More Students can Succeed in Calculus: The Case for Calculus Corequisite Support

By Francesca Henderson

Francesca Henderson

After earning an A in precalculus, my nephew was excited to take calculus during his first year at a historically Black university in the South. He was the only member of his football team to take calculus, and he felt privileged to be starting his STEM journey with calculus. However, the reality did not live up to what he imagined. Although the lectures were engaging, and he understood the concepts, he was not scoring well on his tests and quizzes. He wondered how it was possible to understand the calculus content but still have low scores. His professor sat him down, full of compassion, and told him, “It’s not the calculus you are struggling with, it's the algebra.”

His initial reactions included anger, confusion and disappointment because, after all, he was spending hours and hours working on problems, meeting with his tutor, and attending office hours without seeing any rewards for his effort. Fortunately, his story has a happy ending. He found a tutor who provided him something called “just-in-time instruction,” meeting with him each week to review algebra topics related to the calculus content he was learning in class. Now, he is one year away from earning his bachelor’s in engineering.

He was fortunate that his university had a system in place for supporting student athletes in their coursework. But what about other students? Each year, hundreds of thousands of students take calculus classes, and a large percentage of them struggle. Because of this, many students do not complete the STEM degrees they had aspired to, and many of those are students of color. A recent report I co-authored, Charting a New Course: Investigating Barriers on the Calculus Pathway to STEM, examines this challenge.

Among the questions probed by the report, published by Just Equations and the California Education Learning Lab, are: What could it look like to provide students who are differently prepared with the support they need to succeed and thrive in calculus courses? What if the system was designed so that students could strengthen algebra skills AND learn calculus concepts simultaneously?

Corequisite models can be a way of doing both. The model provides students access to college-level coursework without requiring them to take non-credit remedial math courses. As research began to show that remedial math sequences were not increasing students’ success in college math, corequisite strategies were designed to create more equitable access for students to take college-level math courses. Several research studies have shown that corequisite models are much more effective than traditional remedial courses in boosting success rates in courses such as college algebra, precalculus and statistics. In Tennessee, according to a report by the Community College Research Center, students in corequisite math were much more likely to pass math compared to students in the traditional prerequisite track. The University System of Georgia found positive results when comparing completion rates of students in their traditional prerequisite model (23%) in 2012-2013 to students in the corequisite model (55%) in 2015-2016. According to Complete College America,“ corequisite remediation is doubling and tripling gateway college math courses in half the time or better.”

But most of the research on corequisite models has focused on courses like College Algebra and Statistics. What do we know and what do we want to know about the effectiveness of corequisites in calculus?

Charting a New Course highlights this question and points to a few programs that utilize a corequisite model in their calculus instruction. These models show different ways of approaching corequisite support for students.

Model #1

At Appalachian State University in North Carolina, a calculus support course is available to all students enrolled in calculus. Students are able to opt into the support course. According to the university’s website, approximately 6 percent of students enrolled in calculus take the course, which offers support with prerequisite skills, calculus concepts, and “self-regulation” to help students adopt college-level study skills. For this model, the corequisite support covers not only math concepts, but also navigating college more broadly.

Model #2

Clarkson University in upstate New York has been utilizing a corequisite model for Calculus I for over a decade. Based on its success, the math department has expanded the model to Calculus II. Clarkson initially places all calculus students into a Co-Calculus support course, which provides a “just-in-time” review of algebra concepts that are needed to learn calculus. An online course syllabus shows a week-by-week progression of the Co-Calculus class, which teaches algebra concepts related to the calculus topics for that week. After four weeks, students have an opportunity to test out of the support course or remain enrolled. This model is different than the first because instead of opting in, students must test out.

Model #3

The University of Cincinnati advises a subset of mainstream calculus students to take a supplementary session, where students work in small groups on tasks created by faculty but facilitated by graduate students. Calculus students who enrolled in a corequisite had higher course success rates than those who did not. The university also has a calculus with precalculus option, in which students enroll in a four-credit calculus section as well as a two-credit-hour supplementary session focused on precalculus. To place into calculus, students need a 740 on the new SAT or a 29 on the ACT, but those with a 700 or 28 may enroll in the precalculus version. The campus is refining this option, because the rates of students continuing to calculus II have been lower than expected.

These models show that corequisites can be structured and implemented in various ways, depending on the students and the college context. More research is needed in different settings to test the efficacy of these programs compared to placing students in traditional prerequisites such as College Algebra and Precalculus. One opportunity is through the California Education Learning Lab’s new request for proposals, Seeding Strategies to Close the Calculus Equity Gap, which will award 25 or more grants of up to $100,000 for STEM departments at California public higher education institutions to address equity gaps in calculus success. The corequisite approach is not the only way to provide support to students toward equity, but it is a model that should be seriously considered by math departments and programs invested in supporting more students to move into STEM fields. The students will likely be very grateful for concurrent support, just like my nephew.

On February 3, 2022 the webinar Closing the Calculus Equity Gap will host a discussion with leading scholars and educators on the role college calculus plays in achieving racial and gender equity in STEM and how educators and policymakers can support student success in STEM pathways. It will be held 12:00pm - 1:15pm PST and is organized by California Learning Lab.

Francesca Henderson is a career math educator serving in various capacities, namely math instructor, curriculum writer, department chair, and research associate. Her current research focuses on the fidelity of which corequisite models are implemented in postsecondary mathematics education.

References

Ran, F. X., & Lin, Y. (2019). The effects of corequisite remediation: Evidence from a statewide reform in Tennessee. Community College Research Center. https://ccrc.tc.columbia.edu/publications/effects-corequisite-remediation-tennessee.html

Mejia, M.C., Rodriguez, O., & Johnson, H. (2020). A new era of student success at California’s community colleges. Public Policy Institute of California. https://www.ppic.org/wp-content/uploads/a-new-era-of-student-access-at-californias-community-colleges-november-2020.pdf

Logue, A.W., Douglas, D., & Watanabe-Rose, M. (2019). Corequisite mathematics remediation: Results over time and in different contexts. Educational Evaluation and Policy Analysis, 41(3), 294-315. https://doi.org/10.3102%2F0162373719848777

Appalachian State University:

http://www.appstate.edu/~marlandes/MathPathways/Calculus1.html

Clarkson University: https://www.clarkson.edu/sites/default/files/2018-05/calculus.pdf

University of Cincinnati:

https://www.artsci.uc.edu/departments/math/courses/continuum/stem.html#course-4 and email communication from Dr. Ricardo Moena, Professor and Director of Entry-Level Mathematics