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Encouraging Curiosity, Self-Directed Study and Belonging in Penn Students: The Directed Reading Program in Math

Mona Merling

The Directed Reading Program Model

The Directed Reading Program (DRP), now running for an eighth semester in the Penn mathematics department, has a very simple model. The program pairs undergraduates with graduate students for one-on-one reading projects over the course of a semester. Penn advertises proudly their six-to-one student faculty ratio, and even better, there is an almost two-to-one graduate student to undergraduate student ratio across the University. However, undergraduates rarely get a more meaningful interaction with a graduate student in their field of interest than the usual TA sessions and office hours. The DRP offers undergraduate students an opportunity for sustained one-on-one interaction as they follow their own interests and it offers graduate student volunteers an opportunity to be a mentor. During the course of the semester they develop and carry out a reading project, usually covering a topic that is not part of a core class in the curriculum. The Directed Reading Program at Penn’s mathematics department has grown to about twenty-five to thirty pairs per semester with topics covering both applied and pure mathematics. The program website, which lists all current and previous projects, gives a great overview of the breadth of subjects being studied each semester. 

The mentor and mentee have weekly meetings for which the mentee independently prepares for a few hours each week. At the end of each semester, there is a presentation session in which the undergraduates give short talks on what they have learned. This is not viewed as an assessment but as a celebration of the work done over the course of the semester: we provide dinner, we invite the entire department, and presenters invite their friends. I have always attended these presentation sessions with great excitement and every time I have been blown away by the wide range of topics, as well as the delivery and the substance of the presentations. They demonstrate how engaged, dedicated, and high-achieving our undergraduates are, and of course, the excellent mentorship they have received from their graduate student mentors through their learning journey and with preparing the presentations.

The Directed Reading Program offers an experience that deviates from the usual classroom, instead more closely resembling that of graduate school research in mathematics. The undergraduates are building the fundamental skills of self-study, communicating effectively what they have studied during the weekly hour meeting with their mentor, and preparing the end of term presentation. They are also offered the freedom to pursue a topic that excites them while still getting guidance from a more experienced mathematician. Moreover, the interaction with their graduate student mentors offers a glimpse into graduate student life, and often the mentoring extends from math guidance to offering advice about graduate school or summer program applications. The DRP can constitute a ramp to research mathematics. More immediately, the mentors can help their mentees connect with a faculty member to pursue an honors degree. 

The Directed Reading Program was started at the University of Chicago, but similar programs now run in about twenty mathematics departments around the country. There is also a DRP network which hosts a website for sharing resources. After a successful pilot DRP that I co-organized at Penn together with a graduate student, Thomas Brazelton, and our then undergraduate chair Dennis DeTurck in fall 2019, the DRP has been solidly in the hands of our graduate students who mentor the students and organize the program. The program is thriving thanks to the graduate students’ dedication and to the enthusiasm of the undergraduates for pursuing extracurricular opportunities to learn mathematics. My first experience with the DRP was when I was a graduate student myself at the University of Chicago, where I served as an organizer and mentor for the program. I still recognize the influence of my own experience in the Directed Reading Program to this day. This was my first mentoring experience and it has certainly shaped my mentorship style. I am thrilled that our graduate students here also have the opportunity to engage in valuable mentoring experiences through the DRP.

Inclusivity and Belonging in the Mathematical Community

The DRP network page explains how Directed Reading Programs can broaden participation in mathematics, but how without careful leadership it can also reinforce stigmas. Our graduate student organizers have done a fantastic job making the DRP at Penn live up to its potential to be inclusive. This shows in the make-up of the program, in which about half of the participants are women and historically underrepresented minorities in mathematics, in stark contrast with most advanced math classes. I share the opinion expressed by the organizers of the DRP network that “DRPs can help mitigate mechanisms that promote long-standing stigmas—especially those surrounding underrepresented groups in mathematics—that are often triggered in traditional classroom settings.” 

In my experience, the DRP helps build a sense of belonging and offers self confidence for both the mentors and the mentees. The freedom that the DRP offers, the individualized and more personal experience, and the lack of assessment via traditional methods like tests, I think, are all conducive to the wonderful results that we witness during the final presentations because they allow each participant to grow as a mathematician during the course of the semester at their own pace and and let them take charge of the direction. 

I think that sometimes the stress of assignments, deadlines, and upcoming tests can hamper a deeper learning of the material and genuine intellectual engagement. Strict course formats can steer students away from pursuing material that interests them specifically. On the other hand, the DRP gives students the freedom to slow down and really immerse themselves in any little detail, or pursue some tangential question that piques their interest and see where it leads. This is a lot closer to how math research really is, and again, it is sometimes hard to discover the joy of this exploration in the classroom because of the constraints of usual class formats. I am happy that students have an opportunity to experience this side of math in their undergraduate studies at Penn and that the DRP is offering a welcoming environment for it.

I believe that the benefits of a Directed Reading Program are not exclusive to mathematics, and such a program could be a meaningful addition to many other departments. Students commonly associate a range of different fields with high stakes exams and assessments. A program like DRP can provide undergraduates with a much better sense of how we know what we know. By interacting so closely with graduate students, the mentees also get a much better idea of what graduate school and research is like. A Directed Reading Program can make a field more accessible to students who are historically underrepresented in that field, and at the same time offer a hands-on, meaningful mentoring experience for graduate students. At Penn, Wharton has already started a DRP modeled on the mathematics DRP. These programs can encourage a more meaningful learning experience for Penn students in addition to regular classes.

Mona Merling is an assistant professor in the department of mathematics.

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This essay continues the series that began in the fall of 1994 as the joint creation of the College of Arts and Sciences, the Center for Teaching and Learning and the Lindback Society for Distinguished Teaching. 

See https://almanac.upenn.edu/talk-about-teaching-and-learning-archive for previous essays.

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