One of my new undergrad advisees asked me how to participate in a philosophy discussion class. This is not something I usually teach explicitly, and it was never taught to me explicitly, and why not? Because a discussion with skilled participants makes all the difference.
This particular student is not shy--he's an officer in his fraternity. So he's not asking for help with that. He's asking about quality, and he pointed out that he doesn't want to imitate what some students do because he thinks the way they participate wastes class time. He might be right! But he also might have a mistaken idea about what a good or bad comment is.
Since I wrote a lot for him, I thought it would be worth copying here:
If you go to a public lecture, you will see that our faculty members each have their own style for asking questions. Actually, most of us have a toolbox that includes a few different question types. For instance, one of us usually asks an apparently simple question of clarification which he has carefully planned so that the speaker will say something controversial, and he follows up with the question "So do you realize that the implication of what you're saying is the usually undesirable outcome X?" Others often ask the speaker if they have examined the connection between what they're saying and some other philosopher. One of us comes right out and says "I disagree with your starting assumptions."
So developing a style for engaging in public is a good thing to think about—we've all done that, maybe explicitly or maybe we just let our style emerge over time.
The first thing to do, then, is to watch what other students (and professors) do, and start evaluating the kinds of questions/comments and the ways of saying them which you think are especially effective or ineffective. Then practice one kind of question yourself. Even if you just have one kind of question/comment that you feel comfortable making, and which you can fashion to fit different circumstances, then you're in good shape.
One of the things you should ask yourself is whether you are better at reacting to other people or better at expressing a thought that is independent of what other people have said. Because depending on the answer, you'll need to be mentally prepared to jump in in different ways. Usually professors give an opening for the latter strategy. Either at the beginning or at the end, they ask "Is there anything about this reading you didn't understand?" or "Is there something else about this debate that we should cover?" And that's your cue.
If you're better at reacting, then you just have to be ready to let your spring-loaded question get tripped and come out your mouth. For instance, I'm better at reacting than starting a conversation, but as an undergrad I used to be really, really slow to respond, and then I would leave every class thinking "Why didn't I just say what I was thinking?" I had to practice being faster, and that's how I developed the bad habit of talking over other people. In some circumstances, it's rude, and in other circumstances, it's how to get heard.
The second thing to do is to have a couple of strategies and types of questions in mind, and the kind that you start developing will depend on the above choice. If you can react, professors LOVE it when one student calls another student out (but in a gentle, respectful, kind way) for saying something that doesn't make sense. Your participation goal is not necessarily to interact with the professor—it's just as good (and probably better) to interact with other students. For instance: "Pat, I think what you just said about the evil demon is really interesting, but you also said that Descartes is an empiricist. I'm curious if you could say more about that because I think of Descartes as a rationalist."
Another thing that professors LOVE is if you can make a connection with a different class day. This is something that can sometimes be prepared ahead of time. "I found myself following along with Marx when he makes a point about the power of the proletariat. But just last week I had a positive feeling toward Nietzsche when he wrote about the powerful individual. Yes, I want to be a powerful individual, but I also want to stand in solidarity with my people. Professor, is there a tension here? What do you make of it?"
Which reminds me—some but not all professors like to be asked what they think about a controversy or interpretation. Well, really everyone likes to be asked, but some will refuse to say.
Finally, you can always ask questions of clarification. "I didn't really get how the revolution is supposed to happen, especially if the ruling class controls the means of public communication. What am I missing?" Or more simply "What is the proletariat? I read this but I'm still confused." Or an interesting one "Is this idea supposed to apply to our time? And if it does, who would the proletariat be right now? The 99%? The 47%? Just people who are homeless?" Asking these kinds of questions does not make you look stupid (although you should do the reading and not just ask basic questions without reading). It makes you look like you're paying attention to details.
So the summary is:
You can improve participation by
1. planning ahead
2. recognizing the openings and invitations that apply to the kind of comment/question you're best at
3. practicing one particular kind or style of comment/question over and over again until it feels natural to you.