tells us what the year is
Lex Fridman (1:00:26.440)
and then we'll supplement these big activities with.
Lex Fridman (1:00:29.120)
So they're being used and teachers really like them
Lex Fridman (1:00:34.360)
and are really happy about them.
Jo Boaler (1:00:36.160)
I just always want more.
Lex Fridman (1:00:37.440)
And I guess one of the things I would like for YouCubed,
Jo Boaler (1:00:40.200)
one of my personal goals is that every teacher of maths
Lex Fridman (1:00:43.600)
knows about YouCubed.
Jo Boaler (1:00:45.400)
At the moment, lots of teachers who come to us
Lex Fridman (1:00:48.440)
are really happy they found it
Lex Fridman (1:00:49.760)
but there's a lot of other teachers
Lex Fridman (1:00:51.200)
who don't know that it exists.
Jo Boaler (1:00:53.520)
I hope this helps.
Lex Fridman (1:00:54.920)
Yeah.
Jo Boaler (1:00:55.960)
From a student perspective and not in the classroom
Lex Fridman (1:00:59.440)
but at home studying,
Jo Boaler (1:01:03.800)
is there some advice you can give
Lex Fridman (1:01:07.360)
on how to best study mathematics?
Lex Fridman (1:01:09.760)
So what's the role of the student outside the classroom?
Lex Fridman (1:01:13.720)
Yeah, I think one thing we know is a lot of people
Jo Boaler (1:01:17.520)
when they review material,
Lex Fridman (1:01:19.680)
whether it's maths or anything else,
Jo Boaler (1:01:21.320)
don't do it in the best way.
Lex Fridman (1:01:23.640)
I think a problem a lot of people have
Jo Boaler (1:01:25.800)
is they read through maybe a teacher's explanation
Lex Fridman (1:01:28.920)
or a way of doing maths and it makes sense.
Lex Fridman (1:01:32.800)
And they think, oh yeah, I've got that.
Lex Fridman (1:01:33.840)
And they move on.
Lex Fridman (1:01:36.320)
But then it's not until you come to try
Lex Fridman (1:01:38.840)
and work on something and do a problem
Jo Boaler (1:01:40.520)
that you actually realize you didn't really understand it,
Lex Fridman (1:01:42.520)
just seemed to make sense.
Lex Fridman (1:01:44.760)
So I would say,
Lex Fridman (1:01:47.280)
this is also something that neuroscientists talk about,
Jo Boaler (1:01:50.600)
to keep giving yourself questions
Lex Fridman (1:01:53.400)
is a really good way to study.
Jo Boaler (1:01:56.560)
Rather than looking through lots of material,
Lex Fridman (1:01:59.320)
it's always like giving yourself lots of tests
Jo Boaler (1:02:02.480)
is a good way to actually deeply understand things
Lex Fridman (1:02:05.360)
and know what you do and you don't understand.
Lex Fridman (1:02:07.560)
So would the questions be in the form of
Lex Fridman (1:02:11.320)
the material you're reviewing
Lex Fridman (1:02:12.960)
is the answer to that question?
Lex Fridman (1:02:14.440)
Or is it almost like beyond,
Jo Boaler (1:02:16.040)
it's the polygon thing they mentioned for a square.
Lex Fridman (1:02:18.880)
Is it almost like, I wonder what is the bigger picture?
Lex Fridman (1:02:22.760)
I was kind of asking like, how is this extended and so on?
Lex Fridman (1:02:26.200)
Yeah, that would be great.
Lex Fridman (1:02:28.680)
And it's a similar,
Lex Fridman (1:02:30.200)
I mean, a question I get asked a lot is about homework.
Lex Fridman (1:02:32.480)
What is a good thing for kids to do for homework?
Lex Fridman (1:02:34.960)
And one of the recommendations I give
Jo Boaler (1:02:36.960)
is to not have kids just do lots of questions for homework,
Lex Fridman (1:02:42.800)
but to actually ask them to reflect on what they've learned.
Lex Fridman (1:02:46.080)
Like, what was the big idea you learned today?
Lex Fridman (1:02:49.680)
Or what did you find difficult?
Lex Fridman (1:02:51.880)
What did you struggle with?
Lex Fridman (1:02:53.480)
What was something that was exciting?
Jo Boaler (1:02:58.160)
Then kids go home and they have to kind of reflect
Lex Fridman (1:03:01.120)
in a deeper way.
Jo Boaler (1:03:02.440)
A lot of times, I don't know if you had this experience
Lex Fridman (1:03:04.520)
as a math student, lots of people do.
Jo Boaler (1:03:06.640)
Kids are going through math questions,
Lex Fridman (1:03:08.800)
they're successful, they get them right,
Lex Fridman (1:03:10.920)
but they don't even really know what they're about.
Lex Fridman (1:03:13.960)
And a lot of kids go through many years of maths like that,
Jo Boaler (1:03:17.160)
doing lots of questions,
Lex Fridman (1:03:18.200)
but that really knowing what even the topic is
Jo Boaler (1:03:21.960)
or what it's about, what it's important for.
Lex Fridman (1:03:24.400)
So having students go back and think at the end of a day,
Lex Fridman (1:03:28.760)
what was the big idea from this maths lesson?
Lex Fridman (1:03:31.640)
Why is it important?
Lex Fridman (1:03:33.320)
Where would I find that in real life?
Lex Fridman (1:03:36.040)
Those are really good questions
Jo Boaler (1:03:37.920)
for kids to be thinking about.
Lex Fridman (1:03:39.920)
It's probably for everybody to be thinking about.
Jo Boaler (1:03:42.400)
I think most of us go through life
Lex Fridman (1:03:44.320)
never asking the bigger question,
Jo Boaler (1:03:48.160)
always those layers of why questions
Lex Fridman (1:03:51.600)
that kids ask when they're very young.
Jo Boaler (1:03:54.160)
We need to keep doing that.
Lex Fridman (1:03:55.960)
Like whatever the term is,
Jo Boaler (1:03:59.680)
you call first principles thinking,
Lex Fridman (1:04:01.400)
some people call it that,
Lex Fridman (1:04:03.320)
which is like, why are we doing it this way?
Lex Fridman (1:04:08.560)
So one nice thing is to do that
Jo Boaler (1:04:11.760)
because there's usually a good answer.
Lex Fridman (1:04:13.360)
The reason we did it this way
Jo Boaler (1:04:15.360)
is because it works for this reason.
Lex Fridman (1:04:17.760)
But then if you want to do something totally novel,
Jo Boaler (1:04:20.960)
you'll say, well, we've been doing it this way
Lex Fridman (1:04:26.320)
because of historical reasons,
Lex Fridman (1:04:28.600)
but really this is not the best way to do it.
Lex Fridman (1:04:30.520)
There might be other ways.
Lex Fridman (1:04:32.240)
And that's how invention happens.
Lex Fridman (1:04:34.440)
And then you get, that's really useful
Jo Boaler (1:04:36.480)
in every aspect of life, like choosing your career,
Lex Fridman (1:04:40.440)
choosing your, I don't know, where you live,
Jo Boaler (1:04:44.800)
who your romantic partner is, like everything.
Lex Fridman (1:04:47.760)
Everything, yeah.
Lex Fridman (1:04:48.960)
And I think it probably starts doing that in math class.
Lex Fridman (1:04:54.240)
That would be good if we started doing that.
Jo Boaler (1:04:56.280)
I mean, I wonder, I probably didn't do very much of that
Lex Fridman (1:05:00.960)
for most of my education, asking why,
Jo Boaler (1:05:03.760)
except for later, much later in the subjects
Lex Fridman (1:05:08.160)
on grad school when you're doing research on them.
Jo Boaler (1:05:12.240)
When you're first tasked with doing something novel
Lex Fridman (1:05:15.080)
using this or solving a problem
Jo Boaler (1:05:18.040)
really outside the classroom,
Lex Fridman (1:05:19.960)
they have to publish on it.
Jo Boaler (1:05:20.800)
It's the first time you think,
Lex Fridman (1:05:22.560)
wait, why are these things interesting, useful?
Lex Fridman (1:05:27.040)
Which are the things that are useful?
Lex Fridman (1:05:29.440)
And yeah, I guess that would be nice
Jo Boaler (1:05:31.680)
if we did that much earlier, the quest of invention.
Lex Fridman (1:05:35.240)
Yeah, yeah, I mean, one of the sad pieces of research data
Jo Boaler (1:05:39.680)
I think about is the questions kids ask in school goes down
Lex Fridman (1:05:45.800)
like in a linear progression from, in the early years,
Jo Boaler (1:05:51.400)
you can't stop kids asking those questions,
Lex Fridman (1:05:53.800)
but they learn not to ask the questions.
Jo Boaler (1:05:56.720)
I think you told somewhere about an early memory
Lex Fridman (1:06:00.000)
you had in your own education where you asked the question,
Jo Boaler (1:06:04.680)
or maybe that was an example you gave,
Lex Fridman (1:06:06.280)
but it was shut down.
Jo Boaler (1:06:07.440)
Oh, yeah.
Lex Fridman (1:06:08.920)
You've listened to something I said, yeah.
Jo Boaler (1:06:12.160)
I don't remember where it was, but it caught me.
Lex Fridman (1:06:15.200)
Yeah, I remember it really vividly.
Lex Fridman (1:06:17.680)
Or can you tell the memory?
Lex Fridman (1:06:19.840)
Yeah, I was, it's funny, I can remember.
Jo Boaler (1:06:21.800)
It must've really impacted me in that moment
Lex Fridman (1:06:23.960)
because you know how there's lots of hours of school
Jo Boaler (1:06:26.320)
you don't remember at all, but anyway,
Lex Fridman (1:06:29.040)
I can remember where I was sitting and everything.
Jo Boaler (1:06:30.720)
I was in a high school maths class,
Lex Fridman (1:06:33.360)
although they don't call it that in England,
Lex Fridman (1:06:35.280)
and the teacher said,
Lex Fridman (1:06:39.040)
and it was like the first class of this teacher's class,
Lex Fridman (1:06:41.960)
and he said, ask if you have any questions.
Lex Fridman (1:06:44.360)
So at one point I put my hand up and I said,
Jo Boaler (1:06:46.840)
I have a question, and he said something like,
Lex Fridman (1:06:49.240)
that's your question?
Lex Fridman (1:06:53.840)
And I was like, oh, okay,
Lex Fridman (1:06:55.400)
I'm not asking any more questions in this class.
Lex Fridman (1:06:57.400)
And that hit hard in a way where you didn't wanna,
Lex Fridman (1:06:59.960)
the lesson you learn from that is I'm not gonna ask.
Jo Boaler (1:07:02.040)
Yeah, that was absolutely the last question I'm asking.
Lex Fridman (1:07:06.320)
And that was, yeah, he was the chair of the maths department.
Jo Boaler (1:07:12.040)
I remember that really well.
Lex Fridman (1:07:13.720)
So maybe because of that experience,
Jo Boaler (1:07:18.080)
one of the things we encourage when we teach kids
Lex Fridman (1:07:20.400)
is asking questions, and we value it when they ask questions
Lex Fridman (1:07:23.040)
and we put them up on walls and celebrate.
Lex Fridman (1:07:27.960)
It's funny because I wish there was a feedback signal
Jo Boaler (1:07:31.400)
because he probably, to put a positive spin on it,
Lex Fridman (1:07:35.040)
he probably didn't realize the negative impact
Lex Fridman (1:07:37.440)
he's had in that moment, right?
Lex Fridman (1:07:38.720)
If he only knew, see, this is probably
Jo Boaler (1:07:41.160)
when you're more mature in grad school.
Lex Fridman (1:07:44.120)
I had an amazing professor named Ali Shakafande
Jo Boaler (1:07:46.960)
in computer science, and he would get,
Lex Fridman (1:07:49.960)
he would encourage questions,
Lex Fridman (1:07:51.240)
but then he would tell everybody
Lex Fridman (1:07:52.440)
how dumb their questions are.
Lex Fridman (1:07:54.280)
But it was done, I guess if you show,
Lex Fridman (1:07:57.360)
if you say it with love and respect behind it,
Jo Boaler (1:08:00.760)
then it's more like a friendly, humorous encouragement
Lex Fridman (1:08:03.720)
for more questions.
Jo Boaler (1:08:05.080)
Yeah, it's an art, right, to do it, to write.
Lex Fridman (1:08:07.880)
And then you have to time it right
Jo Boaler (1:08:10.200)
because that kind of humor is probably better
Lex Fridman (1:08:13.080)
for when you're in grad school
Jo Boaler (1:08:15.440)
versus when you're in the early education.
Lex Fridman (1:08:18.000)
Right.
Jo Boaler (1:08:18.840)
Well, and I guess kids or young people get
Lex Fridman (1:08:22.320)
whether somebody's doing it to be funny or, you know,
Jo Boaler (1:08:27.320)
I mean, this is why teaching is so hard.
Lex Fridman (1:08:31.160)
Even your tone can be impactful.
Jo Boaler (1:08:35.120)
It's so sad because for that particular human,
Lex Fridman (1:08:39.680)
the teacher, you just had a bad day,
Lex Fridman (1:08:42.760)
and one statement can have a profound negative impact.
Lex Fridman (1:08:45.920)
I know, sadly, that there's a lot of maths teachers
Jo Boaler (1:08:50.120)
who have that kind of approach,
Lex Fridman (1:08:51.960)
and I think they're suffering from the fact
Jo Boaler (1:08:56.000)
that they think people are math people, not math people,
Lex Fridman (1:08:58.200)
and that comes across in their teaching.
