Austin K. A. (2000)Comment on... "The rebirth of proof in school
mathematics in the United States" by Eric Knuth |
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The author reports that the majority
teachers feel proof is not appropriate for all
students. I would suggest a possible explanation for this :
teachers believe proof is hard because they have seen only
hard proofs. THEOREM Some people may dismiss this proof because it is not like the well-known proofs, say, in geometry. However that would be like dismissing shallow learner swimming pools because they are not like olympic pools. In fact this proof above shares the same pattern as the harder well-known proofs, namely, Pattern: ... The Theorem states the following.the LIST (or SET) the theorem is about; The difference between the easy and
the hard proofs is that in the latter the list/set is too
large for us to write down all the elements and so we have
to use the techniques of proof - language, symbols and
logic. |