It's time to finally bring the scientific method to teaching.
As with a lot of things in science, there's more dogma about teaching than rigorous study of what techniques actually work and help students learn.
There's a nice study (doi: 10.1187/cbe.14-06-0095) that lays out effective teaching practices and references of studying showing that these practices are actually effective. As opposed to a lot of 'active learning' studies, these are studies that tweak one single thing at a time (e.g. allowing students to think before answering a question) to study its effectiveness without a lot of other confounding factors. I'm sort of summarizing / combining a lot of the techniques in the paper and fusing it with what I've done in the classroom.
My experience has been in TAing a lecture course. I was in charge of the discussion. My only requirement was that I give a quiz every class. I usually ended up giving the students problems to work on during class. Ideally, these should be harder or as hard as exam problems. Some suggestions from the paper above:
let students think about the answers themselves first
then put the students in small groups
This encourages participation on a level that's less intimindating than the entire class. It also allows students to learn from other students.
don't hint at the answers
This is just asking for students not to care: why should they try if you're just going to give them the answer?
Students need to be held accountable. I suggest randomizing your roster several times and whenever you have a question to the class, call the next person on the list. Give points as long as the person is present and answers. Cold call on people after they'd had a chance to discuss things in their group.
explain why wrong answers are wrong
Saving the A is the right answer doesn't go far enough. Just as important as explaining why the right answer is right is explianing why the wrong answers were incorrect. This can avoid a lot of confusion
be nice and let your students know that you care about their learning
This is what the paper referenced above called 'apprehension reduction'. You need to make students feel comfortable to admit that they don't know something and comfortable to make mistakes.
Something I've wanted to try but haven't gotten a chance to try to having the students write down one thing they still don't understand at the end of the class period. At the beginning of the subsequent class period, you would then try to clarify the one or two main misconceptions. This also helps you gauge how well you're explaining things and you get a sense of where the class is as a whole. Admitting that you don't know something on an index card is a lot easier than admitting you don't know something to the entire class.