Lex Fridman (1:09:01.040)
But on the flip side, one positive statement.
Lex Fridman (1:09:03.400)
Yeah.
Jo Boaler (1:09:04.240)
Keep them going.
Lex Fridman (1:09:05.080)
That's right.
Jo Boaler (1:09:05.920)
That is the flip side of that.
Lex Fridman (1:09:07.240)
And I myself had one teacher who was really amazing
Jo Boaler (1:09:11.320)
for me in maths, and she kept me in the subject.
Lex Fridman (1:09:14.840)
I probably wouldn't have left it.
Lex Fridman (1:09:16.320)
Who was she?
Lex Fridman (1:09:17.160)
She was, her name was Mrs. Marshall.
Lex Fridman (1:09:20.840)
And she was my A level maths teacher.
Lex Fridman (1:09:27.680)
So I was in England.
Jo Boaler (1:09:30.080)
You do lots of subjects till you're 16,
Lex Fridman (1:09:32.040)
and then you choose like three or four subjects.
Lex Fridman (1:09:35.320)
So I had chosen maths, and you go to higher levels,
Lex Fridman (1:09:41.440)
probably equivalent more to a master's degree in the US
Jo Boaler (1:09:44.640)
because you're more specialized.
Lex Fridman (1:09:46.160)
But anyways, she was my teacher,
Lex Fridman (1:09:48.720)
and for the first time in my whole career in maths,
Lex Fridman (1:09:52.680)
she would give us problems
Lex Fridman (1:09:54.320)
and tell us to talk about them with each other.
Lex Fridman (1:09:58.000)
And so here I was sitting there at like 17,
Jo Boaler (1:10:01.000)
talking with friends about how to solve a math problem,
Lex Fridman (1:10:04.000)
and that was it.
Jo Boaler (1:10:04.840)
That was the change that she made,
Lex Fridman (1:10:07.800)
but it was profound for me
Jo Boaler (1:10:10.000)
because like those calculus students,
Lex Fridman (1:10:13.360)
I started to hear other people's ways of thinking
Lex Fridman (1:10:16.200)
and seeing it, and we would talk together
Lex Fridman (1:10:17.920)
and come up with solutions.
Lex Fridman (1:10:19.840)
And I was like, that was it.
Lex Fridman (1:10:20.680)
That changed maths for me.
Jo Boaler (1:10:23.240)
It wasn't some kind of personal interaction with her.
Lex Fridman (1:10:25.520)
It was more like she was the catalyst
Jo Boaler (1:10:29.200)
for that collaborative experience.
Lex Fridman (1:10:32.040)
I mean, yeah, the many ways teachers can inspire kids.
Jo Boaler (1:10:34.960)
I mean, sometimes it's a personal message,
Lex Fridman (1:10:36.920)
but it can be your teaching approach
Jo Boaler (1:10:39.840)
that changes maths for kids.
Lex Fridman (1:10:42.400)
You know, Cal Newport, he wrote a book called Deep Work,
Lex Fridman (1:10:48.520)
and he's a mathematician, a theoretical computer scientist,
Lex Fridman (1:10:51.480)
and he talks about the kind of the focus required
Jo Boaler (1:10:55.720)
to do that kind of work.
Lex Fridman (1:10:58.080)
Is there something you can comment on?
Jo Boaler (1:11:01.760)
You know, we live in a world full of distractions.
Lex Fridman (1:11:04.920)
That seems like one of the elements that makes studying,
Lex Fridman (1:11:08.400)
and especially the studying of subjects
Lex Fridman (1:11:10.280)
that require thinking like maths does, difficult.
Jo Boaler (1:11:14.480)
Is there something from a student perspective,
Lex Fridman (1:11:17.400)
from a teacher perspective that encourages deep work
Lex Fridman (1:11:20.640)
that you can comment on?
Lex Fridman (1:11:21.480)
Yeah, I think giving kids really inspiring deep problems,
Lex Fridman (1:11:28.320)
and we have some on our website,
Lex Fridman (1:11:31.440)
is a really important experience for them.
Jo Boaler (1:11:35.040)
Even if they only do it occasionally,
Lex Fridman (1:11:38.200)
but it's really important.
Jo Boaler (1:11:40.080)
They actually realise, I do, I give a problem out often
Lex Fridman (1:11:44.360)
when I'm working with teachers, and I say to them,
Jo Boaler (1:11:47.040)
all right, I'm gonna check in with you after an hour.
Lex Fridman (1:11:49.800)
And they're like, an hour?
Jo Boaler (1:11:51.480)
They think it's shocking.
Lex Fridman (1:11:53.520)
And then they work on this problem,
Lex Fridman (1:11:55.400)
and after an hour, I say, okay, how are we doing?
Lex Fridman (1:11:57.880)
They're like, an hour's gone by?
Lex Fridman (1:12:00.600)
How is this possible?
Lex Fridman (1:12:02.000)
And so everybody needs those like rich deep problems.
Jo Boaler (1:12:07.000)
Most kids go through their whole maths experience
Lex Fridman (1:12:10.680)
of however many years, never once working on a problem
Jo Boaler (1:12:14.880)
in that kind of deep way.
Lex Fridman (1:12:16.680)
So the undergrad class I teach at Stanford, we do that.
Jo Boaler (1:12:21.680)
We work on these deep problems every session.
Lex Fridman (1:12:25.160)
And the students come away going, okay,
Jo Boaler (1:12:27.200)
I never wanna go back to that maths relationship I had
Lex Fridman (1:12:30.120)
where it was just all about quick answers.
Jo Boaler (1:12:32.000)
I just don't wanna go back to that.
Lex Fridman (1:12:34.520)
And so we can all, all teachers can incorporate
Jo Boaler (1:12:39.720)
those problems in their classrooms.
Lex Fridman (1:12:41.280)
Maybe they don't do them every day,
Lex Fridman (1:12:42.560)
but they at least give kids some experience
Lex Fridman (1:12:46.080)
of being able to work slowly and deeply
Lex Fridman (1:12:49.760)
and to go to deeper places and not be told
Lex Fridman (1:12:55.680)
they've got five minutes to finish 20 questions.
Jo Boaler (1:12:58.680)
Well, part of it is also just the exercise
Lex Fridman (1:13:02.720)
of sitting there and maintaining focus
Jo Boaler (1:13:05.320)
for prolonged periods of time.
Lex Fridman (1:13:07.040)
That's not often, I mean, that's a skill.
Jo Boaler (1:13:11.960)
It's a skill that also could be discouraging.
Lex Fridman (1:13:16.000)
Like if you don't practice it,
Jo Boaler (1:13:18.120)
just sitting down for 10 minutes straight
Lex Fridman (1:13:20.520)
and maintaining deep focus could be exceptionally challenging.
Jo Boaler (1:13:23.480)
Like if you're really thinking about a problem
Lex Fridman (1:13:26.600)
and I think it's really important to realize
Jo Boaler (1:13:29.240)
that that's a skill that you can just like a muscle,
Lex Fridman (1:13:31.880)
you can build, you can start with five minutes
Lex Fridman (1:13:33.520)
and goes to 10 minutes to 30 and to an hour.
Lex Fridman (1:13:36.680)
And to be successful, I think in certain subjects
Jo Boaler (1:13:39.000)
like mathematics, you wanna be able to develop that skill.
Lex Fridman (1:13:42.520)
Otherwise you're not going to get
Jo Boaler (1:13:46.640)
to the really rewarding experience
Lex Fridman (1:13:49.680)
of solving these problems.
Jo Boaler (1:13:52.400)
Definitely.
Lex Fridman (1:13:53.520)
There was a survey done of kids in school
Jo Boaler (1:13:55.880)
where they were asked, how long will you work
Lex Fridman (1:13:57.480)
on a maths problem before you give up
Lex Fridman (1:13:59.000)
and decide it's not possible to solve it?
Lex Fridman (1:14:02.440)
And the result on average across the kids was two minutes.
Jo Boaler (1:14:10.720)
Yeah, that's a bad sign, but that was a powerful sign
Lex Fridman (1:14:15.360)
that they need to learn to not give up so quickly.
Jo Boaler (1:14:19.480)
Yeah, we mentioned offline
Lex Fridman (1:14:22.760)
because we've been talking so much about visualization,
Jo Boaler (1:14:25.520)
Grant Sanderson, Three Blue One Brown.
Lex Fridman (1:14:29.200)
So he's inspired millions of people
Jo Boaler (1:14:32.040)
with exactly the kind of way of thinking
Lex Fridman (1:14:35.480)
that you've been talking about.
Jo Boaler (1:14:36.640)
Yeah, I love his work.
Lex Fridman (1:14:38.960)
Converting sort of mathematical concepts
Jo Boaler (1:14:42.680)
into visual, like visually representing them,
Lex Fridman (1:14:48.080)
exploring them in ways that help you illuminate
Jo Boaler (1:14:51.000)
like the concepts.
Lex Fridman (1:14:53.280)
What do you think is the role of that?
Lex Fridman (1:14:55.040)
So he uses mostly programmatic visualization.
Lex Fridman (1:14:58.000)
So it's the thing I mentioned where there's like animations
Jo Boaler (1:15:01.320)
created by writing computer programs.
Lex Fridman (1:15:05.560)
Like what do you think, how scalable is that approach?
Lex Fridman (1:15:08.440)
But in general, what do you think about his approach?
Lex Fridman (1:15:10.480)
I think it's amazing.
Jo Boaler (1:15:11.880)
I should work with him.
Lex Fridman (1:15:14.680)
I can share some of our visuals
Lex Fridman (1:15:17.040)
and he can make them in that amazing way.
Lex Fridman (1:15:20.960)
So part of his storytelling,
Jo Boaler (1:15:23.040)
part of it is creating the visuals
Lex Fridman (1:15:26.360)
and then weaving a story with those visuals
Jo Boaler (1:15:29.400)
that kind of builds, like there's also,
Lex Fridman (1:15:32.080)
I mean, there's also drama in it.
Jo Boaler (1:15:34.960)
You start with a small example
Lex Fridman (1:15:36.520)
and then you kind of, all of a sudden there's a surprise.
Jo Boaler (1:15:39.560)
Yeah, yeah, yeah.
Lex Fridman (1:15:41.080)
And it really, I mean, it makes you fall in love
Jo Boaler (1:15:43.440)
with the concept.
Lex Fridman (1:15:45.560)
He does talk about that.
Jo Boaler (1:15:48.440)
His sense is like some of the stuff,
Lex Fridman (1:15:50.800)
he doesn't feel like he's teaching like the core curriculum,
Jo Boaler (1:15:57.320)
which is something, he sees himself
Lex Fridman (1:16:01.000)
as an inspirational figure.
Lex Fridman (1:16:03.600)
But because I think it's too difficult
Lex Fridman (1:16:05.760)
to kind of convert all of the curriculum into those elements.
Lex Fridman (1:16:09.600)
And probably you don't need to.
Lex Fridman (1:16:11.000)
I mean, if people get to experience mathematical ideas
Jo Boaler (1:16:15.920)
in the way that he shares them, that will change them.
Lex Fridman (1:16:20.000)
And it will change the way they think.
Lex Fridman (1:16:21.600)
And maybe they could go on
Lex Fridman (1:16:22.840)
to take some other mathematical idea
Lex Fridman (1:16:25.040)
and make it that beautiful.
Lex Fridman (1:16:26.320)
Well, he does that.
Jo Boaler (1:16:28.920)
He created a library called Manim and he open sourced it.
Lex Fridman (1:16:32.920)
And that library is the, people should check it out.
Jo Boaler (1:16:36.400)
It's written in Python
Lex Fridman (1:16:39.520)
and it uses some of those same elements.
Jo Boaler (1:16:41.960)
Like it allows you to animate equations
Lex Fridman (1:16:44.040)
and animate little shapes.
Jo Boaler (1:16:45.640)
Like people that, you know,
Lex Fridman (1:16:47.600)
he has a very distinct style in his videos
Lex Fridman (1:16:50.320)
and what that resulted in,
Lex Fridman (1:16:51.640)
even though from a software engineer perspective,
Jo Boaler (1:16:54.160)
the code he released is not like super well documented
Lex Fridman (1:16:57.760)
or perfect, but him releasing that,
Jo Boaler (1:17:01.760)
now there's all of these people educating it.
Lex Fridman (1:17:05.200)
And the cool, to me personally,
Jo Boaler (1:17:06.800)
the coolest thing is to see like people they're not,
Lex Fridman (1:17:11.120)
you know, don't have like a million subscribers
Jo Boaler (1:17:13.760)
or something is they have just a few views in the video,
Lex Fridman (1:17:17.440)
but it just seems like the process of them
Jo Boaler (1:17:21.520)
creating a video where they teach
Lex Fridman (1:17:24.360)
is like transformative to them from a student perspective.
Jo Boaler (1:17:27.200)
It's the old Feynman thing,
Lex Fridman (1:17:28.360)
the best way to learn is to teach.
Lex Fridman (1:17:30.280)
And then him releasing that into the wild is,
Lex Fridman (1:17:33.720)
it shows that that impact.
Jo Boaler (1:17:35.800)
Yeah, absolutely.
Lex Fridman (1:17:37.480)
I think just giving people that idea
Jo Boaler (1:17:39.840)
that you can do that with maths and other subjects,
Lex Fridman (1:17:42.920)
there's bound to be people all around
Jo Boaler (1:17:45.680)
who can create more, which is cool.
