Choosing problems for spaced proof review
Spaced proof review takes a lot of effort to implement even if done correctly. One of the mistakes one can make is to choose problems which aren't worth solving over and over. (By "problems", I mean math problems, i.e. the exercise or theorem statement or whatever.)
Properties of good problems:
- The problem is easy
- The problem is "fun"
- The problem is fundamental/important
Easy/fun problems are good for helping you build up and keeping the habit of spaced proof review.
Properties of bad problems:
- There's a lot of fiddly details that are challenging to get right on the spot.
- Problems which give you a sense of dread or some sort of "ugh" reaction.
for proofs that still feel a bit like sorcery — i wonder if it's a good or bad idea to put these into anki as proof cards. i feel like there are benefits and drawbacks:
- trying to recall something you've half-digested is generally painful, and i don't think it's the good kind of pain (it's the pain of bad posture, not the pain of a good workout). it's like, you've stored this knowledge in a badly structured way, and that is the reason you're having trouble recalling it. once you understand the natural way to do the thing, it will become easy to memorize.
- but maybe the way you get to the compacted/good structure is to struggle hard with trying to memorize the bad form of it. once you return to it a few times, you've sort of smoothed out the roughest parts; it kinda makes sense, and now that your brain isn't thrashing every time you think about the problem (because you've memorized the general shape of it) you can actually think about the problem. i have the sense that for many things, i just gave up on even adding them to anki, therefore i never was able to bring my understanding to a mature form (so i completely forgot everything). keeping it in anki is a nagging mechanism to perfect your understanding.
- i still feel though like working on new problems feels more rewarding/exciting than proving existing problems in anki.
I think it's an open question to me how to decide which problems to review in spaced proof review, or e.g. what percentage of problems you solve should be written up as a card in Anki.
Which proofs/exercises do I add as cards? I tend to prefer simple exercises and important exercises. If an exercise involves a lot of tedious detail, I tend to skip it (I might start making cards that just ask for the main point/insight for these tedious exercises).