Revisiting the Calculus of College Prerequisites

It’s time to push reset on the controversy in California over whether college students should take calculus prerequisites. For more than a year, the debate has been centered on an enrollment pattern pursued by a tiny minority of students—the one-half of 1 percent of STEM majors who take a calculus course despite no record of having taken Algebra II in high school. 

At this year’s MAA MathFest, I led a discussion about the role of prerequisites in calculus success and observed that there is considerable room for consensus on broader issues that affect the majority of STEM students. With a pause on major changes by California’s community college system for the next year, there is an opportunity to focus on those central issues rather than the outlier issues that have dominated discussion. 

First, for those who haven’t followed it, here’s a recap of the debate: Analysts, myself included, have pointed out that sequences of college calculus prerequisites—the current norm for students who are considered unprepared for calculus—may not serve all students well. Given that courses such as precalculus and college algebra may function to weed out students from the calculus sequence, we have argued that more research is needed to understand how to best support success in calculus for students who are considered unprepared to take it when they enter college—including which, if any, prerequisite courses can actually boost their paths to STEM careers. 

Along came a 2024 report by the Research and Planning Group for California Community Colleges (RP Group) that drew scrutiny for one of its many findings: It showed that community college STEM majors without a high school Algebra II class on their transcripts who enrolled directly in calculus passed calculus at higher rates than their counterparts who started in a prerequisite course. As with research on remedial math, much of that effect was due to attrition—that is, students exiting the sequence, even if they were passing courses, before reaching calculus. Vastly different takes on the RP findings sparked much of the controversy. 

One camp—including many equity advocates—concluded that all students should be placed directly into calculus courses, even if they had never taken Algebra II. Prerequisites such as college algebra and precalculus serve as gatekeepers that can block the aspirations of capable students, including large numbers of marginalized students, they argued. 

The other camp—including many math faculty at California community colleges and public universities—objected strenuously to the idea of not allowing students to take prerequisite courses. For students who hadn’t taken Algebra II or a more advanced math course, skipping the equivalent of two years of high school math to take calculus would set them up for failure, they said, even if the students simultaneously take a corequisite course. In a resolution, California State University math chairs even questioned the “integrity and reliability” of the RP Group’s research. 

A few things have become clear: While both sides are passionate, the myopic focus on an outlier group ultimately is more confounding than illuminating. (A similar dynamic—also focused on students skipping Algebra II—hobbled discussions of university admissions policies back in 2023.) As surprising as it may be that some students with no Algebra II or higher math course on their records could be taking and passing calculus, policy solutions should not be driven by data on six-tenths of 1 percent of students—230 out of around 36,000 STEM majors. Or the four-tenths of a percent of students—142, to be exact—who ultimately succeeded in this route. 

It is important to acknowledge what we don’t know, as David Bressoud rightly noted in July 2024. Rather than taking the 142 students as representative of all Algebra II skippers, we need to admit that we don’t know much about those students or how they were able to succeed in calculus. For example, did they find some other means to acquire Algebra II knowledge that doesn’t show up on their transcripts? Were they simply more proficient, more confident, or more interested in math than other students? We may find out more soon, as the RP Group is conducting further research on this question. 

The stakes are high for the interpretation of the coursetaking data: A state law says that students cannot be placed into calculus prerequisites unless they are highly unlikely to succeed without them. Depending on the interpretation of “highly unlikely,” precalculus and college algebra courses could all but disappear from community colleges in the state. Hence the doomsday reaction from some faculty. But the high stakes are all the more reason for dispassion. 

In a stay of execution of sorts, the college system in December 2024 delayed its initial implementation plan, for the time being allowing colleges to require up to two prerequisites for students without Algebra II. Data collected over the next two years will determine future system guidance on prerequisites. 

In the meantime, based on exchanges at MathFest, here are some areas for possible consensus: 

• No placement system is perfect. There is always a risk of underplacement and overplacement.
• Overplacement can be harmful. Faculty often worry about this, because students who struggle (unproductively) in a course may not succeed academically, and may end up leaving the STEM path or leaving college altogether. 
• Underplacement also carries risks—particularly the risk of lengthy prerequisites that lead students to exit the path or college altogether. This problem has been less visible until recently, but it often affects students of color, which is why the equity camp has its focus here. 
• It is possible that some students can succeed in calculus without having taken Algebra II. We can acknowledge this without claiming that the same applies to every student who stopped taking math in high school before reaching Algebra II. 
• It is possible that some students could benefit from taking prerequisites, particularly courses that they haven’t already taken in high school. The RP Group report showed this possibility, even though RP did not find a data category that could identify those students in advance. 
• Lastly, students should not be required to repeat courses that they have successfully passed in high school. Statements from community college math leaders at MathFest suggest that this idea is not controversial.

These agreements would ideally allow us to focus on the vast majority of students—those who have taken at least Algebra II in high school. There is growing evidence that such students can succeed in calculus with some academic support. 

Experiments in California with placing students directly into a form of supported calculus have yielded positive results: Cuyamaca College, where most incoming students have taken at least Algebra II, offers direct placement into a calculus course with corequisite support for all students interested in calculus. Sonoma State University students, for whom Algebra II is an admission requirement, are placed into either a one-semester calculus course or—for those with less preparation—a two-semester version. 

Both campuses have reported success with these patterns, consistent with prior research on precalculus. Independent research is still needed to confirm those findings. More analysis on how to define “highly unlikely,” a sore point for some math faculty, could also be key. 

If corequisite calculus proves to be an effective strategy for students who have taken Algebra II, it would become easier to resolve the question of how best to serve students who haven’t taken the course. A maximum of one prerequisite, as recommended by Complete College America, might be the logical outcome. 

Current policy allows another 14 months of research on calculus prerequisites before any new measures take effect. This is the time for building consensus, not focusing on outliers.