Why Some Universities Are Making Calculus Optional
Calculus has been the gateway to STEM majors for half a century. A growing number of universities are reconsidering whether it should be, with data showing that many students who fail calculus would succeed...
Historically, calculus has served as the standard gateway to the STEM majors in US universities for at least fifty years. Many of the engineering, physical sciences, life sciences, computer science, and economics majors require calculus as a prerequisite to the introductory courses in these departments. Additionally, the calculus sequence often serves as a filter determining whether or not a student can continue in a particular major or whether that major is just too mathematically intensive for the student and they should consider other, non-quantitative majors.
US universities are moving to provide alternative paths into STEM majors that do not require students to complete a traditional calculus sequence by the end of their second year of college. This shift to “calculus later” or “calculus alternative” programs is being driven by a growing body of evidence that traditional calculus is not well matched to the mathematical requirements of many STEM fields and that it unfairly keeps too many well-intentioned students with adequate backgrounds in science and in mathematics out of STEM majors because their mathematical training has not been quite right or has come too late. Plan ahead.
What Traditional Calculus Looks Like
The typical calculus sequence for first year university students that are interested in entering into a STEM major is a sequence of three courses that were solidified by university calculus sequences in the 1960s. The typical sequence of courses for the calculus sequence taught in universities is the following: 1) Calculus I (Derivatives), 2) Calculus II (Integrals), and 3) Calculus III (Multivariable Calculus). These sequences focus on the analytical techniques for calculating the derivatives and integrals of functions and are usually taught by focusing on the formal proofs of the limit-based foundations for these calculations. A major focus in these types of courses is on teaching students the many different techniques for performing symbolic manipulations to solve a wide variety of calculus problems.
Contrary to the popular image of the tools of calculus, most scientists and engineers use only the most basic derivatives and a few methods of numerical integration. They recognize when to apply calculus, as opposed to other methods of analysis, and are familiar with a few of the formulas that define calculus. They make little use of the variety of techniques for integration by parts, of partial fractions, or of trigonometric substitution that are stressed in most introductory calculus courses. It works. It works.
The Failure Rate Problem
By far the most commonly-used gateway course in STEM (science, technology, engineering, and mathematics) majors is calculus. Although no single course has a higher failure rate than calculus among gateway courses for which data is available, in part because so many students take it, 25–35% of students who start calculus fail to pass the first course. Indeed, failure in calculus is a major reason that students leave STEM majors, a trend that is particularly true for students from underrepresented groups in STEM majors. A longitudinal study at the University of Florida found that 41% of the students who failed calculus in their first year of college left STEM majors in the two years following their failed calculus course, even though in other respects they would have been good candidates for STEM majors and were even interested in pursuing STEM careers.
On the other hand, so many students fail Calculus only to leave the majors and never return to a STEM major, even if they were adequate in other math classes and had indicated interest in a career in a STEM field. Some numbers: in a longitudinal study of students who did not pass Calculus I at the University of Florida, 41% left STEM majors within two years of failing Calculus I, even though they were otherwise prepared for other STEM majors and had indicated prior interest in a career in a STEM field. That does not seem to be a good use of the time of students who are trying to figure out how to be successful in college and go on to careers in which they will be useful.
What they do at work as opposed to what they use at work is vastly different from the vast majority of calculus “how to” books, including this one.
The Alternative Paths
A number of universities are now offering what could be called alternative paths to the traditional calculus required by engineering, physical and life sciences, computer science and some economics majors at US universities. The University of California, Irvine has created a “Mathematics for the Life Sciences” sequence of courses for students in biology and biochemistry. These students can substitute into the life sciences math sequence after their first year of calculus for fewer credits of pure calculus and, more importantly, for several semesters of biostatistics and modeling.
In response to the lack of appropriate mathematical preparation of their students for computer science, the faculty at Indiana University have been piloting a new “Computational Mathematics” track of study for computer science majors. This alternative track of study for calculus replaces the usual study of the analytical techniques for and formal proofs of derivatives and integrals found in traditional calculus with a focus on the discrete mathematics, numerical methods, and the specific calculus topics most frequently used in algorithmic work.
