As longtime college math faculty in San Diego County, we were taken aback by the news about first-year students struggling with middle school math at UC San Diego.
The idea that students might score poorly on a placement test or get answers wrong in an algebra class was no surprise. That some students, especially those from under-resourced schools, have difficulty with school mathematics is not news to us. As community college instructors, we see a diverse set of students with a wide range of math skills.
What concerns us most is how the campus has been responding. The focus of a recent faculty report seems to be more on measuring just how underprepared students are rather than examining what the campus can do to serve them.
At Cuyamaca College, our mindset has been completely different. Over the last four years, we have redesigned our calculus classes to improve student learning. Until fall 2023, the majority of students who wanted to take calculus started off in precalculus. Since then, students pursuing science, technology, engineering and mathematics majors have had the chance to enroll directly in a calculus class with extra support in the form of a concurrent class. Students have been remarkably successful in this just-in-time approach. We don’t use a placement test and we don’t have remedial courses. Yet the number of our STEM graduates is growing.
For many STEM majors, calculus is the first step in a long sequence of courses. Our redesign has led to significant enrollment growth in Calculus II and Calculus III as well as key physics and engineering courses. We already see a more diverse and more robust path of students positioned to transfer to four-year universities in STEM fields.
Our experience bears out research showing that longer sequences of prerequisite courses often serve to weed students out of STEM pathways. At Cuyamaca, 25% of students who take Precalculus are able to pass Calculus I within two semesters. Since our redesign, students can take Calculus with Support instead: 79% of those taking the new course pass Calculus I in one semester. This is now what the majority of our students do.
Skeptics may ask if the new course is watered down — or less rigorous than what we taught previously or what is offered at other colleges and universities. Our answer is no. When we track these students into subsequent calculus, physics and engineering courses, they are doing just as well and, in some cases, better than students who started in Calculus I without support.
What is different about our courses is the intensive professional development we provide. Faculty work together to shift their classes from traditional lectures to more engaging, student-centered classroom approaches. Initially, our colleagues worried that students would be overwhelmed with the math. We learned that many students were failing because of outside factors — anything from food insecurity to housing instability was interfering. This is why we worked intentionally to create a supportive environment that fosters both learning and belonging.
Our just-in-time approach to the curriculum has been another key to our success. We used to frontload material in precalculus, similar to UCSD’s approach. As every math teacher knows, the students want to know why they are learning the material and where they will use it. This is because precalculus is often taught without context, so students don’t understand how it may prepare them for future math or science courses. The just-in-time approach helps them understand and apply it better.
For example, rather than finding the slope of a secant line in the abstract, students are asked questions about how to find the velocity of a falling pumpkin when it hits the ground or the speed of a rocket going through space at a specific point in time. To do this, we need to find the slope of a tangent line, which requires finding the slope of a secant line and the limits of those.
Plus there are topics in precalculus such as matrices, determinants, vectors and solving nonlinear systems of equations that students don’t need for Calculus I. Any teacher who has taught Calculus II and Calculus III — where these topics are used — will tell you that they have to review those topics in class. So we teach them there, continuing the just-in-time approach.
What is clear to us is that our students are college students. They are here because they want a higher education. We have decided to turn the mirror around and look at our practices rather than focus on their math background to see how we can best support them.
Marshall, Ed.D., is dean of math, science and engineering at Cuyamaca College. Polakoski, Ed.D., is mathematics department co-chair at Cuyamaca College.