Academic Peace Circles fall under the umbrella of Restorative Practices, which evolved from Restorative Justice. The fundamental premise of restorative practices is that people are happier, more cooperative and productive, and more likely to make positive changes when those in authority do things with them, rather than to them or for them.
Using Circles is not new, but applying Circles to an instructional environment allows a teacher to reap the benefits of restorative environment without sa