Link to previous posts: Pt1 Pt2

I’ve been doing a lot of soul-searching about this Inside Out course lately because of a growing dissatisfaction that I’m having about the class and also that some students are expressing.

One of the things I really wanted to do was to create a mathematics class that rehumanizes rather than dehumanizes, and I think that while students are generally feeling very positive about the class, I do feel like I am slipping into prior habits about teaching mathematics.

In previous class sessions, we have been sitting in four groups of 4-5 students and I have been visibly randomly assigning students to the groups for the purpose of having students work with each other and recognize each others’ mathematical talents.

This past Friday, one of my students suggested that we sit in one large circle instead of smaller groups. The result of that was that students generally still worked with the people that they happened to sit next to (there were still about 5 6 clumps of people) but there was also a small number of students who were quicker than the rest in making mathematical connections who were talking across the whole room. That increased interaction added another layer to the small group interactions because it helped to spread ideas faster across the room. It also, however, had the effect of reinforcing a particular kind of mathematical competence in the classroom–the kind where mathematical competence is associated with being quick or fast at getting answers. And, that is something that I’m really trying hard to break away from–I want students to be able to see themselves as being mathematical brilliant in lots of different ways, not just being quick and fast.

I cannot blame this narrow view of mathematical competence on this large circle classroom arrangement. Certainly a lot of it comes from the larger society and the way that many of us learn mathematics in schools–we are taught to value speed and accuracy and to associate that as being smart. But, I also take responsibility in the way that I have been designing the tasks that students are doing.

The materials I’ve been creating for this Introduction to Number Theory are derived from the 2009 Park City Mathematics Institute Teacher Leadership Program morning mathematics class (book version). Because of the mathematical preparation level of the students in the course, I have removed many pieces of the original PCMI course materials so that the main thrust of the work that we’ve been doing has been to tabulate various number-theoretic functions, determining if they are multiplicative or not, and looking for patterns.

The problems in and of themselves, are not group worthy. They can be done by individuals working on their own, and they are presented in numerical order so there is a sense of completing problems in a sequence, one by one. The design of the materials, therefore, reinforces the very thing that I am trying to avoid: a perspective on mathematical competence that values speed and accuracy. Some students in the class get farther along than others in the course, and it’s become clear who those students are. Other students turn to those students for help, which is great, but I don’t see the reverse happening as often.

At the end of each class, I have been spending about 15 minutes in a whole-group discussion in which students share out their mathematical observations and questions, and give gratitude to each other. I was trying to steer students in pointing out the different ways that we all are mathematically competent. Most of the comments lately have been along the lines of “I’m really grateful to XX for explaining YY to me so clearly.”

All of this is really not germane to teaching a course in a prison; this kind of thing happens in math classrooms all around the world. I’m hyper-focused on creating a more humanizing course mainly because I’m teaching in what might be the ultimate dehumanizing environment: a prison. But, the reality is that we need to work toward more rehumanizing classrooms all around the world.

So, what to do? One way to make a classroom more rehumanizing is to listen to your students and find out what they want and need. I did that last Friday by asking them to answer three questions anonymously: (1) What mathematical connections are you still wondering about in this class? (2) What can I (your instructor) do to make this class more awesome? (3) What can you do to make this class more awesome?

Generally, students’ comments about the class were positive. However, there were some comments about the course feeling repetitive (we keep doing the same kind of activity over and over again) and people wondering what the point of this mathematics is. Both of those I will try to address in this Friday’s class. Not sure yet how as it’s only Tuesday. 🙂 Stay tuned.

Another thing that I have heard from students in this facility is that there are other mathematics courses that are being offered by a local community college, but they are often very introductory courses. Some students are ready for and are yearning for more advanced courses. I have inadvertently compounded this problem by adding yet another introductory course (in number theory), because I assumed that there were students who would not be ready to dive more deeply into mathematics. There definitely are students whose mathematical preparation is not sufficient for them to dive as deeply into this course as I originally intended, but then they are others who are ready for this course and more.

