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Summary: Proof as Method: A New Case for
Proof in Mathematics Curricula
M.S. Thesis
Erica K. Lucast
24 February 2003
Abstract
In recent years there has been a call to reform mathematics education to
produce what the NCTM calls "mathematical literacy" for all students. One
of the NCTM's Standards involves the use of problem solving as a method
of learning mathematics. In this thesis I put forward the hypothesis that
proof is valuable in the school curriculum because it is instrumental in the
cognitive processes required for successful problem solving. My view of proof
does not supersede, but rather supplements, the traditional arguments for
teaching proof. The evidence I present here draws on those traditional argu-
ments as well as evidence from cognitive psychology concerning the role of
metacognition in learning. The picture of proof that emerges emphasizes a
role in mathematical discovery which mathematicians have noted but which
is overlooked in educational literature.
Contents
1 Problem Solving and Metacognition 8
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