In these activities, students are faced with a problem that has no
straightforward, reliable method of solution. Finding the right
answer is not as important as the experience of looking for answers
and evaluating the quality of the answers that they do find.
Some
questions that may prove useful in evaluation student performance are:
How frustrating is it for the student not to find a quick solution to
the problem?
How does the student cope with that frustration?
What strategies does the student use to solve the
problem?
What makes the student abandon one strategy and try another?
Can the student describe the strategies that were used and comment on
their effectiveness?
The purpose of discussing proof and mathematical truth is to expose
students to these notions, and to make them familiar with the roles
that certainty and uncertainty play in mathematics. Although students
should be learning to articulate their reasoning processes, they
should not be expected to produce flawless proofs. They should
recognize that the question, ``Do we know this for sure?'' is one that
mathematicians continuously ask.
