> Date sent: Wed, 12 Mar 97 23:55:28 -0700 > From: Lou Talman <email@example.com> > To: alper@Csli.Stanford.EDU, firstname.lastname@example.org > Subject: Re: Plausibility Arguments> <snip>
> The really interesting, and difficult, question is this: How should > we deal with students who invent their own "plausible, convincing > arguments" supporting "outright falsehoods"? > > The question is interesting because students who are capable of > such things (almost always innocently, of course) are very interesting > people to teach. > > The question is difficult because it means we must recognize the > outright falsehood> <snip> > I maintain that the most effective way to deal with the situation is to > present the "prover" with an example that clearly contradicts what has > allegedly been proved. And then step aside. > > At least for a while. Noticeably longer than the "prover" likes. > > --Lou Talman > That strategy was used regularly in a graduate topology class I took years ago. The professor, Lawrence Fearnley, was a master at creating a diagram or sketch. His usual approach was to listen carefully to the student present am argument. Then if no one, including the student presenter, saw the error, he would step to the board and draw. His comment was usually something to the effect that "Let me see if I can illustrate." Then he would produce a sketch, step back himself, and look at your argument and his sketch, and wait. Very effective. The "step aside" strategy that you suggest is powerful.
Oh, yes. Sometimes he WAS just illustrating something that had been done correctly, so we always examined his drawings VERY carfully.
Of course, we were trying to present good mathematical proofs, not just plausibility arguments, but the counter-example strategy is effective in both settings. In fact, we often were presenting plausibility arguments with loopholes where we should have been doing mathematical proofs.
Steve Cottrell Mathematics Supervisor K-12 Davis School District 45 East State Street Farmington, UT 84025