Today many academics are participating in #ShutDownSTEM, forgoing our usual academic work to instead work on how to improve the current dismal state of STEM (Science, Technology, Engineering, and Mathematics) with regard to racism, especially as it harms black people. This is part of a larger reaction to the uprising sparked by the police murder of George Floyd. If, as we say in the slogan, black lives matter, then black lives matter in the academy and we should back up our words with action.
For my contribution to this effort, I did some preliminary data analysis on one step in the STEM pipeline, namely calculus classes. Mathematicians often like to say that what we do is devoid of political or social content. Perhaps that is true for some of our research—it’s difficult to see, for instance, how set-theoretic potentialism could possibly have anything to say about racism in the USA—but we do more than just research. We also teach. Even if one believes that the content of a calculus class is neutral, that does not mean that the actual practice of how we teach calculus is neutral.
In US institutions it is common for the calculus sequence to act as the gatekeeper to certain majors. The requirement that these majors take calculus is, of course, pedagogically sound; if you need to know calculus to understand X science, then you need to take calculus to major in X science. But these classes often have high fail rates and whether a student gets through these classes is a major determiner of whether they go on to graduate with a degree in that major, of whether they change majors, drop out, etc.
The hypothesis I wish to look at—and which I think the preliminary data support—is that this calculus gatekeeping is not racially neutral. That is, the hypothesis is that mathematics departments are overseeing part of why black people are underrepresented in STEM fields. There is a real problem here, and to solve it we must be willing to face its reality. If that requires giving up the false idea that mathematicians are detached from the political world—detached from culpability in the problems society faces—so much the better.
This blog post is laid out as follows. I discuss some factors I think contribute to calculus—and mathematics more broadly—as racial gatekeeper to STEM. I then give some thoughts on how we might begin to change things for the better. As an appendix I discuss the bit of analysis I did to get some preliminary support for thinking this is a factor.
Why is calculus a gatekeeper?
In this section I give two suggestions for why calculus would be a racial gatekeeper for STEM. Namely, those two suggestions are (1) cultural views on what mathematics is and who can do it and (2) differences in pre-tertiary education. Of course, to a large extent this section is speculative, and I would not claim that these are the only two factors.
Let me discuss the first suggestion first. A common view among Americans is that mathematics is an innate skill; either you have it or you don’t. Anecdotally, a common response to me telling a new acquaintance that I teach math is some form of I hate math/I could never do math/I’m not a math person.
For something stronger than anecdotes, consider this 2015 article in Science about the gender gap in STEM fields. Quoting the abstract (emphasis mine):
Some scientific disciplines have lower percentages of women in academia than others. Leslie et al. hypothesized that general attitudes about the discipline would reflect the representation of women in those fields (see the Perspective by Penner). Surveys revealed that some fields are believed to require attributes such as brilliance and genius, whereas other fields are believed to require more empathy or hard work. In fields where people thought that raw talent was required, academic departments had lower percentages of women.
In this study, mathematics ranked second on disciplines thought to require innate giftedness (with philosophy as number one). To determine this score, the study asked practitioners of a discipline about both their own views and what they think others in their discipline believe. But I hope it is uncontroversial to say, at least in mathematics, that these same attitudes are found more broadly. It is not just mathematicians who think that genius is necessary to succeed in mathematics, it is society as a whole.
The trouble is that genius is neither a gender-neutral nor race-neutral label. The archetypal genius is a white man. The archetypal mathematician is a white man. If students come through our calculus classes with the idea that you’re either a math person or you’re not, then combined with racial stereotypes about who is a math person then that will lead to a racial gap in outcomes. And a racial gap in who succeeds in calculus classes will then cause a racial gap in who gets STEM degrees, due to calculus’s role as gatekeeper.
