The broad aim of this research is to characterize the views of proof held by college calculus students and their two types of teachers mathematics graduate students and professors. The analysis is based on an examination of the ways in which people in all three groups produce and evaluate different types of solutions to a proof-based problem from a college calculus course. Initial results indicate a subtle but fundamental difference in the way university level teachers and students view proof. To the teachers a proof is the connection between an idea and the representation of the idea the representation used being a function of the norms of a particular mathematical community. To the students, who have not had many mathematical experiences outside of school mathematics and who may not understand the underlying mathematics, the proof is simply the representation. (Author)