I started a Math Circle for K-12 teachers last year with three of my colleagues. Roughly, a Math Circle is just a place where people get together and work on interesting math problems. So far, it has been a wonderful experience. I got to fly to Denver to get some training, and we have had a great time putting it together.
We have started off by focusing on 6–12 teachers, and we have had only a tiny bit of success. We have seen a total of four different teachers, with two of the teachers being dedicated regulars (and a third possibly joining them now). This could be a little weird, with a 2-to-1 professor-to-teacher ratio, but it has not been. The sessions have been a lot of fun, and the actual dynamic is that one of the professors leads the session and everyone else acts as a student (and the leader of the session is often a student, too, since s/he also often has not thought too deeply about the problems). We have been meeting 3–4 times per year.
Our budget so far has been $0, although we have tried to get several grants. The National Association of Math Circles has been supportive, though, even sending us a Math Circle starter pack. We hope to get some money to provide dinners for the teachers eventually. We are able to offer them “continuing education” credits, which helps them renew their teaching licenses (these don’t cost us anything; we just get a little help from the chair of our Education Department, who needs to sign them).
The Math Circle has been a fun and interesting experience with a shockingly low start-up cost and time investment. Let me know if you have questions about starting one.