At 10:37 AM -0700 5/30/01, Wayne Bishop wrote: > >If you think that Barry Simon's article was not primarily about the >importance of *proof* in mathematics, not even Euclidean geometry in >spite of its title let alone some genuflection to the two-column >proof format, I believe that you are missing his point. In >effect, yes, you *are* criticizing proof itself, perhaps >inadvertently, but that is the effect. For someone quite >knowledgeable about geometry, that is amazing, even tragic, but that >makes it no less true. > >Perhaps you would clarify your message by offering some concrete >examples of proof as you would like to see it developed in the >precollegiate mathematics curriculum? If you have thoughts for >improving it at the university level, those remarks would be helpful >as well. Tossing a grenade into Simon's article while claiming that >proof is central to mathematics is not.
The fact that Wayne is trying to weasel his way out of yet another lie is not surprising. That he shields his ample body with Barry Simon effigy is appalling.
The issue of proof being central to mathematics is a red herring (the only kind Bishop recognizes). No one is arguing that it is not. On the other hand, the issue of what constitutes proof is wide open. The argument is that there is no reason to emphasize two-column proof in geometry classes at the exclusion of other approaches. "Two-column" is an emphasis on format, perhaps even formal organization of thought, but not on "proof". As such, the "two-column" issue is irrelevant to mathematics (when was the last time any mathematician was forced to adhere to the two-column format the way that some teachers make students do?).
But there is more at issue here as well. Proof may be central to mathematics, but WHEN does it become central to mathematics EDUCATION? Certainly one should not wait until college to get a notion of proof--that is far too late. Waiting to talk about it until a formal course in Euclidean Geometry (yet another red herring, but more on that elsewhere) is also inappropriate. The question, however, remains--when should students be 1) exposed to proof, 2) able to recognize a proof, 3) able to affect a proof? My experience tells me that (1) happens around grade 6 in US schools--about the same time as in other countries. However, (2) and (3) only happen for select few, not even all of those intending to become mathematics majors in college. The latter appears to be Barry Simon's concern. Wayne's concern, on the other hand, is just to plop his robust ego into a bucket to make waves.
So let Wayne's bleating continue, but, if we want to have a productive discussion of proofs, ignore his posts.