What you described is exactly how number bond is taught in Singapore math. From concrete to pictures and to abstract. Maybe you just don't like the name/jargon, but kids need some definition as a short hand at some point, right? I don't see how what you described is any different than the number bond teaching is in Singapore math. Once the kids figured out all the number bonds up to 10, they can easily decompose a number to make 10s for hard addition and subtraction problems.
You're correct that I'm complaining about how it's explained (
specific to the CC). The number bond approach seems to be used by the Common Core as a means to teaching a concept (existence of equivalent sums), rather than as an algorithm for
displaying these sums, which is what it is. That's the problem.
US math education has a way of making straightforward topics unnecessarily complex. Ideas are presented out of order, concepts are mashed up together, and individual algorithms are treated as critical routes to understanding, rather than as techniques for getting an answer.
The thing is, it all looks pretty at first glance. The textbooks are colorful and friendly and have lots of nice photographs in them. If you're familiar with something from another system, you might look at one and think, "Oh, they use x [e.g. number bonds], like SM does. Great." But when you look closely, you see that they present things out of context, mix too many ideas in one go, and make such a mess, even HG+ kids feel like they can't understand math concepts
that they figured out for themselves when they were 3 or 4, and start to hate it.
I'm going to compare a SM presentation of number bonds with that in a CC book. I strongly suspect that the SM book will present ideas one step at a time in a logical manner. I doubt the same will be true of the CC book. I say this because I've done this several (umpteen?) times already over the years and the result is always the same: Common Core or not, mass-use books produced by Big Ed make a mess of things.
