on May 19, 2003
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.