Progress through Calculus
There is a growing body of research pointing to why students are leaving STEM fields in general and first-year mathematics courses in particular. Contrary to common belief, introductory mathematics courses are not serving as a filter for students who are academically unprepared. Instead, students leaving STEM fields often cite poor instructional experiences in introductory level courses as the primary reason for their departure. Unfortunately, many of these studies are focused on either a limited number of institutions, a small number of students, or a single course. What is currently missing is a national portrait of studentsﾒ Precalculus through calculus curricular experiences and how these experiences relate to what is known about effective programs that support student success.
In a previous NSF funded study, Characteristics of Successful Programs in College Calculus (CSPCC), we found that institutions with more successful Calculus I programs shared seven factors, ranging from coordination with pedagogical autonomy, departments supportive of active learning, and substantive graduate teaching assistant training. The overall goal of the Progress through Calculus (PtC) project is to investigate, at a national level, department-level factors that influence student success over the entire progression of the introductory mathematics courses, which we refer to as the Precalculus to Calculus 2 (P2C2) sequence.
The PtC project is being conducted in two phases. Phase 1 is a census survey of all mathematics departments that offer a graduate degree in mathematics. Phase 2, which has yet to begin, will be case studies of departments implementing changes to their P2C2 sequence. Survey analysis includes descriptive statistics (counts, frequencies, means, standard deviations) followed by additional descriptive methods (e.g., Multiple Correspondence Analysis; clustering; Principal Components Analysis) to reveal patterns in the census data. Our aim is to identify models of existing P2C2 programs in their entirety rather than simply identifying patterns within individual components.
Analysis of the census survey data will address the following three research questions:
1. How do mathematics departments prioritize the importance of the seven characteristics found in the CSPCC study?
2. How do mathematics departments characterize their implementation of the practices of successful programs identified in CSPCC study, what changes are being considered, and why?
3. What instructional format and structures (e.g., bridge courses, stretched out calculus) are currently in place in the P2C2 sequence and how common are they nationally?
The findings paint a national portrait of studentsﾒ curricular experiences with Precalculus and single variable calculus, as well as the viewpoints held by departments of mathematics about that experience. We see that departments are not unaware of the value of particular features, but that they are not always successful at implementation. Our work not only reveals what is currently happening, but also what is changing, how, and why. We note that many institutions reported in open-ended questions that they want to make improvements, but are not sure how. This project is revealing not only what is happening in mathematics departments at the national scale, but also illuminating ways of reaching institutions interested in change.
In phase one of the project we intended to conduct a census survey of all departments that offer a graduate degree in mathematics. However, 25 institutions were on the MAAﾒs ﾓdo not email/contactﾔ list and since the invitation to participate in the survey was sent through the MAA, we decided not to include these institutions.