Let me begin with a short addition to yesterday's post. It's ok to teach the "shortcuts" in math--change the inequality sign when multiplying/dividing by a negative number, "invert and multiply", "a negative times a negative is a positive". What's absolutely not OK is to teach those shortcuts but not to teach why they work.
There are some algorithms, though, that are so handy, so useful, and so easy to learn, that they can reasonably be taught as "this is the way to do it". Third graders don't need to understand why the long division algorithm works, they just need to learn it (and it is possible, but perhaps it requires a superteacher like Mrs. Barton for all students in a class to learn it). They should learn multi-place multiplication, too. They should learn the algorithms that have been used for centuries not because they've been used for centuries, but because they work and are the most efficient algorithms humans have come up with. When someone comes up with a better algorithm for division, I'll support it, but until then I'll merely applaud those who search for one.
This algorithm is not "the one". Holy crap. Is there any rational, sober person who honestly thinks this method is better, easier to learn, and/or more efficient than the so-called traditional method? The academics who came up with that have been out of 3rd grade too long. Mrs. Barton would look down her nose at that method--and continue to teach students as she always had, which was effectively.