2024 ASEE Annual Conference & Exposition

Integrating Precalculus into Calculus II and Its Outcomes

In many calculus courses, a lack of precalculus skills can be a major hindrance to student success. At our institution, lots of students often take Calculus II directly after graduating from high school, with varying levels of precalculus preparation. As a result, many students consistently make precalculus-related errors in their calculus courses, which leads to increased academic challenges and reduced confidence. However, practical constraints like extended graduation timelines and financial limitations have prevented a dedicated precalculus course.

To foster a more inclusive and equitable learning environment, the purpose of this research is to offer precalculus practice opportunities that are accessible to all students, allowing them to improve their precalculus skills without becoming overwhelmed. This is accomplished by integrating precalculus instruction into the curriculum of Calculus II and evaluating its impact.

More specifically, our research seeks to address the following key questions:

1. How, if at all, do students' precalculus skills improve throughout the semester with this intervention? Do such improvements differ based on sociodemographic characteristics (i.e., gender, URM, first generation)?

2. To what extent, if any, does the integration of precalculus and prior precalculus/calculus knowledge associate with Calculus II performance?

3. How do students perceive the intervention? Do these perceptions differ based on factors such as sociodemographic, precalculus experience and calculus experience?

To facilitate the integration of precalculus skills into the Calculus II course, our research team has developed a comprehensive list of precalculus learning objectives. We have also created four different comparable assessment versions that cover all these learning objectives. During each Calculus II class, we utilize three-minute lecture slides to introduce or review one or two precalculus objectives. Students are then given the opportunity to take the corresponding assessment and are allowed up to four attempts to achieve at least 80% mastery of all the precalculus learning objectives.

To assess the effectiveness of this incorporation, we analyzed student performance across the four different assessment versions to gauge improvements in precalculus skills and explore their correlation with calculus final exam performance. In addition, an end-of-semester survey was deployed to investigate students' perceptions and attitudes towards this intervention.

This research project is partially supported by HHMI Inclusive Excellence 3 (IE3) Learning Community, underscoring our commitment to fostering inclusivity and enhancing student outcomes in first year mathematics education