Can I just say that if I'd known that Anna's method was okay, I'd have been a lot less angsty as a child while learning mathematics?
That method really reminds me of the Singapore Mathematics approach-- it's largely visual, and relies very very little upon learnt algorithms so much as on concepts that underlie those algorithms.
For example, the notion that dividing by a fraction is the same thing as multiplying by the inverse of that fraction-- that is a thing that few children now ever learn. They know HOW to do it mechanically, all right-- but the ones that don't know WHY tend to (IME) struggle to retain it without ongoing practice. It's crippling when they begin to do advanced algebra or basic quantitative science.
On the one hand, I'm glad that someone, somewhere is doing it right. {sigh}
On the other, it just makes me feel sulky toward-- well, the US system, I suppose.
