Using funding made available by the Maths Stats & OR Network we have produced a guide to provide mathematicians with an accessible introduction to some ideas from the mathematics education research literature. We intend this to be particularly useful for new lecturers enrolled on PGCHE programmes but we also think it would be of interest for experienced lecturers looking for further insight into their students’ thinking. The guide focuses upon three ideas that we use to structure our own thinking as university mathematics lecturers about what students need to learn in order to succeed in undergraduate mathematics. Specifically we concentrate on what they need to learn in order to make sense of their early encounters with abstract definitions and proofs which we see as key to making a successful transition to university-level mathematical thinking.
