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…

This study proposes methods of reporting results of physics conceptual evaluations that more fully characterize the range of outcomes experienced by students with differing levels of prior preparation, allowing for more meaningful comparison of the outcomes of educational interventions within and across institutions. Factors leading to variation…

Effective mathematics teaching elicits and uses evidence of student thinking to assess progress toward mathematical understanding and adjusts instruction continually to support and extend learning (National Council of Teachers of Mathematics, 2014). However, as teachers march through content in precalculus, they tend to rely heavily on traditional…

This work presents an evaluation of a unified Calculus 1 course in a large Brazilian federal university. By course unification we mean having all the sections following the same weekly schedule, under the same syllabus and common assessment. We analyse two sets of data: pass rates relative to the 9 semesters prior to the unification and to the…

Digital Game-Based Learning (DGBL) demonstrated a positive impact on students' motivation, engagement, knowledge acquisition, and many other areas. However, all the benefits DGBL can offer for the classroom do not seem to be enticing enough to persuade classroom instructors to implement DGBL in their classroom. There is a disconnect between…

This article includes a case study describing our innovative teaching technique of assigning reading journals in a first semester calculus course (Calculus I), as well as an exposition about and recommendations arising from our subsequent experiences implementing similar methods in Junior and Senior mathematics courses. In the primary case study…

Homework is prevalent in mathematics courses, as are cumulative final exams. This study incorporated the memory science concepts of the "testing effect" and "spacing effect" in the homework and final exam of college mathematics courses. By replacing some new homework problems with review problems, students had additional…

This paper presents a case study conducted by two universities seeking to explore Open Education Resources (OER) in their precalculus course. Students not only gained access to their textbook for free on the first day of class, but also Lumen OHM, an online mathematics assessment platform. The majority of students involved in the study were…

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 this paper, we assess the pedagogical approaches we employ in our US-based undergraduate mathematics courses during the COVID-19 pandemic. Our goal is to share anecdotal evidence on the use of math journals, oral exams, and learning portfolios in the synchronous online mathematics classroom. We reflect on our experience using artifacts of…

Inequities in student access to trigonometry and calculus are often associated with racial and socioeconomic privilege, and often influence introductory physics course performance. To mitigate these disparities in student preparedness, we developed a two-pronged intervention consisting of (1) incentivized supplemental math assignments and (2)…

The goal of the present study is to investigate the impact of procedural and conceptual teaching on students' mathematical performance over time. For this purpose, implicit differentiation and integration by parts were taught in two different ways to first-year university students of two different calculus courses: one course with Conceptual…

As university instructors update modes of teaching and student engagement in STEM classes, concerns often arise about student resistance to different methods of teaching and learning. This research examines what it looks like from a student perspective to experience a shift in attitude by exploring the case of Dane, a white male student who…

In this classroom note, we describe the use of a wiki to aggregate student solutions to calculation-based mathematics problems. We outline the setup of the wiki used to support this project, the administrative issues involved in running a wiki, and student reaction to the wiki project. We will describe how students participated, and were assessed,…

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…