|There's more than one way to do things|
What is Learning, as opposed to Education, as opposed to Studying? And what are their merits?
I've gone through the "education mill" and the big problem I see is they push people too fast throught the system. There is a big difference between memorizing ways to solve problems, and gaining a conceptual understanding of the problem. Usually once a student sees the concepts underlying a problem, the answer becomes almost obvious. There is a quote by someone ...If you know how(and/or why) to ask the question, you already are on the path to the answer.
But concepts take a long time to settle in, and usually in early school you just want to force the vocabulary of the problem, into the student's minds. Therefore we have memorization as an early teaching technique.
Do you really want to teach the concept of number systems to pre-college level students? No, you just want them to learn the rules of math and algebra, so they can handle the equations shown to them in other classess.
I still can quote from memory the solution to the quadratric equation..... x equals -b plus or minus the square root of b squared minus 4ac all over 2a.
If they understood the concept, they probably would be able to derive the equation themselves.....but that would take too long...so they push the kids thru school as fast as possible. (In Perl analogy, howlong did it take you to realize what a hash was, and why should you use it? For the longest time, I said to myself...arrays can do it all)
Another good example which I see, is the concept of measuring space and areas. If you could take the time to impress on someone, what the concept of space is, that is it is a 3 dimensional quantity, it almost becomes obvious to them that the volume is $x*$y*$z, and they never forget. But if you don't pass on the concept of dimensional views, they need to memorize and you can stump them easily by giving them an area($x*$y) in ft^2 and a ceiling height, and asking for the room volume.
Now of course, there are real world problems to teaching concepts to people under 20....at that age, the only concept that is important, is the color of Mary-Sue's underpants. :-)
I'm not really a human, but I play one on earth. flash japh