Former Van Vleck Assistant Professor, Natasha Rozhkovskaya, now an Associate Professor at Kansas State University, recently wrote the first guide to math circles for elementary school children. She was interviewed in the blog for Scientific American about math circles in general, their beginnings and their widespread popularity.

http://blogs.scientificamerican.com/budding-scientist/from-russia-with-math-for-kids/

Our own Math Circle: https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle