```Date: Dec 15, 1992 9:37 AM
Author: Bernie Ivens
Subject: Proofs - My Thoughts

PROOFS-  My Thoughts1.  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 provabletheories based on terms(undefined or defined), assumptions (axioms orpostulates), and previously proven theories(theorems, propositions,etc.)3. Any methodology - discovery, constructions, discussions,experimentation which will help students of geometry understand morecompletely is wonderful. Let's follow these eye opening discoveries withproving the concepts in an organized way. Let's document, keep recordscarefully, use previously developed ideas to help develop new ideas. 4.  I wonder if that part of the mathematics educational community thatwants to eliminate or greatly diminish the use of proofs is succumbing tothe frustration of many instructors. (to avoid the word PROOF some textsuse flowcharts, conjecture- "a rose is a rose")5.  SOME QUESTIONS	a).  Are we just interested in students learning a body of informationor are we also interested in a logical development justifying conclusionsthat 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 inthe past?	d).  A high school in Pennsylvania has a 5 month geometry course- noproofs at 	 all. Is that the way we should go?I have taught geometry for 30 + years. I have enjoyed combining theexcitement of students exploring and discovering with the excitement ofproofs- and I think, very successfully.ANY OPINIONS OUT THERE?Bernie IvensThe Geometry ForumSchool LiaisonSwarthmore College, PAivens@forum.swarthmore.edu
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