> For example, I don't think that kids who struggle with common core math and then switch to the "normal way" (the way their parents learned) will have a leap in ability the way that kids who switch from three-cueing to phonics do.
I'm not quite sure that's true. In my city, there is a local charter school that teaches math with only Common Core methods. The local public school teaches primarily Common Core, but also supplements it with Houghton-Mifflin workbooks of the sort that we learned 30 years ago. By 4th grade, the public school's math proficiency rates are 20 points higher than the charter school's. They draw from similar socioeconomic demographics - if anything, the charter school parents tend to be a bit more affluent and involved in their kids' educations than the public school's.
As said elsewhere, there's not really such a thing as common core mathematical methods.
The main way they differ from what came before is that the CC standards expect students to be able to explain more of what they're doing and why, which is pushing a lot of people building curriculum to emphasize visual methods, bar models, etc. But that's not part of CC per se.
By "common core methods", I'm lumping together a bunch of approaches where, in the words of the immortal Tom Lehrer, "the important thing is to understand what you're doing rather than to get the right answer".
Understanding what you're doing is important. Understanding what you're doing on the way to getting the wrong answer is not really, unless your goal is to get the wrong answer. IMHO, getting the right answer should be the starting point for math education. It's not all of math education - there is a vital role for understanding what you're doing. And wrong answers have their place as well - it's actually very illuminating to work out what happens in number systems where 1/0=1 or 1/0=0 or is anything other than undefined, and then show how that means that every number is equal to every other number. But the big lesson from working these lessons is usually that mathematical conventions are what they are because it makes other branches of math simpler, and they could be otherwise (that's the whole point of having axioms), but then you'd have to deal with the consequences, which is often that certain results we take for granted don't hold.
In software engineering, we have a saying: "Make it work, make it right, make it fast." It means that you don't shoot for perfect code up-front. There's too much learning involved in just making useful code. But once you have something that works, you can anchor your explorations around something that already has a quantum of utility. At that point, you work on simplifying the approach, making it understandable, cutting out abstractions that aren't necessary and adding abstractions that make the problem shorter. And then when you're done with that, you add optimizations to make the program run faster, but only if necessary.
The point of starting with working code is to bound the search space, though. If you don't have that, you can find that you spin your wheels forever and never generate anything useful. Likewise, the point of phonics is to get you somewhere close to the right word. It bounds the search space, while whole-word or 3-cue approaches leave the beginning reader guessing indefinitely. And the point of drilling math problems until you're at least familiar with basic arithmetic is so that you can enter the conversation about "What does this all mean? Why do these approaches give the same answer? What happens if I take a slightly different set of axioms?" with knowledge of what that answer was in the first place.
> By "common core methods", I'm lumping together a bunch of approaches where, in the words of the immortal Tom Lehrer, "the important thing is to understand what you're doing rather than to get the right answer".
Well, maybe that's really misdirected then, isn't it? Because the actual Common Core standards aren't really behind your complaints.
I don't really agree with the rest of what you say, though. Rote and math drilling are very important, but understanding is pretty important so you know what method to select. IMO, a good math class is 1/3rd rote, 1/3rd intuition/pictures, and 1/3rd efforts to add rigor.
It's worth noting the whole lot of the world introduces pictures and geometric methods early, like some of these curriculums are trying to do, and gets better results in math education than we have. Though I don't really think most US teachers know how to do that well, yet.
> Understanding what you're doing is important. Understanding what you're doing on the way to getting the wrong answer is not really, unless your goal is to get the wrong answer.
Everyone wants the right answer. A huge proportion of our population basically gives up on math at some point from 4th to 7th grade; they decide they're bad at it, and this self-assessment is more predictive of their future performance than their actual performance. This is really a general pedagogical thing rather than being rooted in standards or even curriculum, but a lot of the reason some teachers and programs are trying to celebrate partial success is to reduce this problem. The background trend is particularly harmful to girls, who for a variety of reasons tend to self-assess more harshly than boys.
In any case, this all has very little to do with Common Core, other than it started happening in the same decade. (Buying new textbooks to align with a new standard is a good chance to change things.) And it's really confusing to those of us with some domain knowledge who can't figure out the specific, non-CC reason why a particular person is complaining.
My background: I advise on math curriculum selection and development at a small private school; I coach a competitive MS math team that routinely wins (crushes— we are 4% of the local MS pop but had 8/12 of the top students last year) regional competition despite us being tiny. Our elementary school that feeds us adopted visual and explanatory methods early, and devoted a whole lot of effort at getting good at teaching this way. (Note, we didn't abandon rote practice. Also note that we are not really required to align with state standards, but for math we could do so with very little change).
We get a huge proportion of our student body through AP Calc; my eldest did it in 8th grade.
I'm not quite sure that's true. In my city, there is a local charter school that teaches math with only Common Core methods. The local public school teaches primarily Common Core, but also supplements it with Houghton-Mifflin workbooks of the sort that we learned 30 years ago. By 4th grade, the public school's math proficiency rates are 20 points higher than the charter school's. They draw from similar socioeconomic demographics - if anything, the charter school parents tend to be a bit more affluent and involved in their kids' educations than the public school's.