A lot of the problem people associated the Common Core math is the problem of the reform math. Unlike Val, I am quite okay with decomposing numbers and number bonds. That is how I do mental math and it feels natural to me.
The problem is that it’s important to see a concept through the eyes of someone who’s never met it before. Not doing this, I think, is a stumbling block in a lot of American math education programs. Number bonds is a good example. It’s abstract, and abstraction doesn’t mix well with 6-year-olds. The concept needs to be as obvious as possible, and this just isn’t the case with number bonds. That they work for a gifted adult as an algorithm isn’t honestly relevant to teaching a concept to a little kid.
It’s much easier to have the teacher put 3 blocks on her right and two on her left. “Okay kids, how many blocks here (pointing)?” “THREE!” How many here? “TWO!”
“Now I put them together. How many blocks?”
“FIVE!”
“See? I combined 3 and 2 and got 5. Addition means combining things.”
What do number bonds offer that this simple demonstration doesn’t? IMO, bonds are unnecessary and may turn a simple idea into something confusing. Why use an abstract concept on six-year-olds when a simple concrete one will do the job better?
Decomposing numbers has the same basic problem. The idea is obvious to an intelligent adult, but that doesn’t make it so for a kindergartner. Again, it’s too abstract. Think about little kids who tear a piece cheese into several pieces and tell you that they have more cheese now. They decomposed the cheese, but didn’t see that they still have the same amount of cheese, because the idea is too abstract for them.
