- 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.