Lex Fridman (1:17:48.720)
Yeah, definitely.
Lex Fridman (1:17:49.640)
So I recommend that people do like JavaScript or Python.
Lex Fridman (1:17:52.600)
You can build like visualizations of most concepts
Jo Boaler (1:17:56.400)
in high school math.
Lex Fridman (1:17:57.720)
You can do a lot of kinds of visualizations
Lex Fridman (1:18:00.000)
and doing that yourself.
Lex Fridman (1:18:01.480)
Plus, if you do that yourself, people will really love it.
Jo Boaler (1:18:04.360)
People actually, people love visualizations of math.
Lex Fridman (1:18:09.240)
Cause they, I mean, it's something in us
Jo Boaler (1:18:11.160)
that loves patterns, loves figuring out difficult things
Lex Fridman (1:18:14.280)
and the patterns in there then are unexpected in some way.
Jo Boaler (1:18:19.000)
Yeah.
Lex Fridman (1:18:19.840)
Have you ever noticed that hotels
Lex Fridman (1:18:22.040)
are always filled with patterns?
Lex Fridman (1:18:24.240)
I was just noticing at the hotel I'm in now,
Jo Boaler (1:18:26.360)
all of their carpets are pattern carpets
Lex Fridman (1:18:28.720)
and then they have patterns on the walls.
Jo Boaler (1:18:30.920)
Yeah.
Lex Fridman (1:18:31.760)
So, yeah.
Jo Boaler (1:18:33.080)
We humans love the symmetry and patterns,
Lex Fridman (1:18:36.440)
the breaking of symmetry and patterns.
Jo Boaler (1:18:38.840)
Yeah.
Lex Fridman (1:18:39.920)
And then it's funny that we don't see mathematics
Lex Fridman (1:18:42.880)
as somehow intricately connected to that, but it is, right?
Lex Fridman (1:18:45.960)
I mean, that's one of the perspectives
Jo Boaler (1:18:47.360)
that I love students to take is to be a pattern seeker.
Lex Fridman (1:18:51.040)
In everything.
Jo Boaler (1:18:51.880)
In, yeah, certainly in all of maths.
Lex Fridman (1:18:53.840)
I mean, you can think of all of maths
Jo Boaler (1:18:55.320)
as a kind of subject of patterns
Lex Fridman (1:18:57.160)
and not just visual patterns, but, you know,
Jo Boaler (1:19:01.600)
when you think about multiplying by five
Lex Fridman (1:19:05.720)
and the fact you can, you know,
Jo Boaler (1:19:08.120)
if you're multiplying 18 times five,
Lex Fridman (1:19:11.280)
you can instead think of nine times 10.
Jo Boaler (1:19:14.680)
That's a pattern that always works in mathematics.
Lex Fridman (1:19:17.240)
You can halve a number and double a number.
Lex Fridman (1:19:19.080)
And so, yeah, I just think there are patterns everywhere.
Lex Fridman (1:19:21.320)
And if kids are thinking their role is to see patterns
Lex Fridman (1:19:24.760)
and find patterns, it's really exciting.
Lex Fridman (1:19:28.440)
What do you think about like MIT OpenCourseWare
Lex Fridman (1:19:31.960)
and the release of lectures by universities?
Lex Fridman (1:19:36.280)
I think it's good.
Jo Boaler (1:19:37.880)
I think it's good.
Lex Fridman (1:19:38.720)
I think that is what started the MOOC I did
Jo Boaler (1:19:43.800)
was using that platform.
Lex Fridman (1:19:46.040)
So you ultimately think like the Udacity models
Jo Boaler (1:19:48.720)
is a little bit more effective
Lex Fridman (1:19:50.440)
than just a plain two hour lecture.
Jo Boaler (1:19:52.440)
I think there's definitely,
Lex Fridman (1:19:53.600)
you can bring in good pedagogy into online learning.
Lex Fridman (1:19:57.000)
And I think the idea of putting things online
Lex Fridman (1:19:59.560)
so that people all over the world can access them is great.
Jo Boaler (1:20:02.720)
I don't think the initial excitement around MOOCs
Lex Fridman (1:20:06.000)
sort of democratizing education
Lex Fridman (1:20:08.280)
and make it more equal came about
Lex Fridman (1:20:11.840)
because they found that the people taking MOOCs
Jo Boaler (1:20:14.040)
tended to be the more privileged people.
Lex Fridman (1:20:17.000)
So that was, I think there's still something to be found
Jo Boaler (1:20:20.880)
in that there's still more to be done
Lex Fridman (1:20:22.800)
to help that online learning reach those principles.
Lex Fridman (1:20:27.640)
But definitely, I think it's a good invention.
Lex Fridman (1:20:31.800)
And I have an online class that's for kids,
Jo Boaler (1:20:35.080)
that's a little free class that gives them.
Lex Fridman (1:20:36.960)
What's the topic?
Jo Boaler (1:20:37.960)
It's called How to Learn Maths.
Lex Fridman (1:20:39.480)
How to Learn Maths.
Jo Boaler (1:20:41.680)
It shows maths as this visual creative subject
Lex Fridman (1:20:44.360)
and it shares mindset and some brain science
Lex Fridman (1:20:47.080)
and kids who take it do better in maths class.
Lex Fridman (1:20:51.200)
We've studied it with like randomized controlled trials
Lex Fridman (1:20:54.160)
and given it to middle school kids
Lex Fridman (1:20:57.240)
and other middle school kids who don't take it
Lex Fridman (1:21:00.000)
but are taught by the same teachers.
Lex Fridman (1:21:01.320)
So their teachers are the same.
Lex Fridman (1:21:02.920)
And the kids who take the online class
Lex Fridman (1:21:04.840)
end up 68% more engaged in their maths class
Lex Fridman (1:21:08.680)
and do better at the end of the year.
Lex Fridman (1:21:10.480)
So that's a little six session, 15 minute class
Lex Fridman (1:21:15.080)
and it changes kids maths relationships.
Lex Fridman (1:21:18.920)
So it is true that we can do that with some words
Jo Boaler (1:21:24.840)
that aren't, it's not a huge change to the education system.
Lex Fridman (1:21:30.320)
Do you have advice for young people?
Jo Boaler (1:21:33.120)
We've been talking about mathematics quite a bit
Lex Fridman (1:21:35.920)
but in terms of their journey through education,
Jo Boaler (1:21:39.200)
through their career choices, through life,
Lex Fridman (1:21:41.760)
maybe middle school, high school, undergrad students,
Lex Fridman (1:21:46.040)
of how to live a life they can be proud of?
Lex Fridman (1:21:50.520)
I think if I were to give advice to people,
Jo Boaler (1:21:54.160)
especially young people, my advice would be to always,
Lex Fridman (1:21:59.400)
it sounds really corny,
Lex Fridman (1:22:00.440)
but always believe in yourself
Lex Fridman (1:22:03.360)
and know that you can achieve
Jo Boaler (1:22:05.240)
because although that sounds like obvious,
Lex Fridman (1:22:07.880)
of course we want kids to know that they can achieve things.
Jo Boaler (1:22:10.320)
I know that millions of kids who are in the school system
Lex Fridman (1:22:13.760)
have been given the message, they cannot do things.
Lex Fridman (1:22:17.160)
And adults too, they have the idea,
Lex Fridman (1:22:20.520)
oh, I did okay in this, I went into this job
Jo Boaler (1:22:23.200)
because those other things I could never have done okay in.
Lex Fridman (1:22:26.840)
So actually when they hear,
Jo Boaler (1:22:28.480)
hey, maybe you could do those other things.
Lex Fridman (1:22:31.440)
Even adults think, maybe I can.
Lex Fridman (1:22:34.960)
And they go back and they encounter this knowledge
Lex Fridman (1:22:38.000)
and they relearn things and they change careers
Lex Fridman (1:22:40.680)
and amazing things happen.
Lex Fridman (1:22:42.560)
So for me, I think that message is really important.
Jo Boaler (1:22:45.840)
You can learn anything.
Lex Fridman (1:22:47.680)
Scientists try and find a limit.
Jo Boaler (1:22:50.040)
They're always trying to find a limit,
Lex Fridman (1:22:51.120)
like how much can you really learn?
Lex Fridman (1:22:52.400)
What's the limit to how much you can learn?
Lex Fridman (1:22:54.160)
And they always come away not being able to find it.
Jo Boaler (1:22:56.400)
People can just go further and further and further.
Lex Fridman (1:22:59.400)
And that is true of people born with brain,
Jo Boaler (1:23:04.400)
areas of their brain that aren't functioning well
Lex Fridman (1:23:06.280)
that have what we call special needs.
Jo Boaler (1:23:08.640)
Some of those people also go on to develop
Lex Fridman (1:23:10.880)
and do amazing things.
Lex Fridman (1:23:12.680)
So I think that really experiencing that,
Lex Fridman (1:23:17.280)
knowing that feeling, not just saying it,
Lex Fridman (1:23:19.440)
but knowing it deeply, you can learn anything
Lex Fridman (1:23:24.080)
is something I wish all people would have.
Jo Boaler (1:23:28.600)
Actually also applies when you've achieved
Lex Fridman (1:23:30.600)
some level of success too.
Lex Fridman (1:23:32.400)
What I find, like in my life with people that love me,
Lex Fridman (1:23:36.240)
when you achieve success,
Jo Boaler (1:23:37.840)
they keep celebrating your success
Lex Fridman (1:23:40.280)
and they want you to keep doing the thing
Jo Boaler (1:23:42.640)
that you were successful at,
Lex Fridman (1:23:44.960)
as opposed to believing in that you can do something else,
Jo Boaler (1:23:49.080)
something big, whatever your heart says to do.
Lex Fridman (1:23:51.560)
And one of the things that I realized the value of this,
Jo Boaler (1:23:57.760)
quite recently, which is sad to say,
Lex Fridman (1:24:00.400)
is how important it is to seek out,
Jo Boaler (1:24:03.160)
when you're younger, to seek out mentors,
Lex Fridman (1:24:04.920)
to seek out the people,
Jo Boaler (1:24:07.520)
surround yourself with people that will believe in you.
Lex Fridman (1:24:10.680)
It's like a little bit is on you.
Jo Boaler (1:24:14.040)
It's like, you don't get that sometimes
Lex Fridman (1:24:18.200)
if you go to grad school,
Jo Boaler (1:24:20.080)
you think you kind of land on a mentor,
Lex Fridman (1:24:22.240)
maybe you pick a mentor based on the topic
Jo Boaler (1:24:24.440)
they're interested in.
Lex Fridman (1:24:25.680)
But the reality is the people you surround yourself with,
Jo Boaler (1:24:28.960)
they're going to define your life trajectory.
Lex Fridman (1:24:32.400)
So select people that believe in you.
Lex Fridman (1:24:35.480)
And get away from people who don't believe in you.
Lex Fridman (1:24:38.640)
Sometimes parents can be that, they can love you deeply,
Lex Fridman (1:24:41.840)
but they set, it's the math thing we mentioned,
Lex Fridman (1:24:46.280)
they might set certain constraints on the beliefs
Jo Boaler (1:24:50.120)
that you have.
Lex Fridman (1:24:50.960)
And so in that, if you're interested in mathematics,
Lex Fridman (1:24:55.080)
and your parents are not that interested in it,
Lex Fridman (1:24:56.800)
don't listen to your parents on that one dimension.
Jo Boaler (1:24:59.600)
Exactly.
Lex Fridman (1:25:00.800)
Yeah, and if people tell you you can't do things,
Jo Boaler (1:25:02.880)
you have to hear from other people who believe in you.
Lex Fridman (1:25:06.640)
I think you're absolutely right about that.
Lex Fridman (1:25:09.200)
So sad the number of people who've had
Lex Fridman (1:25:11.280)
those negative messages from parents.
Jo Boaler (1:25:14.040)
In my Limitless Mind book, I interviewed quite a few people
Lex Fridman (1:25:16.840)
who'd been told they couldn't do math,
Jo Boaler (1:25:18.520)
sometimes by parents, sometimes by teachers.
Lex Fridman (1:25:21.720)
And fortunately, they had got other ideas
Jo Boaler (1:25:24.880)
at some point in their life,
Lex Fridman (1:25:26.040)
and realized there was this whole world
Jo Boaler (1:25:28.520)
of mathematical thinking that was open to them.
Lex Fridman (1:25:32.240)
So it's really important that people do connect
Jo Boaler (1:25:37.360)
with people who believe in them,
Lex Fridman (1:25:39.120)
however hard that might be to find those people.
Lex Fridman (1:25:41.920)
What do you hope the education system,
Lex Fridman (1:25:44.880)
education in general, looks like 10, 20, 50,
Lex Fridman (1:25:48.000)
100 years from now?
Lex Fridman (1:25:49.640)
Are you optimistic about this future?
Jo Boaler (1:25:51.720)
Yeah, I definitely have hope.
Lex Fridman (1:25:53.080)
There is, change can happen in the education system.
Jo Boaler (1:25:56.600)
In recent years, it's been microscopically slow.
Lex Fridman (1:26:03.320)
But I do actually see change happening.
Jo Boaler (1:26:07.320)
We were talking earlier that data science is now
Lex Fridman (1:26:10.840)
a course you can take in high school instead of algebra two.
Lex Fridman (1:26:14.280)
And that's pretty amazing because that content
Lex Fridman (1:26:17.640)
was set out in 1892 and hasn't changed since then.
Lex Fridman (1:26:22.080)
And so now we're actually seeing a change
Lex Fridman (1:26:25.120)
in the content of high school.
Lex Fridman (1:26:26.880)
So I'm amazed that that's happening
Lex Fridman (1:26:29.480)
and very happy it's happening.
Lex Fridman (1:26:31.280)
So change is very slow in education usually,
Lex Fridman (1:26:33.960)
but when you look ahead and think about all that we know,
Lex Fridman (1:26:38.960)
and all that we can offer kids in terms of technology,
Lex Fridman (1:26:42.960)
you've got to think that 100 years from now,
Jo Boaler (1:26:46.960)
education will be totally different to the way it is now.
Lex Fridman (1:26:50.960)
Maybe we won't have subject boundaries anymore
Jo Boaler (1:26:54.400)
because those don't really make much sense.
Lex Fridman (1:26:57.400)
And it's interesting to think how certain tools
Jo Boaler (1:27:00.880)
like programming, maybe they'll be deeply integrated
Lex Fridman (1:27:03.960)
in everything we do.
Jo Boaler (1:27:04.800)
Yeah, you would think that all kids are growing up
Lex Fridman (1:27:07.360)
learning to program and create.
Lex Fridman (1:27:11.040)
So I just think, I mean, the system of schooling
Lex Fridman (1:27:14.360)
we have now, people call it a factory model.
Jo Boaler (1:27:17.240)
It's not designed to inspire creativity.
Lex Fridman (1:27:21.960)
And I feel like that will also change.
Jo Boaler (1:27:25.560)
People might look back on these days
Lex Fridman (1:27:27.360)
and think they were hilarious,
Lex Fridman (1:27:28.800)
but maybe we'll in the future,
Lex Fridman (1:27:32.200)
kids will be doing their own programming
Lex Fridman (1:27:33.600)
and they'll be able to learn things
Lex Fridman (1:27:35.080)
and find out things and create things
Jo Boaler (1:27:37.120)
even as they're learning.
Lex Fridman (1:27:37.960)
And maybe the individual subject boundaries will go.
Jo Boaler (1:27:44.320)
Data science itself coming into the education system
Lex Fridman (1:27:47.360)
kind of illustrates that because people realize
Jo Boaler (1:27:50.440)
it doesn't really fit inside any of the subjects.
Lex Fridman (1:27:54.960)
So what do we do with it?
Lex Fridman (1:27:56.280)
Where does it go and who teaches it?
Lex Fridman (1:27:59.840)
So it's already raising those kind of questions
Lex Fridman (1:28:03.080)
and questioning how we have these different subject boundaries.
Lex Fridman (1:28:07.560)
So you've seen data science be integrated
Lex Fridman (1:28:09.320)
into the curriculum?
Lex Fridman (1:28:10.640)
Yes, it's happening across the United States as we speak.
Jo Boaler (1:28:14.080)
I wonder how they got initiated.
Lex Fridman (1:28:15.480)
Like how does change happen in the education system?
Lex Fridman (1:28:18.360)
Is it just a few revolutionary leaders?
Lex Fridman (1:28:20.880)
It does, I think so.
Jo Boaler (1:28:22.320)
I think so.
Lex Fridman (1:28:23.160)
It's been an interesting journey
Jo Boaler (1:28:24.520)
seeing data science take off actually.
Lex Fridman (1:28:26.600)
There was a course that was developed in 2014
Jo Boaler (1:28:32.240)
by some people who thought data science
Lex Fridman (1:28:34.240)
was a good idea for high schoolers.
Lex Fridman (1:28:36.640)
And then after some kids took the course
Lex Fridman (1:28:39.480)
and nothing bad happened to them,
Jo Boaler (1:28:41.320)
they went to college and people started to accept it more.
Lex Fridman (1:28:46.320)
And then this was a big piece of the change in California.
Jo Boaler (1:28:49.480)
The UC system communicated.
Lex Fridman (1:28:52.040)
They sent out an email last year,
Jo Boaler (1:28:53.600)
the 50,000 high schools saying, we now accept data science.
Lex Fridman (1:28:57.080)
Kids can take it instead of algebra two.
Jo Boaler (1:28:59.120)
That's a perfectly legitimate college pathway.
Lex Fridman (1:29:01.960)
So that was like a big green light for a lot of schools
Jo Boaler (1:29:05.640)
who were like wondering about whether they could teach it.
Lex Fridman (1:29:08.520)
So I think it happens in small spaces and expands.
Jo Boaler (1:29:12.280)
It goes viral.
Lex Fridman (1:29:13.480)
Yeah.
Jo Boaler (1:29:14.320)
In this modern age.
Lex Fridman (1:29:15.160)
Then it goes viral.
Jo Boaler (1:29:16.000)
California's ahead, I think in creating courses
Lex Fridman (1:29:21.000)
and having kids go through it, but it's suddenly,
Jo Boaler (1:29:25.360)
when I last looked, there were 12 states
Lex Fridman (1:29:27.400)
that were allowing data science as a high school course.
Lex Fridman (1:29:29.720)
And I think by next year, that will have doubled or more.
Lex Fridman (1:29:35.040)
So change is happening.
Jo Boaler (1:29:38.400)
Joe, as I said, I think mathematics
Lex Fridman (1:29:41.920)
is truly a beautiful subject.
Lex Fridman (1:29:45.120)
And you having an impact on millions of people
Lex Fridman (1:29:48.560)
and you having an impact on millions of people's lives
Jo Boaler (1:29:52.200)
by educating them, by inspiring teachers to educate
Lex Fridman (1:29:56.160)
in the ways that you've talked about
Jo Boaler (1:29:57.960)
in multidimensional ways, in visual ways,
Lex Fridman (1:30:01.440)
I think is incredible.
Lex Fridman (1:30:02.440)
So you're spreading beauty into the world.
Lex Fridman (1:30:06.040)
So I really, really appreciate
Jo Boaler (1:30:07.520)
that you spend your valuable time with me today.
Lex Fridman (1:30:09.240)
Thank you for talking.
Jo Boaler (1:30:10.080)
Thank you.
Lex Fridman (1:30:10.920)
It was really good to talk to you.
Jo Boaler (1:30:12.560)
Thanks for listening to this conversation with Joe Boller.
Lex Fridman (1:30:15.280)
To support this podcast,
Jo Boaler (1:30:16.680)
please check out our sponsors in the description.
Lex Fridman (1:30:19.520)
And now let me leave you with some words
Jo Boaler (1:30:21.400)
from Albert Einstein.
Lex Fridman (1:30:23.640)
Pure mathematics is the poetry of logical ideas.
Jo Boaler (1:30:27.960)
Thanks for listening and hope to see you next time.
Lex Fridman (20:00.720)
I said, no, don't put it on a stamp.
Jo Boaler (20:03.560)
It's, but your words are really important.
Lex Fridman (20:07.960)
And kids are sitting in classrooms all the time thinking,
Lex Fridman (20:12.480)
what does my teacher think of me?
Lex Fridman (20:13.880)
Does my teacher think I can do this?
Lex Fridman (20:17.240)
So it turns out it is really important
Lex Fridman (20:19.520)
to be saying to kids, I know you can do this.
Lex Fridman (20:22.560)
And those messages are not given enough by teachers.
Lex Fridman (20:27.600)
And really believe it.
Lex Fridman (20:28.960)
And believe it.
Lex Fridman (20:29.800)
Yeah, it's like.
Jo Boaler (20:30.640)
You can't just say it, you have to believe it.
Lex Fridman (20:32.440)
I sometimes, cause it's like,
Jo Boaler (20:36.520)
it's such a funny dance,
Lex Fridman (20:38.000)
cause I'm almost such a perfectionist.
Jo Boaler (20:39.560)
I'm extremely self critical.
Lex Fridman (20:41.320)
And I have one of the students come up to me
Lex Fridman (20:43.600)
and it's clear to me that they're not even close to good.
Lex Fridman (20:49.360)
And it's tempting for me to be like,
Jo Boaler (20:52.280)
to sort of give up on them mentally.
Lex Fridman (20:54.320)
But the reality is like,
Jo Boaler (20:55.840)
if you look at many great people throughout history,
Lex Fridman (20:58.920)
they sucked at some point.
Jo Boaler (21:00.360)
Yeah, exactly.
Lex Fridman (21:01.200)
And some of the greatest took nonlinear paths
Jo Boaler (21:04.200)
to where they sucked for long into later life.
Lex Fridman (21:08.760)
And so always kind of believing that this person
Jo Boaler (21:11.960)
can be great.
Lex Fridman (21:13.240)
Exactly.
Jo Boaler (21:14.480)
You have to communicate that,
Lex Fridman (21:15.800)
plus the fact that they have to work hard.
Jo Boaler (21:17.600)
That's it, yeah.
Lex Fridman (21:19.000)
Yeah, and you're right.
Jo Boaler (21:19.920)
Silicon Valley where I live is filled with people
Lex Fridman (21:22.720)
who are dropouts at school,
Jo Boaler (21:24.520)
or who had special needs, who didn't succeed.
Lex Fridman (21:28.800)
It's very interesting that have gone on
Jo Boaler (21:30.720)
to do amazing work in creative ways.
Lex Fridman (21:34.240)
I mean, I do think our school system is set up
Jo Boaler (21:36.600)
to value good memorizers who can reproduce
Lex Fridman (21:42.680)
what a teacher is showing them,
Lex Fridman (21:44.720)
and push away those creative deep thinkers,
Lex Fridman (21:49.160)
often slower thinkers, they think slowly and deeply.
Lex Fridman (21:53.600)
And they often get the idea early on
Lex Fridman (21:55.320)
that they can't be good at maths or other subjects.
Lex Fridman (21:59.000)
So yeah, I think many of those people
Lex Fridman (22:02.320)
are the ones who go on and do amazing things.
Lex Fridman (22:05.160)
So there's a guy named Eric Weinstein.
Lex Fridman (22:08.280)
I know many mathematicians like this,
Lex Fridman (22:09.800)
but he talks a lot about having a nonstandard way
Lex Fridman (22:16.040)
of learning.
Jo Boaler (22:17.680)
I mean, a lot of great mathematicians,
Lex Fridman (22:19.680)
a lot of great physicists are like that.
Lex Fridman (22:22.080)
And he felt like he became quickly,
Lex Fridman (22:24.640)
he got his PhD at Harvard,
Jo Boaler (22:26.360)
became quickly an outcast of the system.
Lex Fridman (22:28.560)
Like the education, especially early education system,
Jo Boaler (22:32.200)
didn't help him.
Lex Fridman (22:33.120)
Is there ways for an education system
Lex Fridman (22:37.840)
to support people like that?
Lex Fridman (22:40.320)
Is it this kind of multidimensional learning
Lex Fridman (22:42.400)
that you mentioned?
Lex Fridman (22:43.240)
Absolutely, absolutely.
Jo Boaler (22:44.280)
I mean, I think education system still uses an approach
Lex Fridman (22:48.040)
that was in classrooms hundreds of years ago.
Jo Boaler (22:50.320)
The textbooks have a lot to answer for
Lex Fridman (22:53.720)
in producing this very uninspiring mathematics.
Lex Fridman (22:58.320)
But yeah, if you open up the subject
Lex Fridman (23:00.720)
and have people see and solve it in different ways,
Lex Fridman (23:02.960)
and value those different ways.
Lex Fridman (23:05.320)
Somebody I appreciated a lot
Jo Boaler (23:07.280)
is a mathematician called Mary Mizikani.
Lex Fridman (23:09.680)
I don't know if you've heard of her.
Jo Boaler (23:10.560)
She won the Fields Medal.
Lex Fridman (23:12.480)
She was from Iran.
Jo Boaler (23:14.480)
First woman in the world
Lex Fridman (23:15.560)
to win the Fields Medal in mathematics.
Jo Boaler (23:17.800)
She died when she was 40.
Lex Fridman (23:19.480)
She was at Stanford.
Lex Fridman (23:21.240)
But her work was entirely visual.
Lex Fridman (23:24.840)
And she talked about how her daughter
Jo Boaler (23:27.600)
thought she was an artist
Lex Fridman (23:28.760)
because she was always visualizing.
Lex Fridman (23:30.680)
And I attended,
Lex Fridman (23:33.680)
she asked me to chair the PhD defense
Jo Boaler (23:35.800)
for one of her students.
Lex Fridman (23:37.440)
And I went to the defense in the math department.
Lex Fridman (23:40.280)
And it was so interesting
Lex Fridman (23:41.440)
because this young woman spent like two hours
Jo Boaler (23:45.280)
sharing her work.
Lex Fridman (23:46.800)
All of it was visual.
Jo Boaler (23:47.800)
In fact, I don't think I saw any numbers at all.
Lex Fridman (23:50.480)
That's awesome.
Lex Fridman (23:51.320)
And I remember that day thinking,
Lex Fridman (23:53.440)
wow, I could have brought her like 13 year old
Jo Boaler (23:55.920)
into this PhD defense.
Lex Fridman (23:56.960)
They would not recognize this as maths.
Lex Fridman (24:00.280)
But when Maryam Izzakhani won the Fields Medal,
Lex Fridman (24:03.720)
all these other mathematicians were saying
Jo Boaler (24:05.640)
that her work had connected
Lex Fridman (24:07.920)
all these previously unconnected areas of maths.
