There is a very technical math ed word for the sort of knowledge that Polya wants is: robust knowledge. The opposite term is fragile knowledge. Fragile knowledge fall apart easily when challenged bvy a teacher or a problem for which an incorrect answer is computed. Robust knowledge is confidently defended by a student and used appropriately even for problem types never seen before.
Lynn Carlson, Ph.D. Asst. Professor, Mathematics SUNY Oswego
>________________________________ >From: Roberta M. Eisenberg <firstname.lastname@example.org> >To: email@example.com; firstname.lastname@example.org; email@example.com; firstname.lastname@example.org >Sent: Friday, September 7, 2012 10:40 AM >Subject: A Quote from Polya > > >FYI ? Some words of wisdom from the master problem solver. (Known for his famous book, How to Solve It.) > > >Bobbi Eisenberg > > >Pedantry and mastery are opposite attitudes toward rules. To apply a rule to the letter, rigidly, unquestioningly, in cases where it fits and in cases where it does not fit, is pedantry ... . To apply a rule with natural ease, with judgment, noticing the cases where it fits, and without ever letting the words of the rule obscure the purpose of the action or the opportunities of the situation, is mastery. -George Polya, professor of mathematics (1887-1985) > > > > >