0:00:11.436,0:00:12.415
Hello.

0:00:12.415,0:00:17.866
So I'm here to tell you that what you[br]have believed about your own potential

0:00:17.866,0:00:22.200
has changed what you have learned,[br]and continues to do that,

0:00:22.200,0:00:26.577
continues to change your learning,[br]and your experiences.

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So, how many people here --[br]let's get a show of hands --

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have ever been given the idea[br]that they're not a math person,

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or that they can't go onto[br]the next level of math,

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they haven't got the brains for it?

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Let's see a show of hands.

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So, quite a few of us.

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And I'm here to tell you[br]that idea is completely wrong,

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it is disproven by the brain science.

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But it is fueled by a single myth[br]that's out there in our society

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that's very strong and very dangerous.

0:00:54.817,0:00:58.429
And the myth is that there's[br]such a thing as a math brain,

0:00:58.429,0:01:00.717
that you're born with one, or you're not.

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We don't believe this[br]about other subjects.

0:01:03.027,0:01:07.337
We don't think we're born[br]with a history brain, or a physics brain.

0:01:07.337,0:01:08.908
We think you have to learn those.

0:01:08.908,0:01:11.668
But with math, people,[br]students believe it,

0:01:11.668,0:01:14.148
teachers believe it, parents believe it.

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And until we change that single myth

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we will continue to have widespread[br]underachievement in this country.

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Carol Dweck's research[br]on mindset has shown us

0:01:24.638,0:01:27.538
that if you believe[br]in your unlimited potential

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you will achieve at higher levels[br]in maths, and in life.

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And an incredible study on mistakes[br]show this very strongly.

0:01:35.458,0:01:39.887
So Jason Moser and his colleagues[br]actually found from MRI scans

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that your brain grows[br]when you make a mistake in maths.

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Fantastic.

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When you make a mistake,[br]synapses fire in the brain.

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And in fact in their MRI scans

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they found that when people[br]made a mistake synapses fired.

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When they got work correct[br]less synapses fired.

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So making mistakes is really good.

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And we want students to know this.

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But they found something else[br]that was pretty incredible.

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This image shows you[br]the voltage maps of people's brains.

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And what you can see here[br]is that people with a growth mindset,

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who believe that they had[br]unlimited potential,

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they could learn anything,

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when they made a stake,[br]their brains grew more

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than the people who didn't believe[br]that they could learn anything.

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So this shows us something that brain[br]scientists have known for a long time:

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That our cognition, and what we learn

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is linked to our beliefs,[br]and to our feelings.

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And this is important for all of us[br]not just kids in math classrooms.

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If you go into a difficult situation,[br]or a challenging situation,

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and you think to yourself:[br]"I can do this. I'm going do it."

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and you mess up or fail,

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your brain will grow more,[br]and react differently

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than if you go[br]into that situation thinking:

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"I don't think I can do this."

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So it's really important that we change[br]the messages kids get in classrooms.

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We know that anybody can grow their brain,

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and brains are so plastic,[br]to learn any level of maths.

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We have to get this out to kids.

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They have to know that mistakes[br]are really good.

0:03:14.930,0:03:17.721
But maths classrooms[br]have to change in a lot of ways.

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It's not just about[br]changing messages for kids.

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We have to fundamentally change[br]what happens in classrooms.

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And we want kids to have a growth mindset,

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to believe that they can grow,[br]and learn anything.

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But it's very difficult[br]to have a growth mindset in maths.

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If you're constantly given short, closed[br]questions that you get right or wrong,

0:03:36.020,0:03:38.531
those questions themselves

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transmit fixed messages about math,[br]that you can do it or you can't.

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So we have to open up maths questions

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so that there's[br]space inside them for learning.

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I want to give you an example.

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We're actually going to ask you[br]to think about some maths with me.

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So this is a fairly typical problem,[br]it's given out in schools.

