Date: Mar 13, 1997 1:55 AM
Author: Lou Talman
Subject: Re: Plausibility Arguments
Ted Alper wrote:
> ...at all but the most rigorous level, one
> can construct plausible, convincing arguments of outright
> falsehoods. I think one should try to confront students with such
> arguments sufficiently often to at least make them suspect the
> existence of levels of reasoning beyond those they are being
> challenged to master.
Purposeful construction of misleading arguments strikes me, in most
instances, as misguided showmanship. There is a place for such
constructions at post-calculus levels, where proof begins to become
central to instruction. (I maintain that proof is important, but not
*central* until then.)
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 (*whatever it may be*) for what it is. (So much
for the theory that knowing how to teach is more important than knowing
what to teach!) Then we must be able to deal effectively with the
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.