Lex Fridman (24:11.240)
And so, but when she was,
Lex Fridman (24:14.240)
she also shared that when she was in school,
Jo Boaler (24:16.120)
when she was about 13,
Lex Fridman (24:17.640)
she was told that she couldn't do maths.
Jo Boaler (24:21.040)
She was told that by her teacher.
Lex Fridman (24:22.680)
Is this is Iran?
Jo Boaler (24:23.960)
She grew up in Iran.
Lex Fridman (24:24.800)
In Iran, yeah.
Lex Fridman (24:26.080)
So I love that.
Lex Fridman (24:27.360)
To be told you can't be good at maths
Lex Fridman (24:29.320)
and then go on and win the Fields Medal is cool.
Lex Fridman (24:33.880)
I've been told by a lot of people in my life
Jo Boaler (24:37.120)
that I can't do something.
Lex Fridman (24:38.200)
I'm very, definitely nonstandard.
Lex Fridman (24:41.040)
But all it takes,
Lex Fridman (24:42.280)
that's why people talk about like the one teacher
Jo Boaler (24:45.360)
that changed everything.
Lex Fridman (24:46.200)
That's right.
Jo Boaler (24:47.040)
All it takes is one teacher.
Lex Fridman (24:48.000)
That's right.
Jo Boaler (24:48.840)
That's the power of that.
Lex Fridman (24:53.040)
So that's like, that should be inspiring to teachers.
Jo Boaler (24:55.800)
I think it is.
Lex Fridman (24:57.520)
You as a single person, given the education system,
Jo Boaler (25:00.000)
given the incentives,
Lex Fridman (25:00.960)
you have the power to truly change lives.
Lex Fridman (25:03.240)
And like 20 years from now,
Lex Fridman (25:04.960)
I feel as a medalist will walk up to you
Lex Fridman (25:06.640)
and say thank you.
Lex Fridman (25:07.480)
Yeah, so you did that for me.
Jo Boaler (25:09.320)
Yeah, absolutely.
Lex Fridman (25:10.320)
And I share that with teachers
Jo Boaler (25:12.120)
that even in this broken system
Lex Fridman (25:15.520)
of what they have to do for districts and textbooks,
Jo Boaler (25:19.760)
a single teacher can change kids maths relationship
Lex Fridman (25:22.880)
or other subjects forever.
Lex Fridman (25:26.440)
What's the role of the parents in this picture?
Lex Fridman (25:29.560)
Let's go to another difficult subject.
Jo Boaler (25:31.640)
Yeah, that is a difficult subject.
Lex Fridman (25:34.080)
One study found that
Jo Boaler (25:38.400)
the amount of maths anxiety parents had
Lex Fridman (25:42.720)
predicted their child's achievement in school,
Lex Fridman (25:46.640)
but only if they helped with homework.
Lex Fridman (25:51.200)
So...
Jo Boaler (25:52.560)
Oh, that's so funny.
Lex Fridman (25:57.000)
There are some interesting implications for this.
Jo Boaler (25:59.800)
I mean, you can see how it works.
Lex Fridman (26:01.240)
If you have maths anxiety
Lex Fridman (26:02.480)
and you're helping your kids with homework,
Lex Fridman (26:03.840)
you're probably communicating things like,
Jo Boaler (26:06.200)
oh, I was terrible at this at school.
Lex Fridman (26:09.080)
And that's how it gets passed on to kids.
Lex Fridman (26:12.400)
So one implication is
Lex Fridman (26:14.560)
if you have a really bad relationship with maths,
Jo Boaler (26:16.920)
you hate maths, you have maths anxiety,
Lex Fridman (26:19.040)
just don't do maths homework with your kids.
Lex Fridman (26:22.840)
But we have on our website,
Lex Fridman (26:25.840)
we have a little sheet for parents
Jo Boaler (26:28.480)
of ways to interact around maths with your kids and...
Lex Fridman (26:33.720)
That's ucubed.org.
Jo Boaler (26:36.560)
That's ucubed.org, yes.
Lex Fridman (26:39.280)
So one of the things I say to parents
Jo Boaler (26:40.920)
when I give parent presentations is
Lex Fridman (26:42.960)
even if you hate maths,
Jo Boaler (26:44.680)
you need to just fake it with your kids.
Lex Fridman (26:46.760)
You should be always endlessly optimistic
Lex Fridman (26:49.960)
and happy about doing maths.
Lex Fridman (26:52.200)
And...
Jo Boaler (26:54.040)
I'm always curious about this.
Lex Fridman (26:55.440)
So I hope to have kids one day.
Jo Boaler (26:57.840)
I don't have kids currently.
Lex Fridman (27:00.840)
Are parents okay with like sucking at maths
Lex Fridman (27:04.080)
and then trying to get their kid
Lex Fridman (27:06.400)
to be better than them essentially?
Lex Fridman (27:07.840)
Like, is that difficult thing for a lot of parents?
Lex Fridman (27:09.960)
It is difficult.
Jo Boaler (27:10.880)
To have like, it's almost like an ego thing.
Lex Fridman (27:12.840)
Like, I never got good at this
Lex Fridman (27:15.120)
and I probably should have.
Lex Fridman (27:16.840)
And yeah, I mean, to me, you wanna celebrate that,
Lex Fridman (27:20.840)
but I know a lot of people struggle with that.
Lex Fridman (27:23.840)
Like coaches in sports,
Jo Boaler (27:25.920)
to make an athlete become better than them,
Lex Fridman (27:29.680)
it can be hard on the ego.
Jo Boaler (27:31.760)
Yeah.
Lex Fridman (27:32.680)
So do you experience the same with parents too?
Jo Boaler (27:35.680)
I think, I mean, I haven't experienced parents
Lex Fridman (27:38.000)
worrying that their kids will be better than them.
Jo Boaler (27:40.800)
I have experienced...
Lex Fridman (27:42.800)
I have experienced parents
Jo Boaler (27:45.560)
just having a really bad relationship with maths
Lex Fridman (27:47.920)
and not wanting to help,
Jo Boaler (27:50.280)
not knowing how to help, saying things.
Lex Fridman (27:54.000)
Like another study showed that when mothers
Jo Boaler (27:56.680)
say to their daughters,
Lex Fridman (27:58.120)
I was bad at maths in school,
Jo Boaler (28:00.080)
their daughter's achievement goes down.
Lex Fridman (28:02.440)
So we know that kids pick up on these messages
Lex Fridman (28:05.280)
and which is why I say you should fake it.
Lex Fridman (28:08.400)
But also I know that lots of people
Jo Boaler (28:10.160)
have just had a really bad relationship with maths,
Lex Fridman (28:12.320)
even successful people.
Jo Boaler (28:15.120)
The undergrads I teach at Stanford
Lex Fridman (28:17.520)
have pretty much always done well in maths,
Lex Fridman (28:21.040)
but they come to Stanford thinking maths
Lex Fridman (28:24.040)
is a set of methods to memorize.
Lex Fridman (28:28.200)
And so, so do many parents believe that.
Lex Fridman (28:31.440)
There's one method that you memorize
Lex Fridman (28:34.320)
and then you reproduce it.
Lex Fridman (28:36.880)
So until people have really had an experience
Jo Boaler (28:40.080)
of what I think of as the other maths,
Lex Fridman (28:42.280)
well, until they've really seen
Jo Boaler (28:43.760)
that it's a really different subject,
Lex Fridman (28:48.640)
it's hard for them to be able to shift their kids
Jo Boaler (28:51.280)
to see it differently.
Lex Fridman (28:52.640)
Is there for a teacher,
Jo Boaler (28:55.040)
if we were to like systematize it,
Lex Fridman (28:57.920)
is there something teachers can do
Lex Fridman (28:59.800)
to do this more effectively?
Lex Fridman (29:01.400)
So you mentioned the textbook.
Jo Boaler (29:04.040)
Yeah.
Lex Fridman (29:04.880)
So what are the additional things
Jo Boaler (29:07.200)
you can add on top of this whole old school
Lex Fridman (29:10.000)
traditional way of teaching that can improve the process?
Lex Fridman (29:14.720)
So I do think there's a way of teaching maths
Lex Fridman (29:17.560)
that changes everything for kids and teachers.
Lex Fridman (29:21.680)
So I'm one of five writers of a new framework
Lex Fridman (29:25.480)
for the state of California, a new maths framework.
Jo Boaler (29:27.600)
It's coming out next year.
Lex Fridman (29:29.240)
And we are recommending through this maths framework
Jo Boaler (29:32.280)
that people teach in this way.
Lex Fridman (29:33.880)
It's called teaching to big ideas.
Lex Fridman (29:37.520)
So at the moment, people have standards
Lex Fridman (29:42.520)
that have been written,
Lex Fridman (29:43.440)
and then textbooks have taken these standards
Lex Fridman (29:45.760)
and made not very good questions.
Lex Fridman (29:48.840)
And if you look at the standards,
Lex Fridman (29:50.480)
like I have some written down here,
Jo Boaler (29:53.040)
just reading the standards,
Lex Fridman (29:54.560)
it makes maths seem really boring and uninspiring.
Lex Fridman (29:57.760)
What are the kind of, can you give a few examples?
Lex Fridman (30:00.880)
So this is an interesting example.
Jo Boaler (30:03.160)
In third grade, there are three different standards
Lex Fridman (30:06.160)
about unit squares.
Jo Boaler (30:10.480)
Okay.
Lex Fridman (30:11.640)
So this is one of them.
Jo Boaler (30:12.600)
A square with side length one unit, called a unit square,
Lex Fridman (30:16.120)
is said to have one square unit of area
Lex Fridman (30:18.760)
and can be used to measure area.
Lex Fridman (30:20.560)
And that's something you're expected to learn?
Jo Boaler (30:23.400)
That is something, so that's a standard.
Lex Fridman (30:25.600)
The textbook authors say,
Jo Boaler (30:26.920)
oh, I'm gonna make a question about that.
Lex Fridman (30:28.400)
And they translate the standards into narrow questions.
Lex Fridman (30:32.160)
And then you measure success by your ability
Lex Fridman (30:33.960)
to deliver on these standards.
Lex Fridman (30:36.880)
So the standards themselves, I think of maths
Lex Fridman (30:40.240)
and many people think of maths in this way
Jo Boaler (30:41.800)
as a subject of like a few big ideas
Lex Fridman (30:44.760)
and really important connections between them.
Lex Fridman (30:48.200)
So you could think of it as like a network map
Lex Fridman (30:50.400)
of ideas and connections.
Lex Fridman (30:52.600)
And what standards do is they take that beautiful map
Lex Fridman (30:55.800)
and they chop it up like this into lots of little pieces
Lex Fridman (30:58.720)
and they deliver the pieces to schools.
Lex Fridman (31:01.000)
And so teachers don't see the connections between ideas,
Jo Boaler (31:05.240)
nor do the kids.
Lex Fridman (31:06.400)
So anyway, this is a bit of a long way of saying
Jo Boaler (31:08.400)
that what we've done in this new initiative
Lex Fridman (31:11.840)
is we have set out maths as a set of big ideas
Lex Fridman (31:16.080)
and connections between them.
Lex Fridman (31:17.520)
So this is grade three.
Lex Fridman (31:20.840)
So instead of there being 60 standards,
Lex Fridman (31:25.120)
we've said, well, you can pull these different standards
Jo Boaler (31:29.640)
to get in with each other
Lex Fridman (31:32.200)
and also value the ways these are connected.
Lex Fridman (31:38.040)
And by the way, for people who are just listening,
Lex Fridman (31:39.840)
we're looking at a small number of like big concepts
Jo Boaler (31:44.000)
within mathematics, square towels,
Lex Fridman (31:46.400)
measuring fraction, shape and time,
Lex Fridman (31:49.040)
and then how they're interconnected.
Lex Fridman (31:51.680)
And so the goal, this is for grade three, for example.
Jo Boaler (31:55.040)
Yeah, and so we've set out for the state of California,
Lex Fridman (31:58.960)
the whole of mathematics K10
Jo Boaler (32:02.520)
as a set of big ideas and connections.
Lex Fridman (32:05.120)
So we know that teachers, it works really well
Jo Boaler (32:08.480)
if they say, okay, so a big idea in my grade is measuring.
Lex Fridman (32:15.560)
And instead of reading five procedural statements
Jo Boaler (32:19.160)
that involve measuring, they think,
Lex Fridman (32:21.440)
okay, measuring is a big idea.
Lex Fridman (32:22.560)
What rich, deep activity can I use
Lex Fridman (32:25.360)
that teaches measuring to kids?
Lex Fridman (32:27.880)
And as kids work on these deep, rich activities,
Lex Fridman (32:30.440)
maybe over a few days,
Jo Boaler (32:32.600)
turns out a lot of maths comes into it.
Lex Fridman (32:35.800)
So we're recommending that let's not teach maths
Jo Boaler (32:40.120)
according to all these multiple statements
Lex Fridman (32:43.400)
and lots and lots of short questions.
Jo Boaler (32:45.560)
Instead, let's teach maths
Lex Fridman (32:47.480)
by thinking about what are the big ideas
Lex Fridman (32:49.240)
and what are really rich, deep activities
Lex Fridman (32:52.240)
that teach those big ideas.
Lex Fridman (32:53.720)
So that's the, like how you teach it
Lex Fridman (32:55.880)
and maximize learning.