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I want you to think about it differently.[br]So we have three cases of squares.

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In case 2 there's more squares[br]than in case 1,

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and in case 3 there's even more.

0:04:04.492,0:04:06.502
Often this is given out with the question:

0:04:06.502,0:04:10.892
"How many squares would there be[br]in case 100, or case n?"

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I want you to think[br]of a different question.

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I want you to think without any numbers[br]at all, or without any algebra.

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I want you to think entirely visually,

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and I want you to think about[br]where do you see the extra squares?

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If there are more squares[br]in case 2 than case 1, where are they?

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So if we were in a classroom, I'd give you[br]a long time to think about this.

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In the interest of time,[br]I'm going to show you some different ways

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people think about this, and I've given[br]this problem to many different people,

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and I think it was my undergrads[br]at Stanford who said to me --

0:04:45.422,0:04:46.943
or one of them said to me:

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"Oh, I see it like raindrops.[br]Where raindrops come down on the top.

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So it's like an outer layer,[br]that grows new each time."

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It was also my undergrads who said:

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"Oh no, I see it more [br]like a bowling alley.

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You get an extra row,

0:05:03.964,0:05:07.554
like a row of skittles[br]that comes in at the bottom."

0:05:07.554,0:05:10.125
A very different way of seeing the growth.

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It was a teacher, I remember,[br]who said to me it was like a volcano:

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"The center goes up,[br]and then the lava comes out."

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[Laughter]

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Another teacher said: "Oh no,[br]it's like the parting of the Red Sea.

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The shape separates, and there's[br]a duplication with an extra center."

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I remember this was --[br]Sorry, this one as well.

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Some people see it as triangles.

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They see the outside growing[br]as an outside triangle.

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And then there was a teacher[br]in New Mexico who said to me:

0:05:49.744,0:05:55.345
"Oh it's like Wyane's World,[br]Stairway to Heaven, access denied."

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[Laughter]

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And then we have this way of seeing it.

0:06:04.636,0:06:07.006
If you move the squares,[br]which you always can,

0:06:07.006,0:06:09.058
and you rearrange the shape a bit,

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you'll see that it actually[br]grows as squares.

0:06:11.468,0:06:14.158
So, this is what I want to illustrate[br]with this question:

0:06:14.158,0:06:18.006
"When it's given out in maths classrooms,[br]and this isn't the worst of questions,

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it's given out with a question of:[br]"How many?" and kids count.

0:06:20.996,0:06:22.166
So they'll say:

0:06:22.166,0:06:24.876
"In the first case there's 4.[br]In the second there's 9."

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They might stare at that column of numbers[br]for a long time and say:

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"If you add one to the case number[br]each time and square it,

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then you get the total number of squares."

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But when we give it to students,[br]and high school teachers,

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I'll say to them when they've done this:

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"So why is that squared?[br]Why do you see that squared function?"

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They'll say: "No idea."

0:06:47.717,0:06:51.727
So this is why it's squared.[br]The function grows as a square.

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You see that squaring[br]in the algebraic representation.

0:06:55.677,0:06:59.967
So when we give these problems to students[br]we give them the visual question.

0:06:59.967,0:07:01.987
We ask them: "How they see it?"

0:07:01.987,0:07:05.587
They have these rich discussions,[br]and they also reach deeper understandings

0:07:05.587,0:07:08.398
about a really important[br]part of mathematics.

0:07:08.398,0:07:10.918
So we actually need a revolution[br]in maths classrooms.

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We need to change a lot of things.

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And part of the reason[br]we need to change so much

0:07:15.708,0:07:18.167
is because research[br]on maths teaching and learning

0:07:18.167,0:07:20.237
is not getting into schools[br]and classrooms.

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And I'm going to give you[br]a stunning example now.

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So this is really interesting.

0:07:27.729,0:07:30.619
When we calculate --[br]Even when adults calculate,

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where a brain area[br]that sees fingers is lighting up,

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we're not using fingers,

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but that brain area[br]that sees fingers lights up.

