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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.

... the one key ingredient that is rarely communicated is that math, seen from just the right angle, with correct lighting, is fun.

I wouldn't want to quibble with that, but what is usually said is that so and so or such and such MAKES math, or science, fun. This drives me crazy. The current fad is to load up the exposition with slang and cute talk. Cf. the JPL MSL page. They have a blog page for Curiosity, where Curiosity herself blogs in the first person. They also explain its construction using human metaphor, without deviation: Its legs, its eyes, its brain ...

And if I may go ahead and quibble, is fun really the point? Puzzles and such are fun, I guess, so you can have mathematical fun, but this is just by the way. You yourself spoke of the beauty. I never really feel that way about it though, to be honest. It's certainly gratifying. It's an "itch" really. Newton was asked how he was able to arrive at his celebrated results and he replied, "By thinking on them constantly."

I agree heartily.

There’s one additional angle here: Too many public school teachers are “scared” of math.

My wife went to a teaching program about eight years ago for two years - since she already had her BS, she needed only the teaching method and state-mandated classes to get her cert.

Well, she dropped the whole idea of teaching. She was horrified by how blatantly *stupid* most teaching candidates are. They’re terrified of math. When my wife tried to help these women learn math, she got not shortage of attitude blown back on her.

She came away from the whole experience thinking (with justification) that public school teachers are a) incompetent and b) are proud of it.