Progress through Calculus
This project will build on the insights from Characteristics of Successful Programs in College Calculus to explore the factors influencing student success over the progression of introductory mathematics courses that begins with Precalculus and continues through the full year of single variable calculus. This sequence, required of most STEM majors, will be referred to as Precalculus to Calculus II (P2C2). Two research questions will be investigated using a national census survey of universities offering advanced degrees in Mathematics, case study visits to selected universities, and the gathering of longitudinal data.
What are the programs and structures of the P2C2 sequence as currently implemented? How common are the various programs and structures? How varied are they in practice? What kinds of changes have recently been undertaken or are currently underway?
What are the effects of structural, curricular, and pedagogical decisions on student success in P2C2? Success will be assessed on a variety of measures including longitudinal measures of persistence and retention, performance in subsequent courses, knowledge of both precalculus and calculus topics, and student attitudes.
The answers to these questions will be leveraged to develop a theoretical model that can be used to guide departments in deciding how to allocate resources so as to most effectively improve student success in Calculus. While much is now known about why students leave STEM fields, there is little connection between this theoretical knowledge and the actual structures and programs of the P2C2 sequence. This project will provide that link, helping departments to more rationally decide how to invest their limited resources. Under the auspices of the Mathematical Association of America, a national census survey of institutions offering graduate programs in mathematics will produce a comprehensive picture of the ways that P2C2 sequences are structured and implemented across the country. Detailed case studies will investigate connections between aspects of P2C2 structures and student success. Success will be assessed using a variety of measures that will characterize it along multiple dimensions, including retention and student learning. The CSPCC project identified seven characteristics of more successful Calculus I programs at PhD granting institutions. The PtC project case studies will build on insights from CSPCC by exploring connections between these characteristics (as applied to P2C2) and student success. This design is well suited to provide practical insights into the changes to P2C2 programs that have the potential to produce various types of success outcomes.