I agree with ColinsMum-- the explaining IS the part that must happen in order to do higher math.
There's not a right "method."
But there is a right way to communicate what you are using as a method.
It has to be valid as a set of instructions for another person in order to be correct, basically.
But it's the intuitive jumps that lead to the higher math being discovered in the first place. The explanations are how you prove to others that the jump was correct, and the road map that lets others follow in your footsteps.
DS is math-intuitive, and it does get very frustrating, trying to get him to "show his work". I just asked his new teacher, in her "syllabus questions" homework, what happens if he doesn't have any work to show? Many things happen in that boy's head, and some of them are scary.
If she wants the answers out of there, she's going to have to get them herself, because when I try, it makes my brain melt.
