I know the semester is off to a good start when I can get students to voluntarily share personal stories out loud in a class of 250, and when I have to cut off the discussion because too many students want to share.
As a professor and someone who cares deeply about high-quality instruction, I find it incredibly satisfying to see students eagerly engaging with the material. But that kind of discussion doesn't just happen organically. Rather, there are things instructors can do to encourage students to speak up in class (especially in large classes) and to feel comfortable doing so.
Here's what I'd suggest:
1) Set the tone early. Don't just use the first day of class to review the syllabus. Start with a mini lesson that gets students thinking and talking and sharing. Include small group or partner discussion questions and a few questions that ask for more public responses.
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2) Start with low stakes. Ask brainstorming questions that produce a list of responses and don't require knowledge of the readings. On the first day of my intro sociology class, I lead off by asking: "What are some reasons students might drop out of high school?" Students can easily come up with a long list (everything from laziness and lack of motivation to bullying and homelessness).
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3) Learn students' names. When I call on students for answers, I ask their name and then repeat it back to them to make sure I've got it right. In my big class (250), it's a small gesture that can make students feel seen. In my "small" class (80), I also take attendance every class period by calling names aloud. For me, that's the fastest way to learn students' names, and I usually know at least 60% of them by week 3.
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4) Give students in-class discussion materials. Blog posts and video clips and short podcasts are great. For students, those materials provide a concrete, easily accessible, culturally-relevant jumping off point for a discussion.
On the first day of my Intro Sociology class, I show this 30-second PSA featuring Lebron James. Then I ask students to turn to a classmate and talk about what it implies about why students drop out of school. After about 2 minutes of discussion, I ask for volunteers to share (usually "students drop out because they're lazy or don't care about school"). Then I refer back to our list of possible causes of dropout and talk about the difference between structure and agency.
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5) Don't worry about looking stupid. Sharing relevant personal stories is a great way to show students how to engage with the material. And if they're funny or embarrassing stories, that's even better. Letting yourself be seen as human and fallible helps students (especially first generation students and students of color) feel comfortable coming to you for help and support and engagement.
In my Sociology of Childhood class, we read Allison Pugh's work on children's "economies of dignity" and the shame kids feel when they can't join the conversation with their peers. I tell students about how, in sixth grade, my Language Arts teacher asked for "brand names" for a MadLib-style group writing assignment. The teacher went around the room, and my classmates suggested things like "Gap" and "Reebok" and "Esprit" (it was the 90s). When it got to me, I had no idea what to say, so I read the label ("Lower East Sides") off the back of my Payless-brand shoes. That of course prompted peals of laughter and incredulous claims of "I've never heard of that!" from my peers. I was mortified, sinking red-faced into my chair.
A related point (and thanks to Helena Alden for bringing this up on Twitter): Share your failures. It's important for students to know that, as instructors, we don't know everything, can't do everything, make mistakes, and don't always achieve what we set out to achieve.
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6) Don't make students worry about looking stupid. I never cold-call students - I don't want them to be afraid to come to class. If I ask a question and no one raises their hand, that's on me. It could mean they didn't do the reading, but in my experience it more often means the question wasn't clear or students are afraid of looking stupid if their answer is wrong.
A related point (and thanks to MartaAH for this suggestion): Avoid asking students to speak for their entire group (race, ethnicity, gender, sexual orientation, disability status, etc.). By not cold-calling, you can ensure that students only share if they want to contribute to the conversation and if they feel comfortable doing so.
I should add here that I do require students to participate in my "small" (80-student) class. But they have the option to participate either by speaking in class or by posting/discussing links to course-relevant materials on Canvas. Either way, they need instances of participation over the course of the semester to get full-credit. I've found that having the option of online participation really helps students who might never feel comfortable speaking in front of the group, no matter what I do in class.
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7) Large group discussions work best with open-ended questions. If you want to ask questions with a single correct answer (especially in a large class), ask them privately instead of publicly. Polling apps like Top Hat are great for this. You can easily get a sense of whether students understand a concept without making them risk publicly getting it wrong.
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8) Validate students' answers. Reiterate what each student shares and gently redirect/clarify if the point is off-topic, unclear, or problematic in some way. Then connect each student's point to the larger discussion/topic before moving on to the next student. Like learning students' names, this approach helps students feel seen when they talk in class. That approach is also beneficial for the students who are listening. It helps them see the connection between what their classmates share and what they're supposed to get out of the lesson. It also helps the listeners feel reassured that you as the instructor aren't going to let racist, sexist, classist, or otherwise insensitive responses go unaddressed.