When two people talk about mathematics problem solving, they may not be talking about
the same thing. The rhetoric of problem solving has been so pervasive in the mathematics
education of the 1980s and 1990s that creative speakers and writers can put a twist on
whatever topic or activity they have in mind to call it problem solving! Every exercise of
problem solving research has gone through some agony of defining mathematics problem
solving. Yet, words sometimes fail. Most people resort to a few examples and a few
nonexamples. Reitman (29) defined a problem as when you have been given the
description of something but do not yet have anything that satisfies that description.
Reitman's discussion described a problem solver as a person perceiving and accepting a
goal without an immediate means of reaching the goal. Henderson and Pingry (11) wrote
that to be problem solving there must be a goal, a blocking of that goal for the individual,
and acceptance of that goal by the individual. What is a problem for one student may not
be a problem for another -- either because there is no blocking or no acceptance of the goal. Schoenfeld (33) also pointed out that defining what is a problem is always relative
to the individual.