This Tuesday I attended the LMS Education Day, a yearly event focussing on how we teach mathematics to our undergraduates. The topic this year was curriculum development: are our curricula ready for the 21st century?

I learned two things during this day: First, every department is struggling to adapt to students that are less prepared for a mathematics degree than the department is used to teaching. Second, the introduction of subject-level TEF evaluations in 2019/20 is going to be a really big deal.

The issue of adaptation is an interesting one. It is not specific to a class of universities. Universities that lowered entry requirements in recent years from ABB to BBB have to rethink what they are teaching and how they are teaching it. Sometimes student engagement is a problem, sometimes material has to be moved from year 1 to year 2. But also Russell group universities are finding that teaching methods and assessment structures that worked in the past have become less effective.

I came away from the day with the feeling that to some extent everyone is struggling. As lecturers and professors we all know mathematics and we all want to impart this knowledge to the next generation. But certainty seems to be draining away. People are becoming unsure what to teach, who to teach it to, how to teach it and what the purpose of the teaching is. Few students who study mathematics will become mathematicians; for many a mathematics degree is a prerequisite to getting a job. Independent of the admission standards there is pressure in every department to keep dropout rates low. And then there are NSS scores, which often enough come to not only measure but define the quality of teaching.

This, ultimately, is the environment in which teaching happens and in which decisions are being made what to teach and how teach it. It is also an environment that is alien to mathematics itself. And so uncertainty creeps in. If students are not learning mathematics to become mathematicians, what should we teach them? Is the $\epsilon$-$\delta$-notion of convergence really necessary for a job in X? What about Galois theory? Galois theory may have provided the proof that one cannot square the circle and become the foundation of modern algebra, but is it not too difficult for an undergraduate? If a department is measured by its dropout rate and its NSS scores, maybe we can ease the students’ workload a bit; sacrifice a bit of rigour to gain a bit of happiness?

How should we teach mathematics? There were lively debates at the Education Day on this subject. Are lectures a thing of the past? Should we abandon lectures for more active modes of learning? The paper by Freeman et al. was quoted several times. The paper is a meta-analysis of studies comparing traditional lectures with “active learning” methods and comes out strongly in favour of active learning. The department in Edinburgh uses for all first and most second year teaching the flipped classroom methodology. Other departments have not gone this far, but have made steps in the same direction. The question should not be: lecture or active learning? The question should be, where is the right balance between lecturing and active learning. Maybe not the flipped classroom, but just a tilted one. Which is incidentally the title of a brilliant article by Lara Alcock.