During recitation sections, should I ask students for help in coming up with the answer? Typically when teaching recitation sections (in lower level applied math classes), I bring a problem or two, and ask students to fill in the steps in the solution.  Usually 4 or 5 people (out of 10-15) are engaged in this process.

On the one hand, I think the engaged students benefit from the class discussion, and enjoy it more than listening to a lecture.

On the other hand, I worry that the students who don't participate in the discussion will find it boring, or get confused (because sometimes the other students suggest wrong approaches, and I humor them a bit before explaining why it's wrong).  It also makes the problem-solving process longer than it could be, and in that time I could cover more types of problems or just let students go home early.

What do you think is the best practice?  (And is it different in regular lectures than in recitation sections?)
I really like working problems with students, because I think that actually working a problem is a very good way to engage more deeply with the material.  That said, you've put your finger on two very important problems: engaging the whole class, and dealing with incorrect solutions.

My approaches to these two problems:


Engaging the whole class: you don't have to have everybody talk, but you have to give an opportunity for everybody to talk.  In fact, I think it's often better not to call on individual students, and thereby put them on the spot.  But you can promote engagement by calling on subsets of the class, e.g., "Let's hear from somebody who hasn't spoken yet", "somebody on the left side of the room", "one of you folks in the back".  This gives you ways to make sure the confident students don't dominate and allow less confident students space to step forward.
Dealing with incorrect solutions: Honest mistakes are golden, for every one highlights a way in which a student is misunderstanding the material.  Depending on the nature of the mistake, you can take a number of different approaches.  With some mistakes, you can just follow through to illustrate how things go wrong, then use that as a contrast.  With others, you can go Socratic and ask the student questions that lead them to understand the correct answer more deeply.  Yet others give you a chance to segue into an explanation of common misunderstandings.  I say, cherish the mistakes, give the student positive feedback for speaking and thinking even as you tell them they are wrong, and turn them into opportunities for deeper understanding.  


To me, the flip side of the problems you highlight are, in fact, the best reasons to ask students to help work problems in small recitations.  Solved well, they can present students with some of the best guided learning opportunities in an entire course.