From: Rick Norwood
To: Teacher2Teacher Public Discussion
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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