Now let me discuss the second suggestion. As anyone who has taught calculus at a public university knows, students come into the class with wildly different backgrounds. Of course this is not unique to mathematics classrooms, but it is especially salient due to how mathematics classes build so much on material from previous classes. Some students are amply prepared, having had strong mathematics education from their high school years and before. Others come in under-prepared, and are asked to learn calculus while also learning the algebra they should have already been taught. To use my institution as an example, our mathematics department has recently implemented a learning assistant program for our calculus classes targeted at exactly this problem. We have found that under-preparation is a common reason for students to fail or withdraw, and so we offer them extra-curricular instruction to review/learn for the first time material that should have been taught earlier.
Pre-tertiary education in the USA is far from being free of racial bias. Indeed, there is a high level of de facto racial segregation in our schools. And resources are distributed inequitably, with black students getting less resources than black students. This is compounded by other inequities. For instance consider police in schools and the school-to-prisons pipeline. For some black students the effect of all this is that they do not go to college. But even for those that do, their education is still harmed, causing them to be less prepared for university calculus classes than their more privileged peers. Being less prepared then puts them in a more difficult position in their calculus classes, making them more likely to fail or withdraw. This then means that fewer black students will pursue and graduate with degrees in majors with a high calculus requirement.
What is to be done?
If my two suggested factors in why calculus is a racial gatekeeper are indeed part of the explanation, then this suggests how we might better teach calculus. Let me swap the order and address the second factor first.
This problem is bigger than mathematics departments in universities. As long as pre-tertiary education is racially inequitable, we will see the consequences in universities. But there are steps we can take now.
The most basic is to see that we are part of a larger system, and that we need solidarity across the whole system. As university educators we need to stand with high school and earlier educators. For an example, let me pick on Hawaiʻi. In 2018 there was a ballot initiative to allow the legislature to implement a tax on investment properties to fund public schools. (Unlike most US states, Hawaiʻi does not fund schools through property tax, but rather most funds come from excise taxes.) The union for University of Hawaiʻi faculty opposed this ballot measure. On the one hand, it’s understandable that the union would stand for the immediate financial interests of its members, some of whom would be paying the new tax. On the other hand, better funded elementary and high schools in the state would better prepare students to attend our university, thus making our jobs easier and allowing us to better serve our students. (But this is somewhat moot, as the state supreme court shut down the ballot initiative before it could be voted on.)
But beyond this sort of larger solidarity, we can act locally. To again use University of Hawaiʻi as an example, we can and should do stuff like the learning assistant program I mentioned in the previous section. If students—disproportionately black students—come into our calculus classes under-prepared, then we can do something about that. Rather than saying it’s not our problem we can provide supplemental resources/instruction to help students fill in the gaps from when their high schools underserved them. At the UH Mānoa mathematics department we’ve used undergraduate peer mentors as learning assistants for this, but I’m sure there are other approaches to be tried.
Peer mentors also are relevant for how we could address the other factor. Part of the challenge with breaking the view that mathematics requires innate, unteachable talent is who is presented to students as an example of a mathematician. Mathematics education at and before the level of calculus suffers from an overabundance of dead white guys. Students learn names like Leibniz or L’Hôpital or Euler or Gauss. Among the living, their instructors are disproportionately likely to be white and to be male, as are their TAs, to a lesser extent. We can and should fix the gender/race ratio in mathematics so that mathematicians better reflect the broader population. But it is hopeless to try to fix an early stage in the STEM pipeline by waiting until the end stage is equitable. Mathematics undergraduate populations are more representative of the student population as a whole than mathematics instructors are. I think it’s fair to suggest that a black student who has a black learning assistant helping out at recitation sessions is more likely to see themselves as someone who can do math than the black student who only sees white people teaching them math.
Another way to address the math requires innate talent myth is in how we communicate to our students. Let me use myself as a cautionary example. In teaching calculus, the occasional clever trick comes up. For instance, to determine the derivative of the sine function you can use a trig identity. I want my students to see that there is a logic behind the rule for the derivative, that mathematics consists of structured understanding not just random facts. But I also want to communicate to them they are not expected to reproduce this sort of clever trick on exams (as otherwise they spend time worrying about rather than studying what they do need to know). A way I’ve handled this is to make an off-hand comment like “How would you think of this trick? Well a clever person figured it out once and we can use his work and see that the logic is sound without needing to reproduce his thought process.” I now think, after reflecting in the course of writing this blog post, that this has the side effect of reinforcing the math requires innate talent myth, and so will have to have a new way to handle this sort of thing.
