Inquiry-Based learning (IBL) is a fairly well-known term in the United States (US) describing a range of student-centered or active pedagogical approaches in mathematics. However, the 'big tent' definitions of IBL mean that there is much variation in IBL users' instructional practices, variation which we set out to codify. Cluster analysis of…

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 examined college calculus instructors' preferences in solving two calculus tasks to examine college calculus instructors' use of important cognitive roots in understanding derivatives of function. Our results showed that only one instructor consistently uses cognitive roots while other instructors either focus on algebraic methods or…

Although the secondary-tertiary transition has been investigated in mathematics education research with different focuses and theoretical approaches, it remains a major issue for students in the transition. With success in a science, technology, engineering, or mathematics (STEM) major at stake, we investigated a novel approach to support the…

Using the tools of praxeological analysis and didactical transposition analysis, the treatments of the Fundamental Theorem of Calculus in one Norwegian, Grade 13 textbook is analysed, with a particular focus on the development of the logos block of the FTC. The terms structure, functioning and utility, first introduced by Chevallard in 2022, is…

Designing and implementing purposefully developed tasks have been linked to students' understanding of mathematical topics. We report on design principles and intentions that guided the development of "inquiry-oriented tasks." Through a qualitative analysis of the tasks, we identified seven themes that encapsulated these design…

We study the augmented reality sandbox (ARSB) as an embodied learning environment to foster meaning making in the context of bivariable calculus. We present the case of Tiago, a first-year bachelor chemistry student, performing a series of tasks based on embodied design, including perception-based, action-based and incorporation-based tasks.…

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…

Studies of discourse are prevalent in mathematics education, as are investigations on facilitating change in instructional practices that impact student attitudes toward mathematics. However, the literature has not sufficiently addressed the operationalization of the commognitive framework in the context of Calculus I, nor considered the…

The National Science Foundation identified a shortage of STEM professionals in the United States. There is a dire need to promote STEM education to secure high-paying and skilled jobs for the country's residents and the overall healthy economy. This shortage is partly due to students' low retention and persistence to graduate in STEM fields. Due…

Researchers have demonstrated a much-needed shift in pedagogical practices to incorporate literacy strategies. This dissertation provides additional empirical evidence to expand the body of research by utilizing a comparative readability analysis that examines the academic language of a popular calculus textbook. A sample from the published…

In this paper we discuss the important Abel's summation formula, which is a very powerful tool for analysing series of real or complex numbers. We derive from it an integral test which may be useful in cases where the classical integral test may not be applied. We also discuss how this new integral test may be used when one is dealing with…

According to the MAA Instructional Practices Guide, deep learning requires student engagement with content both inside and outside the classroom. Hence, mathematics instructors must work to engage students in the learning experience. Higher education research often equates engaged learning and active learning, but what does engaged learning mean…

The expectations gap -- the difference between the level at which high schools prepare students and the preparation colleges expect -- is believed to be accountable for hindering access to, and success in, higher education. It has been largely attributed to misalignment of priorities and lack of communication among policy makers and educators and…

The paper presents analyses of multivariable calculus learning-teaching phenomena through the lenses of DNR-based instruction, focusing on several foundational calculus concepts, including "cross product," "linearization," "total derivative," "Chain Rule," and "implicit differentiation." The…