by Brian Katz
In Mathematics, more than in any other field, themes of gender, race, religion, and sexuality seem irrelevant. We push abstraction further than any other discipline, so ignoring these themes may be necessary for our disciplinary work. And yet, understanding the relationship between these themes and our professional lives or our students lives has clearly become important. I have very few, if any, answers to this problem, but I share my thoughts in the hope that we can collect the kernels of a solution spread throughout the community of practitioners.
This article starts off abstractly but eventually moves to a few anecdotes that I’d like to understand better and finishes with some questions for the reader to consider.
I believe that it is impossible to completely segregate a part of a person’s identity from his/her experience in any domain. When I am a student, a teacher, or a colleague, I am all of myself, not just the parts most important to that role. I find it useful to think of each person as a collection of voices that sometimes say contradictory things. In certain situations, it may be useful to listen to certain voices and turn down the volume on others. As a person who has made it this far in the field of mathematics, I have become comfortable focusing on the seemingly “neutral” voices while working. However, I am always a gay, Caucasian man. I have always thought of myself as Caucasian instead of white or Anglo-Saxon because I look like my Russian immigrant relatives. Since moving to the MidWest to work at a christian-affiliated university, “white” hasn’t seemed nuanced enough. My dark coloring and (Jewish) last name have led to a few awkward conversations that make me think that I am perceived as other by my students and some colleagues. There are a host of other voices/themes that could have appeared on this list; I’m not sure if it is important that all of the themes pertain to parts of my identity that are absolutely beyond my control. I’m sure it’s important to consider both the kinds of themes that are assumed to be visible (like race and gender) and those that are not (like socioeconomic status and sexual orientation).
In some fields there is a vibrant sub-field that connects the discipline to these themes above: history and African-America history, for example. This distinction quietly asserts that the main field is race neutral; research into what is being called “white privilege” has shown that there is actually a huge constellation of measurable benefits enjoyed by the racial group that was previously considered neutral. In short, silence on the issue was previously considered not to be a bias, but that position seems untenable now.
But there are no similar sub-fields of mathematics; I currently can’t see how there could be any. It seems to me that almost every other field contains at least some questions for which these themes are central, so there will at least be a few times at which we as department members and teachers will have the opportunity to discuss the themes as they arise naturally from disciplinary issues. For example, discussions of gender, race, and sexuality will clearly arise in biology because of their relationships to reproduction and heritability; even socioeconomic themes will arise in discussions of public health (if those happen). And yet, these themes are clearly important for individual practitioners, for the hiring and retention of faculty, for the history of mathematics, and for the instruction of students.
Perhaps the actual discipline of mathematics has no generalizable relation to these themes. Even if this were true, it does not mean that the experience of individuals doesn’t connect it to these themes for them; instead it would mean that there are random connections that are either very small or that cancel each other out. It seems to me that our complete silence on the themes, especially in the classroom, assumes that there cannot be connections. I would prefer that we find a way to validate these connections in the classroom instead of ignoring them. Our silence is enough to squelch any discussion, I think. (I suspect that I am speaking too broadly about what happens in classrooms, but it’s all I know.) I have absolutely no idea how to do this without essentially activating stereotype threat and making things much worse.
I also don’t see how the themes arise in a physics classroom from disciplinary query, but I do know that physics is taught with a much greater emphasis on its historical context, which opens many doors. Perhaps this model could offer us some insight. However, I often describe mathematics as “revisionist history”, referring to both the accumulation of “facts” and the way that it’s written. I place great value in clear writing, which can be very different from a narrative of discovery, and on the axiomatic method, which can over-write the hard work of previous scholars by shifting the starting point. I don’t know if I’m willing to compromise this, and I don’t know to what extent it can be blended with a more historically aware style.
I was originally attracted to mathematics because of its abstract, crystalline beauty, because of its emphasis on linguistic precision, and because of the universality and permanence of its truths. In short, my connection is philosophical and aesthetic. In his 2007 TED talk, Steven Pinker argues that aesthetes claim “art is on the decline” because elite art has consciously divorced itself from the human universals that used to be its bread a butter. While I think that he could have been much more careful (and I’d like to read the book “The Blank Slate”), I think his point is certainly a factor. Perhaps this factor is also at the heart of the disconnect between math faculty and students. Are we elite artists who can’t seem to remember that many people come to the studio wanting to make something beautiful and representational?
