Stephanie,
Our son is 12 and refuses to show his working for math also. What is starting to work a little is a discussion we had a week ago.
We started by telling DS that while he understood what he had done on his homework, we couldn't understand it. We talked about how when he answers a question in Other classes, he often has to write a sentence or two. Those sentences have to follow the grammar, spelling, and punctuation rules or they are not easily understood by anyone reading the answers. The same thing is true in math, if he doesn't write the answers out in a recognizable form and show his thought process then it is much harder for anyone reading his answers to understand what he did.
In DS's case, he can do so many of the steps in his head that it looks like he picked an answer out of the air. So we are having DS teach us the material and we only write down the steps he explains. Once he saw the answers we were getting following his directions, he started getting a little better about showing more of his work. However, it is still a work in progress