I think I will need to be rethink the course a bit. I will probably shift the course material away from the PCMI materials and incorporate other materials related to number theory. I will need to include more practical applications uses of the mathematics that we’re learning. And finally, I think I will need to more explicitly address the idea of mathematical competencies, perhaps by providing a partial list of the ways that students have been mathematically brilliant in the class.

Link to previous post: Pt1

Teaching a math course inside of a prison is surprisingly unremarkable. Once we get into the classroom and starting doing mathematics, it’s easy to forget that you’re in a prison. We’re just a bunch of people learning mathematics together.

There are only several real complications I’ve encountered so far: (1) logistics, (2) limits on what we can learn about each other, and (3) much greater heterogeneity in my students’ prior experiences with and attitudes toward mathematics.

There are some significant logistical issues to figure out. My “outside students” and I have to drive from our campus to the prison each week (costs covered by Harvey Mudd College), make sure we’re dressed accordingly, don’t have cell phones or any other contraband, have proper identification, and follow any rules dictated by the prison.

There are some limits on what we can learn about each other. My outside students and I never ask for sensitive information from our inside students: the length of their sentences, what they did to wind up in prison, etc. It’s wonderful if an inside student choose to share that kind of information, but we don’t inquire. Both the inside and outside students are asked not to use their last names in this class. This is so that outside students aren’t tempted to look up information about the inside students, and the inside students don’t continue having a personal relationship with the outside students after the course is over (a rule of the Inside-Out Prison Exchange Program).

This past week, I was reminded about the great heterogeneity of mathematical experience that exists in our classroom. As you can imagine in any group of adults, there were are some people with positive attitudes toward mathematics, and some with negative views. Some of these stories came out during our first class meeting when we shared our experiences with each other about mathematics.

This past Friday, I got a bit of a shock. A student asked me, “What’s that little number next to that number?” He had not seen an exponent before. I was taken aback, not by his lack of experience with exponents, but that I had been so oblivious to that up to this point. There have been some exponents that have appeared in the course materials so far, but this question didn’t come up yet. We quickly talked about exponents and the student was fine and continued working. But, I was a bit shocked and still am a bit unsettled.

In the description for this number theory course, I wrote that some fluency with high school algebra would be required. It could be that some people are taking the class anyway, even if they aren’t fluent with high school algebra. Or it could be that some students have taken high school algebra in the past but have forgotten it. Either way, the reality is that there are students in this course that have very different experiences with mathematics. Some are just (re)learning about exponents and others are making sophisticated connections about what they’re learning. It’s my job as the instructor to make sure that we are all learning mathematics together regardless of our prior experiences; that is a pretty big challenge, however.

Other complications I’ve experienced so far are not germane to teaching Inside-Out. For example, if a student misses a class, I have to find ways to help them find out what they missed so that they can participate in class. My outside students and inside students have both missed classes for various reasons. Outside students have missed class due to illness or travel. Inside students sometimes cannot come to class because their dormitories are on “lock down” during our class.

There is one more significant difference between teaching courses at the Harvey Mudd and teaching through the Inside Out program. The pedagogy that we use in this course is quite different. As I mentioned in the first part of this post, I am not lecturing in this course. We do mathematics together through carefully sequenced problem sets that take into account what we learn during each class meeting and what students are wondering about. I do enjoy teaching in this way and wish that more of my Mudd courses could be taught this way. The pressure of having to “cover” a pre-determined body of material in a prescribed amount of time prevents me from fully teaching in this problem-based approach. One day, I would like to figure out how to teach in this humane way in my Mudd courses.

This semester, I’m teaching a course entitled “Introduction to Number Theory” through the Inside-Out Prison Exchange Program. In short, what that means is that every Friday, I take a group of students from the Claremont Colleges (the “outside students”) with me to the California Rehabilitation Center to join 15 incarcerated students (the “inside” students) in learning some introductory topics in number theory.

