Proof: Dr. Hubbard’s Impact Is Continuous
By Ankita Mohapatra (University of Michigan, Ann Arbor, MI)
Interviewee: Diana Hubbard (Brooklyn College (CUNY), Brooklyn, NY)
Dr. Hubbard steps into my classroom wearing colorful earrings and a t-shirt dress, looking decidedly young enough to fold her frame into a student desk. But she smiles and introduces herself.
“Welcome to Math 351, Principles of Analysis. My name is Diana and I will be your instructor.”
She takes pink chalk to the board: A sequence ?? converges to a real number x if ∀? > 0, ∃? such that |??− ?| < ? for n > N. Then she asks us to draw our understanding.
With that first chalked line on the board, Dr. Hubbard challenged me to redefine my understanding of a basic math term. She invited us to leave prejudice at the door, discouraged us from referring to analysis texts we might cross online, and expected us to be fully present in class body and mind every single day. I knew then my perspective on mathematics would evolve throughout the semester.
Michigan Mathematics introduced IBL (Inquiry-Based Learning) courses like Math 351 to champion student involvement in mathematics as an investigative journey. Unlike in traditional lecture, IBL asks small student groups to progress through worksheets with building questions under the instructor’s guidance. Dr. Diana says, “I think the general idea behind [IBL] is you learn math by doing it, not by watching it.” As a non-auditory learner also struggling with attention deficit and hyperactivity, Dr. Hubbard’s IBL methods actively engaged me throughout the class period and motivated me to be an asset to my teammates.
The department awarded Dr. Hubbard its Juha Heinonen Outstanding Postdoctoral Assistant Professor Teaching Award last April and invited her to teach an IBL course called Introduction to Proof for Master of Education students. The course was filmed for future IBL workshops, and portions were observed live at the concurrent UM Math Department IBL Workshop. Dr. Hubbard believes there is something rewarding about active learning built into IBL, explaining that “what [instructors] really want is student ownership of the material – students are more motivated if they really can see themselves in what they’ve produced.”
Dr. Diana’s interest in pedagogical methods is not a standardized commodity. In mathematics academia, large research institutions will hire individuals for their research contributions, with quality of undergraduate teaching likely an afterthought. However, Dr. Hubbard entered the career with equal motivation toward education and research.
“They satisfy different elements of my personality,” she says. “Teaching is more of a people-oriented puzzle… with research you’re a little more at sea.” Dr. Hubbard researches low- dimensional topology and knot theory, exploring questions related to braid theory, contact geometry, and Khovanov and Floer-type homology theories. Despite being relatively young in her mathematical career, her works have been published in five journals, and she’s mentored several students in their own published works.
Dr. Hubbard doesn’t point to her talks and awards when I ask her about her proudest moments. Instead she tells me earnestly, “If you see your students having these ah-hah moments, that’s how you know things are going well.” She points to one example when a female student commented to her after an IBL class that the most vocal, confident people don’t always actually know what they’re talking about, and that she should stand up for what she believes during group work. “I remember being really pleased that she’d had this observation – she was such a strong and creative student, but I think she didn’t think of herself as really strong at the beginning of the course,” Dr. Hubbard recounts.
Since her own schooldays, Dr. Diana has gone beyond the classroom to support budding mathematicians through mentorship and outreach programs. She was the first woman in the mathematics PhD program at Boston College, and a woman named Beth Romano entered the following year. They were the only females until four women joined a few years later. Diana and Beth pioneered the Sophie Germain society to establish regular meet-ups and foster an environment where women felt comfortable and valued. Today, the society has grown under a new moniker and continues generating a space focused on the issues with being a woman in a male-dominated field.
When I ask her about those issues, she tells me about a class where she was the only female student and the professor would refer to her as “Girl” while her male counterparts would be addressed by name. “Those experiences made me expend emotional and mental energy convincing myself that I really did belong, energy that would have been better spent doing math, or having fun, or really anything else at all!” exclaims Dr. Diana. Nonetheless, she points to her wonderful experiences in programs specifically made for and by women in mathematics. Dr. Hubbard will tell you it’s not just about women, it’s about diversity. “Mathematical and pedagogical talent pops up everywhere in all different kinds of people,” she argues. “Doing mathematics involves a lot of creativity, and it’s not like if one person doesn’t think of something, someone else definitely will.” The goal is to encourage every mathematically-inclined person to pursue those interests, unencumbered by roadblocks like race, gender, economics, first-gen status, creed, orientation, or sickness.
Does diverse participation shake anything outside dusty math journals read only by persons with three letters preceding their names? Dr. Hubbard argues, “students in a Calculus I class will go off and become doctors and teachers and lawyers and government officials and parents.” High quality mathematical training, from persons with unique backgrounds and communication styles, resonate with a broader audience. That value never diminishes, since students carry that logical aptitude and appreciation for mathematical balance forward into their careers and lives.
I sat in the last class Dr. Hubbard taught at the University of Michigan. The close of the semester brought two momentous occasions to Dr. Diana’s life: she was preparing for a shift to the Big Apple to start as a tenure-track Assistant Professor at Brooklyn College, CUNY, and she was expecting a baby girl.
Wanting to celebrate the developments, and showcase my newfound comfort around Greek letters, I sourced a gel pen and a thank-you card and wrote:
Pf. for Continuity: ∀ difficulty threshold ε > 0, ∃ professor δ > 0 s.t. if student attends office hours, and/or distance from professor does not exceed Gmail Wi-Fi range, then guidance received subtracted from student’s initial confusion level leaves perception of difficulty < ε.
QED
