Mounting evidence of the effectiveness of active learning strategies has prompted many mathematics departments to start engaging in transformational change efforts. Change, however, especially change in instructional practice, is a challenging endeavor. Some departments are using coordination of multi-section courses as a vehicle to enact changes…

In this paper, we investigate leadership related to the instruction of lower division undergraduate courses at five university mathematics departments with strong calculus programs. We use social network analysis to identify patterns of influence on instruction, using the relations: advice seeking, instructional material sharing, discussion of…

This paper reports a study of university students' experiences of learning mathematics in an introductory differential equations course that takes an inquiry approach to learning and teaching. The students are on a trajectory leading toward a bachelor's degree in mathematics to be followed by a year-long teacher education credential program. The…

This study explores how the goals and enactment of three tailored calculus courses, referred to as course variations (standard calculus, life sciences calculus, and physics calculus), at the same university impact students' mathematical identity. In this mixed-methods study, we draw on the framework of figured worlds to interpret how students'…

Precalculus and single-variable calculus courses are a critical early juncture for the success of science, technology, engineering, and mathematics (STEM) students in the United States (US). The default course structure is often a required three-term sequence of precalculus, differential calculus, and integral calculus. In this paper we analyse…

While the number of studies of flipped classrooms has increased, they have primarily addressed the efficacy of using such an approach on student outcomes, often failing to account for the classroom activities and learning theories used to design the curriculum. This study begins to fill this gap in the literature by uniting the at-home video and…

The authors present findings from a recently completed census survey of all mathematics departments in the United States that offer a graduate degree in mathematics. The authors report the viewpoints of departments about characteristics shown to support students' success as well as the extent to which these characteristics are being implemented in…

This paper is based on a large-scale empirical study designed to investigate Calculus I programmes across the United States to better understand the relationship between instructors' concerns about coverage, instructional practices, and the nature of the material covered. We found that there was no association between instructors feeling pressured…

In this paper we address practical questions such as: How do symbols appear and evolve in an inquiry-oriented classroom? How can an instructor connect students with traditional notation and vocabulary without undermining their sense of ownership of the material? We tender an example from linear algebra that highlights the roles of the instructor…

This article presents a case study that details the successes and lessons learned by faculty and administrators at San Diego State University (SDSU) who are in the process of implementing a substantial improvement to the Precalculus to Calculus 2 sequence. Improvement efforts have been informed by national studies of successful programs and center…

We investigate the nature of Calculus I homework at five PhD-granting universities identified as having a relatively successful Calculus I program and compare features of homework at these universities to comparable universities that were not selected as having a successful program. Mixed method analyses point to three aspects of homework that…

The Riemann sum definition of integration is ubiquitous in college calculus courses. This, however, is not the only possible way to define an integral. Here, we present an alternative mean-based definition of integration. We conjecture that this definition is more accessible to students. In support of this proposition we first present a…

We present findings from case study analyses at five exemplary calculus programs at US institutions that offer a doctoral degree in mathematics. Understanding the features that characterize exemplary calculus programs at doctoral degree granting institutions is particularly important because the vast majority of STEM graduates come from such…

This paper provides an exposition of the unfolding and growing complexities of student and instructor gesturing over time. Specifically, it provides an account of how different forms of gestures, all related to the same mathematical idea, can create a chain of signs that support and enhance increasingly sophisticated understanding of one important…

A substantial percentage of college students who enrol in Calculus I intending to take more calculus decide at the end of the semester not to continue with calculus. This represents a huge loss in terms of the need for more students to pursue a major in one of the science, technology, engineering and mathematics (STEM) disciplines. In this report…