Talking Math at Graterford Prison

Last week I gave a very unusual math talk. It was at Graterford Prison, a maximum-security men’s prison in the Philadelphia area, and my colleague Katie Haymaker and I were there to talk about math. Villanova runs a degree-granting program at Graterford, bringing several professors to the prison each week to teach classes leading to an Associates or Bachelor of Arts degree. The courses and degree requirements are the same as those for the on-campus students (with the exception of lab requirements). The program has granted 63 degrees since it began in 1972, and usually enrolls between 50 and 60 students at a time.

Katie and I were at Graterford as part of the Professor Speaks program. About once a month, a professor gives a talk to the group on a topic of their own choosing. These talks have covered all kinds of topics, though never math (as far as I could tell). We were there to talk about how the math that we love is probably not what they think of as math–that math isn’t about learning formulas or performing on tests, but instead about exploration and logical reasoning and fun. We expected some skepticism, as usual.

However, speaking at Graterford was not the usual talk experience, in so many ways. We set out for the prison in the late afternoon, following the wonderful Kate Meloney, a professor in Villanova’s Department of Sociology and Criminology who took over running the Graterford program this year. Katie was driving, and I wasn’t paying much attention to where we were going. Until all the sudden suburbia vanished from the landscape and was replaced by an enormous concrete wall that went on and on and on. We eventually pulled into a parking lot and found an entrance that really could have belonged to any kind of institution. Following Kate’s tips, we left everything but our drivers’ licenses and a pile of photocopied handouts in the trunk of the car. Inside, we were told we’d have to wait until 6 PM, so we sat down on some benches. Having never been in a prison before I was very curious and fairly nervous, so it was nice that I got to sit on the bench and watch people come and go for a while. A sign above the security screening area said “SECURITY IS NOT CONVENIENT.”

Eventually we were called into the screening area. We had submitted our clearance documents a couple months before, and Kate and some alumni in Graterford had made the arrangements for the talk, so everything went fairly smoothly. The security officers were very polite and professional and very, very serious. We basically had to sign in, get marked with a special ultraviolet pen, and walk through a metal detector: less invasive than the airport. My shoes set off the detector so I had to kick them through, then walk through barefoot, which seemed oddly informal. We walked for what seemed like a really long time through the institution. A chaplain who escorted us said it was a quarter mile from the entrance to the prison chapel. The President and several other members of the Graterford Villanova Alumni chapter (all currently incarcerated) were there to meet us. They told us that the former President, one of Kate’s close contacts inside Graterford, had just been placed in transitional housing in preparation for his release. Everyone was very happy to hear this, of course. The guys set up some chairs, seemingly more than we could possibly need. In the spirit of optimism we had made 30 handouts. Realistically we expected 15 or so people. At first it seemed we wouldn’t even get that, though the people who were there we very friendly. Most of them introduced themselves and thanked us for coming.

even split try 2

Even Split, one of the puzzles we shared at Graterford. The object is to fill in all the boxes with the numbers 1 through 4, so that each number appears exactly once in each row and column. The sum of the numbers in the shaded boxes should be 20, and the sum of the numbers in the white boxes should also be 20.

The chairs filled up as the cell blocks gradually released people for the evening. There was no blackboard or projector—just a lectern and microphone. Since trying to say much about math without visual aids is hard, we decided to keep the talk to a minimum and go straight for the fun with some puzzles. The 30 handouts disappeared and we had to ask people to share with their neighbors. The handouts set up four puzzles we’d chosen to demonstrate that math was more than arithmetic and algebra. We luckily had recently attended a conference about math circles, which gave us some great ideas. We used two puzzles we learned about from Josh Zucker (Even Split, a very cool puzzle due to Thomas Snyder, and a mad veterinarian puzzle), and two classics (a counterfeit coin puzzle and the good old limited measuring cups puzzle). We hadn’t known for sure if the audience would have access to pencils, so we chose mostly puzzles that they could work on without writing anything down. Luckily most people brought pencils and pens with them. Our tag-team introductory “lecture” only lasted about 15 minutes, and we set them to work on Even Split.

We were nervous—how would this go over? If the audience didn’t bite on the puzzles we were pretty much lost, since we didn’t plan anything else. However, they did like the puzzles, more than we could have hoped for. The atmosphere was like a really fun normal classroom, when all the students know each other and buy into your activity and seem to be working just for the fun of it. Many people were familiar with Sudoku and so with the basis for the Even Split puzzle, but some were not, so Katie and I walked around the room helping different people and groups sort out various snags. Several people solved the puzzle and called us over to check their solutions. After a few minutes Katie talked through a couple of steps to start the puzzle, and the room was really responsive. People spoke up to explain the logic as she asked questions at the mic. After warning them, she showed the solution, but some people looked away, wanting to finish it for themselves first.

Next up was the counterfeit coin puzzle.  You might know this one: there are three piles of three coins each. One of the piles is all counterfeit and the other piles are all real. The counterfeit coins weigh 11 grams, while the real coins weigh 10, and you want to find the fake stack in just one weighing. I explained that you had a digital scale with only one weighing left on the battery. Sometimes my students get confused about whether I mean balance scale or what, so I spent some time laboring over this point. The audience seemed to find this fairly funny, and somebody called out “we know how a digital scale works,” which then struck me as kind of funny also, given the large percentage of people in prison for drug crimes. But then I felt weird laughing at this, not totally sure what they had been laughing at, and so I just rushed right on to further explain the puzzle… This was only one of many moments of unsureness and strange questions I had in preparing and giving this talk—I felt that I was working within a potentially very different culture, with rules that I didn’t understand.

