One need only consider the cultural impact of the recent film *Hidden Figures* to see the need to expand our cultural understanding of who can engage in mathematics, writes Sara N. Hottinger.

My relationship to mathematics has never been easy, nor has it been consistent. Sometimes I disliked math and did not think I could achieve success. Sometimes I loved mathematics and could not imagine doing anything else with my life. I’m sure I am not alone: we all have math stories to tell.

My earliest memory of mathematics is attending a remedial class the summer after kindergarten. I remember asking my mother what “remedial” meant. By third grade, it was well established that mathematics was not one of my strengths, and I was tracked into the lowest-level math class. In middle school, I began to do better in mathematics, and I discovered, to my surprise, that I enjoyed it.

After doing well on a competency test and achieving high marks in class, I told my eighth-grade math teacher that I wanted to enroll in the honors section of high school algebra. She told me that was not a good idea and encouraged me to take the nonhonors section.

During my sophomore year of college, I declared an undergraduate major in mathematics after a chance conversation with my calculus professor, one of several supportive math faculty members who told me I had a talent for mathematics. I earned a bachelor’s degree in mathematics and graduated with honors, after completing my senior thesis in knot theory. Yet I chose to pursue a doctoral degree in feminist studies, in large part because I never really believed that I could become a mathematician.

My experiences are not uncommon. The scholarship on pedagogy in the mathematics classroom shows, time and again, the impact teachers have on the students in their classrooms. Experiences like mine -- the discouraging middle school teacher or the professor who offers a word of praise -- certainly play a role in determining whether a student succeeds in math.

But mathematical success depends on more than just what happens in the classroom. Our individual relationships to mathematics develop in a complex cultural context, and we need to move beyond the classroom if we want to understand the ways that mathematical success has been limited to a select group. While my own classroom experiences have had a profound impact on my successes and failures in mathematics, it was only when I started to understand those experiences within a larger cultural context that I gained insight into how my own relationship to mathematics influenced my decision to leave the field.

One of the most profound memories I have of my undergraduate mathematics education is of failing multiple times, almost to the point of giving up and changing my major. At the small liberal arts school where I did my undergraduate work, the course that separated the math majors from everyone else was linear algebra. If you could succeed in linear algebra, you could succeed in the mathematics program.

Midway through the semester, I was on the verge of dropping the course and changing my major when things turned around for me. I had struggled to complete the homework and usually had to seek help from my professor. After about six weeks, however, that struggle resulted in a sudden ability to understand the problems and proofs that I encountered in our textbook. It was like a click inside my head -- a light switch turned on in a room that had previously been dark.

That moment taught me many things: the thrill of succeeding after hard work, the seduction of mathematical clarity, and the beauty of mathematical rigor. I enjoyed mathematics before that moment, but I truly loved it afterward.

The experience that I had in linear algebra shaped my understanding of intellectual labor in general. It was a moment I remembered in graduate school as I struggled to understand difficult feminist and cultural theory. I knew that if I kept working at it, the reading would get easier and comprehension would not require so much time and toil.

When I teach theory to my students, I tell them about this moment in my linear algebra class -- the hard work that came before it, the multiple failures and the fact that I didn’t give up, and the moment the light turned on in my head. It has helped me to understand that intellectual ability is not necessarily something that only some of us are born with, as our society likes to tell us; rather, it is something all of us can continually work to improve.

**A Gendered Perception**

Education scholars have found that our perception of natural ability versus hard work is gendered, especially in mathematics. Female students claim they are not good at mathematics because they always have to work so hard to succeed. Male students do not discuss how hard they work; instead they claim their success in mathematics comes naturally. In addition to preventing girls and women from understanding themselves as mathematicians, the perception that mathematical intelligence is a natural ability can serve as a stumbling block for marginalized groups when they find they need to struggle in order to understand.

In general, the men in my undergraduate program were no more successful than I was at mathematics, but what I remember most about the atmosphere of competition I experienced there is the confidence the male students had in the performance of their work, whether or not the end result was actually correct.

