"My examples about atoms filling their shells ,and
I think (and I'm interested to know if anyone
thinks I am wrong on this one), that refraction
is like a marching bandŠ are rather different ,
as they are 'models' that are not useful
approximations but conceptually quite unlike the
target scientific thinking. - Keith"
The bigger question I don't think this discussion has addressed is that most secondary physics students won't major in physics. (Or better still, most secondary students won't ever take another course in physics!) I agree completely that we need to put greater emphasis on the fact that we ARE teaching imperfect models and analogies. BUT, I would say that many of these things are taught as they are because a majority of students will never have to "unlearn" the models taught in high school or even many introductory college physics classes.
I'm not sure it's reasonable to adopt/require more complex models/analogies when a majority of students will not have to "unlearn" simpler ones. I would consider Keith's "marching band" and "filled shell" examples sufficient and graspable as an explanation of refraction and simple chemistry for a vast majority of the population. I won't defend significant figures, but will say that for math-challenged students, "real" error analysis dramatically compounds the mathematical difficulties (and fear!) students already have with physics and physical science. For many students at the secondary level, a simple conceptual understanding IS the "target scientific thinking."
To me, there is a vast difference between building a foundation for a future physicist and introducing the broader population to the ideas of physics, and most secondary schools necessarily focus on the broader population. That's why physics majors have to "unlearn."
Mike Meyer
Senior Lecturer
Michigan Technlogical University
mrmeyer@mtu.edu