I'm the principal of a school, and the answers to the questions should be level-specific (elementary, middle, or high school) and grade specific, if you know what grade is being advertised.
My peers in elementary school focus on literacy questions, social skills development issues, and effective management of the volumes of paperwork.
For middle school interviews, I focus on interdisciplinary planning examples (how to bring reading strategies into all subject areas) , classroom management skills (be specific with the set up of the room and past experiences with disruptive students), and specific ways that you communicate to parents, in both positive and negative situations.
High school principals look at college prep effectiveness in lesson plans for upper levels, and more behaviour management with lower levels. They also want to know how you will help in maintaining a safe and orderly campus (being in halls after school, walking students out the doors, etc.)
These hints apply for any teaching job, on any level:
• Be enthusiastic--nothing kills an interview like a teacher with no passion---smile, and give examples of meaningful connections with students
• Be specific with examples of great lessons/outcome, innnovative projects you have done, and "out of the box" strategies that worked.
• Be honest--you may want to give an example of something that didn't work out the way you wanted it to, and then give the lesson YOU learned. Interviewers will find it refreshing.
• Save the "My philosophy on education is....." routine. It's boring, and no matter how you feel, it is always akin to a canned response. If someone asks for your philosophy, consider it a rookie question, make your answer brief, and move on.
• DON'T say, "I'll take any teaching job--I just want to get started." When I hire someone, I want them to know that my STUDENTS and their respective age of development come first, not the paycheck. If you want middle school, only interview for that level, not high school or elementary (assuming you have the appropriate certification).
• Assuming that you have been successful in moving your student up in standardized test, bring the % and quote them.
• Make sure that the private school will give you a good recommendation. I always check references.
Good Luck!