Why lecture and how? When you start teaching maths to STEM students it is important to establish first what the students know and what they don’t. The school curriculum changes all the time and you might attract different cohorts in different years, whatever the reason, no two intakes are exactly the same. You can then decide how “to deliver content”, so that as many as possible would understand it. Not just decide, it is important to experiment too to see what explanation work best. It is important to “facilitate” a lot of “unlearning”, to clear students’ minds of half-digested half-truths. Most of them didn’t understand the basic maths symbols when they start, so originally they cannot be expected to follow maths textbooks or pre-recorded presentations on their own. So, I am a great advocate of lectures delivered in the form of a Socratic dialogue.