I have shared puzzles many times, and they don’t always go great. If the class looks back blankly and doesn’t seem intrigued, it can be hard to give them any direction or encouragement without ruining the whole thing. It’s much easier to give hints or ask questions if people are really trying on their own. The Graterford students stepped up. However, some people got the puzzle FAST. Way faster than I had solved it the first time around. The people who got it didn’t yell out the answer or anything—they helped the other guys by asking questions and giving hints.

The hour passed really fast. We told them that the last two puzzles were a Christmas present, and that we’d hopefully be back in January to talk about some more. I am really looking forward to going back—this was no contest the most fun I’ve ever had giving a talk, and the students were extremely kind and welcoming.

On the way out, we passed a group of new inmates, in different colored jumpsuits. To the other side, I glanced into what looked like a residential cellblock, where a man was standing at the bars, looking out. This was the most stereotypical prison image of the entire visit. I felt that if I were in prison, I would be dying for a space of intellectual exploration and for the chance to earn a degree. I was told later that some of the alumni took 15 or 20 years to get their degrees, waiting for classes that fulfilled certain requirements. The students apparently always do their reading and homework, often twice. The Graterford program means a lot to the students. And many of the professors who teach in the program say it is overall an incredibly positive experience, life changing.

When I was writing this blog entry, I emailed Katie to ask what she thought about our visit. She wrote, “I feel like before we visited it was difficult for me to get past the ‘convict’ label and to accept that everyone there was just a normal person – probably because we are told that they aren’t normal by society, or by the media, or whoever. And of course we were sufficiently warned to be cautious and avoid potential scams. But once you and I were actually there working one-on-one with the guys, it was much easier to view each of them as individuals. Rereading that, I feel like it’s so obvious that it’s a non-statement.” I felt the same way—obviously the students are individuals, but from the outside, we know almost nothing about them. My visit was a positive experience, but I still feel a bit unmoored by the realization of how little I knew about the prisoners and their lives before visiting, and how little I know still. Before my visit I knew that the prison was there, but in some essential way I could fuzz my vision on the people inside. Inside, though, the people came alive as individuals, living complex lives, in an isolated world right within our city.

I haven’t taught a course there, but I hope that I can in the next few years. At Villanova, we are lucky that if the department chair agrees, classes that faculty teach at Graterford count toward the regular teaching load. I’m not really sure how this works at other Universities. Has anybody out there ever taught in a college in prison program? Or spoken to a non-mathematical audience that turned out to be really great? I would love to hear about it in the comments.

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2 Responses to Talking Math at Graterford Prison

  1. Avatar Steve Malbasa says:

    Hello Beth,

    I am chasing a Ph. D. in mathematics, and I now teach school in a juvenile detention facility in Ohio. My students are incarcerated, and many of the have (cough) treated school as optional for most of their lives. I rarely get all the way through algebra I in the school year.

    I do sometimes get a student who is very talented in mathematics or another STEM field, and I have done one-on-one with these young men and women, but the exercises that seem to work the best are the ones that I find outside of a textbook. I spoke to my students about the P NP problem earlier this year. I set the hook early in my lecture, and told them about the $1M bounty on the head of the prize, and gave a brief history of the millennial problems and what the P NP problem can do if it is shown that the two parts equal each other.

    My final activity is that I give them a set of 20 numbers that sum to 3000. I offer a candy bar prize (believe me, that is a big deal to them) to anyone who can break down these 20 numbers into two groups of 10 numbers, each of which sum to 1500. This obviously is very difficult, and I use my motivational tricks, cajoling, and backslapping to keep them focused. I’ve done this a few times, and only had two students who succeeded. One was a very smart young man, and one was… I’ll be diplomatic about his abilities; he will probably continue to be incarcerated most of his life, but he solved my problem.

    Since they would have to, in theory, go through 20! possibilities, I usually give everyone a candy bar after the exercise, and tell them that I was able to put this puzzle together in about 15 minutes, but solving it would be extremely hard, even if they had a computer with a lot more firepower than my laptop. It does a pretty good job of illustrating the difference between a P and NP problem, and even gets a few positive remarks from them.

    I wouldn’t want to have to stay in jail outside of an 8 hour workday, but spending time with those who are interested in the material is always a privilege, even in the land of orange polyester clothes and shower shoes.


    • Avatar bmalmskog says:

      Hello, Steve! Thanks for your really thoughtful comment. Your experiences with incarcerated youth are very interesting. It sounds like you need to use every method you can find to keep them motivated and engaged. You bring some really neat stuff into the classroom–doing P vs NP is a great idea! When Katie and I gave our talk, it was key that everyone in the audience came because they wanted to. I think it would be much much more difficult to engage an audience that was forced to come to class, just one more thing they have absolutely no choice about. I am impressed that you are able to teach creatively in that environment.

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