Math Circles are a form of education outreach and enrichment through which mathematicians and mathematical scientists share their passion. The Circles combine significant content with a setting that encourages a sense of discovery and excitement about mathematics through problem solving and interactive exploration. Ideal problems are low-threshold, high-ceiling; they offer a variety of entry points and can be approached with minimal mathematical background, but lead to deep mathematical concepts and can be connected to advanced mathematics.
In Teaching Circles you would do the same thing. You would take an activity you were especially excited about that week or an upcoming week and go through the activity with your peer teachers. You gain valuable feedback on different activities ranging from hands on, manipulatives, technological, and uncommon types of education. Teachers can explain their thinking what would work better next time and make adaptations for their students.
This model helps younger teachers gain insight on activities that master teachers are doing in their classroom, it also helps veteran teachers see different ways of incorporating things into their teaching as well. It helps get teachers who have been teaching 20+ years to try new things to share with the group.
Most importantly if you were to do this building wide, you could see what other teachers are teaching in your building and how you can help them pre-teach material. If you knew the chemistry teacher was teaching the periodic table of elements, the history teacher could pre-teach Dimitri Mendeleev, the English teacher could incorporate vocabulary using the periodic table of elements, a math teacher could add and subtract atomic weights. By incorporating lessons that we do everyday and broadcasting to others we get a tighter sense of community.