As a student (of courses in mathematics) I really most enjoyed when the teacher had good pedagogical skills - being able to give "Ahaa" moments in their explanations when stuck on a problem and actually "see the connections" between the theory from the lectures and the workbook problems to solve. This can of course be achieved in several ways - drawing good parallels, by showing other well-chosen examples which aid the bottom-line understanding. I have not taken any courses on pedagogy but perhaps try to find out how countries with working educational systems do. Finland is one example of such.
A pedagogue should know and have true interest in optimizing the exchange of knowledge and understanding from lectures/classes to students. I am sure there are tons of material on techniques for memorization/understanding/maintaining or planting seeds of enthusiasm and learning interest/cognitive theories etc. Sometimes the solutions are simple, sometimes not, but let me bring an example:
The brain (especially a tired student's one) needs to be activated to actually learn/understand and create new neuron connections). There are many ways this can be achieved, but keep in mind /why/ I remembered the following:
We had a lecturer who, when some really important concept to understand and remember was about to be explained, brought out an arsenal of different tricks. One time he had a bike with the steering wheel connected to the back wheel which everyone who dared could try during the break and which the lecturer himself tried out several times. Yes, people sat up straight, started laughing and they immediately had the focus on the lecturer and the bike. That focus then remained for 10-15min, enough time for him to present the very important concept he had in mind. And I had no trouble remembering or understanding it, because the brain is associative and every event and data which is presented before us while something out-of-the-ordinary happens will have /much/ greater chances to be remembered - that info might be important, so that's why the brain tries to suck it up and absorb like a sponge.
Do not make the classes too monotonic. People cannot keep their concentration for too long anyway (there is much research done at this point too) and it is very enjoyable for the brain to alternate the way it learns. Like, reading theory for a while, then watching a video clip where more is explained and shown in a multi-media fashion, then the teacher may continue on the problem on the board etc.
The bottom line: Just sitting in the same way doing math is great at some times (like when at home in the kitchen with a large cup of tea, with no crowds of people walking about etc so that you can really concentrate for hours) but at the University class where you actually have access to a teacher for help, that time should be used with care to address the ways people learn and avoid the pitfalls which make their brains ignore new incoming information.
Most importantly I think that teachers and lecturers should have a deeper level of communication and both should be well-informed of what was said and done on teh lecture as well as the mathematics class afterwards. This is something I really missed when studying (not too many years ago, got my degree in 2011). It really seemed that way too often "the left hand/right part of brain did not know what the right hand/left part of brain was up to" at the University. Poor intercommunication between lecturers/teachers/students, low level of feedback possibilities from students and student rarely had any non-imaginary possibility to influence the course - it was always like "thanks for your feedback (if any), we will try to address this for the upcoming years.." Yay :/
Another problem that I often scratched my head about was that every lecturer/teacher (especially lecturer) always thought that their course /was the most important course and the only course (worth to concentrate on) for the students. While in fact as a student you probably have three or four simultaneous courses and all are equally important. Basically, attitude. Attitude does a whole lot!
When I had to go to the lecture where I knew that the lecturer enjoyed tormenting the students instead of working /with/ them, I had a completely negative setting in the brain even before the class/lecture...affecting the knowledge exchange very negatively of course.
The above are just feedback, "a student's diary" if you will, from IRL and not anything I have looked up officially or anything like that.