[danielbarla]

I think the problem is that not enough time is spent explaining these very common techniques - what the rationale behind them is, hot to intuit that it could be applied to a specific problem, and how to get from that intuition to the actual answer / application.

Often, there's a very large skill gap between the student and the teacher (especially at college level, where many of the career mathematicians live and breathe maths), and these things are hand-waved away as obvious. Even worse is when the teacher doesn't actually know, and is just presenting the material straight from a guide. The way most course material seems to be set up is to skip over the middle part, and as a result the best short term strategy is to learn it as a bag of tricks.

I love maths, but I think its universal applicability and beauty get lost due to the way it's generally taught.