{"id":1982,"date":"2017-05-18T17:13:19","date_gmt":"2017-05-18T21:13:19","guid":{"rendered":"http:\/\/blogs.ams.org\/phdplus\/?p=1982"},"modified":"2017-05-21T16:42:05","modified_gmt":"2017-05-21T20:42:05","slug":"topics-in-core-mathematics-at-graterford-prison","status":"publish","type":"post","link":"https:\/\/blogs.ams.org\/phdplus\/2017\/05\/18\/topics-in-core-mathematics-at-graterford-prison\/","title":{"rendered":"Topics in Core Mathematics at Graterford Prison"},"content":{"rendered":"

Topics in Core Mathematics sounds like the blandest possible math class.\u00a0 The course title is meant to convey the one important aspect of the class for many students: this class fulfills the core math requirement for the College of Liberal Arts and Sciences.\u00a0 Box checked.\u00a0 However, the advantage of blandness is that it can be the base for anything.\u00a0 This spring, my colleague Katie Haymaker and I taught TCM at Graterford State Correctional Institution<\/a>, a maximum-security prison in the Philadelphia area.\u00a0 I\u2019ve written before about a talk we gave there<\/a> and our math circle at Graterford<\/a>, but this was our first chance to offer a course for college credit, through the Villanova Graterford program. Villanova is one of a large handful of US colleges and universities, including Bard College, Cornell University, and many community colleges,<\/a> that bring professors into correctional institutions to offer classes for credit.\u00a0 This is one way of offering higher education to prisoners; other schools, like Adams State in Colorado, offer correspondence courses.\u00a0 Villanova\u2019s program even gives faculty members full teaching credit for teaching at Graterford, which I have heard is fairly unusual. The goal of Villanova\u2019s program is to be as similar to an on-campus degree as possible, with the same rigorous requirements in courses, and often the same professors teaching on-campus and off.<\/p>\n

Some blog readers might have a chance to teach a course in this setting, though I realize that many will not.\u00a0 Some things about this process and course can give some wider early-career insights, though.\u00a0 For example, Katie and I would never have taught this course if Katie hadn\u2019t been hanging out\/networking at one of the monthly Faculty Friday happy hour events organized by the university.\u00a0 That\u2019s how she first met Kate Meloney<\/a>, who runs the Villanova Graterford program.\u00a0 Going to university-wide events like this has paid off for me in just meeting cool people, and sometimes these people connect me with something I\u2019d never have known about otherwise.\u00a0 Also, co-teaching a course was a great experience for me.\u00a0 I had never attempted it before, and it turned out to be very rewarding.\u00a0 We were also very lucky that the dean of our college gave us both full teaching credit for the course.\u00a0 Before this, I didn\u2019t know that I could apply for double-credit co-teaching with a colleague.\u00a0 I would definitely recommend it, especially if you can convince Katie to teach with you.<\/p>\n

Our experiences might also be interesting\u00a0if you are simply trying to teach a core math\u00a0course on campus, since our course was attempting to be as much like an on-campus course as possible, though without much technology or access to office supplies. \u00a0We designed our course around the text\u00a0The Heart of Mathematics<\/a>, by Ed Burger and Michael Starbird.\u00a0 We chose this book because I had used it with great joy in a Math for Liberal Arts course at Colorado State University as a graduate student. The idea of HoM is to \u201cmake mathematics fun and satisfying for everyone,\u201d according to the back cover.\u00a0 I like the book because it starts with puzzles and works through some of the most fun big ideas of mathematics, without emphasizing computation or requiring any calculus or even much pre-calculus.\u00a0 Our plan was to basically avoid anything that looked like what the students had experienced before as \u201cmath,\u201d and hopefully thereby avoid the twin issues of past algebra difficulty and math anxiety.<\/p>\n

