I remember in early elementary being told I could not add 7 and 8 by taking 3 away from the 8 and adding it (the 3) to the 7 to get 10 then taking the resulting 5 (from 8-3) and adding it to the 10 to get 15. The teacher said it was "too complicated" and "probably wouldn't work when you get to higher math." So I shut up and just kept doing it in my head. A few years ago, I saw in one of DS's math books, *my* technique being taught under the heading "redistribution."
My point is that elementary school teachers are often not very strong in math and don't feel comfortable evaluating alternative methods. I'm not saying that all teachers are, but enough are that I'd be careful confronting her.
We actually used home school curriculum for math that I sent to school in 4th and 5th (and he did during math time) until DS had self-paced up to the point he could take algebra with a real high school certified math teacher this year (in 6th). His teachers were at least vocal about the fact that DS was better than them at math and they were not comfortable teaching him at his level. So they were happy with our solution. (Math is actually his weakest subject, but his teachers were all very comfortable with humanities and were happy to give him quite differentiated assignments in class--reading Thomas Jefferson essays, for example. That was fine with them, but math freaked them out.)
And when the work got harder, he started showing his work, because he needed to, not because someone told him he should.
