Here is the full transcript and summary of Stanford mathematics professor Jo Boaler’s TEDx Talk presentation: How You Can Be Good At Math, And Other Surprising Facts About Learningat TEDxStanford conference.
Listen to the MP3 Audio:
TRANSCRIPT:
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.
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 amount of university students who have good finger perception predicts their calculation scores. And the amount 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.
So there’s lots of other research that’s not known by teachers and schools. We also know that 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.
So 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 them about mindset and mistakes. But we also taught them creative, visual, beautiful maths. And 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 clip:
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.
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!
[Video ends]
So we need to get research out to teachers. We need a revolution in maths teaching. And 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 clip:“Math class last year was notes, and just handouts, and your own little box — you were just boxed in. You were like 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.
Want a summary of this talk? Here it is.
SUMMARY:
Jo Boaler’s TEDx Talk, titled “How You Can Be Good At Math, And Other Surprising Facts About Learning,” challenges prevailing misconceptions about math and learning. Boaler argues that the belief in a “math brain” is a dangerous myth that hinders learning. She highlights key points from her talk:
1. The Myth of the Math Brain: Boaler asserts that the idea of a “math brain,” implying that one is born with an innate ability for math, is false and unsupported by brain science. This myth perpetuates a fixed mindset about math abilities.
2. Mindset Matters: Carol Dweck’s research on mindset demonstrates that believing in one’s unlimited potential leads to higher achievement in math and life. Boaler emphasizes that mistakes are valuable for learning and can stimulate brain growth.
3. Visual Mathematics: Boaler advocates for a shift in math education towards visual and creative approaches. She presents an example where students are encouraged to think visually about math problems, fostering deeper understanding and discussions.
4. The Importance of Finger Perception: Boaler discusses the significance of finger perception in math learning, which is often discouraged in schools. Research shows that good finger perception predicts math achievement, yet students are made to feel that it’s “babyish.”
5. Changing Math Classrooms: Boaler calls for a revolution in math classrooms, emphasizing that research on effective math teaching and learning needs to reach educators. She shares a successful case where students improved their math skills by 50% after being taught with a growth mindset and creative, visual math techniques.
6. Empowering Students: Boaler shares the perspective of a middle school student who describes the shift from a rigid math environment to an open, collaborative one. The student expresses newfound confidence in his math abilities and a sense of working together to create a better future.
7. Belief in Unlimited Potential: Boaler concludes by emphasizing the importance of believing in one’s potential. She suggests that focusing solely on teaching methods or standards neglects the critical factor of students’ self-belief in their abilities.
In her TEDx Talk, Jo Boaler calls for a transformation in math education, emphasizing the need to break free from the myth of the “math brain” and promote a growth mindset among students. By embracing visual, creative, and collaborative approaches to learning, Boaler believes that all students can unlock their unlimited potential in math and beyond.
