Number bond basically is just how many different addition problems give you the same answer. Decomposition is the natural extension of that.
That's not what I've seen. But either way, why add a layer of complication to simple process?
Extend the demonstration and move a block from the group of two to the other group. Now you have four on one side and on the other, yet when you combine them, there are still 5 blocks. "See? There are different ways of making a group of five." Next: hand out blocks ask the kids how many ways they can combine things to get a group of 4 or 6 or 7 or whatever. Bonus: see who can put all their blocks on one side and none on the other.
This idea, once ingrained, can be extended naturally and logically to writing out sets of sums that equal a single number. It can also extend to the commutative property without using that term explicitly (e.g. four blocks on the left vs. four blocks on the right).
Again, why use abstraction when concrete will do? Kids need a solid foundation in concrete ideas and basic operations before they can move to the abstract and truly understand topics like algebra.
As for decomposition being a natural extension, it starts in Kindergarten. There's nothing to extend from when you're at square one. Plus, kindergarten is an age when kids think they have more cheese when they tear the cheese into pieces.
It might be tripping up the parents who grew up in a different environment, but the kids don't have any issues with this concept if this is how they are taught.
Okay, that's a bit insulting, and there's no need for that.
That said, this accusation has been used frequently by people defending poorly thought-out math programs:
you just don't understand it. Yes, I understand it. The engineers complaining about Everyday Math understood it, too. Etc. I also understand that in teaching concepts of basic arithmetic, simplicity wins over abstraction.
