posted by:

Judith Fonzi
on May 13, 2003
at 5:08PM

subject:

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 ?

