How you can be good at math, and other surprising facts about learning | Jo Boaler | TEDxStanford — Transcript

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1. 0:00Translator: Bob Prottas Reviewer: Leonardo Silva
2. 0:11Hello.
3. 0:12So I'm here to tell you that what you have believed about your own potential
4. 0:17has changed what you have learned, and continues to do that,
5. 0:22continues to change your learning, and your experiences.
6. 0:27So, how many people here -- let's get a show of hands --
7. 0:29have ever been given the idea that they're not a math person,
8. 0:33or that they can't go onto the next level of math,
9. 0:35they haven't got the brains for it?
10. 0:37Let's see a show of hands.
11. 0:40So, quite a few of us.
12. 0:41And I'm here to tell you that idea is completely wrong,
13. 0:46it is disproven by the brain science.
14. 0:48But it is fueled by a single myth that's out there in our society
15. 0:52that's very strong and very dangerous.
16. 0:54And the myth is that there's such a thing as a math brain,
17. 0:58that you're born with one, or you're not.
18. 1:00We don't believe this about other subjects.
19. 1:03We don't think we're born with a history brain, or a physics brain.
20. 1:07We think you have to learn those.
21. 1:08But with math, people, students believe it,
22. 1:11teachers believe it, parents believe it.
23. 1:14And until we change that single myth
24. 1:17we will continue to have widespread underachievement in this country.
25. 1:21Carol Dweck's research on mindset has shown us
26. 1:24that if you believe in your unlimited potential
27. 1:27you will achieve at higher levels in maths, and in life.
28. 1:31And an incredible study on mistakes show this very strongly.
29. 1:35So Jason Moser and his colleagues actually found from MRI scans
30. 1:39that your brain grows when you make a mistake in maths.
31. 1:43Fantastic.
32. 1:44When you make a mistake, synapses fire in the brain.
33. 1:47And in fact in their MRI scans
34. 1:49they found that when people made a mistake synapses fired.
35. 1:52When they got work correct less synapses fired.
36. 1:56So making mistakes is really good.
37. 1:59And we want students to know this.
38. 2:00But they found something else that was pretty incredible.
39. 2:03This image shows you the voltage maps of people's brains.
40. 2:08And what you can see here is that people with a growth mindset,
41. 2:12who believe that they had unlimited potential,
42. 2:14they could learn anything,
43. 2:16when they made a mistake, their brains grew more
44. 2:19than the people who didn't believe that they could learn anything.
45. 2:23So this shows us something that brain scientists have known for a long time:
46. 2:28That our cognition, and what we learn
47. 2:31is linked to our beliefs, and to our feelings.
48. 2:35And this is important for all of us not just kids in math classrooms.
49. 2:39If you go into a difficult situation, or a challenging situation,
50. 2:42and you think to yourself: "I can do this. I'm going do it."
51. 2:46and you mess up or fail,
52. 2:48your brain will grow more, and react differently
53. 2:52than if you go into that situation thinking:
54. 2:55"I don't think I can do this."
55. 2:57So it's really important that we change the messages kids get in classrooms.
56. 3:03We know that anybody can grow their brain,
57. 3:07and brains are so plastic, to learn any level of maths.
58. 3:10We have to get this out to kids.
59. 3:12They have to know that mistakes are really good.
60. 3:14But maths classrooms have to change in a lot of ways.
61. 3:17It's not just about changing messages for kids.
62. 3:20We have to fundamentally change what happens in classrooms.
63. 3:23And we want kids to have a growth mindset,
64. 3:25to believe that they can grow, and learn anything.
65. 3:28But it's very difficult to have a growth mindset in maths.
66. 3:31If you're constantly given short, closed questions that you get right or wrong,
67. 3:36those questions themselves
68. 3:38transmit fixed messages about math, that you can do it or you can't.
69. 3:42So we have to open up maths questions
70. 3:44so that there's space inside them for learning.
71. 3:47I want to give you an example.
72. 3:48We're actually going to ask you to think about some maths with me.
73. 3:51So this is a fairly typical problem, it's given out in schools.
74. 3:55I want you to think about it differently. So we have three cases of squares.
75. 4:00In case 2 there's more squares than in case 1,
76. 4:02and in case 3 there's even more.
