> Two tests. One at the beginning of the year, one at the end.

Is it the same test (same questions) or a different test? I would guess same type of questions.

Also what if the students are already top performing and don't improve but actually get a slightly worse. (As in they all get 95% and then, well a few get sick and skip a few months from school and now the class gets 94%).

I guess I am still confused at how average expected improvement is supposed to work reliably across all those population models.

Do we assume the school-wide population of students is uniform enough to calculate a meanigful average improvment from it which can be applied very classroom individually.

There are a lot of school districts that have very mixed populations (economic, ethnic, cultural) backgrounds.

Same about the state. Some states districts that maybe very rural and undeveloped mixed in with a metropolitan area some place across the state.