So I had never heard of the box method of multiplication/division either, but having looked it up, recognize it as similar to the method I and most of my siblings developed on our own for doing mental math. I think most of us think of it as multiplying/dividing "from the left". Similar to mental addition/subtraction, which we also do "from the left," but with some alterations involving making 10s, 100s, etc., in a technique I have also seen in some Common Core math curricula (it's in Singapore Math, too). (My apologies if this makes no sense without an example.) I still use the conventional algorithms (except for long division, where I use a modification of the traditional method that skips straight to the remainders) when computing on paper, though.
Anyway, I agree that the issue isn't the multiple methods per se--I teach my children multiple methods for anything I can, and let them pick by the problem--it's mandating that every method must be demonstrated on every problem. I would rather see them learn to select the most expedient method for the problem, and for their cognitive style.
Curiously, the one area of math that USA students are good at, compared to the international average, is procedural knowledge. Perhaps we are attempting to dismantle that, too?
