Dept of Education: Work Harder Not Smarter

I'm sure many feel this way about the school system in Canada or the US. Both systems are based on the same practices with few alterations. Core subjects (Math, Science, Language Arts, Social) with a few sprinklings of fun subjects thrown in to keep kids entertained. The problem I am seeing with this strategy is that children are taught to do what the teacher does and do it over & over & over, ad infinitum.
When that child who can recite or redo what the teacher has "taught" (because very few children actually understand the mechanics/reasons behind the theory), they graduate High School and go to university. This university now expects for the reasoning behind methods to be understood without reteaching the subjects.
A few of the children probably have twigged to the understanding of concepts that were not explicitly explained. But the majority of those children (and I have to admit that I am one when it comes to mathematics) recite and give back the teacher what they want, but if asked the same question in another way cannot work their way through and come up with an answer because they lack the underlying principles and/or theory that was implicit in the work but not stated.
And now that university expects them to know this stuff...

Luckily I have the ability to self-teach (or probably more likely avoid classes where there is material I do not understand), and this has not been a problem in acquiring my education so far. But I have seen it come up in a number of places. I have a nasty habit of forgetting most things taught in one semester by the next (unless pummelled into my head over & over & over), even if I DO understand the concepts. I usually pick up quicker the next time it is explained and have that "Oh yeah!" moment.
But how do you teach the underlying principles & to retain material that is absolutely critical in the future? And more importantly, teach this to a wide range of ages & learning abilities...