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…

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…

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…

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…

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…

In calculus courses, instructors often use the end-of-section problems in a textbook in homework assignments or other course assessments. As a result, these problems influence the teaching and learning of calculus. In this study, we examine the levels of cognitive demand of these problems in a mainstream calculus textbook and classify them within…

From 2012 to 2019, the proportion of undergraduate economics degrees denoted as "Econometrics and Quantitative Economics" (STEM-eligible) conferred annually increased from 1 percent to 22 percent. The authors present results from a survey of the 73 institutions conferring at least one STEM-eligible economics degree in 2017 or 2018. They…

An onto-semiotic analysis of the mathematical connections established by one in-service mathematics teachers and university students when solving a problem about launching a projectile using the derivative was carried out. Theoretically, this research was based on the articulation between the Extended Theory of Mathematical Connections and the…

Literature has established that some learners encountered difficulties solving first order ordinary differential equations (ODEs). The use of error analysis in teaching ODEs is believed to make essential contribution towards calculus knowledge development. This paper therefore focuses on analyzing pre-service teachers' (PSTs) errors and…

A few case studies have suggested students' struggles with the "temporal order" of epsilon and delta in the formal limit definition. This study problematizes this hypothesis by exploring students' claims in different contexts and uncovering productive resources from students to make sense of the critical relationship between epsilon and…

We investigate the challenges students face in the transition from calculus courses, focusing on methods related to the analysis of real valued functions given in closed form, to more advanced courses on analysis where focus is on theoretical structure, including proof. We do so based on task design aiming for a number of generic potentials for…

Foundational undergraduate courses in chemistry and mathematics are gateways to a number of lucrative majors and pre-professional programs. Historically, however, students often struggle with these disciplines and can benefit from alternate approaches to examining their learning strategies. This article describes the use of exam…