In terms of being embarrassed, if you tell your students that you are expecting them to read ahead and only ask questions on subjects you've already explained, everyone should know the answer.
Of course, some students won't really understand exactly what the teacher is asking, might have problems talking in front of people, etc. What I would suggest, then, is to make sure that if someone doesn't know a problem, you immediately move on to another student (i.e. don't badger one student if they don't know the answer).
If you find that a student frequently passes on answering questions, that would be a great indication that they might not be understanding the issues, and that would be a good time to schedule a meeting with them to get it sorted out (via email or something, to avoid singling that student out in front of his/her peers).
Of course, some students won't really understand exactly what the teacher is asking, might have problems talking in front of people, etc. What I would suggest, then, is to make sure that if someone doesn't know a problem, you immediately move on to another student (i.e. don't badger one student if they don't know the answer).
If you find that a student frequently passes on answering questions, that would be a great indication that they might not be understanding the issues, and that would be a good time to schedule a meeting with them to get it sorted out (via email or something, to avoid singling that student out in front of his/her peers).