Thanks for the offer! Yes, this sounds interesting. One of the things I've tried to get out of my math tutoring experience was to see how the teacher looked at the problem before beginning to actually solve it and see if it works out. But they never actually thought out loud for me to understand their thought process; also, I often can't tell what mental resources someone else uses when solving a difficult/tricky math problem. (Experience? Sudden insight? Additional notions I don't yet have?)