**by David Cruz-Uribe, Department of Mathematics**

Diversity and inclusion really have nothing to do with the subject of mathematics, per se. Mathematics is among the most abstract and universal of human disciplines. Pure mathematicians work hard to strip their subject of anything contingent, anything to close to the “real world.” Attempts to decolonize mathematics, or to construct a feminist algebra [1] notwithstanding, pure mathematics is remarkably free of cultural influences.

This does not, however, let math instructors, or those who teach STEM subjects entirely off the hook. There are two things that intrude upon the ideal nature of our disciplines: they are applied to the real world, and they are done by human beings. While pure mathematics exults in its abstraction, the discipline of applied mathematics is firmly committed to applying these abstractions to analyzing real world phenomena. And, more to the point, even in pure math courses, particularly at the lower level, students demand that we give “real world” examples. This requires instructors to be cognizant of who their students are and what is in their background knowledge coming into our classes.

Let me begin with a silly but real example. In an introductory calculus course, I realized as I was finishing an exam that it totaled 99 points. I didn’t want to increase the value of any particular problem, so at the end of the exam I added a one point question:

*True of False: Brett Favre is the greatest quarterback who ever lived.*

I was a diehard Packer’s fan, Favre had led the Packers to two consecutive Super Bowls, so I figured that this was a perfectly reasonable question. During the exam, one of my best students came up and said to me, in a somewhat worried voice: “*I don’t know who Brett Favre is*!” Oops. I solved this problem by marking the problem incorrect if they put false but giving everyone the point regardless of their answers. But in retrospect, I realized that what I thought was well known, my cultural capital, was not automatically shared by my students. Since then, I have tried to make sure that my examples are either familiar to all my students, or I explain them in class. Thus, when discussing the hyperbolic paraboloid [2], if I compare it to a Pringle’s chip, I make sure my students know what a Pringle is. (Turn about is fair play: once, a British student responded by asking, “*that’s a brand of crisp, isn’t it?*” I had to ask her what a crisp was.)

Math instructors also need to realize that how we perceive things is not necessarily how our students do. A pointed example of this comes from my undergraduate days. One of the graduate TAs was teaching calculus and decided to “liven up” the standard homework problems with a series of word problems about the misadventures of the royal baker. Unfortunately, he started with the mildly off-color — a problem about working with “dill dough”— and went rapidly downhill from there. But, while some students found it funny, others were put off by it, and there were complaints. I am not sure how the chair or graduate director handled this, but the story problems came to a sudden end.

I am pretty sure he meant nothing in particular by this: I knew him fairly well and he was a nice guy, except for a sense of humor that was eccentric even by the standards of mathematicians. But what was funny to him was crass and offensive to at least some of his students. This is easy to avoid, with a bit of care. When teaching introductory statistics, I created a series of problems and examples about Wanda the waitress and her boyfriend, Bob the Barista, but I worked at keeping them light-hearted and inoffensive. (After one semester, a student asked on his student evaluations if Bob ever proposed to Wanda.)

At this point, a more curmudgeonly reader might be fuming that I am demanding that all instructors be politically correct — and maybe I am, depending on what you mean by that particular shibboleth. But really, a big step towards diversity and inclusion in the classroom is recognizing that some (many?) of our students are not like us, having both different cultural knowledge and expectations, and different perceptions of social interactions. Acknowledging this, and treating them with dignity and respect will go some way to making the math (or STEM) classroom a welcoming place.

## References

[1] *Toward a feminist algebra,* Mary Anne Campbell and Randall K. Campbell-Wright, in Teaching the Majority: Science, Mathematics, and Engineering That Attracts Women, edited by Sue V. Rosser. New York, Teachers College Press, 1995.

[2] See https://en.wikipedia.org/wiki/Hyperbolic_paraboloid

*David Cruz-Uribe is Chair of the Department of Mathematics. *