The Hidden Cost of Calculus Prerequisites

It’s no secret that we are in the midst of a student debt crisis. Seventy percent of students who receive a bachelor’s degree have education debt by the time they graduate. In 2017, 68 percent of bachelor’s degree holders of the class of 2016 owed $30,800 or more in federal student loan debt. Many approaches to solving this crisis rightly focus on the cost of education itself and addressing predatory private colleges and lending practices. But what else may unnecessarily cost students time and money, and put them at risk of not getting a college degree? 

We know from existing research that lengthy remedial sequences are linked with reduced student success, exponential attrition, and billions of dollars in costs to students. What if Calculus prerequisite sequences have the same problem—creating additional, burdensome costs for students, as well as unnecessary barriers to STEM careers? Addressing this issue is especially relevant in the wake of the COVID-19 disruptions that compromised students’ exposure to advanced math in high school. 

That’s why we looked at math department websites and 2022-2023 course catalogs from all 23 California State University (CSU) campuses and interviewed CSU math leaders as part of Staying the Course: Examining College Students’ Paths to Calculus, a new Just Equations report. Staying the Course analyzes how the CSU system structures its Calculus prerequisite sequences and the impact of these courses on student attrition.

One of the report’s more dramatic findings is the variety in calculus sequence lengths across the CSU system. We found that one CSU campus requires students to take up to four semesters of math before they reach Calculus. Imagine spending two years—or a year and a half if you enroll in summer courses—of your undergraduate career just trying to get to the actual course you need for your degree. Long on-ramps to Calculus were a theme in our Staying the Course findings, with many students taking two or more prerequisites before reaching their first calculus course. 

We also found that sequences and paths across campuses were confusing, and that there is little transparency about how long these paths might be. This lack of transparency can be an issue for students who may not realize that their score on a placement exam could add an additional semester or two to their degree plan and therefore don’t study. As a result, many students are wasting time and money—not to mention the potential mental, physical, and emotional resources required—on these extra courses. 

The strategy of lengthening sequences to improve student success in fact proves wasteful and likely ineffective—assuming that the end goal is actually for students to learn calculus and earn a STEM degree. Part of the problem is the reliance on placement tests to restrict access to calculus courses. While faculty justify this approach as a way to ensure that students admitted to Calculus are prepared to succeed, there needs to be a greater emphasis on how the courses themselves can support success. When you pick out only the highest scorers from a flock of students, you are admitting the fraction of students into a calculus course that have the highest probability of doing well in the course. As it turns out, large proportions of students in college Calculus I courses have already taken a calculus course in high school. 

All of this interferes with fostering and supporting a diverse, talented STEM workforce. Attrition is a major barrier to STEM, disproportionately affecting women and minoritized students. The more unnecessary steps and costs there are on the way to a STEM degree—such as four prerequisite courses to get to Calculus—the more likely we are to lose diverse minds that could bring innovation and change to the STEM fields. 

Staying the Course only scratches the surface of this issue as it relates to Calculus prerequisites. The report calls for further research to ensure that campuses’ prerequisite approaches are effective in promoting success in Calculus and in STEM fields. This means addressing the significant unseen costs on students. In a time when students are facing a financial crisis and an education crisis spurred by COVID-19, supporting students means giving them the most transparent and effective pathways toward their desired degrees.