I agree, I don't see how this actually teaches how multiplication actually works. It's a clever method to avoid solving the problem the classic way of using a memorized multiplication table and breaking down the problem into smaller segments. I don't even see how this saves you time once you get up to speed on either method. The only difference is that with my old school way I can explain to you why I get the answer I calculated while this method doesn't seem to offer that ability.
I hate to disappoint you, but mathematics is nothing but a gigantic collection of tricks, rules, games and the like written in language impenetrable to outsiders.
If a mathematical paper had said something about graphical isomorphisms with a two-dimensional lattice, the average person would have been impressed, without understanding a word of it. But show them children doing it and suddenly it's a cheap trick.
Actually, thanks. That gives me an idea for the next time I have to explain higher math. I'll just find a way to show it to children first. They're usually easier to teach, anyhow.
No, if that's how I came across then that's not what I intended. Although, I feel you're a bit selective in your snips in an effort to make some kind of point. I know how multiplication works, but the memorization of the table speeds up the process. I was simply trying to say that this method was not much different, nor more superior, than table memorization.
My comment about not teaching how multiplication works is aimed at the statement made that this method is how Japanese students learn to multiply, as in the title of this thread.