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Thanks, Doug, for a presentation triggering a rich exchange, and all for the resulting conversation.  I like the modeling approach a lot, not so much because of the math emphasis as because of the more general "open-ended transactional inquiry" approach, one that incorporates the making of observations, the creation of ways to make sense of observations ("stories"), the sharing of stories to take advantage of conflicts, and the resulting (and continuing) revision of stories.  This, it seems to me, is easily and desireably transferrable to other subjects than physics (not only other sciences but all teaching contexts), if we are willing/able to commit ourselves to the objective of encouraging the development of "autonomous thinkers" ("inquirers").

Concerns about performance on standardized exams and about parents/school boards/kids wanting "the answers" are one set of barriers, but our conversation (and a recent one in an interdisciplinary group on evolving systems) suggests that an additional barrier is within ourselves.  To one degree or another, we all tend to feel beholden to our own disciplinary background/experience/expertise.  And that in turn, if nothing else, creates a tension between encouraging the development of peoples' ability to think for themselves and our own sense that there is some particular model/story that students need to acquire in order to better think for themselves.  The problem with our thinking there is a "right" model/story is its contribution to students/parents/school boards thinking of education in those terms as well.  Maybe we need to do a little more soul-seaching on our own deep conceptions of inquiry and education?  Could we give up the idea that there is a particular place students need to get to, and be content with their getting from where they started to any of a number of possible ("valid") new places?  For more along these lines, see "Bagging placement at both beginning and end."