These programs have impressive outcomes for students as well as universities who offer alternative mathematical preparation for STEM majors and students. For instance, students in the alternative tracks of Calculus pass the class at a higher rate than their counterparts in the traditional Calculus track. In addition, these students also persist in STEM majors at higher rates. Students in the alternative tracks also reported higher levels of preparation for subsequent classes in their STEM major than did students in the traditional Calculus track.
The Curriculum Question
A second issue for those interested in alternatives to the traditional calculus sequence for scientists and engineers is that of the curriculum in subsequent terms. Data from the 2025 evaluation of 15 alternative sequences suggests that in the life sciences and computer science sequences students who had taken statistical-and-modeling sequences as part of their alternative calculus sequence performed as well or better in upper-division courses for their major than their counterparts who had taken a traditional calculus sequence. In engineering, however, the story is quite different: in the mechanical engineering, electrical engineering, and aerospace engineering sequences studied, students performed worse in upper-division courses for their major in those sequences in which symbolic manipulation was not a major component of the alternative calculus sequence than their counterparts who had taken a traditional calculus sequence. The implication of this data is that while alternative sequences to the traditional calculus sequence for scientists and engineers are appropriate for some fields, they are not yet appropriate for others.
In contrast, the majority of engineering programs—mechanical, electrical, and aerospace engineering—still require the traditional calculus sequence as they rely heavily on the students’ ability to perform symbolic manipulation in upper-level courses as well as in their professional careers. The new alternative math tracks are largely confined to the life sciences and computer science where the gap between the traditional calculus required for entry into STEM majors and the calculus used in the students’ major is the largest.
What Faculty Think
It’s been found that in fields that have gone with an alternative math track, most faculty members were at first resistant but are now supporters. Biology faculty find that students who have gone through a life science’s math track for their calculus are better prepared for the quantitative parts of their biology major than their counterparts who had taken traditional calculus. A friend who does evaluation at a university said that the best thing that people can do differently than what they are reading is find out what math their major requires and then see what kind of math track their university is offering for that major.
I’ve long recommended that students entering STEM fields skip the pricey precalc course and go straight to the calculus, as recommended by the Math Association of America in the attached MAA report. And a friend who is an Education professor at UMass Boston reports that an investigation found that the best single step to reduce failures in calc would be to drop the “Failure Rate” category from the university statistics.
Mathematics faculty take quite different views on these new tracks, with some arguing that as long as mathematically intensive majors require calculus, the less mathematically intensive can use “applied math” or “computational methods.” The worry here is that, even in the life and social sciences, the mathematics tracks designed for these fields water down the mathematical content of the courses, in the name of relevance, and compromise the students taking these alternative sequences by not preparing them adequately for those more mathematically intensive majors, should the student decide to switch.
What This Means for Students
For students entering STEM majors, the finding that several universities now offer alternative paths to calculus for STEM majors to consider. Students who are entering Engineering, Physics, or Pure Mathematics can still opt for the traditional calculus sequence. However, students who are entering life science majors or majors in which applied mathematics, statistical thinking, and/or computational methods are more prevalent might fare better in alternative calculus tracks for STEM majors if such a sequence is offered by their university. Moreover, such students might achieve their academic goals more quickly.
Studnets can use these findings to help determine whether or not they should sign up for Calculus in the first place. Since different universities have taken different approaches to Math for different majors, students can investigate the mathematics required for their intended major before even enrolling in university. For example, if the intended major requires Engineering, then students should take Calculus and make sure that they have taken enough credits in pure Math as well. On the other hand, for majors that are more applied in nature and do not require as much Calculus, students can investigate alternative Math sequences that may be offered by the university and can potentially have better outcomes in terms of both success in Math and time to degree.
The Broader Pattern
The calculus reconsideration is part of a broader pattern in higher education: the unbundling of gateway courses from the disciplines they once served. The era when one mathematics sequence served all of STEM is ending. The replacement is more diverse and, in many cases, better matched to actual disciplinary needs. The challenge is in helping students work through the choices and making sure that the alternatives do not become a hidden two-tier system in which traditional preparation remains higher-status than the alternatives.
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