For the winter term, I definitely like to change my teaching habits. My idea is to start with a small problem in each session to engage the curiosity of the students. Even if they haven’t yet means to solve the problem they should think about possible paths to solutions. Only after awakening their interest we open the book to look for the theory.
I do not know how this works in the many different classes I have this term. There is a rather small master class for approximation theory, a medium sized class for geometry, another one for optimization, and a huge class of economy students (we are short of professors.) Probably The problems will work well with the smaller class, but may turn out a bad idea in the large classes. We’ll see.