That's an excellent point. He does need to learn how to keep himself entertained, but there are limited options for that when one is in first grade.
Aculady - I've been fighting with the school all year long. They try so hard to make sure that the struggling students are up to speed, sometimes the advanced students fall through the cracks. His teacher tries, within the constraints given by the district. She let him read. When the books became too easy, she let him bring his own books from home. When she realized he was finishing his assignments so quickly that he was spending most of the day reading and getting bored with it, she gave him a journal so he could write stories, and she would occasionally come by and give him pointers on grammar and punctuation (which is not even TAUGHT in first grade here). But he needed some variety. That was why I started sending him to school with a chapter book to read AND his notebook or extra work. He gets bored easily. His teacher has discussed skipping second grade - I don't want to skip him in the middle of the year, but at the end of the year I wouldn't be opposed to moving him to third instead of second. The district is resistant - they think he should be satisfied with 30-40 minutes PER WEEK with the gifted teacher.
OHGrandma - I'm not sure why it didn't also occur to me that I should be thrilled to death that he is spontaneously doing math. (I majored in physics in college - so you can see how a good math background is a BIG issue for me).
So I suppose my only remaining question is, should I be worried about a lack of self-control later on? There are situations in life where kids aren't necessarily entertained, but they have to behave anyway. Any thoughts on whether or not he is likely to learn that if I'm keeping him CONSTANTLY busy?