If I had to summarize all of the somewhat cogent arguments against the CCSSM, they appear to sound something like, "We've done it this way and it works, so why would we try anything else?"
This is how their argument is posed, but it makes a pretty LARGE assumption, that being that mathematics education in America has worked.
It doesn't work.
I understand that it is reassuring in some twisted Lovecraftian way to think that there are some people that are good at math and the rest of the world that will never be good at math, but that's like saying, "there are some people that are good at Japanese and some people that will never be good at Japanese . . . " well yeah, if you assume as a matter of course that it's impossible to teach Japanese except to the people that are already fluent in it.
The fact of the matter is that mathematics IS a language and anybody can be good at it. That doesn't mean that we'll be as good as the absolute best of the world any more than it means that we can be as good as some guitar virtuoso, but we can at least learn power chords and probably the melody to "Ode to Joy".
Everyone can math.
Yes, that is probably going to become a standard saying in my teaching repertoire and maybe even a title of some book down the line. I understand that math is a noun and I'm using it as a verb, deal with it. (Sorry to foreigners that use "maths", it sounds much less cool in your language).
I'll say it again, everyone can math.
At least, they can if they are afforded the opportunity to math, given a reason to math, and taught math in such a way as to not have it sound like gobbledegook, gibberish and doubletalk.
So when we say that the old way of teaching math "works", we're saying that the increasing minority of people that have natural talent in mathematics or are raised in mathematics-speaking households rise to the top and are able to do math by learning it the old way while everyone else flounders, increases math anxiety on a national level, and mathematics becomes increasingly stigmatized and closed off to a majority of Americans—which only compounds the difficulty for the next round of students and the next and the next.
Eventually we have a culture of assumed failure when it comes to mathematics instead of a culture of, "Yes, we can do this!"
So why are we changing math even though you think that it made some sort of sense the old way and the new way makes less sense to you? Because the old way was stupid and it set students up to fail.
Yes, people taught the old way are not going to understand the new way as well at first, but if you learned the old way maybe you couldn't ever get pass power chords because you were taught rote memorization of chords and notes and never understood music theory. Maybe all you can say is "konnichiwa" (but you've got that down pat), but never learned the grammar and mechanics of the Japanese language; this is mathematics in America today for the vast majority of students.
But the CCSSM emphasize the understanding necessary to not just be able to do arithmetic, but to set students up for success in algebra, geometry, calculus, and beyond. We're teaching students the language of mathematics, not just the vocabulary.
Let me know if you have any questions.
(Note: I've ignored the arguments that sound something along the lines of, CCSSM is other people trying to take control of our schools! Besides the politically motivated nature of many of those arguments, the assumption is that your schools were better off before. They weren't. Is CCSSM perfect? Absolutely not, but it is immeasurably better than the system that preceded it and it deserves our support.)