A few schools offer faculty internships. So you will run across enlightened opportunities such as the Kenan-Lewis Internship at Woodberry Forest School in Virginia. Two Kenan-Lewis interns are appointed annually.
This brief video offers three tips to advance your career
Advantages to Working in a Private School
A private school teacher does not have to teach to the test. Public school teachers must focus on preparing their students to do well on state mandated testing as opposed to really teaching them.
Smaller Class Size
Private school class sizes are generally smaller than similar public school classes. You can truly teach a small class of students. Discipline issues are minimal.
Increased Teacher Safety
Teachers feel safer in most private schools because private schools can enforce their discipline codes with impunity. In addition most private schools have a much smaller student population than public schools. It is easier to supervise a smaller group of students.