Curriculum is How Important?
I am agnostic on the issue of Common Core in that I am not fully convinced what we teach matters quite as much as how we teach. It's not that curriculum choices are valueless, indeed they are a deep expression of values. A 'great books' curriculum is only valuable if it embraces great books from all cultures and not just Western books written by the writers from the dominant culture.
However no matter what is taught, at the end of the day, how the what is taught means a hell of a lot more than the what. To paraphrase Maya Angelou, people may forget what you say but they never forget how you made them feel. Teachers that use curriculum as a delivery system for teaching self-worth, confidence, hope, persistence, as well as thinking skills, are always teaching what is important.
The issue with common core may not be the stuff itself but just how little we value what is less measurable by standardized testing. Chiefly they are success skills that, at heart, are always what great teachers are always teaching.