Any scientist who couldn’t explain to an eight-year-old what he was doing was a charlatan.
From Cat’s Cradle by Kurt Vonnegut
As a graduate student, one of my favorite things to do is solve interesting problems. It doesn’t matter if it is a homework problem or a random question from a fellow student (honestly, I think I prefer the random questions). Lately I have realized solving problems is not the only thing that creates a good mathematician. One also needs the ability to articulate ideas and solutions in a way others can understand and relate to.
For the last two semesters I have participated in the NSF Graduate STEM Fellows in K-12 Education (GK-12) Program. The purpose of this program is to interact with students in K-12 and their teachers in order to improve communication and teaching skills. Personally I have visited a middle school once a week and discussed various types of problems with the students. While I was never able to explain my research (Maximal Cohen-Macaulay Modules), I did show the students how to ask meaningful mathematical questions and am still in the process in showing them how to articulate their ideas. For me, this exercise has greatly helped me to identify problems in my own presentation of mathematical thought and forced me to be sensitive to my audience. Although, according to Vonnegut, I am still a charlatan.
I would recommend this type of outreach to any graduate student; speaking in front of someone who has absolutely no prior knowledge is a great experience and helps you focus your thoughts. If you are interested in talking to children about math, you don’t have to wait for the NSF to fund a program. Many schools in your city would love for you to come an volunteer your time; maybe just once a month. Working with middle school kids can be fun and surprising; the students are a lot cleverer than you might think.