A New Kind of Circle: Math Circle at Graterford Prison

This painting was done by a Graterford Math Circle participant, inspired by the question of how to test someone’s claim that they could tell the difference between Pepsi and Coke by smell.

Like many other Math Circles, the Graterford Math Circle just had its first meeting of the fall. The leaders, Katie Haymaker and I, brought a question to the group: How can we understand the lottery, and when can you play to win? Following a plan from Michelle Manes (in turn inspired by Jordan Ellenberg’s book), we ran a mock lottery to illustrate how buying a certain slate of tickets can reduce risk and make the lottery a good investment (under very rare circumstances), but found that the lottery in general is a very bad investment. We talked about the MIT group that made at least $8 million in the Massachussetts lottery. We had several good laughs, students anticipated every “mathematical point” that we’d hoped to make, and I left feeling totally proud of the students, and jazzed about math and math circles. This was all very normal and fun and cool! There were two unusual things about our circle. First, the students are adults, though not teachers or necessarily parents. Second, the circle takes place in the education wing of Graterford Prison, a maximum-security men’s prison about 45 minutes from Philadelphia, where the students are incarcerated.

Katie and I started the Graterford Math Circle in January of this year. We both were interested in starting a new Circle of some kind, and in working with adults, but there is already a wonderful Math Teachers Circle in Philadelphia (also, see my earlier blog post). We were both interested in teaching at Graterford through Villanova’s degree program, but hadn’t had the opportunity yet. So we hit upon the idea of a Math Circle at Graterford. We hoped the Math Circle could teach problem solving techniques, help Graterford students to see mathematics in a new way, and hopefully make students more comfortable in future mathematics classrooms. Since many of the students also have children, I hoped that positive experiences with Math Circle would also influence how the students talk to their families about math, and at least slightly reduce the chance that their children would be anxious about math.

Of course, Math Circles are generally for K-12 students, teachers of K-12 students, or occasionally parents of K-12 students, so our Circle for adult students was really a new model. We were not sure if it would work, honestly. What if the questions were not interesting to these students? What if there were major institutional rules that kept us from being able to create a fun atmosphere? We envisioned armed guards watching sternly and students forced to remain in their seats at all times.

We did a trial run, giving a talk at Graterford to share some puzzles and see if there was enough interest to have a monthly meeting. As I described in my blog post, it was really fun, and convinced us that the Math Circle could work. Our first meeting was in January—we did the Pancake Problem that I described in another blog post. It went over really well! There was a guard in the hallway, but the classroom atmosphere was relaxed and fun. We moved desks, worked in groups, and interacted just like people in any other math circle. We met once a month for the rest of the spring, with groups varying from 4-15 students. These guys are really enthusiastic. Getting them interested in the problems has not been at all difficult—the only difficult parts have been getting into the institution, not being able to use any technology, and getting some of the more outspoken people to delay shouting out answers.

In May, Katie and I went to Graterford’s graduation ceremony. Seven students were graduating from the Villanova program, and many more were receiving GEDs or certificates for vocational training programs. One of our most consistent Math Circle participants was graduating, and was very happy to see us at the event. He sent us (and our department chair) the most beautifully typed (yes, on a typewriter) thank-you letters over the summer. At the latest Math Circle, he brought us three of his summer projects: careful solutions to some of the problems posed in the handouts for three of the spring’s Math Circle topics. For the pancake problem, he had written computer programs to sort stacks of pancakes and to produce disordered stacks. For the puzzles we had brought in our initial talk, he had typed up full solutions to each. His reasoning was very clear and the explanations were excellent. Reading these solutions, I was so impressed with his work, and I felt incredibly happy that we had taken the opportunity to share some of our favorite parts of math with these guys. It feels like recommending your favorite book to someone who really puts in the time and thinks about it, and then tells you that the book now means something to them, too.

This is a flowchart created by a Math Circle member to describe an algorithm to sort a stack of pancakes.

Other members of the circle have also brought extensive and creative work on past problems to later math circles, and they have naturally come upon some really interesting ideas in mathematics. There was sort of an organically developed generating function approach to one problem, and steps towards abstract algebra in another. We also received letters from some of the other guys, including the drawing I included above, inspired by a math circle question on how you could test whether a person could tell the difference between Coke and Pepsi by smell. (adapted from a Math Teachers Circle problem by Amy N. Myers of Bryn Mawr College).

Katie and I are planning (if our Dean approves) to co-teach a math class at Graterford this spring. We were originally planning to suspend the Math Circle for the spring, since we would be busy with teaching, but after last week, I’m not sure I can give it up. This Math Circle only happens once a month, but it really reminds me why I wanted to be a math professor in the first place.