I actually like the common core math curriculum; it’s good at getting across that numbers have meaning beyond themselves (by which I mean represent an amount or measurement of something else) and that you can estimate. If you learn math that way, it’s more intuitive. (It’s the way I naturally think of math, for example.) But I’m sure it’s frustrating for parents who are trying to help with homework and think “wait, this is MATH now?” because it’s a little like having to help with art homework – thinky abstract stuff. You can’t necessarily jump in in the middle.
The main complaints I have seen about “new math” are parents mad that they’re being asked to either (1) estimate rather than do arithmetic (2) fill in boxes or use number cubes to represent amounts visually instead of using arab numerals, or (3) pay attention to significant digits and therefore round off. All of which is stuff that’s not really new.
I see this as being historically similar to when in the 70s a lot of people freaked out over the shift to teaching reading using phonics instead of using the whole word method. (Which some people are still freaking out about, even though it’s been confirmed through a huge amount of experimental evidence that it’s the fastest way to teach reading to the largest group of students.) Lots of “du u no haw to reed gud” etc. I have trouble understanding the degree of outrage (or maybe fear?) people feel over an attempt to move away from rote learning to get kids to think about process.
Like, once kids get the basics of this system, it’s easier for them to invent the next step on their own instead of having to ask a teacher. It’s a deeper level of understanding than “memorize the next multiplication table.” (Full disclosure: I hate memorizing things. By which I mean I hate intentionally memorizing things, by for instance repeating a table of words or numbers over and over, rather than committing to memory naturally as I make mental connections.)