Lex Fridman (32:57.600)
What about like from a school district perspective,
Lex Fridman (33:01.440)
like measuring how well you're doing,
Jo Boaler (33:04.640)
grades and tests and stuff like that.
Lex Fridman (33:07.000)
Do you throw those out or is it possible?
Jo Boaler (33:08.880)
I am not a fan of grades and tests myself.
Lex Fridman (33:13.440)
I think grades are fine
Jo Boaler (33:15.920)
if they're used at the end of a course.
Lex Fridman (33:18.960)
So at the end of my maths course,
Jo Boaler (33:21.000)
I might get a grade because a grade is meant
Lex Fridman (33:23.080)
to be a summative measure.
Jo Boaler (33:24.360)
It kind of describes your summative achievement.
Lex Fridman (33:27.680)
But the problem we have in maths classrooms
Jo Boaler (33:30.040)
across the US is people use grades all the time,
Lex Fridman (33:33.440)
every week or every day even.
Jo Boaler (33:36.360)
My own kids, when they went through high school,
Lex Fridman (33:38.560)
technology has not helped with this.
Jo Boaler (33:40.560)
When they went through high school,
Lex Fridman (33:41.800)
they knew they were being graded
Jo Boaler (33:42.840)
for everything they did, everything.
Lex Fridman (33:45.880)
And not only were they being graded for everything,
Lex Fridman (33:48.120)
but they could see it in the grade book online
Lex Fridman (33:50.400)
and it would alter every class they went into.
Lex Fridman (33:52.880)
So this is the ultimate,
Lex Fridman (33:54.920)
what I think of as a performance culture.
Jo Boaler (33:57.480)
You're there to perform, somebody's measuring you,
Lex Fridman (34:00.120)
you see your score.
Lex Fridman (34:03.720)
So I think that's not conducive for deep learning.
Lex Fridman (34:08.600)
And yes, have a grade at the end of the year,
Lex Fridman (34:10.960)
but during the year,
Lex Fridman (34:12.400)
you can assess kids in much better ways.
Jo Boaler (34:14.600)
Like teachers can, a great way of assessing kids
Lex Fridman (34:18.720)
is to give them a rubric that kind of outlines
Lex Fridman (34:22.080)
what they're learning over the course of a unit
Lex Fridman (34:24.000)
or a few weeks.
Lex Fridman (34:25.760)
So kids can actually see the journey they're on,
Lex Fridman (34:28.760)
like this is what we're doing mathematically.
Jo Boaler (34:31.120)
Sometimes they self assess on those units
Lex Fridman (34:34.360)
and then teachers will show what the kids can do
Jo Boaler (34:40.000)
with a rubric and also write notes.
Lex Fridman (34:42.160)
Like in the next few weeks,
Jo Boaler (34:43.560)
you might like to learn to do this.
Lex Fridman (34:48.160)
So instead of kids just thinking about,
Jo Boaler (34:49.840)
I'm an A kid or a B kid,
Lex Fridman (34:51.160)
or I have this letter attached to me,
Jo Boaler (34:53.200)
they're actually seeing mathematically what's important
Lex Fridman (34:56.920)
and they're involved in the process
Jo Boaler (34:58.600)
of knowing where they are mathematically.
Lex Fridman (35:02.320)
At the end of the year, sure, they can have a grade,
Lex Fridman (35:04.840)
but during the year,
Lex Fridman (35:06.240)
they get these much more informative measures.
Jo Boaler (35:10.160)
I do think this might be more for college,
Lex Fridman (35:14.760)
but maybe not.
Jo Boaler (35:16.320)
Some of the best classes I've had
Lex Fridman (35:18.640)
is when I got a special like set aside,
Jo Boaler (35:23.720)
like the professor clearly saw that I was interested
Lex Fridman (35:27.840)
in some aspect of a thing.
Lex Fridman (35:29.880)
And then I have a few in mind and one in particular,
Lex Fridman (35:34.760)
when he said that he kind of challenged me.
Lex Fridman (35:38.080)
So this is outside of grades and all that kind of stuff
Lex Fridman (35:41.320)
that basically it's like reverse psychology.
Jo Boaler (35:44.880)
I don't think this can be done.
Lex Fridman (35:47.200)
And so I gave everything to do that particular thing.
Lex Fridman (35:50.960)
So this happened to be in an artificial intelligence class.
Lex Fridman (35:54.320)
But I think that like special treatment
Jo Boaler (35:57.600)
of taking students who are especially like excellent
Lex Fridman (36:01.840)
at a particular little aspect,
Jo Boaler (36:03.480)
that you see their eyes light up.
Lex Fridman (36:06.120)
I often think like maybe it's tempting for a teacher
Jo Boaler (36:09.480)
to think you've already succeeded there,
Lex Fridman (36:11.680)
but they're actually signaling to you
Jo Boaler (36:13.400)
that like you could really launch them on their way.
Lex Fridman (36:18.600)
And I don't know, that's too much to expect from teachers
Jo Boaler (36:21.640)
I think to pay attention to all of that
Lex Fridman (36:24.920)
because it's really difficult.
Lex Fridman (36:25.960)
But I just kind of remember who are the biggest,
Lex Fridman (36:30.000)
the most important people in the history
Jo Boaler (36:32.320)
of my life of education.
Lex Fridman (36:34.840)
And it's those people that who really didn't just
Jo Boaler (36:37.880)
like inspire me with their awesomeness, which they did,
Lex Fridman (36:40.400)
but also just they pushed me a little.
Jo Boaler (36:42.840)
Like they gave me a little push.
Lex Fridman (36:45.200)
And that requires focusing on the quote unquote
Jo Boaler (36:47.480)
excellent students in the class.
Lex Fridman (36:50.520)
Yeah, I think what's important though is teachers
Jo Boaler (36:53.840)
to have the perspective that they don't know
Lex Fridman (36:56.040)
who's gonna be excellent at something
Jo Boaler (36:58.480)
before they give out the activity.
Lex Fridman (37:00.320)
Exactly.
Lex Fridman (37:01.160)
And in our camp classes that we ran,
Lex Fridman (37:05.720)
sometimes students would finish ahead of other students.
Lex Fridman (37:10.440)
And we would say to them, can you write a question
Lex Fridman (37:15.280)
that's like this but different?
Jo Boaler (37:19.080)
Oh, and over time we encourage them
Lex Fridman (37:21.440)
to like extend things further.
Jo Boaler (37:24.800)
I remember we were doing one activity
Lex Fridman (37:26.800)
where kids were working out the borders of a square
Lex Fridman (37:30.160)
and how big this border would be in different case sizes.
Lex Fridman (37:33.560)
And one of the boys came up at the end of the class
Lex Fridman (37:36.280)
and said, I've been thinking about how you do this
Lex Fridman (37:38.880)
to the Pentagon.
Lex Fridman (37:40.480)
And I said, that's fantastic.
Lex Fridman (37:42.200)
How do you, what does it look like with Pentagon?
Jo Boaler (37:44.440)
Go find out, see if you can discover.
Lex Fridman (37:47.200)
So I didn't know he was gonna come up and say that.
Lex Fridman (37:49.720)
And I didn't have in my head like this is the kid
Lex Fridman (37:53.560)
who could have this extension task,
Lex Fridman (37:55.600)
but you can still do that as a teacher.
Lex Fridman (37:59.720)
When kids get excited about something
Jo Boaler (38:01.320)
or they're doing well in something,
Lex Fridman (38:03.160)
have them extend it, go further.
Jo Boaler (38:06.200)
It's great.
Lex Fridman (38:07.040)
And then you also, like this is like teacher and coach,
Jo Boaler (38:11.680)
you could say it in different ways to different students.
Lex Fridman (38:13.920)
Like for me, the right thing to say is almost to say,
Jo Boaler (38:18.920)
I don't think you could do this, this is too hard.
Lex Fridman (38:21.320)
Like that's what I need to hear.
Jo Boaler (38:23.080)
It's just like, no, there's immediate push.
Lex Fridman (38:26.320)
But with some people, if they're a little bit more,
Jo Boaler (38:29.200)
I mean, it's all has to do with upbringing,
Lex Fridman (38:31.200)
how your genetics is.
Jo Boaler (38:33.200)
They might be much more, that might break them.
Lex Fridman (38:35.360)
Yeah, that might break them.
Lex Fridman (38:36.200)
And so you have to be also sensitive to that.
Lex Fridman (38:38.320)
I mean, teaching is really difficult for this very reason.
Jo Boaler (38:42.200)
It is.
Lex Fridman (38:43.200)
So what is the best way to teach math,
Jo Boaler (38:47.720)
to learn math at those early few days
Lex Fridman (38:50.760)
when you just wanna capture them?
Jo Boaler (38:53.680)
I do something, actually there's a video of me
Lex Fridman (38:56.320)
doing this on our website that I love
Jo Boaler (38:58.840)
when I first meet students.
Lex Fridman (39:03.160)
And this is what I do.
Jo Boaler (39:04.280)
I show them a picture, this is the picture I show them.
Lex Fridman (39:08.240)
And it's a picture of seven dots like this.
Lex Fridman (39:12.960)
And I show it for just a few seconds and I say to them,
Lex Fridman (39:15.720)
I'd like you to tell me how many dots there are,
Lex Fridman (39:17.640)
but I don't want you to count them.
Lex Fridman (39:19.120)
I want you to group the dots.
Lex Fridman (39:20.800)
And I show it them and then I take it away
Lex Fridman (39:24.120)
before they've even had enough time to count them.
Lex Fridman (39:27.040)
And then I ask them, so how did you see it?
Lex Fridman (39:29.720)
And I go around the room and amazingly enough,
Jo Boaler (39:35.000)
there's probably 18 different ways
Lex Fridman (39:36.960)
of seeing these seven dots.
Lex Fridman (39:39.240)
And so I ask people, tell me how you grouped it.
Lex Fridman (39:42.240)
And some people see it as like an outside hole
Jo Boaler (39:44.320)
with a center dot.
Lex Fridman (39:45.680)
Some people see like stripes of lines.
Jo Boaler (39:49.240)
Some people see segments.
Lex Fridman (39:51.760)
And I collect them all and I put them on the board.
Lex Fridman (39:53.760)
And at the end I say, look at this,
Lex Fridman (39:55.400)
we are a class of 30 kids
Lex Fridman (39:57.240)
and we saw these seven dots in 18 different ways.
Lex Fridman (40:00.240)
There's actually a mathematical term for this.
Jo Boaler (40:01.880)
It's called groupitizing.
Lex Fridman (40:03.760)
Groupitizing?
Jo Boaler (40:04.720)
Yeah.
Lex Fridman (40:05.560)
I like it.
Jo Boaler (40:06.720)
It's kind of cool.
Lex Fridman (40:07.560)
So turns out though that how well you groupitize
Jo Boaler (40:11.840)
predicts how well you do in maths.
Lex Fridman (40:15.480)
Is it a raw talent or is it just something
Lex Fridman (40:18.920)
that you can develop?
Lex Fridman (40:19.760)
I don't think it's raw.
Jo Boaler (40:20.600)
I don't think you're born groupitizing, I think,
Lex Fridman (40:22.600)
but some kids have developed that ability if you like.
Lex Fridman (40:27.280)
And you can learn it.
Lex Fridman (40:28.960)
So this to me is part of how wrong we have maths.
Jo Boaler (40:34.120)
That we think to tell whether a kid's good at maths,
Lex Fridman (40:36.600)
we're gonna give them a speed test on multiples.
Lex Fridman (40:40.600)
But actually seeing how kids group dots
Lex Fridman (40:43.880)
could be a more important assessment
Jo Boaler (40:46.120)
of how well they're gonna do in maths.
Lex Fridman (40:48.200)
Anyway, I diverge.
Lex Fridman (40:49.560)
What I like to do though when I start off with kids
Lex Fridman (40:52.280)
is show them I'm gonna give you maths problems.
Jo Boaler (40:54.520)
I'm gonna value the different ways you see them.
Lex Fridman (40:57.040)
And it turns out you can do this kind of problem
Jo Boaler (40:59.840)
asking people how they group dots with young children
Lex Fridman (41:03.000)
or with graduate students.
Lex Fridman (41:05.400)
And it's engaging for all of them.
Lex Fridman (41:10.480)
You talk about creativity a little bit
Lex Fridman (41:12.080)
and flexibility in your book Limitless.
Lex Fridman (41:15.120)
What's the role of that?
Lex Fridman (41:16.680)
So it sounds like there's a bit of that kind of thing
Lex Fridman (41:19.680)
involved in groupitizing.
Jo Boaler (41:22.600)
Yeah, yeah.
Lex Fridman (41:24.520)
I love this term.
Lex Fridman (41:25.600)
So what would you say is the role of creativity
Lex Fridman (41:28.480)
and flexibility in the learning of maths?
Jo Boaler (41:31.240)
I think what we know now is that what we need
Lex Fridman (41:34.720)
for this 21st century world we live in is a flexible mind.
Jo Boaler (41:42.040)
School should not really be about teaching kids
Lex Fridman (41:44.360)
particular methods but teaching them
Jo Boaler (41:46.200)
to approach problems with flexibility.
Lex Fridman (41:49.440)
Being creative, thinking creatively is really important.
Lex Fridman (41:52.840)
So people don't think the words maths and creativity
Lex Fridman (41:56.960)
come together, but that's what I love about maths
Jo Boaler (42:00.240)
is the creative different ways you can see it.
