on May 13, 2003
Does the mathematical thinking and reasoning involved in "proof" offer
any insights here ?
I find this way of thinking about teachers knowledge helpful.
I have been allowing myself to use the following line of reasoning
(even if it never felt quite right)knowing more mathematics makes one a
more flexible mathematician - therefore if teachers know more
matheamtics they will be more flexible in their ability to use
mathematics and thus be better prepared to do the mathematics called
for in teaching.
The questions you raise and the examples you engaged us in have me now
asking, what is the nature of the mathematics teachers need to know
more of ?
Having taught from Kindergarten through college level mathematics I can
attest to the fact the situations similar to the ones described in the
paper arise at all levels.
So now I'm beginning to wonder about how knowledge of the concept of
"proof" and facility with generating and analyzing "proofs" might
figure into the mathematics that teachers need to know more of. Is the
mathematical thinking employed in proving / understanding proofs
similar to that of analyzing errors or appraising unexpected methods
for their accuracy or applicability ?