This article is about an MSOR Network-funded project with the same title. I describe the construction and initial testing of a DVD resource designed to help mathematicians learn more about their students’ reasoning at the ransition-to-proof level. The DVD uses specially annotated video data together with screens of prompts for reflection to encourage discussion among mathematicians about students’ difficulties and successes. I describe part of the content indicating how a short episode can raise many of the major issues that have been investigated and discussed in the mathematics education literature. I also report on design issues in the structure of the DVD and on mathematicians’ responses to an early version of the content. Finally I describe the progress of the project and outline how I think it might be used in training for new lecturers and for graduate students involved in teaching.
