College Calculus courses are widely-known as “weed-out” courses, and literature reviewed in Just Equations’ recent report—by myself, Melodie Baker and Francesca Henderson in partnership with the California Education Learning Lab—substantiates that reputation. But what can colleges do to better support students taking Calculus and pursuing an interest in STEM (science, technology, engineering, and mathematics)?
Precalculus courses would seem to be the obvious answer—until one looks at actual research. Studies highlighted in our report, Charting a New Course: Investigating Barriers on the Calculus Pathway to STEM, note that placement into college precalculus courses is far from a prescription for STEM success. And, alarmingly, this problem seems to exist in the shadows of many college math departments.
First, the problem: We learned, thanks to a 2015 report by the Mathematics Association of America, that students who take Precalculus are more likely to leave STEM fields. Three studies spanning public universities in four states found that at least a third of students who were successful in Precalculus nevertheless did not continue to Calculus, a requirement for STEM majors. At Arizona State University, for example, 43 percent of declared STEM majors who had earned an A in Precalculus opted out of Calculus. Nearly two-thirds of ASU students in the physical and life sciences who earned a C or higher in Precalculus left those paths. Similarly, at Texas Tech University, a third of students earning a B or higher in Precalculus didn’t take Calculus I.
Equally concerning, even students who do progress from college Precalculus to Calculus do not appear to benefit. In fact, Precalculus may lower their performance, according to a 2014 quasi-experimental study based on records of more than 10,000 Calculus I students. It found that students with weaker high school preparation had a slight but not statistically significant benefit from Precalculus (again, if they took Calculus), but better-prepared students scored six points lower in Calculus if they began the sequence in Precalculus (Sonnert & Sadler, 2014).
Our own analysis of data shared by California’s higher education systems found that Black and Latinx public university students were more likely than other students to take Precalculus before enrolling in Calculus. Students with such enrollment patterns were also less likely to complete STEM degrees. (However, these were correlational, not causal, links, and we had no information on students’ prior preparation. The trends at community colleges were less clear, due to smaller cell sizes for students enrolling directly in Calculus.)
None of the research pinpointed the reasons for Precalculus’ low performance. But interviews we conducted surfaced some theories. One was that placement in Precalculus sends discouraging messages to university students who have already taken the course in high school. Another is that the challenging but dull content turns students off of math and STEM.
But understanding the reasons and what to do about them would require math departments to be focusing on this question. Troublingly, very few are. There is a tendency among math faculty to fixate on course success rates, leaving the more salient issue of students not progressing to the subsequent course in a sequence a largely invisible problem.
In their 2015 chapter, David Bressoud (current director of the Conference Board of Mathematical Sciences) and Eric Hsu (current math chair at San Francisco State University), called out this problem, writing: “Whatever placement policy is chosen, it must be monitored continually. This includes looking at correlations between placement scores and grades in Calculus I… It makes no sense to have a policy in place that directs certain students to Precalculus if Precalculus is, in fact, a dead end for most of the students who take it.”
About a decade ago, similar findings caused higher education leaders to conclude that traditional approaches to remedial education were doing students a disservice. New approaches such as multiple-measures placement and corequisite courses have been replacing traditional remedial math strategies based on a growing body of rigorous research demonstrating that these approaches enable more students to pass college-level math courses.
It’s essential that math departments individually and collectively undertake similar research to examine whether—and, if so, why—Precalculus functions as a dead end.* Possible solutions might include changing the Precalculus course content, modifying instruction to include active learning, as well as mindset strategies to bolster students’ math identity and sense of belonging.
But, if the ultimate goal is to succeed in Calculus, changing the math sequence itself might be more promising. Wright State University in Ohio has designed a math for engineering course in lieu of Precalculus that has greatly increased student outcomes in engineering. Some universities, including University of Cincinnati, Appalachian State University in North Carolina, and Clarkson University in New York, are designing corequisites and other versions of Calculus to support students with weaker preparation. But others, such as San Diego State University and University of California, San Diego are doing the opposite: They are addressing the problem by lengthening the course pathway to Calculus to provide students more preparation.
It is unlikely that such vastly different approaches are both promoting students’ success in STEM. But which is most effective and are there versions of Precalculus that clearly support success in Calculus? The answers can’t become visible until the current problems with Precalculus are taken out of the shadows.
*Just Equations continues to look for rigorous research on the pathways to Calculus. We encourage readers to share with us any research that may shed light on the course pathway to Calculus at firstname.lastname@example.org.