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Thanks for telling me your approach! For all the examples you gave, I feel like those are the sort of thing that become so familiar in the process of working w

Thanks for telling me your approach! For all the examples you gave, I feel like those are the sort of thing that become so familiar in the process of working with those objects (e.g. spending long hours seeking proofs of theorems when I first studied them) that they’d be hard to forget, and I have trouble seeing how such cards would be helpful. I suppose if I just read through the textbooks and sought to memorize the definitions and proofs by rote then this would make sense, but I’ve always been told, and practiced, that the best way to learn the material is to find the proofs myself rather than just reading them straight through. And having done that, the key ideas of the proof, and especially the definitions (which became burned into my brain in the process of working with them) seem to last for months or years without explicit recall. With language learning, it feels much more to me like rote memorization of an arbitrary mapping between labels in one language and labels in the other, so I find spaced repetition much more helpful. I’m not trying to be dismissive here, just genuinely trying to understand. I would love to find a more efficient method for studying math, as it’s the main thing I do right now with my time and I expect at least several more years of it. If I’m missing a better way then I’d really like to know. Thanks very much.

edanm 8y ago
Look, everyone is different. But I did a CS degree about 10 years ago. I learned calculus, and even had to memorize a bunch of proofs for the course. Now I'm not saying that I don't remember anything from the course... but I definitely remember extremely little. Even some of the "base objects" that we studied. (It's not like I'm a mathematician who actively uses this stuff). > I’ve always been told, and practiced, that the best way to learn the material is to find the proofs myself rather than just reading them straight through. Let's be clear, I completely agree with this. I don't just copy into Anki - I study, and then I put into Anki. In fact, just the fact of putting something into Anki tends to make me think about it much more clearly, as I decide what needs to be in there, how to rewrite the proof to be more concise but still understandable by me, etc.
- DavidSJ 8y ago
  > I learned calculus, and even had to memorize a bunch of proofs for the course. I'm curious about this. Did your class require students to find many of their own proofs of key results, or was it more about regurgitating proofs from the textbook?
  - edanm 8y ago
    Short answer is it was the latter. This was Calc 1 in a Computer Science program. Basically, the final exam had something like 6 questions, most of them standard calculation or new proof questions. But 2 questions were "prove this theorem that you learned", e.g. prove the intermediate value theorem or Weierstrauss' theorem or L'Hopital's rule or something. And answering at least one of these was mandatory. The proofs were from a list of about 40 proofs that would be on the test. The effect was that you basically had to memorize 40 proofs before the test, or at least a good chunk of them. I hated this at the time and though it was a total waste of time, but in retrospect, I think this was great way to force students to actually grapple with proofs. It was my first serious proof-based course (though I did proof stuff before in Linear Algebra and Set Theory courses). And in retrospect, this is (part of) how I actually study today, so I guess I liked the idea.

edanm 8y ago

Look, everyone is different. But I did a CS degree about 10 years ago. I learned calculus, and even had to memorize a bunch of proofs for the course. Now I'm not saying that I don't remember anything from the course... but I definitely remember extremely little. Even some of the "base objects" that we studied. (It's not like I'm a mathematician who actively uses this stuff). > I’ve always been told, and practiced, that the best way to learn the material is to find the proofs myself rather than just reading them straight through. Let's be clear, I completely agree with this. I don't just copy into Anki - I study, and then I put into Anki. In fact, just the fact of putting something into Anki tends to make me think about it much more clearly, as I decide what needs to be in there, how to rewrite the proof to be more concise but still understandable by me, etc.

DavidSJ 8y ago
> I learned calculus, and even had to memorize a bunch of proofs for the course. I'm curious about this. Did your class require students to find many of their own proofs of key results, or was it more about regurgitating proofs from the textbook?
- edanm 8y ago
  Short answer is it was the latter. This was Calc 1 in a Computer Science program. Basically, the final exam had something like 6 questions, most of them standard calculation or new proof questions. But 2 questions were "prove this theorem that you learned", e.g. prove the intermediate value theorem or Weierstrauss' theorem or L'Hopital's rule or something. And answering at least one of these was mandatory. The proofs were from a list of about 40 proofs that would be on the test. The effect was that you basically had to memorize 40 proofs before the test, or at least a good chunk of them. I hated this at the time and though it was a total waste of time, but in retrospect, I think this was great way to force students to actually grapple with proofs. It was my first serious proof-based course (though I did proof stuff before in Linear Algebra and Set Theory courses). And in retrospect, this is (part of) how I actually study today, so I guess I liked the idea.