Teacher2Teacher 
Q&A #315 
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From: Alexander Bogomolny To: Teacher2Teacher Public Discussion Date: 2002040313:03:40 Subject: Absence of value of twocolumn 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 twocolumn proofs is entirely misplaced. Acquantaince with twocolumn 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.cuttheknot.com
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