At the core of this vision is the idea that if people (administrators, parents, community members, policy makers, etc) just asked us teachers what we thought would make sense, then we would better be able to prepare our young people for the new future that awaits them.
A few specific aspects of this autonomy are:
1) Teacher control over curriculum - this may be obvious to some teachers, but probably not to some administrators. With control over what to teach every day, I can better serve my students.
2) Teacher control over budgets - imagine a world where we could help purchase new materials not just for our classrooms but for the school. If teachers could come to agreement on if they needed money for trips, new furniture, storage, etc, then we'd understand some of the financial pinches of wasting paper but also how to balance the money we need for good use.
3) Teacher control over hiring/firing - this is a tricky concept that can run us into trouble but I think overall is an intriguing idea that should be pursued. The staff at a given school understands the culture the best and would know if a new hire would work well or not with other teachers.
There were many different aspects on which that these schools were compared (check out the autonomy matrix here) but they all were implemented in slightly different ways. I think it would do districts across the country a great service to trial some of these ideas. Some are scary but all have interesting opportunities.