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Proof in geometry
Posted:
May 25, 2001 1:45 PM
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I have a concern with "proof in geometry" discussions that takes a
slightly different direction than several of the recent posts.
Geometry is not a course in proof, but proof is essential to the
development of geometric understanding. The concepts of
"statement-reason," syllogisms, converses, inverses,
contrapositives, truth tables, are not unique to geometry. In fact
proof is just as essential in algebra, or calculus, or elementary
school arithmetic as it is in geometry. Let me re-state to be
absolutely clear: Proof in geometry is important. Proof in other
courses is also important.
The level of formalism will, of course, be adjusted to the
mathematical setting. Proofs in graduate courses in topology are
very different from reasonable and reasoning arguments presented
to third graders as they learn multiplication tables.
One of the difficulties in my own high school experience back in
the late 1950's was that proof, reasoning, even defense of an idea,
was seldom raised until the geometry course. I'm delighted to see
reasoning and proof as one of the "Standards" in the NCTM
Principles and Standards IN EVERY COURSE.
Steve Cottrell
Mathematics Supervisor K-12
Davis School District
P.O. Box 588
Farmington, UT 84025-0588
Phone 801-402-5123
Fax 801-402-5333
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