In my university, tutorial sessions in physics usually consists in the teaching assistant solving three to six problems in front of the class (less than 30 students per class). Some TAs try to encourage student participation by asking what the next step in solving the problem should be, etc... but the results are usually poor. As a student, I mostly thought that this format for tutorial sessions was a waste of time, especially since most TAs gave the corrected exercises after the tutorial session (as I think they should be doing). I usually stopped attending after a few weeks.
I now find myself in the situation of being a TA for the first time and I don't want to repeat the same mistake as my peers. I want to convince the teacher to let me try a more stimulating format for the tutorial sessions.
I initially wanted to use clickers and ask short multiple choice questions to students, but I may have to abandon that idea since 1) it might be too much of a change for the teacher to accept, 2) take too much time for me to prepare and 3) the university might even not have clickers.
Another idea I had was to go through a single difficult exercise with the students as an example and to leave them the rest of the hour to work in teams on their weekly homework while being available for questions.
What do you think about it? What are some good ways to maximize the usefulness of tutorial sessions and to make them stimulating for students?