[NVDave]

They’re not teaching the latter form in any high school - as you point out, the abstract stuff is for math majors.

The high school variant, as you also point out, can be learned by rote.

And therein lies the issue: The modern teaching methods movement decries “drill and kill,” but want to know something? There are some things where “drills” work just fine. I don’t have to even think about how to multiply numbers up to 15, because we memorized them. If I had to think about how to do multiplication, I would have never made it through all the math involved in electrical engineering.

Here’s the teaching method that would solve most all of today’s problems in education:

http://www.southparkstudios.com/clips/103440/drug-free-treatment

[SpaceBar]

One of the funniest scenes from south park.

[SpaceBar]

They’re not teaching the latter form in any high school...

I hear what you're saying and point taken. Reading all the various responses above by people who have had difficulty with it, reinforces a notion I've had for years that the one key ingredient that is rarely communicated is that math, seen from just the right angle, with correct lighting, is fun. But it's hard to convey that sometimes when the objective seems to be topheavy with "getting the right answer", when the real goal is insight.