Not going meta for developing reliability of problem-solving took a lot of points from me. I just relied on the magical intuition, which was good enough to solve some hard problems (to figure out solution method, without knowing how it was being figured out), but not good enough to reliably solve those problems without errors.
As a result, when I was applying to college, I was afraid of the regular admission exams which I couldn't reliably ace (because of technical errors I wouldn't notice, even though solution methods were obvious), and instead used the perfect score given to winners of Moscow math and physics olympiads, which required solving some hard problems but not solving all problems without errors. Which is a pretty stupid predicament. It just never occurred to me that production of perfect scores can be seen as an engineering problem, and I don't recall any high school teachers mentioning that (even smart college professor teachers administering cram school sessions).
What do you mean by "going meta"?
I feel like the advice in your earlier comment is good for obtaining insight, but I can't see how it would be useful on a test. I haven't taken many tests where I have had enough time to solve each problem in several ways!
I'm eager to learn more if I haven't understood correctly, though.
Lately I've resolved to try harder at teaching myself math so I have a better shot at the international olympiad (IMO). These basically involve getting, say, three really hard math problems and trying your best to solve them within 5 hours.
My current state:
What does the intrumental-rationality skill of LWers have to say about this? What recommendations do you guys have for improving problem-solving ability, in general and specifically for olympiad-type environments? Specifically,