By Luke Tunstall

Something isn’t quite right here, and it’s made me feel uneasy for the last five years.

From my vantage point organizing an institution’s math placement process and creating quantitative support curricula, there’s an elephant in the room that many postsecondary institutions are struggling to address: the increasingly diverse mathematics backgrounds of our incoming students (particularly those with fewer past opportunities to learn mathematics), and the long-term implications of that diversity on the introductory curriculum we offer. If we accept the premise that diversity is generally good, and that all students should have access to a robust and meaningful mathematics curriculum, we can’t ignore the elephant in the room.

By “addressing,” I don’t mean funding summer bridge programs, adding weekly recitations for students with certain placement scores, hiring more tutors, or making content more relevant to students. All of these actions are well intentioned and, in some cases, are what we should always try to do (e.g. connecting content to students’ lives). But they aren’t structural solutions, as they pathologize our students–positioning them as deficient relative to a static standard–rather than the curriculum. We have to confront the reality: Our students today are not those from 20, 10, or even 5 years ago (i.e. prior to the pandemic). Nor is our society.

And that’s OK.

Across the U.S., not only are our students increasingly diverse from a demographic perspective, but they also have more diverse mathematical backgrounds. From the confluence of dual credit programs, AP courses, disparate high-school math offerings, middle-school algebra (sometimes leading to no math in one’s senior year), optional ACT/SAT scores, and a global pandemic that exacerbated existing educational inequities, has emerged an incredibly diverse set of mathematical backgrounds among students in our first-year mathematics courses. Contemporaneous with these changes, diversity, equity, and inclusion (DEI) now reigns supreme in mission statements, enhancement plans, and programming on many college and university campuses. These changes should complement one another. But I don’t think we’re there yet. 

At my own institution, a selective liberal arts college in San Antonio, Texas, we have seen the proportion of students placing into courses below Pre-Calculus (courses which we do not offer!) rise several percentage points in the last two years. In the short term, as a response to the rise in students not placing into our traditional mathematics sequence, we have created a remedial course without a remedial title: Mathematics Skills Workshop. It’s a pass/fail course that serves as an on-ramp to Pre-Calculus and Calculus I. In many respects, it’s similar in principle to bridge programs, or to courses that add additional meeting hours to help “catch students up.” But it adds another semester to students’ mathematics trajectory, and though I’ve genuinely tried to make the course growth-oriented, I will be the first to admit that it’s not a sustainable solution to a larger problem at our institution and many across the U.S.: that we position students with “weaker” mathematics backgrounds as a problem to solve within the confines of our current curriculum–what we’re used to–rather than visioning other possible realities.

For many individuals, myself included, the aforementioned problem seems intractable. How do you construct a new plane while you’re flying the current one? Worse yet, how do you build a new plane if you don’t know what it should look like? I don’t have answers, but in reflecting on the last five years, a few things stand out:

1. Racial diversity (in the U.S.) is inextricably linked to mathematical diversity, so we need to realize that our responses to mathematical diversity can potentially perpetuate racist policies and structures. Here is an example: Suppose that an institution adds College Algebra to its course offerings after determining some students are not ready for Pre-Calculus. Black and Hispanic students are over-represented in the College Algebra course. Whereas Pre-Calculus fulfills the University’s mathematics graduation requirement, College Algebra does not. An effect of this policy is that if a College Algebra student and Pre-Calculus student both decide to switch out of STEM after their first semester, the Pre-Calculus  student is done with that requirement, while the College Algebra student has fulfilled nothing. Though not intentional, one could argue that the policy is racist.

2. Though our students are changing, we don’t have to lower our standards. We can hold high expectations of all of our students while recognizing that as our students and society change, so too should what we expect of them. Importantly, that’s not to suggest that students can’t learn “high-level” mathematics; we know that they can. Carnegie Math Pathways and the Dana Center Math Pathways program exemplify the idea of having high expectations while still meeting students where they are. 

3. A natural follow up question is, what do we do if our students are changing but we shouldn’t make them reach the same finish line as before? We should remember that our students’ needs are changing as well. We don’t have to move the goal post; instead, consider whether we like that goal post at all. Our world is awash in quantitative information, and yet we still ask that they take courses that do little to prepare them for the flood. The quantitative literacy (QL) movement in higher education has certainly taken off in the last two decades, but in many departments, QL courses are targeted at students who don’t need calculus. Research suggests that this is problematic (Elrod and Park 2020). One’s algebra background isn’t all that helpful in a QL course, and so modifying the target audience of a QL-like course could be a viable response to both shifting student backgrounds and societal demands.

While the three remarks above aren’t a schematic for a new plane, I hope that they offer food for thought at your next department meeting or conversation with a colleague.

We work with wonderful students, and they’re constantly changing. Are we?

Luke Tunstall is Director of the Quantitative Reasoning & Skills Center, and Lecturer in Mathematics, at Trinity University. Outside of work, his favorite weekend activities are going to the dog park and watching ice hockey.