Lex Fridman (42:02.880)
And so helping our kids, there's a book I like a lot
Jo Boaler (42:08.600)
by physicists, you probably know this book called Elastic.
Lex Fridman (42:13.920)
You might know it.
Lex Fridman (42:15.800)
And it's about how we want elastic minds.
Lex Fridman (42:18.440)
Same kind of thing, flexible, creative minds.
Lex Fridman (42:21.440)
And schools do very little on developing that kind of mind.
Lex Fridman (42:26.800)
They do a lot of developing the kind of mind
Jo Boaler (42:31.720)
that a computer now does for us.
Lex Fridman (42:35.280)
Memorization.
Jo Boaler (42:36.520)
Memorization, doing procedures, a lot of things
Lex Fridman (42:41.880)
that we spend a lot of time in school on.
Jo Boaler (42:45.320)
In the world, when kids leave school,
Lex Fridman (42:47.480)
a computer will do that and better than they will.
Lex Fridman (42:52.520)
But that creative, flexible thinking,
Lex Fridman (42:54.840)
we're kind of at ground zero at computers
Jo Boaler (42:57.120)
being able to engage in that thinking.
Lex Fridman (42:59.480)
Maybe we're a little above ground zero,
Lex Fridman (43:00.880)
but the human brain is perfectly suited
Lex Fridman (43:05.760)
for that creative, flexible thinking.
Jo Boaler (43:07.520)
That's what humans are so great at.
Lex Fridman (43:09.840)
So I would like the balance to shift in schools.
Jo Boaler (43:12.040)
Maybe you still need to do some procedural kind of thinking,
Lex Fridman (43:15.120)
but there should be a lot more of that creative,
Jo Boaler (43:17.680)
flexible thinking.
Lex Fridman (43:20.160)
And what's the role of other humans in this picture?
Lex Fridman (43:24.000)
So collaborative learning, so brainstorming together.
Lex Fridman (43:29.400)
So creativity as it emerges from the collective intelligence
Jo Boaler (43:33.760)
of multiple humans.
Lex Fridman (43:34.600)
Yeah, super important.
Lex Fridman (43:36.520)
And we know that also helps develop your brain,
Lex Fridman (43:40.600)
that social side of thinking.
Lex Fridman (43:42.360)
And I love mathematics collaboration
Lex Fridman (43:44.920)
where people build on each other's ideas
Lex Fridman (43:47.560)
and they come up with amazing things.
Lex Fridman (43:49.760)
I actually taught a hundred students calculus
Jo Boaler (43:54.080)
at Stanford recently, undergrads,
Lex Fridman (43:56.880)
and we taught them to collaborate.
Lex Fridman (43:59.440)
So these students came in Stanford
Lex Fridman (44:01.280)
and most of them were against collaboration in math.
Lex Fridman (44:04.640)
This is before COVID in person?
Lex Fridman (44:06.240)
Yeah, it was just before COVID hit.
Jo Boaler (44:08.360)
It was 2019.
Lex Fridman (44:10.240)
And this summer.
Lex Fridman (44:12.080)
So you said they're against?
Lex Fridman (44:13.800)
Yeah, so it's really interesting.
Lex Fridman (44:16.720)
So they'd only experienced maths individually
Lex Fridman (44:20.160)
in a kind of competitive individual way.
Lex Fridman (44:22.080)
And if they had experienced it as group work,
Lex Fridman (44:24.640)
it had been a bad experience.
Jo Boaler (44:26.560)
Like maybe they were the one who did it all
Lex Fridman (44:28.800)
and the others didn't do much.
Lex Fridman (44:31.480)
So they were kind of against collaboration.
Lex Fridman (44:33.120)
They didn't see any role for it in maths.
Lex Fridman (44:35.080)
And we taught them to collaborate and it was hard work
Lex Fridman (44:39.720)
because as well as the fact
Jo Boaler (44:42.120)
that they were kind of against collaboration,
Lex Fridman (44:43.520)
they came in with a lot of like social comparison thinking.
Lex Fridman (44:48.440)
So I'm in this room with other Stanford undergrads
Lex Fridman (44:51.440)
and they're better than me or...
Lex Fridman (44:53.480)
So when we set them to work on a maths problem together,
Lex Fridman (44:55.720)
the first one was kind of a disaster
Jo Boaler (44:57.200)
because they put all like, they're better than me.
Lex Fridman (44:59.200)
They're faster than me.
Jo Boaler (45:00.440)
They came up with something I didn't come up with.
Lex Fridman (45:02.560)
So we taught them to let go of that thinking
Lex Fridman (45:05.920)
and to work well together.
Lex Fridman (45:08.560)
And one of the things we did, we decided
Jo Boaler (45:10.760)
we wanted to do a pre and post test
Lex Fridman (45:12.520)
at the end of this teaching.
Jo Boaler (45:13.440)
It was only four weeks long, but we knew
Lex Fridman (45:16.440)
we didn't want to give them like a time test
Jo Boaler (45:18.320)
of individual work.
Lex Fridman (45:19.280)
So we gave them an applied problem to do at the beginning
Lex Fridman (45:23.680)
and we gave them to do in pairs together.
Lex Fridman (45:26.160)
And we gave each of them a different colored pen
Lex Fridman (45:28.560)
and said, work on this activity together
Lex Fridman (45:30.960)
and keep using that pen.
Lex Fridman (45:33.000)
So then we had all these pieces of student work.
Lex Fridman (45:35.120)
And what we saw was they just worked
Jo Boaler (45:37.520)
on separate parts of the paper.
Lex Fridman (45:39.160)
So there's a little like red pen section
Lex Fridman (45:42.000)
and a green pen section.
Lex Fridman (45:43.680)
And they didn't do that well on it.
Jo Boaler (45:45.880)
Even though it was a problem that middle
Lex Fridman (45:48.760)
or high school kids could do,
Lex Fridman (45:49.760)
but it was like a problem solving kind of problem.
Lex Fridman (45:52.680)
And then we gave them the same one to do at the end,
Jo Boaler (45:55.000)
gave them the same colors.
Lex Fridman (45:56.160)
And actually they had learned to collaborate.
Lex Fridman (45:59.160)
And not only were they collaborating the second time round,
Lex Fridman (46:02.080)
but that boosted their achievement.
Lex Fridman (46:04.000)
And the ones who collaborated did better on the problem.
Lex Fridman (46:07.840)
Collaboration is important, having people,
Lex Fridman (46:10.200)
and what was so eye opening for these undergrads
Lex Fridman (46:12.480)
and they talked about it in lovely ways
Jo Boaler (46:15.320)
was I learned to value other people's thinking on a problem.
Lex Fridman (46:19.920)
And I learned to value that other people
Jo Boaler (46:22.280)
saw it in different ways.
Lex Fridman (46:24.280)
And it was quite a big experience for them
Jo Boaler (46:29.440)
that they came out thinking,
Lex Fridman (46:31.680)
I can do maths with other people.
Jo Boaler (46:33.600)
People can see it differently.
Lex Fridman (46:34.800)
We can build on each other's ways of thinking.
Jo Boaler (46:38.280)
I got a chance to,
Lex Fridman (46:39.480)
I don't know if you know who Daniel Kahneman is,
Jo Boaler (46:42.000)
got a chance to interact with him.
Lex Fridman (46:44.080)
And like the first,
Jo Boaler (46:45.360)
cause he had a few,
Lex Fridman (46:46.880)
but one famous collaboration throughout his life
Jo Boaler (46:51.960)
with Tversky.
Lex Fridman (46:52.920)
And just like, you know,
Jo Boaler (46:55.920)
he hasn't met me before in person,
Lex Fridman (46:58.520)
but just the number of questions he was asking,
Jo Boaler (47:01.280)
just the curiosity.
Lex Fridman (47:03.120)
So I think one of the skills,
Jo Boaler (47:05.360)
the collaboration itself is a skill.
Lex Fridman (47:07.920)
And I remember my experience with him was like,
Jo Boaler (47:10.720)
okay, I get why you're so good at collaboration
Lex Fridman (47:14.000)
because he was just extremely good at listening
Lex Fridman (47:17.440)
and genuine curiosity about how the other person
Lex Fridman (47:21.400)
thinks about the world, sees the world.
Lex Fridman (47:23.360)
And then together he's,
Lex Fridman (47:24.920)
he pulled me in in that particular case.
Jo Boaler (47:27.440)
He doesn't know in particular,
Lex Fridman (47:29.320)
like that much about autonomous vehicles,
Lex Fridman (47:31.160)
but he kept like asking all of these questions.
Lex Fridman (47:34.520)
And then like 10 minutes in,
Jo Boaler (47:36.400)
we're together trying to solve the problem
Lex Fridman (47:38.080)
of autonomous driving.
Lex Fridman (47:39.880)
And like, and that, I mean, that's really fulfilling.
Lex Fridman (47:43.080)
That's really enriching.
Lex Fridman (47:43.920)
But it also in that moment made me realize
Lex Fridman (47:46.680)
it's kind of a skill.
Jo Boaler (47:48.160)
Cause you have to kind of put your ego aside,
Lex Fridman (47:50.720)
put your view of the world aside
Lex Fridman (47:52.480)
and try to learn how the other person sees it.
Lex Fridman (47:55.760)
And the other thing you have to put aside
Jo Boaler (47:57.560)
is this social comparison thinking.
Lex Fridman (48:00.640)
Like if you are sitting there thinking,
Jo Boaler (48:03.240)
wow, that was an amazing idea.
Lex Fridman (48:04.800)
He's so much better than I am.
Jo Boaler (48:06.600)
That's really gonna stop you taking on
Lex Fridman (48:09.960)
the value of that idea.
Lex Fridman (48:12.160)
And so there's a lot of that going on
Lex Fridman (48:14.240)
between these Stanford students when they came.
Lex Fridman (48:17.400)
And trying to help them let go of that.
Lex Fridman (48:21.880)
One of the things I've discovered
Jo Boaler (48:24.240)
just because being a little bit more in the public eye,
Lex Fridman (48:27.320)
how rewarding it is to celebrate others.
Lex Fridman (48:31.240)
And how much is going to actually pay off in the long term.
Lex Fridman (48:35.760)
So this kind of silo thinking of like,
Jo Boaler (48:38.160)
I want to prove to a small set of people around me
Lex Fridman (48:41.200)
that I'm really smart and do so
Jo Boaler (48:45.280)
by basically not celebrating
Lex Fridman (48:47.440)
how smart the other people are.
Jo Boaler (48:48.760)
That's actually maybe short term,
Lex Fridman (48:51.480)
it seems like a good strategy, but long term it's not.
Lex Fridman (48:54.520)
And I think if you practice at the student level
Lex Fridman (48:56.440)
and then at the career level, at every single stage,
Jo Boaler (48:58.840)
I think that's ultimately.
Lex Fridman (49:00.440)
I agree with you.
Jo Boaler (49:01.280)
I think that's a really good way of thinking about it.
Lex Fridman (49:04.400)
You mentioned textbooks and you didn't say it,
Jo Boaler (49:11.240)
maybe textbooks isn't the perfect way to teach mathematics,
Lex Fridman (49:15.400)
but I love textbooks.
Jo Boaler (49:16.920)
They're like pretty pictures
Lex Fridman (49:18.560)
and they smell nice and they open.
Jo Boaler (49:19.880)
I mean, I talk about like physical.
Lex Fridman (49:21.640)
Some of my greatest experiences have been just like,
Jo Boaler (49:25.360)
cause they're really well done.
Lex Fridman (49:27.240)
When we're talking about basic, like high school,
Jo Boaler (49:30.440)
calculus, biology, chemistry, those are like,
Lex Fridman (49:34.880)
those are incredible.
Jo Boaler (49:36.840)
It's like Wikipedia, but with color and a nice little.
Lex Fridman (49:40.320)
You must've seen some good textbooks
Jo Boaler (49:41.920)
if they had pretty pictures and color.
Lex Fridman (49:44.520)
Yeah, I mean, I remember,
Jo Boaler (49:46.200)
I guess it was very, very standard, like AP calculus,
Lex Fridman (49:51.200)
AP biology, AP chemistry.
Jo Boaler (49:53.480)
I felt those were like some of the happiest days of my life
Lex Fridman (49:56.080)
in terms of learning was high school.
Jo Boaler (49:58.000)
Cause it was very easy, honestly.
Lex Fridman (50:01.960)
It felt hard at the time,
Lex Fridman (50:03.240)
but you're basically doing a whirlwind tour
Lex Fridman (50:07.080)
of all the science.
Jo Boaler (50:08.400)
Yeah, yeah.
Lex Fridman (50:09.400)
Without having to pick, you do literature,
Jo Boaler (50:12.160)
you do like Shakespeare, calculus, biology, physics,
Lex Fridman (50:17.640)
chemistry, what else?
Jo Boaler (50:19.040)
Anatomy, physiology, computer science,
Lex Fridman (50:23.520)
without like, nobody's telling you what to do with your life.
Jo Boaler (50:26.680)
You're just doing all of those things.
Lex Fridman (50:28.000)
That's a good thing, you're right.
Lex Fridman (50:29.640)
But I remember the textbooks weren't,
Lex Fridman (50:32.440)
I mean, maybe I'm romanticizing the past,
Lex Fridman (50:35.400)
but I remember they weren't, they're pretty good.
Lex Fridman (50:38.640)
But so you think, what role do you think they play still?
Lex Fridman (50:42.000)
And like in this more modern digital age,
Lex Fridman (50:45.480)
what's the best materials with which to do
Lex Fridman (50:48.360)
these kinds of educations?
