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Hello.

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So I'm here to tell you that what you
have believed about your own potential

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has changed what you have learned,
and continues to do that,

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continues to change your learning,
and your experiences.

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

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

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or that they can't go onto
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
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
that's out there in our society

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that's very strong and very dangerous.

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And the myth is that there's
such a thing as a math brain,

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that you're born with one, or you're not.

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We don't believe this
about other subjects.

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We don't think we're born
with a history brain, or a physics brain.

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We think you have to learn those.

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But with math, people,
students believe it,

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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
underachievement in this country.

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Carol Dweck's research
on mindset has shown us

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that if you believe
in your unlimited potential

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

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And an incredible study on mistakes
show this very strongly.

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So Jason Moser and his colleagues
actually found from MRI scans

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

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Fantastic.

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When you make a mistake,
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
made a mistake synapses fired.

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When they got work correct
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
that was pretty incredible.

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

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

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who believe that they had
unlimited potential,

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they could learn anything,

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when they made a stake,
their brains grew more

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

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So this shows us something that brain
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,
and to our feelings.

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

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If you go into a difficult situation,
or a challenging situation,

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and you think to yourself:
"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,
and react differently

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than if you go
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
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,
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
are really good.

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But maths classrooms
have to change in a lot of ways.

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It's not just about
changing messages for kids.

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We have to fundamentally change
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,
and learn anything.

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

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

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those questions themselves

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transmit fixed messages about math,
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
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
to think about some maths with me.

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

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

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

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and in case 3 there's even more.

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Often this is given out with the question:

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"How many squares would there be
in case 100, or case n?"

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I want you to think
of a different question.

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I want you to think without any numbers
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
where do you see the extra squares?

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

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

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

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

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

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or one of them said to me:

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

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So it's like an outer layer,
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 
like a bowling alley.

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You get an extra row,

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like a row of skittles
that comes in at the bottom."

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A very different way of seeing the growth.

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

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

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[Laughter]

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

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

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I remember this was --
Sorry, this one as well.

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Some people see it as triangles.

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They see the outside growing
as an outside triangle.

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

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"Oh it's like Wyane's World,
Stairway to Heaven, access denied."

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[Laughter]

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And then we have this way of seeing it.

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If you move the squares,
which you always can,

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and you rearrange the shape a bit,

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you'll see that it actually
grows as squares.

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So, this is what I want to illustrate
with this question:

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"When it's given out in maths classrooms,
and this isn't the worst of questions,

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

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So they'll say:

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"In the first case there's 4.
In the second there's 9."

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

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"If you add one to the case number
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,
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?
Why do you see that squared function?"

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They'll say: "No idea."

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So this is why it's squared.
The function grows as a square.

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You see that squaring
in the algebraic representation.

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So when we give these problems to students
we give them the visual question.

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We ask them: "How they see it?"

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They have these rich discussions,
and they also reach deeper understandings

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about a really important
part of mathematics.

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So we actually need a revolution
in maths classrooms.

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We need to change a lot of things.

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And part of the reason
we need to change so much

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is because research
on maths teaching and learning

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is not getting into schools
and classrooms.

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

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So this is really interesting.

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When we calculate --
Even when adults calculate,

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where a brain area
that sees fingers is lighting up,

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we're not using fingers,

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but that brain area
that sees fingers lights up.

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So there's a brain area
when we use fingers,

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

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And it turns out that seeing fingers
is really important for the brain.

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And in fact finger perception is --

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Scientists test for finger perception

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by asking them to put
their hands under a table --

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they can't see them touching a finger,

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and then seeing if you know
which finger has been touched.

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The number of university students
who have good finger perception

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predicts their calculation scores.

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The number of finger perception
grade 1 students have

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is a better prediction
of maths achievement in grade 2

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than test scores.

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It is that important.

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But what happens
in schools and classrooms?

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

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They're told it's babyish.
They're made to feel bad about it.

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When we stop children
learning numbers through fingers,

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it's akin to halting
their numerical development.

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And scientists have known this
for a long time.

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And the neuroscientists conclude

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that fingers should be used for students
learning number and arithmetic.

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If we haven't published --

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We published this in a paper
in the Atlantic last week.

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I don't know any educator who knew this.

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This is causing a huge ripple
through the education community.

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There's lots of other research
that's not known by teachers and schools.

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We know when you perform a calculation


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the brain is involved in a complex
and dynamic communication

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between different areas of the brain,
including the visual cortex.

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Yet, maths classrooms are not visual,
they're numerical and abstract.

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I want to show you now what happened

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when we brought 81 students
onto campus last summer,

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and we taught them differently.

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So we taught them about the brain growing.

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We taught about mindset and mistakes.

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But we as also taught them creative,
visual, beautiful maths.

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They came in for 18 lessons with us.

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Before they came to us they had taken
a district standardized test.

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We gave them the same test
at the end of our 18 lessons,

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and they improved by an average of 50%.

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Eighty one students,
from a range of achievement levels,

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told us on the first day:
"I'm not a math person."

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They could name the one person
in their class who was a math person.

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We changed their beliefs.

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And this is a clip from a longer
music video that we made of the kids.

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(Video, Taylor Swift's "Shake It Off")

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But we keep talking

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Can't stop, won't stop solving

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It's like something is growing

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In our minds every time we try again.

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'Cause the haters gonna hate,
hate, hate, hate, hate.

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We will make mistakes,
stakes, stakes, stakes, stakes.

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We're just gonna shake,
shake, shake, shake, shake.

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Shake it off! Shake it off!

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Our method's gonna break,
break, break, break, break.

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It's not a piece of cake,
cake, cake, cake, cake.

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We're just gonna shake,
shake, shake, shake, shake.

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Shake it off! Shake it off!

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We represent things visually,

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Present them to our class clearly

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So that they can see
mmm

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So that they can see
mmm

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We know our brains can grow

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Who cases how fast we go?

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Understanding's what we show
mmm

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Understanding's what we show
mmm

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So we keep trying

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Synapses are firing

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This problem's so exciting

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It's so cool that I want to go
and show the world!

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(Video ends)

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So --

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(Applause)

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We need to get research out to teachers.
We need a revolution in maths teaching.

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If you don't believe me,
come listen to this kid.

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He's a middle schooler,
and we had worked with his teachers

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to shift from worksheet math
to open math with mindset messages.

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This is him reflecting on that shift.

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(Video) Math class last year
was notes, and just handouts,

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and your own little box --
you were just boxed in.

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You were by yourself,
it was every man for themselves.

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But now this year is just open.
We're a whole big --

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It's like a city --

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we're all working together
to create this new beautiful world.

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I think the challenges,
and the future that lies ahead for me --

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If I keep on pushing,

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if I keep on doing this
someday I'm going to make it.

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(Video ends)

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We have focused for so long in education,

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in maths education, on the right way
to teach a fraction,

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on the standards we use in classrooms
which are argued about all the time,

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and we've completely ignored the beliefs
students hold about their own potential.

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And only now
is the full extent of the need

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to attend to that coming to light.

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We all have to believe in ourselves

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to unlock our unlimited potential.

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Thank you.

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(Applause)