When I work on math with my 7yo son, doing problems at the 5-7th grade level, I have noticed that he often fiddles with nearby objects -- and then gets an answer. Part of his brain must have been working on the problem. I have been scolding him for not paying attention, but maybe I should back off and allow a certain of level of fiddling. You can't peek into someone's head, and it's hard to tell what he is thinking about. OTOH, sometimes a child really is just goofing off.
How much "rope" should you give a child who is supposed to be doing academic work?