The Cambridge Method: Struggle First, Understand Later — Transcript

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1. 0:00Everyone tells you just how brilliant
2. 0:02Cambridge is for studying maths.
3. 0:05Cambridge has some of the best
4. 0:06researchers in the world teaching
5. 0:08undergraduate students topics that
6. 0:09they've spent their whole career
7. 0:10studying. But they might be the best at
8. 0:12research, but they're definitely not the
9. 0:14best at teaching. The Cambridge lectures
10. 0:16are fast definition here, a theorem
11. 0:18there, and then a proof left as an
12. 0:20exercise to the reader. Then they move
13. 0:21on, and they expect you to keep up. And
14. 0:24not just to cope, but to be the best in
15. 0:26the world at it. That's the teaching.
16. 0:29That's it. So why do the people who
17. 0:31survive that end up running math
18. 0:33departments and winning fields medals?
19. 0:35Well, Cambridge have a different way of
20. 0:36making the best mathematicians and it's
21. 0:38not teaching but training. Now, let me
22. 0:41be precise because I'm not saying
23. 0:43lectures are bad. They're probably world
24. 0:45class in their field. Some of them have
25. 0:46wrote the thing that they're actually
26. 0:48lecturing on. I'm saying the teaching,
27. 0:50the actual process of moving information
28. 0:52from one brain into another, in my
29. 0:54opinion, is barely attempted. And I
30. 0:57don't think that's an accident. I think
31. 0:58it's kind of the point. Now, if you know
32. 1:01anything about master degree, you're
33. 1:02already probably objecting to what I'm
34. 1:03saying. 12 lectures a week, uh, end of
35. 1:06year exams, proofs left as an exercise,
36. 1:09that's Warick, that's Imperial, that's
37. 1:10Durham, that's every researchheavy math
38. 1:13department in the country. And to be
39. 1:15fair, you're right. So, let me bit more
40. 1:17specific about what makes Cambridge the
41. 1:19extreme case rather than just another
42. 1:20example of the same type. It's the pace.
43. 1:23It's the volume. Material that's a full
44. 1:25module elsewhere is often half a module
45. 1:27at Cambridge. The math tripos covers
46. 1:29more ground faster than pretty much
47. 1:31everywhere else in the world and they
48. 1:33test you on some of the hardest
49. 1:35questions that you've barely been
50. 1:36taught. It does it while assessing you
51. 1:38exactly once in May at the end. Now, in
52. 1:41what way is the teaching bad? Well,
53. 1:43there's 10 to 12 lectures a week in the
54. 1:45first year. You get a new definition, a
55. 1:47new theorem, a proof, next, move on. No
56. 1:49worked examples in the sense that you
57. 1:51know from Alevel. No, let's do one
58. 1:53together. The pace just assumes that
59. 1:55you've read the content ahead of time.
60. 1:56assumes you go home afterwards and spend
61. 1:58eight hours understanding the 55 minutes
62. 2:00they just gave you. And if you don't,
63. 2:02you're behind by Thursday of week one.
64. 2:04Then [music] secondly, nothing you do
65. 2:06actually counts. Example sheets aren't
66. 2:08assessed. Attendance isn't tracked.
67. 2:10There's no coursework other than a bit
68. 2:11of catam in the second year. The entire
69. 2:14year lands on exams in May, which means
70. 2:16the system has no mechanism for noticing
71. 2:18you're drowning in the work until it's
72. 2:20far too late and there's nothing you can
73. 2:22do about it. And then finally,
74. 2:24supervisions. Supervisions are the thing
75. 2:26that Cambridge sells itself on. It sells
76. 2:27it the hardest. And to be fair, it's a
77. 2:29lot more contact time than almost any
78. 2:31other department in the country office.
79. 2:33It's one or two students with an expert
80. 2:35in that field for a full hour. And when
81. 2:37it's good, it's the best teaching in my
82. 2:39opinion in British higher education. But
83. 2:41nothing actually controls that variance.
