This paper is a continuation of an earlier discussion in this journal about adhering to principles of mathematics while presenting function graphs in physics. As in the previous paper, the importance of the vertical line test was examined, this paper delves more in-depth, and it pinpoints a need for presenting graphs with a continuous rate of…

Recently, Wilmer III and Costa introduced a method into the mathematics education research literature which they employed to construct solutions to certain classes of ordinary differential equations. In this article, we build on their ideas in the following ways. We establish a link between their approach and the method of successive…

Flipped instruction has been flaunted as a pedagogical strategy that supports improved learning and retentive abilities of students. Nevertheless, one of the twin challenges reported in the literature, students' failing to complete preparatory work, impedes the efficacy of the model. Thus, learners' motivation and attitude to work are essential…

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…

Studying the effectiveness of remedial courses in higher education has attracted a lot of interest from educational researchers and practitioners. Remediation is associated with significant economic and social costs while the results are usually dubious. In this paper, we apply a widely used method called Regression Discontinuity Design (RDD) to…

Logarithms, pivotal in advanced mathematics and real-world applications, often present challenges to students who resort to rote memorization without grasping their essence. While the emotional dimensions of learning mathematics are increasingly recognized, research in this area remains limited. This dissertation addresses this gap by examining a…

For institutions offering multiple sections of Calculus 1, course coordination allows for consistency among the sections through the reduction of variation of material and/or instructional approaches. Studies on course coordination have shown that a coordinated system can bring benefits to instructors and promote equality for students across…

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…

The equivalent resistance calculation for two circuits in cubic arrangements is solved. Emphasis is placed on the plastic (topological) properties of these circuits. In contrast, the opposite topological behaviour of an analogous arrangement is observed in the calculus of a magnetic field. It is also noted that the solved examples may be used as a…

The literature dealing with student understanding of integration in general and the Fundamental Theorem of Calculus in particular suggests that although students can integrate properly, they understand little about the process that leads to the definite integral. The definite integral is naturally connected to the antiderivative, the area under…

Storytelling has proved to be an effective way of passing on information from one generation to the next. Whether the information relates to history, culture, health, or morality, the story provides a framework so that complex ideas can be better understood and retained. In this article, we consider the role of narrative in the design and…

Students often find the study of electrostatics to be abstract, heavily mathematical, and non-intuitive. This paper describes an inquiry-based approach to teaching electrostatics in an introductory calculus-based physics class that emphasizes the primacy of student conceptual understanding.

Research using the Anthropological Theory of the Didactic suggests different models of how student learning may evolve in the progression of undergraduate mathematics coursework: from elementary courses in Calculus to more advanced courses in Analysis. An ideal model suggests that the theory-driven learning in the latter serves as a natural…

A central goal of introductory physics for the life sciences (IPLS) is to prepare students to use physics to model and analyze biological situations, a skill of increasing importance for their future studies and careers. Here we report our findings on life science students' ability to carry out a sophisticated biological modeling task at the end…

This article explores the parallels between improvisational theater, commonly known as improv, and active teaching. Specifically, it focuses in the impact of improv techniques on instructor and teaching assistant professional development. The implementation of an active teaching seminar is analyzed, where improv techniques were used in developing…