0:07:39.329,0:07:41.508
So there's a brain area[br]when we use fingers,

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and there's a brain area[br]when we see fingers.

0:07:44.088,0:07:49.328
And it turns out that seeing fingers[br]is really important for the brain.

0:07:49.328,0:07:52.999
And in fact finger perception is --

0:07:53.719,0:07:56.031
Scientists test for finger perception

0:07:56.031,0:07:59.161
by asking them to put[br]their hands under a table --

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they can't see them touching a finger,

0:08:01.179,0:08:04.309
and then seeing if you know[br]which finger has been touched.

0:08:04.309,0:08:07.468
The number of university students[br]who have good finger perception

0:08:07.468,0:08:10.378
predicts their calculation scores.

0:08:10.808,0:08:14.561
The number of finger perception[br]grade 1 students have

0:08:14.561,0:08:17.591
is a better prediction[br]of maths achievement in grade 2

0:08:17.591,0:08:19.368
than test scores.

0:08:19.368,0:08:21.337
It is that important.

0:08:21.337,0:08:24.998
But what happens[br]in schools and classrooms?

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Students are told they're not allowed[br]to use their fingers.

0:08:27.798,0:08:30.689
They're told it's babyish.[br]They're made to feel bad about it.

0:08:30.689,0:08:33.922
When we stop children[br]learning numbers through fingers,

0:08:33.922,0:08:37.372
it's akin to halting[br]their numerical development.

0:08:37.372,0:08:39.829
And scientists have known this[br]for a long time.

0:08:39.829,0:08:41.609
And the neuroscientists conclude

0:08:41.609,0:08:47.308
that fingers should be used for students[br]learning number and arithmetic.

0:08:47.308,0:08:48.659
If we haven't published --

0:08:48.659,0:08:51.468
We published this in a paper[br]in the Atlantic last week.

0:08:51.468,0:08:53.458
I don't know any educator who knew this.

0:08:53.458,0:08:57.283
This is causing a huge ripple[br]through the education community.

0:08:59.823,0:09:03.690
There's lots of other research[br]that's not known by teachers and schools.

0:09:03.690,0:09:05.640
We know when you perform a calculation[br]

0:09:05.640,0:09:08.870
the brain is involved in a complex[br]and dynamic communication

0:09:08.870,0:09:13.289
between different areas of the brain,[br]including the visual cortex.

0:09:13.289,0:09:17.748
Yet, maths classrooms are not visual,[br]they're numerical and abstract.

0:09:17.748,0:09:19.529
I want to show you now what happened

0:09:19.529,0:09:22.550
when we brought 81 students[br]onto campus last summer,

0:09:22.550,0:09:24.110
and we taught them differently.

0:09:24.110,0:09:26.430
So we taught them about the brain growing.

0:09:26.430,0:09:29.620
We taught about mindset and mistakes.

0:09:30.030,0:09:34.290
But we as also taught them creative,[br]visual, beautiful maths.

0:09:35.810,0:09:37.815
They came in for 18 lessons with us.

0:09:37.815,0:09:41.181
Before they came to us they had taken[br]a district standardized test.

0:09:41.181,0:09:44.322
We gave them the same test[br]at the end of our 18 lessons,

0:09:44.322,0:09:47.450
and they improved by an average of 50%.

0:09:48.960,0:09:51.621
Eighty one students,[br]from a range of achievement levels,

0:09:51.621,0:09:54.681
told us on the first day:[br]"I'm not a math person."

0:09:54.681,0:09:59.253
They could name the one person[br]in their class who was a math person.

0:09:59.253,0:10:00.782
We changed their beliefs.

0:10:00.782,0:10:06.051
And this is a clip from a longer[br]music video that we made of the kids.