Lex Fridman (50:50.040)
Well, I'm intrigued that you had such a good experience
Jo Boaler (50:52.840)
with textbooks.
Lex Fridman (50:53.680)
I mean, I can remember loving some textbooks I had
Jo Boaler (50:57.080)
when I was learning and I love books.
Lex Fridman (50:59.440)
I love to pick up books and look through them,
Lex Fridman (51:03.040)
but a lot of maths textbooks
Lex Fridman (51:06.480)
are not good experiences for kids.
Jo Boaler (51:08.760)
They, we have a video on our website
Lex Fridman (51:12.840)
of the kids who came to our camp
Lex Fridman (51:14.080)
and one of the students says,
Lex Fridman (51:15.600)
in maths, you have to follow the textbook.
Jo Boaler (51:18.760)
The textbook is kind of like the Bible.
Lex Fridman (51:20.480)
You have to follow it.
Lex Fridman (51:22.400)
And every day it's slightly different.
Lex Fridman (51:25.920)
Like on Monday you do 2.3.2
Lex Fridman (51:28.760)
and on Tuesday you do 2.3.3 and on Wednesday.
Lex Fridman (51:32.480)
And you never go off that.
Jo Boaler (51:35.080)
That's like every single day.
Lex Fridman (51:37.840)
And that's not inspiring for a lot of the kids.
Lex Fridman (51:43.520)
So one of the things they loved about our camp
Lex Fridman (51:45.400)
was just that there were no books.
Jo Boaler (51:46.840)
Even though we gave them sheets of paper instead,
Lex Fridman (51:50.680)
they still felt more free
Jo Boaler (51:53.040)
because they weren't just like trotting through exercises,
Lex Fridman (51:56.600)
exercises, so.
Jo Boaler (51:59.520)
Like what a textbook allows you is like you're,
Lex Fridman (52:03.760)
the very thing you said they might not like,
Jo Boaler (52:06.600)
the 2.3, 2.3, it feels like you're making progress.
Lex Fridman (52:11.080)
And like it's little celebrations
Jo Boaler (52:12.720)
because you do the problem and it seems really hard
Lex Fridman (52:16.160)
and you don't know how to do it.
Lex Fridman (52:17.280)
And then you try and try and then eventually succeed.
Lex Fridman (52:20.920)
And then you make that little step and further progress.
Lex Fridman (52:23.600)
And then you get to the end of a chapter
Lex Fridman (52:26.120)
and you get to like, it's closure.
Jo Boaler (52:28.000)
You're like, all right, I got that figured out.
Lex Fridman (52:29.840)
And then you go on to the next chapter.
Jo Boaler (52:31.320)
I can see that.
Lex Fridman (52:32.240)
I mean, I think it could be in a textbook.
Jo Boaler (52:34.880)
You can have a good experience with a textbook,
Lex Fridman (52:38.960)
but what's really important is what is in that textbook?
Lex Fridman (52:43.160)
What are you doing inside it?
Lex Fridman (52:45.280)
And I mean, I grew up in England
Lex Fridman (52:47.880)
and in England we learn maths.
Lex Fridman (52:50.440)
We don't have this separation of algebra and geometry.
Lex Fridman (52:54.360)
And I don't think any other country
Lex Fridman (52:56.120)
apart from the US has that.
Lex Fridman (52:58.200)
But I look at kids in algebra classes
Lex Fridman (53:01.200)
where they're doing algebra for a year.
Lex Fridman (53:02.720)
And I think I would have been pretty bored doing that.
Lex Fridman (53:05.800)
By the way, can we analyze your upbringing real quick?
Lex Fridman (53:13.040)
Why do British folks call mathematics, maths?
Lex Fridman (53:19.960)
Why is it the plural?
Jo Boaler (53:21.120)
Is it because of everything you're saying
Lex Fridman (53:23.120)
where it's a bunch of subdisciplines?
Jo Boaler (53:25.160)
Yeah, I mean, mathematics is supposed to be
Lex Fridman (53:29.800)
the different maths that you look at,
Jo Boaler (53:34.800)
whether you think of that as topics
Lex Fridman (53:38.040)
like geometry and probability,
Jo Boaler (53:39.760)
or I think of it as maths is just multi dimensional
Lex Fridman (53:45.160)
lots of ways, but that's why it was called mathematics.
Lex Fridman (53:48.720)
And then it was shortened to maths.
Lex Fridman (53:50.480)
And then for some reason it was just math in the US.
Lex Fridman (53:53.360)
But to me, math has that more singular feel to it.
Lex Fridman (53:58.440)
And there's an expression here, which is do the math,
Jo Boaler (54:03.000)
which basically means do a calculation.
Lex Fridman (54:05.240)
That's what people mean by do the math.
Lex Fridman (54:07.480)
So I don't like that expression
Lex Fridman (54:09.360)
because no math could be anything
Jo Boaler (54:11.240)
doesn't have to be calculation.
Lex Fridman (54:12.480)
And so yeah, I like maths
Jo Boaler (54:14.600)
because it has more of that broad feel to it.
Lex Fridman (54:17.280)
Yeah, I love that.
Jo Boaler (54:18.120)
Maths kind of emphasize the multi dimensional,
Lex Fridman (54:20.000)
like a variety of different subdisciplines,
Jo Boaler (54:22.880)
different approaches.
Lex Fridman (54:23.720)
Yeah.
Jo Boaler (54:25.320)
Okay, but outside of the textbook,
Lex Fridman (54:28.640)
what do you see like broadly being used?
Jo Boaler (54:33.640)
You mentioned Sebastian Thrun and MOOCs,
Lex Fridman (54:36.840)
online education.
Lex Fridman (54:37.880)
Do you think that's an effective set?
Lex Fridman (54:39.480)
Can be.
Jo Boaler (54:40.960)
I mean, online, having great teachers online,
Lex Fridman (54:45.080)
obviously extends those teachers to many more people.
Lex Fridman (54:48.080)
And that's a wonderful thing.
Lex Fridman (54:51.480)
I have quite a few online courses myself.
Jo Boaler (54:54.280)
I got the bug working with Sebastian
Lex Fridman (54:56.240)
when he had released his first MOOC.
Lex Fridman (54:59.720)
And I thought, maybe I could do one in maths education.
Lex Fridman (55:03.440)
And I didn't know if anybody would take it.
Jo Boaler (55:06.400)
I remember releasing it that first summer
Lex Fridman (55:08.400)
and it was a free online class
Lex Fridman (55:09.880)
and 30,000 maths teachers took it that first summer.
Lex Fridman (55:13.760)
And they were all talking about it with each other
Lex Fridman (55:16.000)
and sharing it and it was like took off.
Lex Fridman (55:18.000)
In fact, it was that MOOC that got me to create YouCubed
Jo Boaler (55:23.000)
with Kathy Williams, who's the co founder,
Lex Fridman (55:26.120)
because people took the MOOC and then they said,
Lex Fridman (55:28.640)
okay, what now?
Lex Fridman (55:30.680)
I finished, what can I have next?
Lex Fridman (55:33.440)
And so that was where we made our website.
Lex Fridman (55:35.400)
But so yeah, I think online education can be great.
Jo Boaler (55:39.120)
I do think a lot of the MOOCs don't have great pedagogy.
Lex Fridman (55:43.960)
They're just a talking head.
Lex Fridman (55:45.960)
And you can actually engage people in more active ways,
Lex Fridman (55:50.960)
even in online learning.
Lex Fridman (55:53.040)
So I learned from the Udacity principle
Lex Fridman (55:55.920)
when I was working at Udacity,
Jo Boaler (55:57.320)
never to talk more than like five minutes.
Lex Fridman (56:00.200)
And then to ask people to do something.
Lex Fridman (56:03.720)
So that's the sort of pedagogy of the online classes I have
Lex Fridman (56:07.840)
is a little bit of presenting something
Lex Fridman (56:10.520)
and then people do something and there's a little bit more.
Lex Fridman (56:13.200)
Because I think if you have a half hour video,
Jo Boaler (56:15.280)
you just switch off and start doing other things.
Lex Fridman (56:19.200)
So the way Udacity did it is like five, 10 minute,
Jo Boaler (56:22.880)
like bit of teaching with some visual stuff perhaps.
Lex Fridman (56:27.880)
And then there's like a quiz almost.
Jo Boaler (56:29.280)
Then you answer a question, yeah.
Lex Fridman (56:30.600)
Yeah, no, that's really effective.
Lex Fridman (56:34.040)
You mentioned Ucubed, so what's the mission?
Lex Fridman (56:36.120)
What's the goal?
Jo Boaler (56:36.960)
You mentioned how it started, but what's yeah,
Lex Fridman (56:41.440)
where are you at now?
Lex Fridman (56:42.840)
And what's your dream with it?
Lex Fridman (56:44.680)
What are the kind of things that people should go
Lex Fridman (56:47.040)
and check out?
Lex Fridman (56:47.880)
Yeah, we started Ucubed, I guess it was about five years
Jo Boaler (56:51.560)
ago now and we've had over 52 million visitors to the site.
Lex Fridman (56:55.280)
So I'm very happy about that.
Lex Fridman (56:57.400)
And our goal is to share good ideas for teaching
Lex Fridman (57:01.760)
with teachers, students, parents in maths and to help.
Jo Boaler (57:07.280)
We have a sort of sub goal of a raising maths anxiety.
Lex Fridman (57:10.360)
That's important to us, but also to share maths
Jo Boaler (57:13.240)
as this beautiful creative subject.
Lex Fridman (57:15.880)
And it's been really great.
Jo Boaler (57:19.560)
We have lessons on the site, but one of the reasons
Lex Fridman (57:23.560)
I thought this was needed is there's a lot of knowledge
Jo Boaler (57:26.720)
in the academy about how to teach maths well.
Lex Fridman (57:29.120)
Loads and loads of research and journals
Lex Fridman (57:32.360)
and lots of things written up, but teachers don't read it.
Lex Fridman (57:36.360)
They don't have access to it.
Jo Boaler (57:39.040)
They're often behind pay walls, they've written
Lex Fridman (57:43.000)
in really inaccessible ways.
Lex Fridman (57:46.440)
So people wouldn't want to read them or understand them.
Lex Fridman (57:49.240)
So this actually is a big problem.
Jo Boaler (57:51.120)
You have this whole industry of people finding out
Lex Fridman (57:54.200)
how to teach well, not sharing it with the people
Jo Boaler (57:57.360)
who are teaching.
Lex Fridman (57:58.760)
So that's why we made Ucubed.
Lex Fridman (58:01.360)
And instead of just putting articles up saying,
Lex Fridman (58:03.640)
here's some things to read about how to teach well,
Jo Boaler (58:05.760)
we translated what was coming from research
Lex Fridman (58:08.200)
into things that teacher could use.
Lex Fridman (58:10.480)
So lessons, there were videos to show kids
Lex Fridman (58:13.560)
and there were tips for parents.
Jo Boaler (58:16.400)
There were all sorts of things on the site.
Lex Fridman (58:17.960)
And it's been amazing.
Jo Boaler (58:20.600)
As we took inspiration from the week of code,
Lex Fridman (58:24.840)
which got teachers to focus on coding for a week.
Lex Fridman (58:29.520)
And we have this thing called the week
Lex Fridman (58:31.840)
of inspirational maths.
Lex Fridman (58:33.880)
And we say, just try it for a week.
Lex Fridman (58:35.800)
Just give us one week and try it and see what happens.
Lex Fridman (58:39.360)
And so it's been downloaded millions of times.
Lex Fridman (58:42.640)
Teachers use it every year.
Jo Boaler (58:44.560)
They start the school year with it.
Lex Fridman (58:46.520)
And what they tell us is it was amazing.
Jo Boaler (58:49.640)
The kids lights were on, they were excited, they loved it.
Lex Fridman (58:52.960)
And then the week finished and I opened my textbooks
Lex Fridman (58:56.000)
and the lights went out and they were not interested.
Lex Fridman (59:00.000)
Yeah, but getting that first inspiration is still powerful.
Jo Boaler (59:04.160)
It is, I wish, I mean, what I would love
Lex Fridman (59:07.680)
is if we could actually extend that for the whole year.
Jo Boaler (59:11.640)
We're a small team at Stanford
Lex Fridman (59:13.960)
and we're trying to keep up with great things
Jo Boaler (59:17.000)
to put on the site.
Lex Fridman (59:19.640)
We haven't the capacity to produce
Jo Boaler (59:22.480)
these creative visual maths tasks
Lex Fridman (59:24.160)
for every year group for every day,
Lex Fridman (59:25.840)
but I would love to do that.
Lex Fridman (59:27.120)
How difficult is it to do?
Jo Boaler (59:28.560)
I mean, it's to come up with visual formulations
Lex Fridman (59:33.560)
of these big important topics you need to think about
Jo Boaler (59:39.000)
in a way that you could teach.
Lex Fridman (59:43.320)
I mean, we can do it.
Jo Boaler (59:44.720)
We actually, we went from the week of inspirational maths
Lex Fridman (59:47.400)
and we made K8 maths books with exactly that.
Jo Boaler (59:51.920)
Big ideas, rich activities, visuals.
Lex Fridman (59:54.880)
We just finished the last one.
Jo Boaler (59:56.520)
We've been doing it for five years
Lex Fridman (59:58.920)
and it's been exhausting and we just finished.
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