When you look at private high schools, make sure that they "track" kids (have different levels of classes in the same grade) on the humanities side. My kids private HS had that for math, sciences, and foreign languages. But they did NOT track for english or social studies (same classes for everyone). Really a problem for my kids, who are very advanced on the humanities side. Older D not as gifted, so she did okay in spite of this. Second D, it was a big problem. We are not in Philly, but just something to look at.
