All I know is that when some educator or ‘scientist’ comes along and says we HAVE to be able to do something multiple different ways, I wonder why, for what purpose. I've always believed in the Occam’s Razor principle, and would also apply that to methodology.
They seek those with “different thought processes” so they can eliminate the rest?
Children will come up with their own methods for managing mathematics, the methods that work for them. It seems that Common Core attempts to teach them methods directly, instead of teaching them to simply add and subtract and letting them come up with their own methods. That can't work, since the methods a child settles on are not likely to be the same as those taught in Common Core--and Common Core is bypassing the essential skill anyway, which is to perform the number operations in whatever way that works. 5x7=35, no matter how my brain ends up processing it.
The education echelon postulates they can teach children math theory by this method instead of wrote learning and practice, (which they perceive as boring and loses some kids to distraction). This postulate is nothing but VooDoo passed down from upper level academia to prove some elitist doctoral thesis.
Learning to play the piano is done through repetition and practice of fundamentals (scales and such) not theory alone, it’s the same with mathematics.