84. 2:43Sometimes you get someone who transforms
85. 2:45how you think about maths. Sometimes you
86. 2:47get a second year PhD student who is, to
87. 2:50be fair, amazing at what they're
88. 2:51researching, but isn't really up to
89. 2:54scratch with considering how a
90. 2:5519-year-old learns maths. Most of the
91. 2:57time, it's just students desperate not
92. 2:59to embarrass themselves that's forcing
93. 3:00them to keep up with the course. And
94. 3:03even if you get a good supervisor, it's
95. 3:051 hour once a fortnight. It's nowhere
96. 3:07near enough to carry you through an
97. 3:08entire course of something you're
98. 3:10struggling with. that hour is the only
99. 3:12thing that standing between a really
100. 3:14struggling student and a year that they
101. 3:16just can't recover from and just nobody
102. 3:18actually checks whether it's any good
103. 3:19for the student whether they're actually
104. 3:21making any progress. So with all this
105. 3:24going wrong, why does Cambridge end up
106. 3:26with such good mathematicians even
107. 3:27though the teaching seems to be
108. 3:28absolutely non-existent? Well, from what
109. 3:31you'd probably expect and what I did
110. 3:33expect when I went here, non-existent
111. 3:35teaching should lead to the worst
112. 3:36students. However, something happens
113. 3:39when you get no help. When nobody
114. 3:41explains it to you, then you have to
115. 3:43explain it to yourself. And explain
116. 3:45something to yourself is not the same
117. 3:46activity as being explained to. It's a
118. 3:49completely different process and a
119. 3:50different result. With good teaching,
120. 3:53the kind we're all trained to want and
121. 3:54to get from A levels, it hands you a
122. 3:57clean path through the material. You
123. 3:59follow it, it makes sense, you feel the
124. 4:00click. The problem is that by following
125. 4:02somebody else's path, you don't actually
126. 4:05stray from that path. you don't
127. 4:07understand why things work and why they
128. 4:09don't work and you don't find alternate
129. 4:11paths that might just work. Change the
130. 4:14question slightly and the path that you
131. 4:15knew and loved completely disappears cuz
132. 4:18you never built it. You just walk down a
133. 4:19path that somebody else taught you. Now
134. 4:21the reason why Cambridge doesn't like
135. 4:23teaching is because they don't give you
136. 4:24the path. So you work out where that
137. 4:27theorem came from. What breaks if you
138. 4:28drop a hypothesis, why the proof goes
139. 4:30that way and not the obvious way. When
140. 4:33you explain it to yourself, you have to
141. 4:34critique and understand every single
142. 4:36angle to truly understand it. And the
143. 4:39way the example sheets work, you can be
144. 4:40sat with a question for like 6 hours. In
145. 4:43one specific case, I sat with a problem
146. 4:44for 4 days at one point contemplating
147. 4:47how much gravity will affect me if I
148. 4:48jump out of the second story of the
149. 4:50library. But the point is, you get
150. 4:52absolutely nowhere. You learn everything
151. 4:54that doesn't work. And when you finally
152. 4:56get there, you truly understand why it
153. 4:59does work. That six hours of getting
154. 5:02absolutely nowhere is entirely the
155. 5:04point. Everything else is just
156. 5:05scaffolding to help you build towards
157. 5:07the answer. And I'm trying not to be
158. 5:09romantic about suffering. I'm not a
159. 5:11masochist. But there is a name for it in
160. 5:13science. It's called desirable
161. 5:14difficulties. But the short version is
162. 5:17conditions that make learning feel
163. 5:18slower and worse while it's actually
164. 5:20happening produce knowledge that lasts
165. 5:22longer and transfers to more things.
166. 5:26Struggling to understand something
167. 5:27before you're told it beats just being
168. 5:29told. Failing at a problem before you
169. 5:31see the solution always beats just
170. 5:34looking at the solution and going, "Ah,
171. 5:35that's the answer." Now, on the back of
172. 5:37this, there's probably two questions you
173. 5:38might ask. One, aren't students failing
174. 5:41in school because of bad teaching?
175. 5:42Whereas, I've just claimed that bad
176. 5:43teaching leads to good students. And
177. 5:45secondly, does Cambridge actually
178. 5:47produce good mathematicians or they just
179. 5:49have such high standards that they
180. 5:51already let in good mathematicians and
181. 5:53then just take the credit? And to be
182. 5:55fair, you're asking the right questions.
183. 5:57But the second question actually answers
184. 5:59the first. Cambridge does have pretty
185. 6:01much the highest requirements to get in.
186. 6:03I mark step papers. I I know it is a
187. 6:05really hard exam. It's the hardest one A
188. 6:07level students have to go through. It
189. 6:09really pushes students to think
190. 6:10differently and understand the math that
191. 6:12they're doing. So yes, Cambridge does
192. 6:14admit some of the best. But that's
193. 6:15exactly why this method works. Put a few
194. 6:17hundred students like that in one place
195. 6:19and they start trying to outwork each
196. 6:21other. Most of their waking hours go
197. 6:23into the course because everyone around
198. 6:25them is doing the same. that peer
199. 6:27pressure doesn't exist if you don't
200. 6:28admit those people in the first place.
201. 6:31Does that mean it's selection rather
202. 6:32than training? Well, partly yes. I'm not
203. 6:35going to pretend otherwise, but I think
204. 6:37the honest version is that it's both.
