Integrating Precalculus into Calculus II and Its Outcomes

Meiqin Li; Stacie Pisano; Jennifer Felder Marley; Anne M Fernando; Lindsay Wheeler

Download Paper | Permalink

Conference: 2024 ASEE Annual Conference & Exposition
Location: Portland, Oregon
Publication Date: June 23, 2024
Start Date: June 23, 2024
End Date: July 12, 2024
Conference Session: Mathematics Division (MATH) Technical Session 3
Tagged Division: Mathematics Division (MATH)
Tagged Topic: Diversity
Permanent URL: https://peer.asee.org/47659

Request a correction

Paper Authors

biography

Meiqin Li University of Virginia

visit author page

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.

visit author page

biography

Stacie Pisano University of Virginia

visit author page

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.

visit author page

biography

Jennifer Felder Marley University of Virginia orcid.org/0000-0001-5234-0224

visit author page

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.

visit author page

author page

Anne M Fernando University of Virginia

biography

Lindsay Wheeler University of Virginia

visit author page

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.

visit author page

Download Paper | Permalink

Abstract

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

Citation
Format

Li, M., & Pisano, S., & Marley, J. F., & Fernando, A. M., & Wheeler, L. (2024, June), Integrating Precalculus into Calculus II and Its Outcomes Paper presented at 2024 ASEE Annual Conference & Exposition, Portland, Oregon. https://peer.asee.org/47659

TY  - CPAPER
AB  - 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&#39; 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&#39; 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

  

AU  - Meiqin Li
AU  - Stacie Pisano
AU  - Jennifer Felder Marley
AU  - Anne M Fernando
AU  - Lindsay Wheeler
CY  - Portland, Oregon
DA  - 2024/06/23
PB  - ASEE Conferences
TI  - Integrating Precalculus into Calculus II and Its Outcomes
UR  - https://peer.asee.org/47659
ER  -