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.
I would tackle it by clearly defining (or even redefining) the term participation. Particularly I'd advocate for enhancing student's engagement rather than the traditionally defined participation.
Coming out to the board and writing down one's solution or answering the tutor's question on the spot is not the only way we can judge if someone is participating. If the Finance students are indeed less prepared, this is actually an intimidating experience for them, and can cause further withdrawal. Here I list some practices that I have tried and tested, there will be some over-generalizing so bear with me. In your situation the mileage will differ depending on how well you know your students.
First, get them involved in deciding the format of the tutorial. A good way is to send them a poll before or right after the first tutorial. Make the poll anonymous and ask them questions that can help you improve the teaching quality. For example, related courses they have taken, confidence in calculus, how they learn best, issues in the field of finance that interest them, preferred ways to participate (group discussion, showing answer anonymously, etc.)
Once you have the general gist, plan your format around it. You can alter your examples, your ways evaluating participation/engagement, etc.
For instance, make your questions relevant to their field of study. Sometime simply naming your variables with things that they are familiar with improves acceptance. If they are from the business school, case study instead of straight-up "please solve this" exercise would be a good and more familiar option. For example, you can present the challenge first, then data, then the formula. Try to make it as close to their future career experience as possible and this immersive approach may just interest them.
For less prepared students, you can consider group-work and group-self-teaching. For example, a mechanism called jig-saw may be a good choice. Let's say you have four questions and 16 students. Group them into four, and then have each group study one question and get that right. You can tour around and coach them. Then, reshuffle your group so that now the new group has one student from each of the questions (e.g. Q1, Q2, Q3, Q4 as a group) and each of them can take turn to explain his/her approach to the their group members. Each of them is still held accountable and the stake of massively embarrassing themselves is much lower.
Another group-based platform that may work well is message-board. Platforms such as Piazza allows students to contribute to answer a question either with their name disclosed or anonymously. Instructor can then provide feedback. The math symbols may be harder to manage, but Piazza works with LaTeX so it's not that hard to master. You can consider posting the question days before the tutorial so that less confident students can do some extra preparation before meeting you. If coming up to the board and explain the answer is really your way of doing it, then you can also consider assign the question to the students before hand so that they can start working on the one they may be called upon to demonstrate.
There are easier twists and there are elaborated modifications. The overarching tactics can be summarized as:
- Know the learning and communication traits of the generation and cohort you teach.
- Write clear learning objectives and seek feedback on them from other experienced and reputable teachers.
- Engage students flexibly rather than forcing them into a mold of "ideal student" that we or our teachers or our teachers' teachers once conceptualized.
- Make their learning relevant and try your best to make them own their discovery.
- Do not be afraid of setbacks. Changes do not always bring positive reactions, but they are crucial as our audience is ever-changing; the moment we stop trying new teaching methods is the moment we stop being a good teacher.