77. 4:04Often this is given out with the question:
78. 4:06"How many squares would there be in case 100, or case n?"
79. 4:10I want you to think of a different question.
80. 4:12I want you to think without any numbers at all, or without any algebra.
81. 4:17I want you to think entirely visually,
82. 4:19and I want you to think about where do you see the extra squares?
83. 4:23If there are more squares in case 2 than case 1, where are they?
84. 4:29So if we were in a classroom, I'd give you a long time to think about this.
85. 4:34In the interest of time, I'm going to show you some different ways
86. 4:37people think about this, and I've given this problem to many different people,
87. 4:41and I think it was my undergrads at Stanford who said to me --
88. 4:45or one of them said to me:
89. 4:46"Oh, I see it like raindrops. Where raindrops come down on the top.
90. 4:52So it's like an outer layer, that grows new each time."
91. 4:57It was also my undergrads who said:
92. 4:59"Oh no, I see it more like a bowling alley.
93. 5:02You get an extra row,
94. 5:03like a row of skittles that comes in at the bottom."
95. 5:07A very different way of seeing the growth.
96. 5:12It was a teacher, I remember, who said to me it was like a volcano:
97. 5:15"The center goes up, and then the lava comes out."
98. 5:19[Laughter]
99. 5:21Another teacher said: "Oh no, it's like the parting of the Red Sea.
100. 5:26The shape separates, and there's a duplication with an extra center."
101. 5:36I remember this was -- Sorry, this one as well.
102. 5:39Some people see it as triangles.
103. 5:42They see the outside growing as an outside triangle.
104. 5:46And then there was a teacher in New Mexico who said to me:
105. 5:49"Oh it's like Wyane's World, Stairway to Heaven, access denied."
106. 5:55[Laughter]
107. 6:01And then we have this way of seeing it.
108. 6:04If you move the squares, which you always can,
109. 6:07and you rearrange the shape a bit,
110. 6:09you'll see that it actually grows as squares.
111. 6:11So, this is what I want to illustrate with this question:
112. 6:14"When it's given out in maths classrooms, and this isn't the worst of questions,
113. 6:18it's given out with a question of: "How many?" and kids count.
114. 6:21So they'll say:
115. 6:22"In the first case there's 4. In the second there's 9."
116. 6:24They might stare at that column of numbers for a long time and say:
117. 6:28"If you add one to the case number each time and square it,
118. 6:31then you get the total number of squares."
119. 6:34But when we give it to students, and high school teachers,
120. 6:39I'll say to them when they've done this:
121. 6:41"So why is that squared? Why do you see that squared function?"
122. 6:45They'll say: "No idea."
123. 6:47So this is why it's squared. The function grows as a square.
124. 6:51You see that squaring in the algebraic representation.
125. 6:55So when we give these problems to students we give them the visual question.
126. 6:59We ask them: "How they see it?"
127. 7:01They have these rich discussions, and they also reach deeper understandings
128. 7:05about a really important part of mathematics.
129. 7:08So we actually need a revolution in maths classrooms.
130. 7:10We need to change a lot of things.
131. 7:13And part of the reason we need to change so much
132. 7:15is because research on maths teaching and learning
133. 7:18is not getting into schools and classrooms.
134. 7:20And I'm going to give you a stunning example now.
135. 7:22So this is really interesting.
136. 7:27When we calculate -- Even when adults calculate,
137. 7:30where a brain area that sees fingers is lighting up,
138. 7:35we're not using fingers,
139. 7:36but that brain area that sees fingers lights up.
140. 7:39So there's a brain area when we use fingers,
141. 7:41and there's a brain area when we see fingers.
142. 7:44And it turns out that seeing fingers is really important for the brain.
143. 7:49And in fact finger perception is --
144. 7:53Scientists test for finger perception
145. 7:56by asking them to put their hands under a table --
146. 7:59they can't see them touching a finger,
147. 8:01and then seeing if you know which finger has been touched.
148. 8:04The number of university students who have good finger perception
149. 8:07predicts their calculation scores.
150. 8:10The number of finger perception grade 1 students have
151. 8:14is a better prediction of maths achievement in grade 2
152. 8:17than test scores.
153. 8:19It is that important.
154. 8:21But what happens in schools and classrooms?
