>I think we are discussing what is public math. education. >I repeat my motto:
>MATHEMATICAL EDUCATION IS >TEACHING STUDENTS TO SOLVE MATHEMATICAL PROBLEMS.
>Of course, every motto is a simplification. >But my motto has some advantages: >- It fits in two lines. >- It is based on 3000-years old tradition. >- It is difficult to abuse.
>Dennis proposes to concentrate on models rather than problems.
Perhaps I was not clear (then again, perhaps I was). It seems to me that what Euclid and Pythagoris and that crowd were doing was exactly modeling. My problem with Andrei's motto is that it doesn't in its succinctness distinguish between formal mathematics, mathematics applied to problems, and computational or symbol-manipulative exercises. I'd agree that kids should learn to read, understand, appreciate and do proofs, because it promote good thinking in all, as well as being necessary for advanced work in mathematics. But, I don't think that for the majority of students, formal proofs are their own reward, and more than computational exercises are. The Scientific Method is a paradigm or mantra that both informs science education and gives students a home base: they can understand that even though washing out the glassware is a drag, it has a purpose within the SCIENTIFIC METHOD (elimination of irrelevent variables; repeatability;) and that the SCIENTIFIC METHOD pays off. They can read about how the great scientists applied the SCIENTIFIC METHOD, and so on. Yet, in mathematics, even though the great mathematicians of the past were quite conscious of the connection (however tenuous it became) with some phsyical object or phenomenon or whatever, that orientation has been, in my experience (limited, and a bit old, largely lost in higher mathematics education. I've been reading some popular writings on quantum physics, and I find it interesting how symmetry groups and projective geometries were just lying around waiting for physicists to apply them, whereas in fact they had their roots in real physical problems to begin with.
I don't think we need to change any of the directions of mathermatics education (or the directiosn that some would prefer) to adopt "modelling" as an organizing principle. If, that is, it has any value beside's my personal organizational system.