One of their videos features a presentation given by Albany Area Math Circle member Elizabeth Parizh on the social aspects of math circles:
Math Clubs and Their Social Aspect:
A View Inside and Out
Many children today are put off from participating in math activities because it is not popular among school kids. I will describe my own experiences as both a coach and a student in such math clubs, and explains what it is like for kids, and especially girls. I find that this is a very important problem that needs to be solved, because these students are America’s future and need to be prepared to help their country prosper. And yes, this does require math.
Elizabeth's talk was very well received, though unfortunately the videographer's microphone was placed to pick up more of the crowd reaction than of Elizabeth's voice (which came through quite clearly in person.) Her slides are available here.
The other talks and activities at the meeting were also excellent and several of the other featured videos are available here.
Elizabeth also assisted Bard College Professor Japheth Wood in leading sessions on the theory of impartial games designed for middle school and high school teachers. They used the game of Nim to illustrate the ideas of game trees, strategy, and concepts such as the addition of games. More details of that activity, including handouts, are available here. Professor Wood leads the Kingston Math Circle to our south--you may also want to check out his blog, News from the Math Wizard.