[Edit: I have a pair of chips on my shoulder about this, one on my right shoulder and one on my left, as it were, and that's why I sort of blew up here. I really don't think I'm wrong re: the irritant, though. The SMSC referenced, for example, is Spiritual Moral Social Cultural (skills), and it is pretty much exactly as froufrou as you are guessing. You'll also note that every sentence in the post mentions "Japanese" and it's at the most rage-inducing Stuff White People Like level of surface-learning one could imagine, too.)
[Edit: Please up vote tokenadult's comment before this one, because while multiplication is taught by drill2kill here, that comment is better than mine re: math pedagogy generally.]
Within 6 lessons, using Khan Academy, I had him adding four digit numbers in his head, multiplying large numbers, and doing algebra.
He would learn a technique from me or the video, then apply it in practice drills, then review at the next lesson.
Total instruction time was 12-20 hours. I think he did a bit on his own.
I concluded that no one had actually checked to see if he could understand math. North American students hardly try calculations now; they're given calculators at a very early age.
I HATE the fact that American schools force students to do rote computation over and over again, with very little focus on the concepts behind the computations. I hated "math" until my 6th grade homeroom (not math) teacher took the initiative of writing high school level algebra word problems on the board, and not telling us how to solve them until after we attempted them. "A train going from St. Louis is headed toward L.A., and another train from L.A. is headed to St. Louis. they are going 40 mph, when will they pass each other" etc.
Suddenly, when the computation becomes a tool to satisfy an end, rather than the end itself, math becomes interesting.
This is exactly why giving calculators to children who have not yet mastered any method of multiplication is bad.
There is an amusing end to this story. When I entered college, I realized that this pattern-finding approach to solve math was used (in vain for the most part) by many of my classmates to try to game exams. It seems that it had worked well for them through high-school, but failed miserably at college.
That was something that caught me off guard a few years ago. In 2008 I was considering becoming a teacher (high school math/technology). For various reasons I chose a different path, but I sat in on some courses at a friend's school to get a 'day in the life of' feel and an opportunity to talk to other teachers. One class caught me by surprise. It was a 7th grade math course, essentially pre-algebra. However, the students did everything with calculators. The lesson that day was on interest, simple and complex, a way to try and tie the concepts down to real world examples. The students did everything with calculators, not one was using pencil and paper to work out the math (though they all recorded the steps they'd done on the calculators). Talking to the teachers, that was how their curriculum was setup, not just a one off case.
That wasn't what turned me away from teaching, but left me confused about how things had changed so much in the 15 years or so since I'd been in those seats.
EDIT: Did mention complex interest, that part made sense to use the calculator for. My observation was merely attempting to point out the ubiquity of the calculator in the classroom. I'd be interested to see the capability of students after a curriculum like that at doing mental and hand calculations, my understanding is that here in Georgia the various classwide exams they take also permit calculators so the students would have little occasion to demonstrate that skillset.