Enough philosophizing; onward to some real anecdotes.
–My department uses Hughes-Hallett as its calculus textbook for Calc I&II. I have met Deborah Hughes-Hallett, and she is a fascinating woman. Sadly for me, the only part of her essence that I feel like I could articulate to my students is her gender. But I can’t even find a way to bring her up in class. Every scenario I can think of amounts to bringing her up simply to mention her gender. My mother does this occasionally with gay people, and it bothers me that she thinks that it’s an appropriate thing to do. At least I feel free to tell her so, which may not be the case for students to their teacher. In other fields, they refer to texts by their authors’ last names, which can lead to the use of gendered pronouns. In math, we seem to refer simply to “the textbook”. Perhaps I could consciously refer to the textbook by her name to provide that opportunity.
–Twice in the past two years I have had a lower-division course that contained a single black student. Each of them quickly seemed to be isolated from the other students, and I believe that this resulted in a much weaker experience in the class for them. Uri Treisman’s work has shown that students from different racial and socioeconomic backgrounds can have very different expectations about working with peers and that helping them all form useful groups has a huge effect on grades and retention. I have tried to be explicit in helping these classes form groups early, but in both cases the students who needed it most were the least engaged. I don’t know how to broach the subject with a student. If I mention race, I feel like I might be stripping him/her of the right to disconnect race from my classroom, and I’m really worried about tokenism and similar behaviors. If I don’t, it feels like I’m dancing around something, which is probably worse because it connotes that the situation is taboo or even shameful.
–(1) Higher education has a “boy problem”, as the term has been coined. My institution lost more than 10 times as many men as women this year for academic reasons. Most institutions are matriculating significantly more female students than male, and I’ve heard the numbers are worse in terms of applications. (2) Anecdotally, girls used to be silent in math classes; secondary educators have done a good job addressing this issue by supporting the girls. It seems to me that this has left boys with the cultural expectation that they will excel in math without the tools to make it happen. I have taught classes with only a tiny number of men, and they have been visibly intimidated by the women. (3) I recently read an article written for college councilors that put forth evidence that many of the behavioral problems seen in college-aged men are actually strongly related to the development of their gender identities, and many of these behaviors have serious consequences for learning. (4) One of my math classes in college was all male, including the professor. I knew about this going in, and it freaked me out; because of my sexuality, all-male situations tend to make me feel pressured to interpret all behaviors as either confirming or rejecting male stereotypes. I tried really hard to get my female math/sociology friend to sign-up, unsuccessfully. (5) I find myself avoiding student groupings that can be interpreted as being “about gender”, but I don’t really know why. In short, I think gender is really salient in the classroom lives of students but I don’t have a coherent way to think about it.
–I fit several of the gay mannerism stereotypes: spiky hair, high-pitched voice and a singer, lots of wrist movement when I talk. I think my students assume that I am gay, and I prefer this. I am a person who happens to be their teacher; all people have sexual orientations, so I should have one too. (I’m not claiming that these are fixed. I don’t mean to exclude people who actually are asexual, but I may have failed here.) One consequence of the inability to completely segregate parts of the self from the classroom is that students are permitted to include that information as part of their understanding of me, even if we don’t talk about it. It seems, to me, to be questionable ethically to actively try to seem like less than a complete person, especially since I see part of my job as being a role model. Certainly it is part of the goal of college to teach students to engage in academic discourse even about personal and touchy issues, and I think that requires that we model those behaviors and that we be perceived as complete people. However, the student-teacher relationship has a power differential that makes this position very tricky (again, ethically) in certain situations.
I end with a few questions:
- Should the mathematics classroom be a place where we actively engage the students’ race, gender, and sexual orientation (etc) or not?
- Should we, as individual teachers, encourage/allow/discourage/disallow our students to perceive us as people with race, gender, and sexual orientation (etc)?
- What do we need to know and what training could we use to manage these themes effectively?