Abstract: What does it mean to teach mathematics at university level? Does the level matter? Is it different from other levels? I shall visit briefly some trends in the teaching of mathematics at secondary level and use these as a basis for looking at university level. We need to consider who our students are and how teaching at this level relates to the lives, experience and culture of students. One of the factors to be considered is that of institutional organization and expectations. Another important factor concerns the theories on which we base our ideas of learning and teaching and how these affect what teaching does or can look like. Centrally is the question of mathematics itself and how our views on mathematics affect how we teach it. I will offer as examples some research projects into teaching mathematics at my university in the UK and hope that we can use these as starting points for a discussion about teaching.
