What happened to the good old column method?
The spiel is that it gives kids an 'intuitive' sense for math and numbers. On the ground experience seems to indicate that it terrorizes a lot of them and causes psychological issues.
I would have been fine with this common core stuff personally as a kid and would have gotten a kick out of it, but I tended to be at or near the top of my class in grade school when it came to math and science stuff, and even as a kid I was unusually drawn to orthogonal things. As it happened I learned math the old way (though we had abacuses to screw around with which I loved) and I was fine with that also. I never really did lean my times tables though. Oh well...it didn't stop me from getting through differential equations.
Even Wilikon's 'subtraction by adding' thing is tame compared to the absolute idiocy of drawing out a zillion little circles and shit. I am quite confident that some of those lesson plans and schemes were drafted by people with actual malice who simply do not want the population to be numerate. Most enviros themselves are pretty innumerate and there is a great utility to this. They'll buy any bullshit story about a 'consensus of scientist' saying any damn thing.
If one does not reject the hypothesis (or 'conspiracy theory') that the goal of primary education is as much to keep kids from learning very much as it is to teach them things, then the mysterious failures of our education system here in the U.S., where we spend a relatively huge amount of money compared to other nations, then the hypothesis actually has a fair amount of explanatory power. One of the defining things about 'common core' seems to be to cut parents and even teachers themselves out of the loop when it comes to education and have corporations take over with material approved by a central politburo type structure and corporations doing massive data mining and analysis for who knows what purpose.