Few disciplines are as polarizing as math. Everyone seems to have an opinion about it, and those opinions usually veer toward love or hate. A new book argues that part of the problem is how we learn to see math and the people who excel at it: typically male, white and relentlessly objective. Inventing the Mathematician: Gender, Race and Our Cultural Understanding of Mathematics (State University of New York Press) might well also have been called “Reinventing the Mathematician,” because its ultimate goal is to deconstruct our individual and cultural ideas about math -- then build them back up again in a more inclusive fashion.
Author Sara N. Hottinger, interim dean of arts and humanities and a professor of women’s and gender studies at Keene State College, examines mathematical history, math textbooks, portraits of noted mathematicians and the interdisciplinary field of ethnomathematics in her quest to prove that we are all mathematical “subjects.” Her approach is scholarly but also informed by an unusual (but in some ways common) personal story: she considered becoming a mathematician before ultimately pursing a career in women’s studies. The result is a highly readable book that might just change math haters’ minds about math (and, perhaps, make some math lovers more open to critical approaches to the field).
"Everyone can do mathematics," Hottinger said in an email interview. "You may need to work really hard at it and try multiple times before you understand. It may come easier to some of us, but all of us can eventually succeed."
Q: You narrowly missed a career as a mathematician, becoming a gender studies scholar instead. Can you share a little bit about your journey through both disciplines, and why you ended up studying gender in graduate school, as opposed to math?
A: I earned a bachelor’s degree in mathematics and women's studies, graduating with honors in both fields. My major in women's studies was self-designed, because my undergraduate institution, at the time, did not offer a women's studies major. The classes I took in women's studies had a profound impact on me. Reading feminist scholarship empowered me; it changed the way I understood the world and my place in the world. During my senior year, I made the choice to pursue a doctorate in women's studies, rather than mathematics. I distinctly remember thinking that if I became a professor of women's studies, I could share that sense of empowerment with my students.
It is important to acknowledge the agency behind the choices I made. It is also important to study the ways in which the choices we make are shaped, in part, by the culture we live in. That is what my book attempts to do. I made the choice to pursue a career as a women's studies professor for very real and powerful reasons. But I also remember other, smaller choices that led me away from a career as a mathematician. During my junior year, my math adviser encouraged me to apply to the Budapest Semester in Mathematics, a prestigious study abroad opportunity to learn mathematics from leading Hungarian mathematicians. I looked into the program and decided not to apply; I did not think I would be accepted. During my senior year, I worried that I would not pass the subject Graduate Record Examination in mathematics and, as a result, I chose not to apply to graduate programs in mathematics -- despite encouragement from my math professors.
Later, when I read the work of scholars Heather Mendick, Melissa Rodd, and Hannah Bartholomew, I found my undergraduate experiences mirrored in their interviews with female mathematics students. … The dominant ways in which we make meaning, as a culture, do not allow an understanding of femininity to easily coexist alongside an understanding of mathematical achievement.
Q: One might think there's little common ground between gender studies and math, but you bridge the canyon, so to speak. Still, do you have any regrets about not continuing to study mathematics? You note the allure of its simplicity, which is hard to come by in other fields.
A: I love mathematics, and I miss it. When I have time (maybe when I retire!), I would love to take more math classes. But I would never give up my career as an interdisciplinary women's and gender studies professor. I like to ask my upper-level students about their feminist aha moment, and I tell them about my own moment of revelation: a single book changed my life. I was 19, enrolled in my first women’s studies course, and the feminist argument in that book radically shifted the way I understood myself, the world around me and my place in that world. When I chose to pursue a doctoral degree in women’s studies, I remembered that aha moment, and I committed to creating moments like that for my future students.
Not only do I love teaching women's studies, but as a women's studies scholar, I am free to pursue the kind of interdisciplinary projects that interest and sustain me. It was 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 were planted. During my senior year of college, I did an independent study on psychoanalytic theorist and philosopher Jacques Lacan and ended up writing my final paper on the connections between mathematical topology and Lacanian theory. I wrote my women’s studies senior thesis on feminist pedagogies in the mathematics classroom and the ways in which feminist approaches to the teaching of math allowed marginalized students to understand and work with mathematical knowledge in innovative new ways.
I continued this work in my doctoral dissertation, where I made the epistemological argument that mathematical ways of knowing are shaped within communities, using a series of historical case studies to support my argument. And, now, in this book, I consider the cultural construction of mathematical subjectivity and argue that mathematics plays a significant role in the construction of normative Western subjectivity and in the constitution of the West itself.
Q: Even smart people (e.g., Larry Summers) seem to believe that women are inherently worse at quantitative fields than men. Why does this myth, if in fact it is a myth, persist?
A: In my book, I trace the relationship between the construction of mathematical subjectivity and the much broader construction of the subject in Western culture and of the West itself. Mathematics is central to our cultural self-conception, and this becomes clear in the various ways we talk about mathematics, in the stories we tell about the field. These stories both underlie and work to reproduce the discursive construction of the normative subject in Western culture. This intimate relationship between mathematical subjectivity and normative Western subjectivity is why many educators understand achievement in mathematics to be a “gateway” to success in the world. It is also why we, as a culture, have an investment in limiting who can be successful in mathematics. If we maintain a myth that only certain groups can be successful at mathematics, then, as a culture, we also limit access to full subjectivity to people in those groups.
