... but at the same time, if someone is using an alternative method of problem-solving, it is
all the more important to document it thoroughly. 
That is a lesson in good communication skills, if nothing else; it's just not polite to do otherwise.
I like the approach mentioned above of having the child offer "instruction" in his/her method. That reinforces the idea that math and science problem solving can (and should be?) a collaborative exercise as often as it is a solitary one, and that being able to communicate well with others about what you are doing and why is essential to that collaboration.
That can be a hard lesson to learn with other age-mates, but I think it can work well with parental coaching. Great tip!