205. 6:38The system selects the best students and
206. 6:40then it forces those best students to
207. 6:42develop and really learn as quickly at a
208. 6:45scale that nobody would choose to do
209. 6:46voluntarily. A lot of people put
210. 6:48themselves through quite a lot at
211. 6:50Cambridge. A lot of them arrive able to
212. 6:51sit with a hard problem for maybe an
213. 6:53hour, but when they leave, they're able
214. 6:55to sit with a hard problem for like over
215. 6:56a week. That's really important because
216. 6:58that's what research math is. You sit in
217. 7:00front of a problem nobody has ever
218. 7:02solved before. There are no lecture
219. 7:03notes. There's no supervisor who knows
220. 7:05the answer because there is no answer.
221. 7:07You just sit with a problem for days and
222. 7:09days trying to understand it. And the
223. 7:10maths is essentially a three-year
224. 7:12rehearsal for exactly that. It isn't
225. 7:14badly designed teaching. It's
226. 7:16well-designed training that happens to
227. 7:18look identical to badly designed
228. 7:20teaching from the outside. The people
229. 7:21who come out at the end have spent three
230. 7:23years building [music] the specific
231. 7:24muscle that a researching job requires.
232. 7:27Tolerance for not knowing and the habit
233. 7:29of sticking with a problem to find out
234. 7:31that solution. You can't get that from
235. 7:33being spoonfed answers. There is no
236. 7:35version of being taught well that also
237. 7:36teaches you to work without knowing
238. 7:38anything. Okay, so getting on to
239. 7:41probably the most important part of this
240. 7:42video. You don't need to be at Cambridge
241. 7:44to benefit from this system. You can
242. 7:46incorporate these habits into your own
243. 7:48studies. So before you seek for the
244. 7:50solution, sit on it for a while and fail
245. 7:53properly. Don't just give up and then
246. 7:55look for the answer. [music] You need to
247. 7:56give yourself time to make mistakes, try
248. 7:58different methods and struggle. That's
249. 8:01the important part. 10 minutes, half an
250. 8:03hour on paper actually attempting it.
251. 8:06The failure is what makes you fully
252. 8:07understand. the instinct to go and check
253. 8:09the answer as soon as something goes
254. 8:11wrong. It's the exact instinct that's
255. 8:12just costing you because it feels like
256. 8:15efficiency. It feels like you're being
257. 8:16super efficient, finding the answer,
258. 8:17understanding really quickly, but you're
259. 8:19just memorizing their solution. You're
260. 8:21not understanding why the solution
261. 8:22works. [music]
262. 8:23And secondly, bit more of a
263. 8:24controversial one. Hold yourself to a
264. 8:26very high standard. And I'm not saying
265. 8:28do loads and loads and loads of problems
266. 8:30just so that you you've done everything
267. 8:31and you've you've worked really really
268. 8:33hard. I'm saying hold yourself to a high
269. 8:35standard when it comes to your
270. 8:36understanding. See yourself as a
271. 8:38researcher, not just a student. When you
272. 8:41start to learn something new, don't just
273. 8:43accept it because you've been taught it.
274. 8:45Push yourself to develop a deep
275. 8:47understanding of why things work and why
276. 8:49they don't. That's the entire Cambridge
277. 8:52method. It cost you nothing to implement
278. 8:54yourself, and nobody has to teach it to
279. 8:56you, which is kind of more or less the
280. 8:58point of this video. But this is the
281. 9:01exact method I used back when I was in
282. 9:02Alevel to get the highest grades, 5A
283. 9:05starts. I did every module on the
284. 9:07further mass and back then the further
285. 9:09additional math spec and my school at
286. 9:11the time just didn't have anyone who
287. 9:13knew the content to be able to teach it
288. 9:14to me. So I had to learn it myself and I
289. 9:16had to go through this exact method
290. 9:18because I just didn't have the
291. 9:19solutions. I couldn't look anything up.
292. 9:21I just had to struggle with the problem
293. 9:23until I understood them and until I got
294. 9:25the answers right. So yeah, Cambridge
295. 9:28might not have the best teaching, but
296. 9:29the Cambridge method of training rather
297. 9:31than simply teaching produces not only
298. 9:33the best mathematicians in the world,
299. 9:35but also some of the best thinkers,
300. 9:37people who go on to not just study
301. 9:38maths, but maybe philosophy or law. Now,
302. 9:42if you're applying for Cambridge or any
303. 9:43other university for maths, or even if
304. 9:45you're just sitting in first year right
305. 9:46now, quietly wondering whether everyone
306. 9:48else is finding it as hard as you, they
307. 9:50are. It's just nobody wants to say so.
308. 9:52Try and implement some of these ideas.
309. 9:54See if they can help you level up your
310. 9:55math game. see if it helps you with your
311. 9:57university maths. And if you've already
312. 9:58been through the tripost and have a
313. 10:00different view than me, put it in the
314. 10:01comments. I'd actually really like to
315. 10:02read it. See what you thought of being
316. 10:04at Cambridge. But yeah, I'll see you in
317. 10:05the next one. Bye.