We describe the design and evaluation of an innovative course for beginning undergraduate mathematics students. The course is delivered almost entirely online, making extensive use of computer-aided assessment to provide students with practice problems. We outline various ideas from education research that informed the design of the course, and…

We consider how the existence of different signifiers for mathematical objects in different languages manifests in discourse about those objects. Based on the observation that there is a common signifier "derivative" in English used for both the derivative at a point and the derivative function and two phonetically and semantically…

Calculus differential is the basis of mathematics before entering the level of further mathematics, which has a high analysis level. Students have difficulty understanding concepts and have not been able to analyze/predict/realize (self-efficacy) that impact challenges in working on calculus problems. On the other hand, technology has been…

Generalization is a critical component of mathematical reasoning, with researchers recommending that it be central to education at all grade levels. However, research on students' generalizing reveals pervasive difficulties in creating and expressing general statements, which underscores the need to better understand the processes that can support…

It is very common to find in contemporary literature of Differential Equations, the need to incorporate holistically in teaching and learning the three different approaches: analytical, qualitative, and numerical, for continuous dynamical systems. However, nowadays, in some Bachelor of Science that includes only one course in differential…

In Advanced Calculus, our students wonder if it is possible to graphically represent a tornado by means of a three-dimensional curve. In this paper, we show it is possible by providing the parametric equations of such tornado-shaped curves.

Various applied mathematics undergraduate skills are demonstrated via an adaptation of Crank's axisymmetric spherical diffusion model. By the introduction of a one-parameter Heaviside initial condition, the pharmaceutically problematic initial mass flux is attenuated. Quantities germane to the pharmaceutical industry are examined and the model is…

The University Entrance Exam (UEE) has an important impact on how math instructors teach mathematics to prepare students for this exam as well as how their students learn mathematics. Since the UEE is like a bridge between high school and university, its importance becomes twofold. However, research regarding this issue is very limited in…

Income inequality is a central social justice concern, and hence excellent motivation for real-world applications in mathematics classrooms at every level. We describe the "Mathematics for Social Justice" course at Saint Michael's College, giving a specific example of one of the typical social justice projects for the course, and showing…

We present our experience with an open-ended lab activity that we designed for students with a Calculus 1 background. With the goal of learning how scientists study transport in streams, the students collected data on how a pulse of leaves travels down a nearby stream. Students who had little to no experience with data with two independent…

Project-based learning supports unique and authentic problems in differential equations courses. An intuitive, interesting and deep differential equations project is described. The description illustrates a case study of guiding students through a complex project and the technical and personal rewards gained from it. Valuable advice is provided to…

Previous studies have explored students' understanding of the relationship between definite integrals and areas under curves, but not their metacognitive experiences and skills while solving such problems. This paper explores students' mathematical performance, metacognitive experiences and metacognitive skills when solving integral-area tasks by…

This study explored the mathematics beliefs of students enrolled in a first year calculus class at a Midwestern university in the United States. The Indiana Mathematics Belief Scale was administered to 162 students enrolled in a first year calculus class during the first week of school. An exploratory factor analysis (EFA) was performed to examine…

A single laboratory exercise in introductory physics that includes a bit of calculus, a little programming, some breadboard wiring, and making mathematical connections between motion, net force, and power provides a nice STEM experience for students. If you can add in a biomechanics component you hopefully have something that overall can be an…

We discuss an investigation of the difficulties that students in a calculus-based university introductory physics course have with electric field and the superposition principle for the case of a continuous charge distribution and how that research was used as a guide in the development, validation, and evaluation of a tutorial on these topics to…