Something you realize after living in Korea for like even a couple weeks is that shame, or the avoidance of it dictates many a social situation and that in your class, it's really no different. Koreans will feel shame for a myriad of things: appearing not as smart as others, appearing less well-dressed, not doing homework, having weak second language skills, etc, etc. The smarter, more well-prepared students will not show their true colors because they're afraid of making their lesser classmates feel shame. It's a little bit ridiculous at times and often gives me stress, but it's one of those things I've just come to accept about living and working in Korea. Here's how I deal with it:
1. Never put students on the spot. NEVER. Always give students a chance to practice something with a partner or small group before you pick an individual student to answer.
2. I generally choose a team or group to answer and one person has to do it. So, the weaker students can hide behind the stronger ones.
3. Ask for volunteers, but give some sort of incentive. Like a reward system, or telling the students that once you get 5 answers, they're finished for the day.
4. Don't embarrass students for wrong answers. There are plenty of ways to deal with mistakes that don't involve doing this.
5. Never call out of students in front of his or her peers. If you need to discipline someone, do it outside the classroom 1-1.