The distant magnetic field of a magnetic dipole is usually derived via the magnetic vector potential and substantial vector calculus. This paper presents an alternate proof that is less mathematically intensive, and that ties together various problem-solving tricks (the principle of virtual work, observation that only instantaneous quantities…

In a recent submission to "The Physics Teacher," we related how trigonometric identities can be used to find the extremes of several functions in order to solve some standard physics problems that would usually be considered to require calculus. In this work, the functions to be examined are polynomials, which suggests the utilization of…

When learning physics, students need more than just an understanding of mathematical and physical concepts. Integrating the two fields is crucial, as research indicates that students often struggle even when they have a strong grasp of both. In this paper, we use the heat equation as an example from higher education. Given the importance of the…

As attention grows towards the disparities and underrepresentation of minoritized groups within undergraduate STEM education, there is a need for understanding how university calculus program stakeholders perceive the issue of increasing diversity. Calculus is a subject crucial to many STEM disciplines, and thus can play an outsized role in…

This article reports on a study of Kuwaiti college students' knowledge about the concept of functions. It also shows the connections these students make between different representations of functions. The results indicated that most students (96%) were unable to provide a definition of a function and only a third could provide examples of a…

We investigate how an inquiry-oriented, dynamic, open-source calculus textbook shaped one college instructor's planning. We rely on Dietiker et al.'s [(2018). Research commentary: Curricular noticing: A framework to describe teachers' interactions with curriculum materials. "Journal for Research in Mathematics Education," 49(5), 521-532.…

Motivation to learn attracts many researchers in educational contexts. In this study, we propose an instrument tailored towards specifically measuring student motivation in calculus courses at higher education. We outline an extensive instrument development process that was built on (Benson's 1998. Developing a strong program of construct…

The five papers published by Hodgkin and Huxley in 1952 are seminal works in the field of physiology, earning their authors the Nobel Prize in 1963 and ushering in the era of membrane biophysics. The papers present a considerable challenge to the novice student, but this has been partly allayed by recent publications that have updated the…

We conducted a quantitative analysis to determine how the prerequisite path of students taking calculus I impacts their grade performance. We began by investigating the performance of students that took college algebra and trigonometry versus those that took pre-calculus ahead of their credit-bearing calculus I attempt. We concluded that there was…

We present our analysis of 254 Calculus I final exams from U.S. colleges and universities to identify features of assessment items that necessitate qualitatively distinct ways of understanding and reasoning. We explore salient features of exemplary tasks from our data set to reveal distinctions between exam items made apparent by our analytical…

Difficulties presented by students on the concept of instantaneous velocity are well known. This is in part due to instantaneous speed being often defined in terms of the notion of mathematical limit, which may not be clear to many students in introductory physics courses. In this work we present a complementary teaching proposal that can help…

Students are entering postsecondary institutions without the mathematical skills needed to be successful in science, technology, engineering, and mathematics majors (STEM), leading to a shortage of qualified graduates. Consequently, institutions must identify ways to increase satisfaction and performance in mathematics. Mindset theory, with…

In this reflection of teaching, we describe a series of activities that introduce the Taylor series through dynamic visual representations with explicit connections to students' prior learning. Over the past several decades, educators have noted that curricular materials tend to present the Taylor series in a way that students often interpret as…

The COVID-19 pandemic provided students a rare opportunity to use their mathematical knowledge to make sense of a top-of-mind crisis. Based on a report in a major regional newspaper, we designed tasks that require an understanding of infection rates and an interpretation of a misleading claim made in the newspaper. Our analysis of 91 undergraduate…

This paper extends work in the areas of quantitative reasoning and covariational reasoning at the undergraduate level. Task-based interviews were used to examine third-semester calculus students' reasoning about partial derivatives in five tasks, two of which are situated in a mathematics context. The other three tasks are situated in real-world…