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 stake, 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.
(Video, Taylor Swift's "Shake It Off")
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
We know our brains can grow
Who cases how fast we go?
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!
(Video ends)
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.
(Video) 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.
(Video ends)
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)