Date: Mar 12, 1997 7:24 PM
Author: Ted Alper
Subject: Re: Plausibility Arguments
I guess I can agree with what Gary and Lou are saying... Certainly,
there's not much to be said for giving geometry students a jumble of
betweenness axioms at the start of the course.
But I'm still a bit wary of those who are quick to dismiss those
"picky details" as nothing more than that. And textbooks that assume
an air of "rigor" without even an acknowledgement of the subtleties
that have been bypassed do bright students a disservice.
I don't know what the best approach might be -- I'm sure there are
many valid approaches for different students in different
circumstances. In any case, 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.