I'm interested in communicating mathematics to a broad audience.
Math circles (older)
Previously, at Washington University in St. Louis, I was fairly active in the well-established Math Circles program there. I ran activities both at Wash U (on several occasions), and also at the Metamo4ic Math Center (in Ferguson, MO) and Ferguson Middle School.
For an audience of middle school or high school students who have come in on the weekend, I try not to do any lecturing. Instead, I hand students a sheet of paper as they come in, which tells them a new idea, gives an example of the idea, and asks a question about it. Answering the question gets a student the next sheet. Motivated students can work through about 6 to 10 sheets over a relaxed couple of hours. (I suppose this could be described as a “flipped classroom” type active-learning approach, if one likes buzzwords.)
I understand that a version of my approach is now the recommended one for new presenters at the Washington University in St. Louis math circle.
Some of my Math Circles materials: