This paper provides a method for analysing undergraduate teaching of proof-based courses using Toulmin's model (1969) of argumentation. It presents a case study of one instructor's presentation of proofs. The analysis shows that the instructor presents different levels of detail in different proofs; thus, the students have an inconsistent set of written models for their work. Similarly, the analysis shows that the details the instructor says aloud differ from what she writes down. Although her verbal commentary provides additional detail and appears to have pedagogical value, for instance, by modelling thinking that supports proof writing, this value might be better realized if she were to change her teaching practices.