I have heard of common core, but growing up in Texas where it was not adopted, I did not experience it. I have seen examples of kids doing common core math, which must have introduced some new methods for teaching certain math skills. Based on how I've seen math taught with common core, I already have a negative view of it because it has students use 10 steps to solve a problem when only 3 are require. And while it may make each individual step easier, I think they should know how to do the slightly harder steps and get it done in a simpler fashion.
Again, I was not a teacher at the time common core was adopted in the majority of states. As an incoming teacher, I will not be using common core or NGSS since Arizona has developed its own set of standards. I do wonder if they AZ standards have an equivalent to the common core academic language skill standards which would help with language differentiation strategies.