So I'm here to talk about the ways that mathematics teaching and
learning need to change.
So why do we need to change maths teaching and learning?
Many reasons, this is one of them.
We have a nation of maths-traumatized people.
>> [LAUGH] >> Neuroscientists tell us that when
people with maths anxiety see numbers, a fear center lights up in the brain.
And it is the same fear center that lights up when people see snakes and spiders.
>> [LAUGH] >> At the same time,
the problem solving centers of the brain shut down.
So how does maths education need to change?
First of all, many people have the idea that you're born with a maths brain or
your not and that kids can only learn certain levels of mathematics.
And those are completely wrong.
When students struggle in class, they think, I haven't got a maths brain.
And then their brain will actually start functioning differently.
On top of that, people have very fixed ideas about maths.
They think it is a subject of methods to be memorized.
So, unfortunately, our data shows that about 40% of teachers
have these fixed ideas, both about kids and about maths.
And to contrast that, we are in a time of incredible scientific evidence
that tells us our brains are changing and growing all the time.
Even adults of any age, if you go through a focused eight-week training period,
our brains completely change and rewire.
And school students have limitless potential.
Any student in regular school can reach any level of school mathematics.
And I share with teachers more neuroscience than I'll share with you, but
I also share cases.
And one I want to share with you is a young man called Nicholas Lechford.
When he was in first grade, his parents were told he was learning disabled,
had a very low IQ.
They said he was the worst child they had seen in 20 years.
>> [LAUGH] >> Yes, I know, Nicholas just graduated
from Oxford University with a doctorate in applied mathematics.
So we know that this is possible.
We also know that when people go against these really extreme challenges,
that they have a really positive mindset.
I’m sure you’ve heard of the great work of Carol Dweck, who's shown that what you
believe about your potential actually changes your brain, what you learn.
These graphs just show kids going through seventh and eighth grade.
They had the same teachers.
Those who are on this upward trend are kids with a growth mindset,
who believe they can learn anything.
The kids on this lower line are kids with a fixed mindset.
And, as well as the evidence for our brain growth,
we also have really important evidence showing that when we struggle,
when we find something really difficult, those are the best times for our brains.
And, actually, even making mistakes is a really positive time of brain activity.
This was an interesting book,
where they looked at the highest achieving people in different areas and
found that their high achievement was not something they were born with.
But all the people had engaged in a particular kind of practice.
And what was distinctive about it was that they were all pushing at the edge
of their understanding.
Making mistakes, moving on, making more mistakes.
We actually don't want kids in classrooms getting everything right.
We want them struggling and being at this edge of their understanding.
And this incredible evidence came from one of studies of mistakes.
Moser and his colleagues found that, these are voltage maps of people's brains, and
they found a huge activity in the brain when people made mistakes.
Particularly, as you can see here, for people who had a growth mindset.
Their brain activity was much more positive than people with a fixed mindset.
And this is some of the clearest evidence I think we have,
that what you believe about yourself will actually change how your brain works.
And this starts to make sense of those graphs we saw of kids with a growth
mindset always going onwards and upwards.
Their brains are more active when they make a mistake.
But here's the thing, I know in education,
a lot of people have jumped on the mindset bus.
They are telling kids, you can learn anything, just keep trying.
But the problem is,
when those mindset messages hit the wall of fixed mathematics,
maths questions with one answer, one way to get them, those messages fall flat.
So we are in a time, also, when we know that the best brain connections and
brain activity comes about when we see maths in different ways.
From the neuroscience at Stanford, when we work on a maths question,
five different areas of the brain light up.
Two of them are visual pathways.
And thinking visually about maths turns out to be really important.
Also important is when those connections are made between different brain areas.
And we're very fortunate in maths.
We can see it in all sorts of different ways, as numbers, or words, or visuals.
And all of those different ways of seeing maths cause connections to
happen when we think in different ways.
We also know that, and this comes from this new book I like,
that the Western world has valued this kind of algorithmic,
rational thinking forever.
And it's what's taught in schools, but there is a higher level God,
that he describes as this flexible, creative thinking.
And we also know that this rational algorithmic thinking,
we can train computers to do that better than humans.
But they are at ground zero at training computers to engage in creative,
flexible thinking, which is what we need to be teaching our kids in schools.
So what does this mean?
Let's look at a little example.
Do you remember doing this in school?
>> Yeah. >> 1 divided by two-thirds.
You were probably taught to flip and multiply.
What happens when we flip and multiply?
