I have just started teaching a very elementary class for 1st year students on introductory pure mathematics. ( classes at my institution are groups up to 20 students and supplement the lectures. The main purpose is to go over the weekly problem sets )
Since weekly homework assignments are compulsory ( submission is very good, 95% ish ) active participation is encouraged and guaranteed. However I am wondering to what extend it is nevertheless important for students to actively participate DURING the classes as well. They seem to be quite timid and as usual there is nowhere near enough time to cover all the problems from the assignment, so it ends up being a bit of a monologue.
My question is whether this is something I should worry about, or whether it is perfectly acceptable for students to be less outspoken during classes provided they have made a real effort at the assignment.
Moreover, in case somebody with more experience has some advice how I can encourage participation during class without loosing too much time I would really appreciate it ! ( I am somewhat limited in what I can do, as I need to cover a fair bit of ground, so I cannot just turn it into an open discussion session for instance )