participation in 1st year introductory pure maths classes 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 )
 A: I am assuming, from your question, that "small group discussion" are not practical, in terms of the time available in class and the material you need to cover, particularly if you are accountable for covering a lot of material. I take it you don't have the flexibility to emphasize student comprehension at the cost of not covering all the material you are required to cover.
One nice way to motivate participation, and help students overcome the fear of "asking something stupid" (or simply not wanting to draw attention to themselves) is to
Ask the students at the beginning of class (or before class) to hand in a folded sheet of paper (no name required!) with a question they'd like to explore or a concept they'd like clarified: 

E.g., "What one question is most pressing to you, that we might address today?" 

That way, students can ask questions "anonymously", and you can randomly select from the submissions any number of questions to address, depending on the time available. 


*

*As you address the question(s), students' attention will usually perk up! (At least, that has been my experience.) 

*As you work through the questions you select, "think out loud", i.e., try to make explicit how one can approach a problem, and the process involved in solving problems, and that it is normal to test one approach, and that failing, back track, and start anew.

*Students also learn from the questions other students ask that it is "normal" to have questions, to be unsure, or unclear about new material they are encountering.  


No need to force students to write a question: You can make clear that students are free to write "No problems, I got it!"... Or to doodle, or write nothing at all...
This sort of "in-class assignment" will also prompt students to study more actively, by considering questions in advance of class, and prioritizing those that are most pressing. Knowing they will have the opportunity to anonymously pose a question motivates students to engage more actively with the material,the homework, and in class.
Do read @Hans's suggestion, below (comment): Such a strategy can be used at the very end of the class, and it provides nice feedback for you, as well.
A: Here are my 2 cents worth.
With only 20 students, you have a very good opportunity to get students engaged. Know their names, ask them questions (easy ones, try to follow up with a harder one to the same student), call them up by name, get them to ask questions, turn questions from the audience around and ask others to answer them, etc.s 
You will be able to "train" your students to be much less timid within a week. You will get a much better sense of how they are understanding the material. And they are going to understand it better as well.
Since they seem to be eager homework solvers, you can also assign them reading together with (simple) problems on material that you have not covered yet. They will do it and you will have time to go over problems where they have trouble or over more advanced problems. 
Finally ask yourself which purpose of the class is more important: Going over a maximal amount of material or getting students to understand a maximal amount. These two purposes are often at odds, believe it or not.    
A: Beltrame,
Since you have just started teaching the class, I wouldn't worry too much about the lack of class participation for now. I would monitor the level of class participation for a few classes first. As students get to know you better (and you start to know them better), they may become more comfortable asking questions and making points during your lectures. Also, as you say, there may be some students who are better at expressing themselves in written form (i.e. on homeworks, class tests, e-mail, etc.) instead of speaking.
But of course, if one month later, you realise that the level of class participation has dropped even further and is close to 0, then perhaps it might be a good idea to get a colleague or grad student to just sit it in quietly at the back of the class to observe what's going on. They may observe the body language, etc., of students while you are teaching (since you'll be focusing on the lecture material itself) and may be able to give you some feedback on what the students are doing when you teach.
From my experience teaching in a Community College, one idea that seems to work in inducing class participation is to ask small questions (e.g. "what do you think should be the next step here?" when you are doing an example in front of the class) to the class. And you could add in  conditions like "I would like to get an answer from the back 5 rows of the class" or "an answer from the left side of the class please".
Also, I'm not sure if you've already done this, but it's important to let the class know at the start (of term) that you welcome questions. You can say that asking clarifying questions are good because if a student is unsure of something, chances are that a few students in the class are also unsure of the same thing. So it's in the class' best interest for the question to be asked - so encourage them not to be shy to clarify.
Hope these tips help. And all the best for your teaching. Cheers, conan
