2024 ASEE Annual Conference & Exposition

Integrating Precalculus into Calculus II and Its Outcomes

Presented at Mathematics Division (MATH) Technical Session 3

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

Authors

Dr. Meiqin Li University of Virginia [biography]

Dr. Li obtained her Ph.D. in Applied Mathematics from Texas A&M University-College Station in 2017. Dr. Li holds a strong interest in STEM education. For example, she is interest in integrating technologies into classrooms to bolster student success, creating an inclusive and diverse learning environment, and fostering student confidence by redeveloping course curricula and assessment methods, etc. Beyond this, her research intertwines numerical computation, optimization, nonlinear analysis, and data science.
Stacie Pisano University of Virginia [biography]

After receiving a Master of Science in Electrical Engineering from Stanford University, Stacie Pisano worked as an Electrical Engineer and Technical Manager at AT&T and Lucent Technologies Bell Laboratories for 16 years, designing and developing telecommunications equipment. She has been teaching at University of Virginia since 2002, and is currently the Director of the Center for Applied Math.
Jennifer Felder Marley http://orcid.org/0000-0001-5234-0224 University of Virginia [biography]

Jennifer Marley is an Associate Professor of Applied Mathematics at the University of Virginia. She received the B.S. degree in Electrical Engineering from North Carolina State University and M.S. and Ph.D. degrees in Electrical Engineering: Systems from the University of Michigan.
Anne M Fernando University of Virginia [biography]

This paper was submitted to PRIMUS and accepted. I thought the participants at ASEE would appreciate the results as well and sought to present the results as a talk or a poster.
This paper was co-authored with Prof. Katie Gurski Phd (Howard University) and Prof. Timmy Ma Phd (Xavier University). Please see bio sketches below:
Anne Fernando (amf2cb@virginia.edu) received her PhD in Computational and Applied Mathematics from Old Dominion University. She holds an MS in Statistics, an MS in Applied Mathematics from the Georgia Institute of Technology. She was formerly Professor and Chair at Norfolk State University, currently Professor and Director for APMA in SEAS at the University of Virginia. Her research areas include Numerical Analysis, epidemiological modeling and enjoys studying mathematics with students.

Katharine Gurski (kgurski@howard.edu) received MS degrees in Physics and Applied Mathematics at the University of Illinois Urbana-Champaign. She earned her PhD in Applied Mathematics from the University of Maryland. She is a Professor at Howard University. She enjoys collaborative mathematical biology research and introducing undergraduate and graduate students to research.

Timmy Ma (tma@xula.edu) received his PhD in Mathematics from the University of California, Irvine. He held visiting positions at Dartmouth College before joining the faculty at Xavier University of Louisiana, where he is currently an Assistant Professor mentoring undergraduate students in their preparation for graduate school and post-graduate careers.
Prof. Lindsay Wheeler University of Virginia [biography]

Dr. Lindsay Wheeler is Senior Associate director and Assistant Professor in the Center for Teaching Excellence at the University of Virginia. Dr. Wheeler develops, implements, and researches educational development programs and courses to support instructors in redesigning courses.

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