Just a clarification, but the Common Core is a set of standards, along the lines of “by grade X, children shall be able to do Y”. It does not specify any particular method or teaching technique.
It began as a bipartisan effort by the National Governor’s Association to synch up stnadards between states in order to learn from best practices, make it easier to develop and share teaching mterials, and deal with some of the issues that come up when students transfer to a different state. Somewhere along the line, it got turned into a political bogeyman, and now people claim basically everything they don’t like is “Common Core.”
So this is not a “Common Core” technique, because such a thing does not exist.