Transcript Document

Transition to Proof
CUPM: Proof is not something that
can be taught in a single “bridge”
course. It must be developed in every
course.
Me: Proof is part of mathematical
communication, explaining how to
connect a new mathematical insight to
what is already known.
Difference between finding a proof (ie a
personally convincing argument) and
communicating a proof.
Importance of efficiency in proof, but never
at the expense of clarity.
Importance of analyzing one’s own proof
and those of others for “correct, clear,
concise”.
You prepare students by giving them lots of
practice in communicating mathematics.
Communication of mathematical proof has it
own rules. Two of the dominant
characteristics are the use of precise
definition and logical implication. But these
cannot be taught in the absence of
meaningful proofs.