posted by:

Judith Fonzi
on May 19, 2003
at 3:08PM

subject:

The role of proof...

In the previous example where a student develops a "common denominator" algorithm for dividing two fractions Anne suggests that the teacher needed to ask two questions 1) does the algorithm always work; and, 2) how does it relate to the invert and multiply algorithm. This "how does it relate" question is an interesting one. Does a matheamtician need to know how the "common demonitator" and "invert and multiply" algorithms relate  probably not. But, does this classroom teacher need to know  possibly. Knowing a strategy that always works and determining how a unique strategy is related to it could be an approach to determining if the new strategy "always works". This kind of thinking certainly qualifies as mathematics content in my mind and though it may not be unique to teachers (mathematicians search for relationships between the known and the conjecture)it may not be required knowledge for other users of matheamtics.

