[nicoburns]

I have a good friend who works as a high school physics teacher, and this is apparently exactly how they teach: they teach the intuition behind the problems so that the kids can visualise them.

[morelisp]

And this works up until about high school physics, but not too much further. Not only do many interesting mathematical objects lack some intuitive basis, some are interesting specifically because they behave counter-intuitively.

[pfdietz]

Mathematics builds abstractions, but at any level you first see the less abstract things that motivated the abstraction.