How to increase participation in tutorials, as a teaching assistant? I will be a teaching assistant for a couple of "tutorials" this semester. Basically, I just have a list of problems that we have to go over in the tutorial. Last semester, the Calculus for Engineering students were happy to participate, but the Calculus for Finance students were not. The only factor I can think of is that the Engineering students were more prepared. How can I get the students to participate? Should I just stall and not continue until someone raises their hand, and then they'll eventually get the message? Somehow I'm not sure that really works...
I often walk over to a randomly picked student and ask him/her a question. I do that randomly and unpredictably, including corners of the room or sides where students expect to be out of the action, and no student will stay inattentive. Under no circumstances belittle or ridicule, though, no matter how wrong they are, and if the student makes even a partial step in the right direction, give them credit for this. If they are stuck, you can then solicit help from others to further complete the answer.

For students avoiding your eyes, try to pick a question with unclear/ambiguous response. When you then ask the student, they are likely to respond with "I don't know" or similar, and you can then say that they are indeed right, that the answer is indeed unclear (and, of course, you discuss why). This gives them a confidence boost, and the next time you ask them they will be less worried to answer.