I'm going to do the unthinkable: start memorizing mathematical results instead of deriving them.

Okay, unthinkable is hyperbole. But I've noticed a tendency within myself to regard rote memorization of things to be unbecoming of a student of mathematics and physics. An example: I was recently going through a set of practice problems for a university entrance exam, and calculators were forbidden. One of the questions required a lot of trig, and half the time I spent solving the problem was just me trying to remember or re-derive simple things like the arcsin... (read more)

In general there the core principle of spaced repetition that you don't put something into the system that you don't already understand.

When trying to memorize mathematical results make sure that you only add cards when you really have a mental understanding. Using Anki to avoid forgetting basic operations is great. If you however add a bunch of information that's complex, you will forget it and waste a lot of time.

1whales6yNice, and good luck! I'm glad to see that my post resonated with someone. For rhetorical purposes, I didn't temper my recommendations as much as I could have -- I still think building mental models through deliberate practice in solving difficult problems is at the core of physics education. I treat even "signpost" flashcards as opportunities to rehearse a web of connections rather than as the quiz "what's on the other side of this card?" If an angle-addition formula came up, I'd want to recall the easy derivation in terms of complex exponentials and visualize some specific cases on the unit circle, at least at first. I also use cards like that in addition to cards which are themselves mini-problems.
11shminux6yIn 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 [http://en.wikipedia.org/wiki/List_of_trigonometric_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.

Open thread, January 25- February 1

by NancyLebovitz 1 min read25th Jan 2014318 comments

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If it's worth saying, but not worth its own post (even in Discussion), then it goes here.