> Math could be, and I believe is, both independent of and inherently a part > of human experience. I'm not sure we want to get off into this very > theoretical/philosophical debate when we have been primarily dealing with > more directly mathematical issues recently.
Hear, hear! This all began, however, with a genuine pedagogical question, of how -- or why! -- or whether! -- to present to children the notion that mathematical questions can have various answers, according to circumstances or purposes of the moment. For this problem we needed a definition of "mathematical question" and "various answers." I believe I've said about as much as I know about these things, and maybe more. In summary of my own view, I consider it mischievous to put forward any such notion, even while understanding that every *practical* problem in the world is subject to doubtful answers.