I'm an English teacher, so I've rather stayed away from the math side of the Common Core Standards. But I can't help noticing that if you are of a certain age (say, mine) some of it seems vaguely familiar. Let me give you a hint...
(Note: Tom Lehrer is, as the young folks say, the bomb. If you are not familiar with his work, you should acquaint yourself).
So, why this theoretical swinging back and forth of the mathematical pendulum? Because math is not all one thing!
I know. In my discipline, we're used to all sorts of squabbling. Despite the fact that David Coleman and The Corophiles (which might be a good name for a band) seem to believe that all matters of reading, interpreting, and generally messing with literature have been definitively settled, those of us who actually live in that world know better. For example, the notion that author's intent is important or even legitimate may be assumed to be true and settled by CCSS, but actual literary scholars and students can argue about it till the cows come home (which the cows may have consciously intended to do, but on the other hand they may have returned home as a result of cultural pressures and expectations, or as an unconscious expression of patriarchal gender-normative structures).
But math. I always thought math was just, you know, math. And then I got older and I did reading about things like chaos theory and quantum mechanics and building structures and I learned that math is not just math. That there is an ongoing rift of sorts between practical mathematics and theoretical (or pure) mathematics.
If you go to math middle school, the applied mathers will all be sitting at the same lunch table pointing and laughing at the theoretical guys and making fun of them for being the kind of people who like big equations but can't change (or design) a spare tire. Meanwhile, the pure math lunch table is pointing back and mocking the applied guys because they only use math to...ew... make things. Think Big Bang Theory and the abuse Sheldon heaps on Howard for being merely an engineer.
Periodically the ongoing rivalry between these groups spill over into the teaching of math to small children. "It's important," say the pure math guys, "that children learn the principles, grasp the ideas, appreciate and see the pure structure underlying the world of mathy things. It doesn't matter if they can make change; it matters that they see the beautiful mathematical structures and relationships underlying the universe of mathematics."
"No," reply the applied math guys. "It would be really nice if they could figure out how to put together some pieces of wood into a properly measured chair that you can sit in, or figure out how long a train takes to get to Amsterdam. Wrong answers mess up the world."
Children and their parents seem to lean historically toward practical math and getting the right answers. But periodically the theoretical math folks gain the upper hand and push the notion that it's concepts, not correct answers, that matter. The last time they gained the upper hand, we got the new math. This time, they somehow used the launch of CCSS to get their feet in the door again, and so Core math arrived, the bastard grandchild of New Math, desperately trying to get six year olds to grasp the beauty of numerical relationships in the universe of pure math (never mind the answer).
Of course, it's a bit of a false division. Here's one of many rants written about how false a dichotomy it is, but of course, rants like this wouldn't be written or necessary if it weren't a dichotomy that many people observe.
Real Math People undoubtedly understand this better than I, but for my fellow strangers in mathland, I thought a non-mathy explanation might be helpful in grasping why we've been to this weird place of math instruction before, and why we're back there now. And why we undoubtedly won't stay there. If you are of a certain age, you remember what happened to New Math in most places-- schools became very tired of explaining why students were being frustrated by weirdly theoretical homework, but couldn't repeat even a sliver of a times table.