Math and Social Belonging

Philip Gressman, Professor of Mathematics, is one of the instructors who teaches the largest entry-level calculus course at Penn, Math 104. Over the years, he’s seen students struggle with the rigor of the content and wondered how he could mitigate the anxiety related to those challenges.

“It's a math class that a lot of people take,” explains Gressman. “It's also the last math class that a lot of people take. In that sense, it represents the pinnacle of mathematical expectations for a lot of people.”

Those rigorous expectations can cause anxiety. Self-doubt can spiral: Why am I struggling? Am I the only one finding this challenging? Is there something wrong with me that makes this class so difficult?

Last year, Gressman hatched a plan to help his students improve academically. Instead of focusing solely on numbers and equations, Gressman focused on improving feelings of social belonging. The idea was sparked by his participation in Penn’s Center for Teaching and Learning (CTL), which offers programs to help instructors excel in their teaching. As part of a teaching seminar, Gressman read the book Whistling Vivaldi: How Stereotypes Affect Us and What We Can Do by the social psychologist Claude M. Steele. The book focuses on stereotype threat—a situational predicament in which people are or feel themselves to be at risk of conforming to stereotypes about their social group—and how that perceived threat can detrimentally affect performance.

For Gressman, a lightbulb went on.

“People don't usually think about stereotype threat in the context of a math classroom because it seems sterile in terms of psychological factors. But it occurred to me that my classroom was ground zero, a place where people are experiencing anxiety of a social nature in its strongest form, not in its weakest,” Gressman says. “Steele’s book makes a compelling case that the anxiety about not wanting to be seen as confirming a negative stereotype is something that can consume a lot of mental energy and severely limit a student's ability to demonstrate the skills they already have.”

Due to the nature of stereotype threat, Gressman was particularly concerned about his students who were women, first-generation, or from minority backgrounds. Haohua Lyu, C’21, an international student from China who took Math 104 last year, recalls feeling anxious about the challenging content and fearful that he may “end up strengthening the myth that Asians do better in math than others” or perhaps, even worse, that he couldn’t meet the stereotypical expectations that were expected of him as an Asian.

For Gressman, it’s unexpected and rare for students to worry they might do too well in Math 104, but he’s seen worry about doing poorly derail students entirely. He explains, “Many students labor under the semi-conscious or unconscious burden of knowing that strangers or society at large is ready to write them off at the first sign of a struggle because of harmful and pervasive stereotypes like ‘everybody knows that women are not as good at math as men’ or ‘first-generation students don’t have the knowledge to be successful’.”

In response, Gressman added a stealthy intervention into his syllabus, a short writing and reflection assignment inspired by the article “Psychological insights for improved physics teaching’’ by Aguilar, Walton, and Weiman, which outlines a simple, but effective exercise to help mitigate the effects of stereotype threat and increase feelings of social belonging. Ideally, the assignment is a two-part exercise in which students first read thoughts from the previous cohort early in the semester, and then write their own reflections later in the semester. Since Gressman just launched the intervention last year, his current class will be the first to experience both parts of the exercise. For the first part, students received a Midterm Prep Worksheet that includes the following message from Gressman along with reflections from students:

Many new students in Math 104 find themselves facing anxiety about things like their previous academic preparation, difficulty feeling like they belong in the course, shifting understandings of grades and academic standards, or concerns about keeping up in such a fast-paced course. As time goes on, most find that such anxieties are far more common among peers than it initially appeared and that there is a natural adjustment period during which they come to feel more capable and confident in their own ability to succeed. Last November, I asked students to comment on their experience in Math 104 for your benefit.

Students shared reflections such as: “Don’t worry too much about the amount of work and the pressure of grades (even if you do, everyone is worrying about the same things),” and “There is never shame in asking for help from peers, the TA, and/or the professor.” The exercise shows new students that struggle is normal, asking for assistance and working together helps, and that students are not alone or different in their anxieties. Later in the semester, when students write their own reflections, they help the next class to come, while quelling lingering anxieties.

Lyu recalls finding the writing and reflection exercise helpful in calming his own anxieties. He also credits another unique strategy that Gressman employs to increase social belonging as a gamechanger: the SAIL teaching format. SAIL stands for Structured, Active, In-class Learning and, hence the name, has students actively engage with course content through structured activities during class time as opposed to lecturing. Lyu says it’s rare to find a STEM course that uses the SAIL approach, but he believes more should because it brings “vital elements like social interaction and on-the-ground teamwork into training and practices.”

He adds, “I feel like students face much greater stereotype pressure in classes that don’t use the SAIL approach, as sharing experiences and understanding each other through communication are much harder to do. When everyone works on their own, social expectations can become overwhelming for individuals.”

Increasing social belonging in the classroom has an impact, says Gressman. Using the SAIL format and adding the writing and reflection prompt are by no means an experiment or research study, he explains, but anecdotally, he sees a change. More students are feeling comfortable asking their peers for help. Far fewer students are failing his class. Where Gressman used to see a “really long tail of people who were left out and would do extremely poorly, now the distribution of grades at the end of the semester is a lot more compact than it used to be.”

Research shows that small actions like a writing exercise can have big and lasting positive effects. In fact, an intervention during freshman year can impact an entire academic career and have a huge effect on gender and racial gaps in grades.

Gressman sees his classroom work as connected to broader issues around race and gender in mathematics. “Math has a reputation as being one of the ‘purest’ and most impartial intellectual activities out there, but like anything else, it is a tool that can be as easily leveraged to perpetuate systemic inequities. However, it can also be used in service of correcting them. I hope to be part of that correction.”

Gressman is one of the faculty members working on the Bridge to Ph.D. Program, a mathematics master’s program designed specifically for groups that are traditionally underrepresented. The program prepares underrepresented students for direct entry into the Ph.D. program and provides full funding.

“I would like to see mathematics work harder to identify talent in marginalized or excluded communities and pave the way for more students to be equipped to pursue a Ph.D., should they wish to do so,” explains Gressman. “The Bridge to Ph.D. and being aware of the importance of social belonging is a good start.”