Here is the full transcript of Stanford mathematics professor Jo Boaler’s TEDx Talk presentation: How You Can Be Good At Math, And Other Surprising Facts About Learning at TEDxStanford conference.
Listen to the MP3 Audio: How you can be good at math, and other surprising facts about learning by Jo Boaler at TEDxStanford
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.
And 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. And I want you to think about it a bit 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. And often this is given out with the question: “How many squares would there be in case 100, or case n?”
But I want you to think of a different question now. 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. But 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.”
There was another teacher who 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.”
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, and I’ll say to them when they’ve done this: “So why is that squared you think? 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.