This article, Kid's brains reorganize when learning math skills, has a simple take-home message:
Drilling kids on simple addition and multiplication may pay off. "Experience really does matter," said Dr. Kathy Mann Koepke of the National Institutes of Heath, which funded the research.
I see no problem with teaching kids alternative ways to look at how math works, like is done with Common Core curriculum. But doing so instead of teaching math facts is a big mistake.