When it came time to make a decision about graduate school, the prospect of five to seven more years in a similar environment pushed me toward women’s studies. It has been in my attempts to articulate my experiences as an undergraduate mathematics student and to connect my mathematics education with feminist theory that the seeds of my current interdisciplinary intellectual work in the cultural studies of mathematics were planted.

Whether we love it or hate it, I would argue that each of us relates to mathematics more closely than we do to most other disciplines. This relationship manifests itself not only at the level of the individual but also at the cultural level; in the West, mathematics plays an important role in how we conceptualize ourselves. The growth of mathematical knowledge has been called the greatest feat of humanity. Indeed, we define ourselves as human and as civilized by pointing to mathematics; we understand ourselves in relation to it. Many of us even understand the knowledge we produce in relation to mathematics, no matter what our disciplinary affiliation is. We categorize and, often, hierarchize academic disciplines as either more or less quantitative. Many of us feel the need to justify our findings as qualitative, rather than quantitative, without interrogating the value associated with each.

Where does the intimacy of our relationship to mathematics come from? Why does mathematics figure so prominently in our cultural self-conception? We need to address the question of where and how we get our ideas about mathematics and about who can engage with mathematical knowledge.

Mathematics is central to our cultural self-conception in the West; this becomes clear in the various ways we talk about mathematics and in the stories we tell about the field. We learn about what mathematics is from our math textbooks, from the histories we tell and the images we have of great mathematicians, from representations of the field in popular culture, and from cross-cultural examples of mathematical practice. These areas not only contribute to our general cultural understanding of mathematics in the West, but they also contribute to the construction of mathematical subjectivity in ways that limit access to select groups of people.

While some still claim that women and men have different aptitudes for mathematics, many researchers have concluded that biological sex differences in aptitude and achievement in mathematics are minimal to nonexistent. If differences in aptitude and ability do not necessarily force women out of mathematics, then what experiences do young women have in the field and in our wider culture that cause them to leave mathematics at the undergraduate, graduate and professional levels?

**The Need for More Stories**

Researchers have examined women’s experiences within the classroom and in professional settings in an effort to understand why and how young women become alienated from mathematics. The most interesting manifestation of this work looks specifically at how our culture constructs femininity and mathematics as mutually exclusive -- in ways that ensure that girls and women have a difficult time understanding themselves as mathematical knowers.

Young female mathematics students feel forced to choose between their femininity and their identity as mathematicians. In interview transcripts, they either defend their talent as mathematicians in spite of their femininity or claim their identity as women while explaining away their mathematical achievements. But they clearly do not have the cultural tools available to reconcile both aspects of their identity. Some have argued that this may be one reason why young women who have achieved great success in the field nevertheless drop out of mathematics after secondary school.

We need to tell different stories to expand our cultural understanding of who can engage in mathematics. Such stories emerge from the various representations of mathematical knowers that are constructed in mathematics textbooks, in popular culture and in the histories we tell of the field.

For example, while our math textbooks might include more girl characters than they have in the past, we should ask whether those textbooks construct female characters as active mathematical knowers or as passive recipients of mathematical knowledge. When we include portraits of mathematicians in our history of math books, are we including images of female or non-Western mathematicians?

It is important that we identify how limited the cultural construction of the mathematical knower is in the West and then work to create different and more diverse accounts of mathematical knowing. One need only consider the cultural impact of the recent film *Hidden Figures* to understand how revolutionary such stories can be. We need more of these kinds of stories -- stories that give us multiple ways of engaging with mathematics as a field of study and that expand our cultural understanding of who can be a mathematician.

## Bio

*Sara N. Hottinger is interim dean of arts and humanities and a professor of women’s and gender studies at Keene State College. She is the author of* Inventing the Mathematician: Gender, Race and Our Cultural Understanding of Mathematics *(SUNY Press, 2016).*

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