Expanding Calculus Access
Liz KatzAt highly selective colleges, Calculus has become an unofficial prerequisite. It’s seen as an assurance that students are taking the most challenging courses their school offers.
Accordingly, enrollment in Calculus courses started to rise dramatically in the 1990s and 2000s. Calculus enrollment more than doubled from 7% in 1990 to 19% in 2013. This data also documents that Calculus enrollment is not equitably distributed. 6% of Black high school students took Calculus, compared to 18% of white students. In public schools where fewer than 25% of students are eligible for free lunch, 25% of students take Calculus; in schools where more than 75% of students are eligible for free lunch, only 9% of students do.
Access to Calculus is not a reflection of students’ ability to complete higher-level math courses. Often, it’s a reflection of the middle school students attended. That’s because in order to take Calculus in the senior year, students need to have completed Algebra I before starting high school. That’s fairly standard in independent schools, but just 24% of public school students take Algebra I in eighth grade.
As a result, independent high school math placement in ninth grade often aligns with whether or not a student attended an independent K-8, and because white students are dramatically over-represented in independent schools, white students are typically over-represented, first in ninth-grade Geometry, later in twelfth-grade Calculus, and, ultimately, in selective college admissions.
Let’s go back to that course enrollment data. It’s worth noting that these are pre-pandemic numbers, and 2019 is the last year that data was available for this study. We do, however, have access to the number of students who took the AP® Exams in Calculus AB and Calculus BC. (Of course, the number of students who take the AP Exam isn’t equal to the number of students who completed the course, but that data isn’t readily available.)
Between 2009 and 2018, the number of students taking the AP Exam in Calculus (both AB and BC) rose steadily. Since 2019, however, the number of students taking the same exams has dropped each year. Certainly, the pandemic accelerated this trend–but it’s worth noting that the drop started in the last academic year that was unaffected by the pandemic. The pathway to Calculus seems to be narrowing–and that’s not good for equity or achievement.
Math achievement in high school shouldn’t be determined by the education a student has access to in middle school–and it doesn’t have to be. We’re proud that our offerings help schools expand access to Calculus instead of restricting it. Our summer math courses are used by schools to build equity in their academic programs.
Here’s how it can work in a typical math sequence: Students who enter high school without Algebra I take the course as ninth graders. In the summer before tenth grade, they enroll in One Schoolhouse’s Summer Geometry course, which covers a full year of material in eight weeks. (Frequently, schools subsidize or cover the cost of the course as part of their tuition assistance package.) Those students return to school in the fall of tenth grade, ready for Algebra II, on track for Calculus and the college application process in their senior year.
Another option we see frequently shifts summer work a year later. Students take both Algebra I (in ninth grade) and Geometry (in tenth grade) on campus. With a little more academic maturity, these students enroll in Summer Algebra II and complete a full year’s worth of content in the summer before eleventh grade. They’re ready to take Precalculus as high school juniors–the course that’s our third summer equity-boosting option.
We’re excited to be one of the first programs offering AP Precalculus. When the College Board announced the course, it was with the explicit goal of making an AP mathematics course accessible to students who take Algebra I in ninth grade. There’s another, less obvious reason to consider AP Precalculus as an equity booster: because math is the most tracked subject in American high schools.
When high schools welcome new students in ninth grade, the student’s math placement is an educated guess based on their middle school transcript, test scores, or recommendations. Recommendations and evaluations, however, are subject to unconscious bias. A 2019 study discovered that “teachers displayed no detectable bias when assessing the correctness of students’ solutions; however, when assessing students’ mathematical ability, biases against Black, Hispanic, and female students were revealed.”
The students who are underestimated in the placement process are most likely to be Black or Hispanic girls. As these students goes through their high school math courses, expert teachers will recognize untapped potential. To move to a higher track, however, the student needs to surmount a knowledge gap. Math programs need to provide mobility for students to reach their full potential. For these students, AP Precalculus can fill in the knowledge gap between standard Calculus and AP or honors-level courses in senior year.
Even as the new AP Precalculus course has the ability to open access to AP math courses, it doesn’t question the assumption that Calculus should be the zenith of the high school math curriculum–it cements the assumption instead. Math educators don’t want Calculus to be the solitary endpoint for high school math. The Mathematical Association of America and the National Council of Teachers of Mathematics issued a joint position statement in June 2022 that “a high school calculus course should not be the singular end goal of the PK–12 mathematics curriculum at the expense of providing a broad spectrum of mathematical preparation.” For a great conversation about the high school math curriculum, check out this 2019 Freakonomics podcast episode featuring professor Jo Boaler and College Board CEO David Coleman.
Colleges and universities are also questioning that assumption. How might college admissions offices rethink their allegiance to Calculus? That’s a question math teachers, college counselors, and researchers are trying to answer. A 2021 report sponsored by Just Equations and NACAC, A New Calculus for College Admissions: How Policy, Practice, and Perceptions of High School Math Education Limit Equitable Access to College offers research and proposals to widen the pipeline to advanced mathematics, and to challenge college admissions officers’ assumptions about high school math. Taking Calculus in high school is important for students planning to enter STEM fields, but for others, advanced topics in statistics, data science, or other branches of applied mathematics will be far more useful as undergraduates and professionals.
Until college admissions offices shift their thinking about Calculus, independent schools are stuck with an intractable problem. Highly selective colleges demand that students take Calculus, but students’ ability to take Calculus in high school is inequitable and determined by factors outside of their control. Schools need to ask how they can expand equity and access to provide students with the math knowledge they need to thrive in a rapidly changing world. We’re happy to be one of the answers.