On the first day of class, we explained our plan to the students.\u00a0 As you might expect, someone asked if we would be teaching them anything they could use.\u00a0 Where are the practical applications?\u00a0 I felt that it was important to be clear from the start that applications of the sort you find in a calculus or algebra textbook were truly not the goal of the class.\u00a0 We would teach problem solving techniques that could be broadly applied.\u00a0 We would bring\u00a0puzzles and weird ideas that would hopefully provide fodder for thought and conversation.\u00a0 But we would not be learning to compute the half-life of uranium.\u00a0 We would be learning about ideas, some of them with\u00a0larger relevance.\u00a0 The goal was to take a new perspective on what mathematics could be. \u00a0With that said,\u00a0we started in on\u00a0the puzzles,\u00a0and all skepticism was set aside. \u00a0Arguments, however, were not. \u00a0We had SO MANY arguments about what the puzzles\u00a0intended, what was fair in solving them, and what somebody really would have done in this ridiculous situation. \u00a0But these puzzles and arguments were a great hook. \u00a0This was definitely not what the\u00a0students\u00a0expected from math.<\/p>\n

We eventually did sections on basic combinatorics, number theory, geometry, graphs, and probability from the textbook. \u00a0Highlights were Euclid\u2019s proof that there are infinitely many primes, Diffie-Hellman key exchange, Euler circuits, the Art Galley theorem, and Cantor\u2019s diagonalization argument leading to different sizes of infinity.\u00a0 HoM is a really well-written book, and we used many of their ways of explaining things.\u00a0 We also came up with some of our own material, drawing on our own interests, and found other resources.\u00a0 For example, I wanted to teach the students about cryptography in my own way.\u00a0 So I talked about symmetric ciphers, including encryption using a Viginere square with a keyword, cracking these ciphers, then introduced the idea of a \u201ckey book\u201d which would allow for no repetition of the keyword.\u00a0 The students then used Diffie-Hellman key exchange to agree on a page number in the key book to use for encryption. Here is the original assignment<\/a>.<\/p>\n

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A student’s\u00a0encrypted messages for his partners using Viginere square and key from a page of the book, agreed upon by Diffie-Hellman key agreement.<\/p><\/div>\n

Another smaller activity that was very successful was our simulation of the Monty Hall problem.\u00a0 One of the big constraints of working in the prison is the lack of technology.\u00a0 We couldn\u2019t just write a program to simulate keeping the door or switching a thousand times\u2014we had to come up with some way to physically do it.\u00a0 We ended up splitting the students into pairs and using set cards to stand in for the doors.\u00a0 Two green set cards represented the donkey or can of soup, while a purple set card represented the new car.\u00a0 One player shuffled the three cards and gave the other person a chance to choose a door (by putting a paper clip on a card).\u00a0 The student with the cards would then show an unselected green card, and give the chooser a chance to switch.\u00a0 The groups recorded how many wins and losses they had by switching and staying.\u00a0 In some groups it seemed to make no difference, but when we added up everyone\u2019s results we got very close to the predicted two thirds\/one third proportion.\u00a0 This five-minute activity cemented the concept in a way that my lecture definitely had not.<\/p>\n

Our syllabus included homework, two tests, and a final project\/presentation.\u00a0 The students had presented puzzles in the first two weeks of class, and we wanted to end class with another presentation of some kind, where we could hear a bit from each person as an individual.\u00a0 We decided on a poster session, which had a whole extra set of challenges inside an institution.\u00a0 It wouldn\u2019t be possible to assign the students to complete their posters outside of class, because the materials would be very expensive from the commissary and it wasn\u2019t clear what they would have access to.\u00a0 In the end, we had students pair up and choose a section that we had not covered from the textbook.\u00a0 The students were to read their assigned section and meet with the partner (we had to make sure they were on the same cell block) to plan a poster.\u00a0 They would have an hour on the last day of class to actually construct the poster, followed by an hour and a half poster session.\u00a0 We also asked the students to prepare a sort of elevator speech, a 3-5 minute summary of their topic to accompany the poster.\u00a0 We actually weren\u2019t sure that the markers, poster boards, and glue stick would be allowed into the institution, and we weren\u2019t sure if the poster session would really work, but in the end everything came through and the session was one of the highlights of my semester.<\/p>\n

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Poster on voting paradoxes.<\/p><\/div>\n

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Poster on non-euclidean geometries.<\/p><\/div>\n

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Poster on Euler characteristic.<\/p><\/div>\n

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Poster and origami on platonic solids.<\/p><\/div>\n

