[quote=aeh]My PG sib, who is a STEM worker, never "memorized" trig identities, because it was more efficient to re-derive them from the law of sines and law of cosines than it was to brute-force memorize them, and then retrieve them from the arbitrary storage location that would have resulted from rote memorization.
I'm going to put in an endorsement of memorizing. IMO, it's helpful in some situations (especially for beginners at a subject). For example, when learning a new idea, it's easy to have trouble seeing the big picture because of all the details. If you've memorized a chunk of important information, you don't have to think about it. This gives your working memory that much more space to analyze whatever idea you're struggling with. Alternatively, if you derive something, you have to shift your focus from, say, seeing the big picture of the problem to deriving something that's a small part of it. Sometimes it's hard to get back on track. More concretely, if you've memorized the definition of
integer, you don't have to look it up when the problem asks for integer solutions to a particular equation. Again, the distraction factor is reduced.
Different people have different neural circuitry. For some, deriving may be more efficient. For people like me, memorizing can definitely has its advantages.
So I don't see this question as an either/or proposition.
