Regarding Assumption 4 (the real-world applicability of math): I'd like a Standards definition of what exactly the real world is. For a third-grader who's got at least nine more years of eight-hour school days ahead of her, I would hesitate to suggest that school, and the math we do there, is *not* a major part of the real world.
This is related to Ron's suggestion that teaching at this level may be appropriately couched in terms of a "fantasy world," a la Flatland or MathMagicLand or any number of "made-up" situations which facilitate the math at hand.
We should remember, though, that there's a subtle distinction between doing math in a "made-up" context and creating the impression that there is no relationship between the math done in school and the math waiting to be done, either out of school or in later school math settings. It would not be helpful to have to phrase *everything* in terms of some bizarre-sounding alternative reality. At least not 'til grad school. ;-)
Nevertheless, and even though it most often comes at moments of boredom rather than moments of inquiry, the question, "When are we ever gonna have to use this stuff?" smacks of truth and of a challenge to those of us who have decided that it *is* useful to be able to do math. There's a paradox emerging here, namely that of luring kids into math with its applicability and then asking them to be patient while we do the grunt work necessary to keep math applicable, but I suspect that this paradox can be resolved with a healthy and thoughtful balance of math applied to non-school situations with math done in a fantasy world.
Kreg A. Sherbine | To doubt everything or to believe Apollo Middle School | everything are two equally convenient Nashville, Tennessee | solutions; both dispense with the firstname.lastname@example.org | necessity of reflection. -H. Poincare