Coming back to this to update.
At the PTC, the teacher surprised us by showing an end-of-year test she gave DS for third grade math. He scored 72% correct. She said it was impressive (he answered a question on perimeter correctly) and thanked us for bringing to her attention a couple weeks before that he needed to be tested to determine if he could could move up. So, as of yesterday, DS has been moved from second grade math to third. He's finally going to run up against things he doesn't know, and he's excited!
As for his shouting out answers as being her hesitation in moving him into third grade math, she said he's shown acceptable restraint since we talked and that wasn't a factor any longer. I was glad to hear that!
It was like a weight lifted off my shoulders when she pulled out that end-of-year test. I thought I was going to have to bring the whole subject up again. It was a pleasant surprise.
