Date: Mar 14, 1997 10:04 AM
Author: W Gary Martin
Subject: Re: Plausibility Arguments
Putting two things together (I think): Analying invalid arguments is
certainly important, but the most important invalid arguments are those
produced by the students themselves. The ones suggested by Ted and Andre
are useful "puzzles" to help advance their thinking (and in fact I myself
use some of them), but students are perfectly capable of generating invalid
arguments all on their own power. The advantage in addressing the students'
fallacies is that since they reflect exactly how the students think, it may
more likely change their views.
And one of the best ways of eliciting their faulty reasoning is to give
them statements about whose truth there is a question. Too often students
are only asked to prove "true statements", which tends to short-circuit
proof-making. [As I once heard a student say, "The book is asking me to
prove it. If weren't true, they would ask me to prove or disprove it.
Therefore, it must be true. I'm willing to accept it."] In this way,
"proofs of wrong statements" become more than an adjunct; it becomes part
of the core of having students explore mathematics. Gary
At 18:47 -0500 3/13/97, Ted Alper wrote:
>> I want to continue that proofs of wrong statements are just
>> one kind of useful ways to puzzle children. [...]
>> But all this is just a preparation. What should
>> come next is training in solving problems right - that is so
>> that to avoid all these `miracles'. That is why it is so
>> important for children to solve problems where it is clear how
>> to check the answer and to find out whether it is right or wrong.
>I find nothing to disagree with here. "Proofs of wrong statements"
>are certainly not the main course! They are an anjoyable and useful
>supplement, though, and particularly relevant to this thread of