Comment by jfv

I agree. It's (usually intuitively learned) reasoning that's very similar to the logical reasoning of mathematics. I think if you were to study, say, calculus in a manner typical of a first course in college, you'd be missing out on that sort of problem solving, but you'd definitely get that if you took a proofs-based class in analysis ("This function is continuous on this interval, so it must have a maximum. How can I use that to prove what's being asked?").