How some research mathematicians and statisticians use proof in undergraduate mathematics

The paper examines the roles and purposes of proof mentioned by university research faculty when reflecting on their own teaching and teaching at their institutions. Interview responses from 14 research mathematicians and statisticians who also teach are reported. The results suggest there is a great deal of variation in the role and purpose of proof in and among mathematics courses and that factors such as the course title, audience, and instructor influence this variation. The results also suggest that, for this diverse group, learning how to prove theorems is the most prominent role of proof in upper division undergraduate mathematics courses and that this training is considered preparation for graduate mathematics studies. Absent were responses discussing proof's role in preparing K-12 mathematics teachers. Implications for a proof and proving landscape for school mathematics are discussed.

Research highlights
► The results suggest variation in the role of proof in and among mathematics courses.
► Factors such as the course title, audience, and instructor influence this variation.
► Learning how to prove was the most prominent role of proof mentioned.
► Participants considered proof training as preparation for graduate studies.
► Absent were comments about proof's role in preparing teachers.