More generally, I think that as mathematics instructors we need to be cautious about the values and assumptions we communicate. We should strive to communicate that mathematics is a learned skill. It is hard, but it is something that with time and effort you can learn. Mathematics is a collective human endeavor. It is not and should not be the exclusive domain of smart white dudes.
Black lives matter. Black mathematicians matter. Let’s try to act like it, and not just say it.
Appendix: Some preliminary data analysis
To make the data analysis manageable for a one day project, I chose to look at just the CUNY (City University of New York) system. My reasons were: (1) CUNY is large enough and has enough black students that I should be able to get a large enough sample size without having to aggregate data across multiple sources and (2) I did my grad work at CUNY, so it holds a special place in my heart. I also chose to restrict to looking only at black students and white students. I chose black students because (1) to limit the amount of work necessary from me and (2) this comes out of the context of Black Lives Matter. Presumably similar analysis applies for other racial minorities. And white students were chosen as the “control group”; they represent how students would act in the absence of racism.
The CUNY Office of Institutional Research publishes data about CUNY demographics. In particular I looked at two sources:
I then had to augment these sources with information about the number of credits of calculus required for those majors. This required looking at academic catalogs for CUNY schools, where I used the 2017–2018 catalogs to match the year for the enrollment data. For most majors I used City College, the flagship college of CUNY, as a representative sample. For a few I had to use other schools: Forensic Science is only taught at John Jay College; Statistics and Actuarial Science aren’t majors at CC, so I used Baruch College which does offer them; For Technology majors I used the Bachelors of Technology degrees from NYC College of Technology. I also excluded from consideration a few majors in the list: Plant Science, Neuroscience, and Fire Science were excluded for having too small of enrollment; General Science and Other CIS were excluded because I could not tell which majors were grouped into these categories. I should also mention for full disclosure that City College does not have an Engineering major, but rather many different Engineering majors—civil, mechanical, etc. Fortunately they all have the same calculus requirement.
The tests I used were simple. I looked at the correlation between the number of calculus credits required and measures of inclusiveness for black students. For the latter I used three measures:
The Enrollment Ratio (ER), the number of black students enrolled in the major divided by the number of enrolled white students.
The Degree Ratio (DR), the number of black students getting degrees in the major divided by the number of white students getting degrees.
The Persistence Ratio (PR). For both black and white students I looked at the ratio of degrees versus enrollment, and then I took the ratio of those two ratios.
I think the first two measures need no explanation, but let me say something about the third. Assuming it takes four years to complete a degree then the number of degrees awarded in one year for a major should be approximately one fourth of the number of students enrolled in that major. If that ratio is smaller than 0.25 it suggests a friction between students entering the major and eventually leaving—dropping out, switching majors, or taking a long time to graduate. By comparing these ratios here for black and white students I get a measure of how much this friction is racially biased.
For the correlation coefficients I used the standard Pearson’s r method. This gives a number between –1 and 1, with 0 representing no correlation, 1 representing a strongest possible positive correlation, and –1 representing a strongest possible negative correlation. My hypothesis is that for all three ratios (ER, DR, and PR) the correlation coefficient will be negative. Indeed, that is what I found.
Accordingly, I find that this preliminary data suggests the correctness of my hypothesis. Of course, these p-values are not great—unsurprising given the limitations of my data. For a stronger answer one would want to look at more data; especially, one would want to look at more than just CUNY, and also look at other racial minorities. It would also be useful to compare to non-STEM majors.
Also interesting would be to expand this from just undergraduate calculus to look at mathematics requirements more generally. For instance, some graduate programs, e.g. physics and economics, require substantive mathematics. Do those requirements function as racial gatekeepers?