Only they don't teach him by using Latin terminology (decomposing? Are kindergarten teachers really trying to teach kindergartners by telling them to "decompose"?), they teach him by providing sample problems so kids can figure out what they are supposed to do. I always felt that these 5000 different ways of showing that 4 and 3 is 7 would drive me nuts, but I suppose that is very much a gifted kids problem and most kids will really be helped by building number sense. So it is up to elementary teachers to use some common sense as well in how they, um, actually, teach, ie help both kids who struggle and gifted kids to understand what they are supposed to do, and then maybe not make gifted kids who get it do all 5000 ways but give them something more interesting after the first 300 or so...
As someone who always asked 'why' and got the 'this is how we do it' response, I wish I'd been taught the why better, not just how. I appreciate that my kids have a strong number sense and can explain their maths. It's interesting to me, even their use of terminology that is beyond what I would have expected from kids so young, is cool to me. I never used baby talk with my kids, so why not teach terminology like decompose, number model, mental math, estimating, etc, from the get go, to take away the potential scariness of the big words before you get into abstract math? It might make math less intimidating later.
That said, it is how spiraling (which isn't CCSS specific) affects gifted kids that I struggle with, because my kids want to keep going to master it deeper, not stop and pick it up next year. So they might truly get it right away, beyond the instruction level, and then feel like they aren't learning anything new 1-2 years later when circling back. Whole to part, vs step by step.
The drawing can be frustrating -- DS has asked why he had to draw a picture to explain, and his teacher said it was to show his reasoning and that he's fluent enough to have more than one way to solve a problem. Sometimes that seems tedious, and yet, I find I do that myself when I'm trying to process something, and I've actually learned a few things that I didn't really get (or forgot) from my own education. It also is handy for figuring out where misunderstanding might be occurring.
To have that 'I never thought of it quite like that' moment is pretty cool. And there's this sense that the way you do it isn't wrong, you don't HAVE to do it like I do. It's not just memorizing the chart, pattern or algorithm; it's learning how to do calculations mentally and having a back up mental process for when your memory fails you on that quick answer. Rounding and estimating help you confirm your long work, in case you made a simple calculation error.
I think they're good habits to form, if you can allow for those who show mastery initially to do something beyond the class, rather than forcing too much repetition. The CCSS, from my observation, have given a framework for teachers to differentiate at least a grade above -- they can look at the next year's rubric in that standard and work toward that level of mastery with the top cluster in class.
