Contribution: This article identifies possible ruptures between the ways fundamental notions of exact differential and exact differential equations (EDEs) are employed in mathematics courses and professional engineering disciplines. Background: Engineering students often experience difficulties with mathematics courses which may even lead to…

This study investigates the challenges faced by second-year undergraduate engineering students in understanding Stokes' theorem in vector calculus, focusing on the misconceptions found in interconnected concepts that form its foundation. Stokes' theorem involves the application of line integrals, surface integrals, the curl of a vector field, and…

Why do people shift their strategies for solving problems? Past work has focused on the roles of contextual and individual factors in explaining whether people adopt new strategies when they are exposed to them. In this study, we examined a factor not considered in prior work: people's evaluations of the strategies themselves. We presented…

The anthropological theory of didactics (ATD) provides a lens to view mathematics education by placing mathematical practices within socio-cultural and historical contexts. The significance of institutions, in what regards with educational establishments, societal structures, cultural norms, and historical contexts, influences the perception and…

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…

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…

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…

Given the importance of the ability to use variables flexibly in Calculus and students' difficulties related to various uses of variables, this study examined how variables are treated in calculus class. Data for this study came from graduate teaching assistants' (TAs') classroom teaching, which plays a crucial role in undergraduate students'…

In undergraduate mathematics, deductive reasoning plays important roles in teaching and learning various ideas, and is primarily characterized by the concept of logical implication. This comes up whenever conditional statements are applied, i.e., one checks if a statement's hypotheses are satisfied and then makes inferences. In calculus, students…

Undergraduate students study the topic of binomial series expansion as part of their Calculus course. The purpose of this study was to explore the mental constructions of binomial series expansion of a class of 159 students. Data were collected through a written assessment task by each member of the class. A convenient sample of eleven students…

Our work focuses on the transition from high school to university in the field of calculus. In France, recursive sequences are studied as one of the classical exercises in both institutions. Their studies use different theorems and notions, such as functions, convergence, monotonicity, induction, etc. The work expected at this transition requires…

It is evident that more qualitative research on Advanced Placement [AP] classrooms for students from marginalized backgrounds is needed to uncover how AP practices and pedagogies might better serve students who had been historically excluded from the AP Program. I asked my former calculus students (32 total - 22 participated) from my last three…

The quality of the intra-mathematical connections made by Mexican university students when solving tasks on the derivative was characterized. The typology of mathematical connections and the quality levels of mathematical connections were used. Interviews were conducted based on eight tasks applied to three case studies. The results showed that…

Various studies have concluded that many students have difficulty understanding concepts related to function derivatives. One of the concepts in function derivatives is higher-order derivatives, primarily the nth derivative pattern. This study aims to: (1) identify various types of learning obstacles experienced by prospective mathematics teacher…