This study investigates when and how university students in first-semester introductory calculus interpret multiple representations of the same function. Specifically, it focuses on three tasks. The first task has students give their definitions of 'function sameness', the results of which suggests that many students understand a function as being…

Prior research on students' productive understandings of definite integrals has reasonably focused on students' meanings associated to components and relationships within the standard definition of a limit of Riemann sums. Our analysis was aimed at identifying (i) the broader range of productive quantitative meanings that students invoke and (ii)…

A significant portion of mathematics education research has focused on factors that impact student pursuit of science, technology, engineering and mathematics (STEM). Low rates of STEM student enrollment combined with high drop-out rates have consistently drawn attention from educators, administrators and policy-makers at all levels. Many studies…

Resistor--capacitor (RC) circuit labs help students, but most courses don't include them because of complications and cost. This work presents an easy and inexpensive Arduino-based lab on the charge and energy transfer between two capacitors with different values of the initial electric charge when they are connected through a resistor. Capacitors…

This study investigated how students reason about the partial derivative and the directional derivative of a multivariable function at a given point, using different graphical representations for the function in the problem statement. Questions were formulated to be as isomorphic as possible in both mathematics and physics contexts and were given…

Background and Context: Computer Science has traditionally had poor student retention, especially among women. Prior work has found that student attitudes are a key factor to retention, especially with "weedout" courses such as Calculus. Objective: To determine how student attitudes towards CS 1 and Calculus change over active-learning…

Over the course of the introductory calculus-based physics course, students are often expected to build conceptual understanding and develop and refine skills in problem solving and qualitative inferential reasoning. Many of the research-based materials developed over the past 30 years by the physics education research community use sequences of…

In spring 2018, an inquiry-oriented differential equations course was offered at the Lebanese American University. This paper highlights students' comprehension of some qualitative aspects of differential equations, namely their understanding of the equations and their solutions. It also explores the students' success in moving between the…

We use the Survey of Thermodynamic Processes and First and Second Laws-Long, a research-based survey instrument with 78 items at the level of introductory physics, to investigate introductory and advanced students' difficulties with internal energy, work, and heat transfer. We present analysis of data from 12 different introductory and advanced…

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…

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…

The recent push toward active learning -- engaging students in the learning process -- is meant to benefit students. Yet there is still much to learn about students' perceptions of this phenomenon. We share results from an interview study of students' perceptions of features of two active learning models institutionalized at a large…

Background: We examine the efficacy of an online collaborative problem-solving (CPS) teaching approach in academic performance and student connections with other peers, among first-year engineering calculus students at a Latin American university. Our research uses communities of practice (CoP) to emphasize the social nature of learning and the…

We used student surveys to assess changes in proficiency with integral calculus, calculus self-efficacy, and physics self-efficacy in a second semester course of introductory physics focused on electricity and magnetism. In addition to tracking the fraction of quantitative problems solved correctly on the calculus proficiency survey, we also used…

This study investigated factors influencing Force and Motion Conceptual Evaluation (FMCE) pretest and post-test scores for a sample (N=1116 students) collected in the introductory calculus-based mechanics class at a large eastern land-grant university. Several academic and noncognitive factors were examined using correlation analysis and linear…