This was one of many places where having two professors was invaluable. \u00a0Generally, our co-teaching took the form of alternating lectures.\u00a0 While one person would lecture, the other would sort of join the class, occasionally asking questions, adding some relevant thoughts, and helping to clarify questions from the class when possible.\u00a0 It took a lot of pressure off to share grading responsibilities, and enabled us to model the kind of interactions we wanted to see in group work and class discussion.\u00a0 This poster session would have been much more difficult with one teacher, just for the time involved with having meaningful one-on-one contact with each student.\u00a0 When it was time to start, we asked one member of each pair to stay with the poster while the other person walked around and learned about the other posters.\u00a0 Katie and I had developed a simple rubric for grading the posters and presentations: 5 points each for content depth, content correctness, poster clarity, poster creativity\/visual appeal, and presentation.\u00a0 We assigned numbers as we went, to avoid a later session of agonizingly trying to remember our impressions.\u00a0 Between the two of us, it took about 45 minutes to see all the posters in the first round.\u00a0 We then had the students switch and we each went to the posters we hadn\u2019t seen the first time around.\u00a0 The presentations varied in quality (as presentations do), but a few of them were really strikingly good.\u00a0 The posters also varied, in intent and execution, but again some were exceptionally well done. \u00a0I’ve put\u00a0a few here, but more posters are posted on my website.<\/p>\n

I had more fun teaching this class than I have ever had teaching. The most striking thing about the course was the amount of energy in the classroom throughout the semester. \u00a0The students were engaged and game, willing to dive in to any discussion, to speak up with questions, comments, and occasional complaints, and to try activities for themselves.\u00a0 Every day when I walked out of class, I felt that I had actually\u00a0connected with the students.\u00a0 Along with this gameness, most of the students were fairly mature and serious about learning, while still being ready to make jokes and speak up in class.\u00a0 I wished I could have brought my on-campus\u00a0students, as a demonstration of what a classroom can be\u00a0like.\u00a0 I love working with my on-campus students, but I feel that self-consciousness and expectations of what a college classroom \u201cshould\u201d be can\u00a0really limit their experience.\u00a0 What could college be like if students really engaged\u00a0every minute of class time and saw\u00a0class as a dialogue?\u00a0 I have tried to create this classroom atmosphere in many classes, with varying degrees of success.\u00a0 At Graterford, this atmosphere just happened on its own.<\/p>\n

Debates abound<\/a> about the value of providing a college education, especially a liberal arts education, to incarcerated students.\u00a0 I believe strongly in the value of offering basic, vocational, and college education opportunities to incarcerated people. Educational opportunities are essential to opening viable paths for released individuals.\u00a0I also believe that a college education can open doors in a person’s\u00a0inner life, or at least provide access to some beautiful ideas and an intellectual joy that can be hard to find otherwise.<\/p>\n

Two of the students in our class are graduating this year.\u00a0 Both were really cool students to have in class, and have been working on their degrees for many years.\u00a0 One was actually released in April\u2014we worked with him by phone and mail to finish the course as he navigated the trials of re-entry.\u00a0 He will graduate on Villanova campus this Friday with his friends and family cheering him on.\u00a0 He is working two part-time jobs now, and just sent a text to let us know that he got a new job that he was really excited about.\u00a0 The other graduating student is not getting out right now.\u00a0 I have no idea when he will get out.\u00a0 He was one of the quickest students I have ever worked with, and brought so much to the class.\u00a0 Many of the Villanova graduates at Graterford become leaders in a very active alumni chapter at the institution, and help current and prospective students with classwork and navigating the program.\u00a0 I think this student will bring a lot to the next round of students at Graterford.\u00a0 I hope that our Topics in Core Mathematics course gave him something for himself, too.<\/p>\n

In fact, I know that math infiltrated our students\u2019 lives in unexpected ways.\u00a0 After our class on Cantor\u2019s diagonalization proof, a student told me that he and his wife had a game on the phone–the I-love-you-more game, essentially.\u00a0 He said that where it used to stop at \u201cI love you infinity,\u201d the game now could proceed from \u201ccountable infinity\u201d to \u201creal number infinity.\u201d Awesome.<\/p>\n

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Topics in Core Mathematics sounds like the blandest possible math class.\u00a0 The course title is meant to convey the one important aspect of the class for many students: this class fulfills the core math requirement for the College of Liberal … Continue reading →<\/span><\/a><\/p>\n

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