I'd never heard of this before, but looking up some of the controversy, I found this article: http://www.patheos.com/blogs/friendlyatheist/2014/03/07/abou... It actually makes some sense. I'm still skeptical, but it's sounding like it's just a significant departure from the rote memorization methods I grew up with.
Bah... I can tell you why the first algorithm/example works because of the commutative and associative properties of math. Learning "why" a solution works, doesn't require learning some arcane algorithm. If kids don't learn how to do these problems quickly, they'll never be able to do higher order problems in a timely fashion.
You are not a six year old child learning arithmatic. You have missed the point.
> The problem with that method is that if I ask students to explain why it works, they’d have a really hard time explaining it to me. They might be able to do the computation, but they don’t get the math behind it. For some people, that’s fine. For math teachers, that’s a problem because it means a lot of students won’t be able to grasp other math concepts in the future because they never really developed “number sense.”
Mental methods are taught so that children do understand numbers, which gives them a better grounding for future learning.