In my experience memorization often comes for free when you strive for fluency through repetition. You end up remembering the quadratic formula after solving a few hundred quadratic equations. Same with the trig identities. I probably still remember all the most common identities years out of school, owing to the thousands (no exaggeration) of trig problems I had to solve in high school and uni. And can derive the rest in under a minute.
Memorization through solving problems gives you much more than anki decks, however: you end up remembering the roads, not just the signposts, so to speak, which is important for solving test problems quickly.
You are right that “the reduction in mental effort required on basic operations will rapidly compound to allow for much greater fluency with harder problems”, I am not sure that anki is the best way to achieve this reduction, though it is certainly worth a try.
In my experience memorization often comes for free when you strive for fluency through repetition. You end up remembering the quadratic formula after solving a few hundred quadratic equations. Same with the trig identities. I probably still remember all the most common identities years out of school, owing to the thousands (no exaggeration) of trig problems I had to solve in high school and uni. And can derive the rest in under a minute.
Memorization through solving problems gives you much more than anki decks, however: you end up remembering the roads, not just the signposts, so to speak, which is important for solving test problems quickly.
You are right that “the reduction in mental effort required on basic operations will rapidly compound to allow for much greater fluency with harder problems”, I am not sure that anki is the best way to achieve this reduction, though it is certainly worth a try.