>Second, I think we need to really look at what is important to teach. Is >the algebra, geometry, algebra route really appropriate today? When will >our students learn all the new math that has evolved since world war II? >I think their future will require a lot more discrete math, and a lot >less of the traditional curriculum.
While I certainly agree that the standard curriculum should not be considered unalterable -- and that technological changes and needs should influence what and how one teaches -- I wonder what is meant by "all the new math that has evolved since world war II" in this context. Information theory? The method of forcing? The new methods for doing linear optimization problems? Please explain how any of these things effects 10th graders, let alone 5th or second graders, or how it might influence what they should be doing in class.
(The NCTM standards book has that standard bit of boilerplate around pages 7 or 8 of the introduction -- more than half of all mathematics having been invented since WWII -- but what does that MEAN? Are we counting pages of journal articles? Number of theorems? Are we allowing for redundancy? Most of this math builds on the same foundations that classical mathematics does. The vast amount is specialized knowledge -- generally requiring fairly advanced training to be intelligible and even then only digested by a few who feel a need to explore it. A classical secondary mathematics education (as a start) is hardly a disadvantage in approaching the modern mathematical literature.)
For that matter, discrete math -- regardless of what specific topics one puts under the label -- doesn't REPLACE the traditional curriculum. Discrete math builds upon algebra and geometry fairly extensively.