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Q&A #315

Teachers' Lounge Discussion: Value of two-column proofs

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From: Rick Norwood <norwoodr@etsu.edu>
To: Teacher2Teacher Public Discussion
Date: 2002031808:32:18
Subject: Two-column proofs

The value of a two-column proof is that it forces the student to give
a reason for each statement.  Two-column proofs are one very good way
of introducing students to the idea of proof.  Of course, Euclid did
not use two-column proofs, and I am sure when the NCTM standards say
"less emphasis" they do not mean "abandon entirely" but rather they
are recommening the use of two-column proofs to get students started,
followed by the introduction of flow chart proofs, paragraph proofs,
and other kinds of proofs.  

There have been a number of excellent comments in this thread, and I
would like to second two of them.  First, quality is more important
than quantity.  We need to move away from "a mile wide, an inch deep".
Second, there are many right ways to do anything.  A teacher who
insists that every child do things in only one way is probably
insecure about recognizing whether another way is logical or not.

I have been teaching college classes directly from Euclid, with every
student presenting proofs at the blackboard.  I encourage students to
improve on Euclid's proofs, which they can often do.  In about six
weeks, we can work through book one of The Elements, and it is both a
valuable learning experience and a lot of fun.

	

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