> replaced all the teachers in a school with teachers recruited from the top 5 or 10 percent of all teachers in the country.

My Sister and SO are both teachers and we've had this discussion. They believe that if you took a low performing school, and replaced all the teachers with the best teachers in the country, you would find zero difference.

My sister has been beaten up by students, breaks up fights nearly every day, deals with child protection services, assault from parents, weapons in the classroom, drugs, gang activity, students who haven't eaten or bathed all weekend, etc. She teaches Grade 6. It doesn't matter in the slightest how good of a math teacher she is.

She's has it bad, but I think many people here may be surprised just how common her situation is.