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.
> 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?
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.
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.