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Teachers' Lounge Discussion: Value of two-column proofs

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From: Alexander Bogomolny

To: Teacher2Teacher Public Discussion
Date: 2002040313:03:40
Subject: Absence of value of two-column proofs in geometry

Solving a geometric problem often consists of two steps - analysis and
proof, or analysis followed by construction and verification.

Once a proof has been obtained, it could be described in two columns,
in a flow chart, or paragraph by paragraph. Choose one or all.

The main question is of course how does one get the proofs. And the
fact is that none of the above methods helps answer that question. I
say that the concern about two-column proofs is entirely misplaced.
Acquantaince with two-column descriptions is useful. Knowing how to
use them is a great organizational skill. However, unless one knows
how to prove theorems and solve problems, there is no way to put that
skill to a good use.

The right question to ask is how to teach students to prove things, of
which proof exposition is an important, but not a crucial part.

Alexander Bogomolny
http://www.cut-the-knot.com

 


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