0:10:11.161,0:10:13.741
But we keep talking

0:10:13.741,0:10:16.752
Can't stop, won't stop solving

0:10:16.752,0:10:19.642
It's like something is growing

0:10:19.642,0:10:23.852
In our minds every time we try again.

0:10:23.852,0:10:27.012
'Cause the haters gonna hate,[br]hate, hate, hate, hate.

0:10:27.012,0:10:30.342
We will make mistakes,[br]stakes, stakes, stakes, stakes.

0:10:30.342,0:10:33.212
We're just gonna shake,[br]shake, shake, shake, shake.

0:10:33.212,0:10:35.622
Shake it off! Shake it off!

0:10:35.622,0:10:38.462
Our method's gonna break,[br]break, break, break, break.

0:10:38.462,0:10:41.782
It's not a piece of cake,[br]cake, cake, cake, cake.

0:10:41.782,0:10:44.691
We're just gonna shake,[br]shake, shake, shake, shake.

0:10:44.691,0:10:46.553
Shake it off! Shake it off!

0:10:46.553,0:10:49.585
We represent things visually,

0:10:49.585,0:10:52.583
Present them to our class clearly

0:10:53.003,0:10:55.913
So that they can see[br]mmm

0:10:56.083,0:10:58.622
So that they can see[br]mmm

0:10:58.732,0:11:01.594
We know our brains can grow

0:11:01.594,0:11:04.687
Who cases how fast we go?

0:11:04.687,0:11:07.973
Understanding's what we show[br]mmm

0:11:07.973,0:11:10.763
Understanding's what we show[br]mmm

0:11:10.763,0:11:13.114
So we keep trying

0:11:13.274,0:11:16.152
Synapses are firing

0:11:16.152,0:11:20.383
This problem's so exciting

0:11:20.383,0:11:22.913
It's so cool that I want to go[br]and show the world!

0:11:24.214,0:11:25.443
So --

0:11:25.443,0:11:28.081
(Applause)

0:11:30.045,0:11:33.814
We need to get research out to teachers.[br]We need a revolution in maths teaching.

0:11:33.816,0:11:36.203
If you don't believe me,[br]come listen to this kid.

0:11:36.203,0:11:39.065
He's a middle schooler,[br]and we had worked with his teachers

0:11:39.065,0:11:43.222
to shift from worksheet math[br]to open math with mindset messages.

0:11:43.664,0:11:45.510
This is him reflecting on that shift.

0:11:45.510,0:11:50.535
Math class last year[br]was notes, and just handouts,

0:11:50.535,0:11:54.555
and your own little box --[br]you were just boxed in.

0:11:55.105,0:11:59.515
You were by yourself,[br]it was every man for themselves.

0:11:59.515,0:12:02.878
But now this year is just open.[br]We're a whole big --

0:12:03.558,0:12:04.891
It's like a city --

0:12:04.891,0:12:08.511
we're all working together[br]to create this new beautiful world.

0:12:08.511,0:12:14.865
I think the challenges,[br]and the future that lies ahead for me --

0:12:16.985,0:12:18.365
If I keep on pushing,

0:12:18.365,0:12:23.455
if I keep on doing this[br]someday I'm going to make it.

0:12:24.445,0:12:27.939
We have focused for so long in education,

0:12:27.939,0:12:30.806
in maths education, on the right way[br]to teach a fraction,

0:12:30.806,0:12:34.826
on the standards we use in classrooms[br]which are argued about all the time,

0:12:34.826,0:12:39.516
and we've completely ignored the beliefs[br]students hold about their own potential.

0:12:39.516,0:12:42.156
And only now[br]is the full extent of the need

0:12:42.156,0:12:44.936
to attend to that coming to light.

0:12:44.936,0:12:48.246
We all have to believe in ourselves

0:12:48.246,0:12:51.766
to unlock our unlimited potential.

0:12:51.766,0:12:53.246
Thank you.

0:12:53.246,0:12:55.186
(Applause)