Deliberate practice for learning proof-based math

What would a deliberate practice for math look like? Specifically, while self-studying undergraduate-level and graduate-level proof-based math. (So I'm excluding earlier stages of learning math, and also excluding research work. I'm interested in the latter, but that seems like a much more difficult problem to talk about.)

Some difficulties with applying deliberate practice in this setting

https://commoncog.com/blog/the-problems-with-deliberate-practice/ search "What problems exist for practice in fields where no good training methods exist?"

"ill-defined sub skills" I think applies to math. What even are the separate skills in undergraduate math? ability to read a proof? ability to solve problems? those seem too broad as categories to me. maybe there's like "ability to solve a particular kind of problem". but textbook exercises don't come tagged with specific properties, so you can't really filter on these to improve your skill in particular ways.

undergrad proof problems are generally too long that you can't do drills like "get at least 95% correct on these problems" -- you can't run that many trials to practice.

"lack of feedback" -- this one also applies when self-studying math. the only ways to get feedback are by looking up solutions or by posting to something like math SE. book/subfield-specific discord servers might finally change this, but it will be slow. This is related to Feynman technique fails when existing explanations are bad (when existing explanations are bad, you can't even use techniques like Feynman technique to generate pseudo-feedback).

Parts of the definition of deliberate practice

https://www.lesswrong.com/tag/deliberate-practice

let's look at the requirements:

• purposeful practice:
  • "well-defined goals (such as doing something 3 times in a row with no mistakes)": this, as explained above, is one of the difficulties. proofs are long and take a lot of time to do. you also can't just "regenerate" problems using random number generators the way you can with high school level problems. you can still have a well-defined goal like "solve the problems in this section" i guess, but that doesn't seem to be what this requirement is about?
  • "is focused (the person is intently interested in improving, rather than having their attention elsewhere)": i'm not really sure if this requirement is satisfied... like, i guess you're really focused on solving the problem in front of you, or really trying to understand what the textbook is saying. so maybe that counts? on the other hand, i don't think you are usually consciously aware of like "i'm trying to solve this problem so that i can improve in a specific skill"?
  • "involves feedback": as explained above, this is one of the difficulties.
  • "involves getting out of one's comfort zone, practicing things on the edge of one's ability": i think this one is automatically satisfied. you don't solve problems that are obvious. you're always trying to solve problems that are new, that make you curious (i think one of the things curiosity tracks well is problems that are just at the edge of your ability, that seem "fun" because they are doable).
• "informed by an understanding of how to do well" / "the presence of a theory of skill and practice guided by that theory": i'm pretty vague on what counts as a theory. like, i'm guessing "solve lots of problems and you'll eventually get good at math" isn't a theory (yikes, that sounds like naive practice!).

See also

• Spaced proof review

External links

some links (that i didn't find very helpful, but this is all that i was able to find)

• https://news.ycombinator.com/item?id=2515455
• https://www.reddit.com/r/math/comments/71saol/what_does_deliberate_practice_mean_for_math/
• https://matheducators.stackexchange.com/questions/11104/how-can-i-implement-the-principles-of-deliberate-practise-in-my-mathematical-stu

What links here

• Deliberate practice for math (redirect page) ‎ (← links)