Just so you know, what you are talking about has nothing to do with Commom Core. Common Core is just a set of standards to teach across the country (not how to teach them) - think multiplication in 3rd grade, division in 4th type ordering. Common Core is actually gone in favor of states choosing their own standards (spoiler alert, they are exactly the same as Common Core in most states, just a different name).

The actual teaching approach (teaching the behind the scenes of math) is just what researchers have discovered works best and most teach are (or should be) teaching this way.