Hello.

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

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

continues to change your learning,
and your experiences.

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

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

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

they haven't got the brains for it?

Let's see a show of hands.

So, quite a few of us.

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

it is disproven by the brain science.

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

that's very strong and very dangerous.

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

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

We don't believe this
about other subjects.

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

We think you have to learn those.

But with math, people,
students believe it,

teachers believe it, parents believe it.

And until we change that single myth

we will continue to have widespread
underachievement in this country.

Carol Dweck's research
on mindset has shown us

that if you believe
in your unlimited potential

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

And an incredible study on mistakes
show this very strongly.

So Jason Moser and his colleagues
actually found from MRI scans

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

Fantastic.

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

And in fact in their MRI scans

they found that when people
made a mistake synapses fired.

When they got work correct
less synapses fired.

So making mistakes is really good.

And we want students to know this.

But they found something else
that was pretty incredible.

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

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

who believe that they had
unlimited potential,

they could learn anything,

when they made a mistake,
their brains grew more

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

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

That our cognition, and what we learn

is linked to our beliefs,
and to our feelings.

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

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

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

and you mess up or fail,

your brain will grow more,
and react differently

than if you go
into that situation thinking:

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

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

We know that anybody can grow their brain,

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

We have to get this out to kids.

They have to know that mistakes
are really good.

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

It's not just about
changing messages for kids.

We have to fundamentally change
what happens in classrooms.

And we want kids to have a growth mindset,

to believe that they can grow,
and learn anything.

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

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

those questions themselves

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

So we have to open up maths questions

so that there's
space inside them for learning.

I want to give you an example.

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

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

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

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

and in case 3 there's even more.

Often this is given out with the question:

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

I want you to think
of a different question.

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

I want you to think entirely visually,

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

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

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

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

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

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

or one of them said to me:

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

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

It was also my undergrads who said:

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

You get an extra row,

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

A very different way of seeing the growth.

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

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

[Laughter]

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

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

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

Some people see it as triangles.

They see the outside growing
as an outside triangle.

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

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

[Laughter]

And then we have this way of seeing it.

If you move the squares,
which you always can,

and you rearrange the shape a bit,

you'll see that it actually
grows as squares.

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

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

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

So they'll say:

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

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

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

then you get the total number of squares."

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

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

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

They'll say: "No idea."

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

You see that squaring
in the algebraic representation.

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

We ask them: "How they see it?"

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

about a really important
part of mathematics.

So we actually need a revolution
in maths classrooms.

We need to change a lot of things.

And part of the reason
we need to change so much

is because research
on maths teaching and learning

is not getting into schools
and classrooms.

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

So this is really interesting.

When we calculate --
Even when adults calculate,

where a brain area
that sees fingers is lighting up,

we're not using fingers,

but that brain area
that sees fingers lights up.

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

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

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

And in fact finger perception is --

Scientists test for finger perception

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

they can't see them touching a finger,

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

The number of university students
who have good finger perception

predicts their calculation scores.

The number of finger perception
grade 1 students have

is a better prediction
of maths achievement in grade 2

than test scores.

It is that important.

But what happens
in schools and classrooms?

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

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

When we stop children
learning numbers through fingers,

it's akin to halting
their numerical development.

And scientists have known this
for a long time.

And the neuroscientists conclude

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

If we haven't published --

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

I don't know any educator who knew this.

This is causing a huge ripple
through the education community.

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

We know when you perform a calculation

the brain is involved in a complex
and dynamic communication

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

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

I want to show you now what happened

when we brought 81 students
onto campus last summer,

and we taught them differently.

So we taught them about the brain growing.

We taught about mindset and mistakes.

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

They came in for 18 lessons with us.

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

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

and they improved by an average of 50%.

Eighty one students,
from a range of achievement levels,

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

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

We changed their beliefs.

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

But we keep talking

Can't stop, won't stop solving

It's like something is growing

In our minds every time we try again.

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

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

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

Shake it off! Shake it off!

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

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

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

Shake it off! Shake it off!

We represent things visually,

Present them to our class clearly

So that they can see
mmm

So that they can see
mmm

We know our brains can grow

Who cases how fast we go?

Understanding's what we show
mmm

Understanding's what we show
mmm

So we keep trying

Synapses are firing

This problem's so exciting

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

So --

(Applause)

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

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

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

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

This is him reflecting on that shift.

Math class last year
was notes, and just handouts,

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

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

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

It's like a city --

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

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

If I keep on pushing,

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

We have focused for so long in education,

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

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

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

And only now
is the full extent of the need

to attend to that coming to light.

We all have to believe in ourselves

to unlock our unlimited potential.

Thank you.

(Applause)