155. 8:25Students are told they're not allowed to use their fingers.
156. 8:27They're told it's babyish. They're made to feel bad about it.
157. 8:30When we stop children learning numbers through fingers,
158. 8:33it's akin to halting their numerical development.
159. 8:37And scientists have known this for a long time.
160. 8:39And the neuroscientists conclude
161. 8:41that fingers should be used for students learning number and arithmetic.
162. 8:47If we haven't published --
163. 8:48We published this in a paper in the Atlantic last week.
164. 8:51I don't know any educator who knew this.
165. 8:53This is causing a huge ripple through the education community.
166. 8:59There's lots of other research that's not known by teachers and schools.
167. 9:03We know when you perform a calculation
168. 9:05the brain is involved in a complex and dynamic communication
169. 9:08between different areas of the brain, including the visual cortex.
170. 9:13Yet, maths classrooms are not visual, they're numerical and abstract.
171. 9:17I want to show you now what happened
172. 9:19when we brought 81 students onto campus last summer,
173. 9:22and we taught them differently.
174. 9:24So we taught them about the brain growing.
175. 9:26We taught about mindset and mistakes.
176. 9:30But we as also taught them creative, visual, beautiful maths.
177. 9:35They came in for 18 lessons with us.
178. 9:37Before they came to us they had taken a district standardized test.
179. 9:41We gave them the same test at the end of our 18 lessons,
180. 9:44and they improved by an average of 50%.
181. 9:48Eighty one students, from a range of achievement levels,
182. 9:51told us on the first day: "I'm not a math person."
183. 9:54They could name the one person in their class who was a math person.
184. 9:59We changed their beliefs.
185. 10:00And this is a clip from a longer music video that we made of the kids.
186. 10:11But we keep talking
187. 10:13Can't stop, won't stop solving
188. 10:16It's like something is growing
189. 10:19In our minds every time we try again.
190. 10:23'Cause the haters gonna hate, hate, hate, hate, hate.
191. 10:27We will make mistakes, stakes, stakes, stakes, stakes.
192. 10:30We're just gonna shake, shake, shake, shake, shake.
193. 10:33Shake it off! Shake it off!
194. 10:35Our method's gonna break, break, break, break, break.
195. 10:38It's not a piece of cake, cake, cake, cake, cake.
196. 10:41We're just gonna shake, shake, shake, shake, shake.
197. 10:44Shake it off! Shake it off!
198. 10:46We represent things visually,
199. 10:49Present them to our class clearly
200. 10:53So that they can see mmm
201. 10:56So that they can see mmm
202. 10:58We know our brains can grow
203. 11:01Who cases how fast we go?
204. 11:04Understanding's what we show mmm
205. 11:07Understanding's what we show mmm
206. 11:10So we keep trying
207. 11:13Synapses are firing
208. 11:16This problem's so exciting
209. 11:20It's so cool that I want to go and show the world!
210. 11:24So --
211. 11:25(Applause)
212. 11:30We need to get research out to teachers. We need a revolution in maths teaching.
213. 11:33If you don't believe me, come listen to this kid.
214. 11:36He's a middle schooler, and we had worked with his teachers
215. 11:39to shift from worksheet math to open math with mindset messages.
216. 11:43This is him reflecting on that shift.
217. 11:45Math class last year was notes, and just handouts,
218. 11:50and your own little box -- you were just boxed in.
219. 11:55You were by yourself, it was every man for themselves.
220. 11:59But now this year is just open. We're a whole big --
221. 12:03It's like a city --
222. 12:04we're all working together to create this new beautiful world.
223. 12:08I think the challenges, and the future that lies ahead for me --
224. 12:16If I keep on pushing,
225. 12:18if I keep on doing this someday I'm going to make it.
226. 12:24We have focused for so long in education,
227. 12:27in maths education, on the right way to teach a fraction,
228. 12:30on the standards we use in classrooms which are argued about all the time,
229. 12:34and we've completely ignored the beliefs students hold about their own potential.
230. 12:39And only now is the full extent of the need
231. 12:42to attend to that coming to light.
232. 12:44We all have to believe in ourselves
233. 12:48to unlock our unlimited potential.
234. 12:51Thank you.
235. 12:53(Applause)