I think the lattice multiplication originated in Asia - our school district was parading it around a few years ago as the latest greatest way to teach multiplication. And then, oddly, it disappeared... hmmmmmmmm....
So anyway, my dd is home from school now, so I asked her if she could show me how her teacher had taught her to do long division. She said "Oh! Sure!" and made up a problem (dividing 5 into 12543) and then started to show me how to work it out... the old-fashioned way that we taught her how to divide

So I explained that I wanted to see how she did it with the boxes etc... and she said "Oh! Yeah! I remember that! You use arrays!"... then... "Oh wow, I'm not going to do THAT problem that way - there are too many numbers!". So she decided to show me how to divide 5 into... 25. She started to draw out a 5x5 array, wrote the 5 divided into 25 equation and.... through the pencil down and said "I'm not gonna do that - it's too much work. Why do you want to know?" and then she bounced happily out of the room, after she'd solved the other problem the usual way.
So... I guess she isn't interested in explaining it to anyone... or recommending it as a worthwhile method

polarbear