Date: Dec 15, 1992 9:37 AM
Author: Bernie Ivens
Subject: Proofs - My Thoughts
PROOFS- My Thoughts
1. Students could and should be asked to develop, explore, theorize.
After that process is it possible to prove seemingly great conclusions?
Should we rely on insight, totally?
2. To me the "beauty" of geometry is the development of provable
theories based on terms(undefined or defined), assumptions (axioms or
postulates), and previously proven theories(theorems, propositions,etc.)
3. Any methodology - discovery, constructions, discussions,
experimentation which will help students of geometry understand more
completely is wonderful. Let's follow these eye opening discoveries with
proving the concepts in an organized way. Let's document, keep records
carefully, use previously developed ideas to help develop new ideas.
4. I wonder if that part of the mathematics educational community that
wants to eliminate or greatly diminish the use of proofs is succumbing to
the frustration of many instructors. (to avoid the word PROOF some texts
use flowcharts, conjecture- "a rose is a rose")
5. SOME QUESTIONS
a). Are we just interested in students learning a body of information
or are we also interested in a logical development justifying conclusions
that we make?
b). Do we think students are incapable of learning how to do "proofs"?
c). Do we need to learn how to teach "proofs" better than we have in
d). A high school in Pennsylvania has a 5 month geometry course- no
proofs at all. Is that the way we should go?
I have taught geometry for 30 + years. I have enjoyed combining the
excitement of students exploring and discovering with the excitement of
proofs- and I think, very successfully.
ANY OPINIONS OUT THERE?
The Geometry Forum
Swarthmore College, PA