We reverse the numerator and detonator, we get an answer, it's very efficient.
It's also magical and totally meaningless.
>> [LAUGH] >> Instead, we can look at that value of
1 and think, what happens when we divide that by two-thirds?
We can actually see that one set of two-thirds fits into it.
And then we need another half to also fit in to make one and a half.
It's not just fractions that we can think about visually.
Could you prove that for me?
Of course you could.
You'd need lots and lots of lines of numbers or
we could look at this amazing visual which proves that statement.
And a lovely thing is to have kids think about these things and
how they're connected.
Any mathematics can be taught visually and creatively.
And we have lots of examples on our website.
This is our center at Stanford,
that we were really happy when we had 5,000 people come to the site.
We've now had over 32 million visits in just a few years.
Teachers are excited about this visual, creative mathematics.
That's a book that also shows it.
So other things we have on our website.
We have an online student class taken by a quarter of a million students.
And when we started this class, we found that students who
took it achieved at significantly higher levels in their maths class.
We have teacher courses, lessons that are free on the website
are used in about half of the schools in the US now.
And we realized that textbooks don't actually ever give people
a creative visual maths experience.
So now we're working on our own books, also.
But these are some examples of pictures teachers have taken of kids
working on the materials in our books.
We have an interactive guide on our site that's also free and
shows you how to teach in these ways.
And I wanted to finish with a couple of examples of evidence of what happens when
maths changes.
The first one I want to share with you.
We decided a few years ago to bring 83 students to campus and
give them this different experience of maths.
I asked, what would happen if students stopped thinking that maths
was this list on the left and started thinking it was this list on the right?
So we shared with students what I've shared with you, and
then we taught them creatively and openly.
These were the 83 students when they came to us.
Some of the students had scored zero on a pre-test, some were very high achievers.
We gave them that same test at the end of four weeks with us.
And the students had improved by 2.7 years of school.
I'm very excited, we're repeating this camp this summer,
not only at Stanford, but in camps across the country and the world.
More than 30 actual camps are happening.
They're all going to use our curriculum.
And then I'm most excited about the fact we're gonna connect the kids together
this summer.
So students in Hawaii can explain their maths to kids in Alaska.
It's gonna be very exciting.
And then you may be wondering, okay, I see you can do this at Stanford, but
what about actual teachers in schools?
So I wanted to also share with you, the Central Valley of California, you may
know, is a kind of high-need area with lots of low achievement from students.
The county leader came to me and said,
why don't we get teachers to take your online class?
And I said, great, let's do it.
They had a whole group of fifth grade teachers take it.
And we followed those teachers over a year.
And it was an amazing year because the teachers
completely changed their relationship with maths.
They started to see themselves as capable learners, and
they started to teach differently.
And even inside that year, their students ended up scoring at significantly
higher levels in state tests again.
And you'll see there were a lot of press reports of what happened.
And they all point out that teachers first had to change
their own relationship with maths.
Some of the comments from that study.
This was a teacher saying, I thought it was gonna be great for the kids.
I never expected it to change me.
That's been my greatest revelation in all of it.
And then the kids were thrilled, going, my gosh, he's doing it like that?
It's okay that we struggle?
It's okay that we think differently?
And when I hear quotes like that,
I realized kids did not think it was okay to struggle.
And they did not think it was okay to think differently, which tells us why so
many students underachieve.
The principal of one of the schools announced at a conference recently that
his teachers had quadrupled their test scores that year.
And how they used to fear maths and rush through it, but
now they stay till 7 o'clock at night, discussing cool visual maths problems.
So I'll just finish by telling you I wrote this book, Mathematical Mindsets,
a couple of years ago.
The overwhelming feedback I had from that, people who read that book, was,
you have to get this out to more people.
You have to get it out, not just to maths teachers, but other teachers and parents.
So this is my new book that's coming out in the fall.
It talks about these six principles and how if you take on these different
principles in your life, or in your leading, or in your teaching.
Each of these principles really has the potential to unlock people in
significant ways.
And, of course, if you take on all of them, the potential is very strong.
So I will finish just by saying, a nice quote from Laurene Jobs and
Carol Dweck that they put on there.
But when people take on this different approach, they learn about the ideas,
a significant part of themselves kind of unlocks.
It releases their potential,
the same as it can release the potential of school students and others.
So I'm very excited about the work.
And if you'd like to see more, do come to YouCubed and
have a look at what we're doing, thank you.
>> [APPLAUSE] >> This way.
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