Progress through Calculus

Mathematical Association Of America, Washington DC

Investigators

Abstract

This project of the Mathematical Association of America will build on the insights from a previously funded project "Characteristics of Successful Programs in College Calculus" in order to continue to explore the factors influencing student success over the progression of introductory mathematics courses that begins with pre-calculus and continues through the full year of single variable calculus. This mathematics sequence is required of most STEM majors. There are two focal areas for the research the project will investigate using three distinct methods. First a national census survey of universities offering advanced degrees in Mathematics, second, case study visits to selected universities, and finally, a nationwide effort of the mathematics community for gathering of longitudinal data. Focal Area 1) What are the programs and structures of the pre-calculus to calculus 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? Focal Area 2) What are the effects of structural, curricular, and pedagogical decisions on student success in pre-calculus to calculus? Success will be assessed on a variety of measures including longitudinal measures of persistence and retention, performance in subsequent courses, knowledge of both pre-calculus 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 mathematics departments in deciding how to allocate resources so as to most effectively improve student success in Calculus and persistence in STEM. 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 pre-calculus to calculus sequence. The project will provide that link, helping departments to more rationally decide how to invest their limited resources. A national census survey of institutions offering graduate programs in mathematics will produce a comprehensive picture of the ways that pre-calculus to calculus sequences are structured and implemented across the country. Detailed case studies will investigate connections between aspects of pre-calculus to calculus 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. Traditional dissemination efforts will actively draw upon the resources and reach of the MAA to broadly disseminate findings to the entire mathematics community.