Q: What is the stereotype or common portrait of the mathematician? And why is math incompatible with notions of femininity?
A: Although many mathematicians will acknowledge that this is not at all how they work, mathematics is conceived in our culture to be an individual cognitive activity, where the mathematician, working in isolation, discovers a mathematical theorem using logical, rule-based reasoning to develop and modify the work of those who came before him. Many feminist theorists have argued that a close association exists between masculinity and reason, whereby those traits that are considered central to the activity of reasoning -- logic, neutrality, a lack of emotional connection and a separation between the knower and the object of knowledge -- are also stereotypical traits of masculinity. Thus, reason can only be achieved by denying those traits which are stereotypically considered feminine -- empathy, creativity, intuition, embodiment and connection. Yet to reason well is an achievement that defines what it means to be human, to be a subject in Western culture. Thus we have a very difficult time reconciling the ability to reason, which is a central component in the construction of subjectivity, with our understanding of femininity.
Because mathematics is understood to be the ultimate manifestation of the human ability to reason, mathematical achievement is a clear marker in the construction of an ideal subjectivity. If these multiple associations -- between reason, masculinity, subjectivity and mathematics -- are teased apart, we can better understand why mathematical subjectivity and the ability to succeed in mathematics is so difficult to achieve for those in marginalized groups. For example, if mathematical subjectivity and the ability to reason is constructed within Western culture as masculine, then women will continue to find it difficult to see themselves as mathematical subjects. Women will have to choose between being good mathematicians or being "proper" women. A number of studies have shown that this is, indeed, the position that many girls and women in mathematics find themselves.
Q: What are the cultural and disciplinary consequences of such a myth -- perhaps more aptly what you call "normative mathematical subjectivity" -- especially on historically marginalized groups?
A: If mathematical subjectivity is constructed in ways that prevent women from seeing themselves as mathematical subjects, then we also limit the ability of women to see themselves as full subjects in the broader sense, as well. This is true for people of color, as well. In one of his recent publications, David Stinson’s research on the ways in which African-American students must negotiate what he calls the “white male math myth” demonstrate that for African-American students there are a series of cultural discourses that work to limit who can understand themselves as mathematical knowers.
Erica Walker also makes a powerful argument that mathematical identity needs to be reconciled with ethnic, gender or other identities and that students of color, for example, have to sometimes compromise their ethnic identity in order to fully embrace their academic identity. In much the same way that feminist education scholars have shown, via discourse analysis, the incompatibility between femininity and mathematical achievement, both Walker and Stinson show the complex ways successful black mathematics students must accommodate, reconfigure or resist the discursive construction of a normative white, masculine mathematical subjectivity. By limiting access to mathematical subjectivity in this way, we also limit access to Western subjectivity.
Q: What can teachers of math do to cast off cultural baggage surrounding math and gender?
A: I would argue that teachers of mathematics are doing quite a bit already to ensure that girls are succeeding in mathematics. Recent research shows that girls’ achievements in mathematics stay on par with boys through secondary school. There remains, however, a significant disparity between young men and young women’s participation and success in mathematics at the postsecondary level, leading to what many now call the leaky mathematics pipeline. Young women start dropping out of mathematics during their undergraduate and graduate education.
I argue in my book that we need to expand our focus beyond the classroom and consider the wider cultural discourses that shape our relationship to mathematics. One of the first narratives about mathematics that needs to shift is the one that says only some people can be successful at mathematics. Think about the fact that it is perfectly acceptable for people to say things like, "I just can't do math." Such claims then serve as justification for poor performance in mathematics and the eventual decision to stop taking math classes altogether. We would never accept an equivalent claim about reading, right? Our assumption is that every child can read. Some may have to work harder at it, but eventually everyone should be able to read. We need to start making the same assumptions about mathematics.
I would also love to see more representations in our wider culture of women and people of color working at and succeeding in mathematics. The phenomenal success of the film Hidden Figures is a testament to the power of such representations. But what Hidden Figures also teaches us is that we need to expand our understanding of the history of mathematics. Right now our histories of mathematics center around a narrative of discovery. Only those mathematicians who made a great mathematical discovery or advanced knowledge within the field are counted in those histories. Telling histories of mathematics in that way discounts the many, many women and men who advanced mathematics through excellent, innovative teaching, through translating complex mathematical texts, or through the kind of hard, daily mathematical labor we see represented in the movie. We need more varied stories in our culture of what it means to be successful as mathematical knowers and practitioners.
Q: You have two daughters. How do you approach math at home?
A: I have tried to focus as much, if not more so, on numeracy, as I have on literacy. When they were younger, I played number games with my girls and tried to cultivate their interest in working with patterns and problem solving. When my older daughter started school, I started talking about how much practice is needed to succeed in mathematics. When she started working on a new concept in mathematics and was having difficulty, I told her that the struggle she experienced was normal and expected. And I told her to keep struggling, that when she has struggled enough, understanding will come.
Because that narrative has been central to how we talk about mathematics, she is rarely frustrated by new mathematical concepts these days. She will occasionally ask for an explanation, but I more commonly get a request for more practice problems. She knows now that if she just practices a little bit more, then she will succeed. And I do, of course, have a lot of books and stories and images of women who have been successful at mathematics. The importance of having role models cannot be discounted.