The California Rehabilitation Center (CRC) is a medium-security state prison for men, located in Norco, California. Here’s a painting of CRC by Sandow Birk (held by the Pomona College Museum of Art).

For over 20 years, the Inside-Out Prison Exchange Program, based at Temple University, has brought campus-based college students with incarcerated students for semester-long courses held in a prison, jail or other correctional setting all around the world. What I appreciate most about the organization is the way it approaches education as a collaborative endeavor and not one in which higher education professors and students go to a carceral organization to “help inmates” out of a sense of volunteerism or charity. Our local Inside Out program was started by Pitzer College and is run in part by a group of incarcerated men at CRC who make up our “Think Tank”. The truth is that I and the Claremont Colleges outside students are learning just as much as inside students are, if not more.

How are students selected? All students (inside and outside) are asked to fill out a questionnaire to find out why students want to take this course and what they hope to gain from the experience. There are several Inside Out courses that the Claremont Colleges offer each semester, and all of us instructors figure out how to allow the greatest number of students as possible to take our courses.

What are the goals of this course? While I do want students in this course to learn some interesting mathematics, the underlying goal of this course is for students to learn something about themselves and others through doing mathematics with each other. In particular, I am hoping that students in this class will have a more nuanced and complete understanding of what it means to be mathematically brilliant so that they can recognize that in themselves and others. This is one of the ways that I am hoping to create a rehumanizing mathematical experience for me and my students.

What is the course like? The Inside-Out Program is very particular about the kind of pedagogy we are to use. Lecture-based courses don’t provide for the kind of mutual engagement and co-learning that the program is trying to encourage. Therefore, I’ve structured my course using materials based off of my work with Bowen Kerins, Al Cuoco, Glenn Stevens in 2009 at the IAS/Park City Mathematics Institute Teacher Leadership Program.

On the first day, I tell students that this course is likely to be very different from any other mathematics course they’ve taken. The class is designed so that students learn from and with each other, not directly from me; I spend almost no time lecturing. Instead, the students work in small groups on a set of mathematical tasks during each class period. I’ve designed the tasks to pique curiosity and encourage students to make conjectures and look for patterns—in other words, the tasks are designed to engage students in doing mathematics the way that professional mathematicians do mathematics.

We basically spend almost all two hours of our time together doing math. I interrupt the work from time to time to facilitate students sharing their observations with each other. We close out the time by having a whole-class discussion and share-out about the (1) questions that we’re still wondering about, (2) interesting mathematical observations that we made, and (3) our gratitude toward one another for the contributions that they made to our learning.

Why number theory? Number theory is a wonderful area of mathematics that has a low threshold for entry and high ceiling for exploration. I have designed the course materials so that only experience with high school Algebra is required. Also, I am not at all an expert in number theory, so that allows me to approach things with a fresh perspective and to be surprised along with my students.

What’s it been like so far? We’ve already had four class sessions. We started by looking at the divisors of numbers and we’re currently thinking about modular arithmetic. Both the inside and outside students have been fantastic. Everyone seems to be deeply engaged in the mathematics and in working with each other.

Ideally, I would have had an equal number of inside and outside students, but right now I have 4 outside students and 15 inside students. We have been arranging ourselves in four groups of 4-5 students. This has worked out really well so far.

Unpredictable things happen all the time that prevent people from attending class. For example, during the first class session, parts of the prison were on lock-down so some students were not able to get to class. I have to be flexible and find ways to fold in students when they are able to attend class.

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I hope to write more about my experiences throughout this semester. These are just some preliminary thoughts that I wanted to jot down.

This teaching and learning experience would not be possible without (1) the training and support I received in May 2018 from the Inside-Out Program, (2) support from administrators at the CRC, (3) the amazing students that are currently in the course, (4) and logistical support from the Claremont Colleges, made possible in part by a grant from the Andrew Mellon Foundation.

Next… Part 2