This article uses dynamic software in Excel to demonstrate several ways in which graphical and numerical approaches can be introduced both to enhance student understanding of l'Hopital's Rule and to explain why the Rule actually works to give the "right" answers. One of the approaches used is to visualize what is happening by examining…

In this paper we present two simulations designed with GeoGebra that illustrate dynamically a key concept in Vector Calculus: line integrals of vector fields, along with other associated mathematical properties and applications. Students are not required to know the GeoGebra environment: a user-friendly interface with buttons, functionalities and…

This paper develops the ideas of "The Pedagogical Power of Context: Iterative Calculus Methods and the Epidemiology of Eyam" (French "et al." 2018 "J. Phys. Educ."), where we considered the application of the Euler method to solve epidemiological problems. Our purpose was to convey some examples of school level work…

Simulation is an effective tool for analyzing probability models as well as for facilitating understanding of concepts in probability and statistics. Unfortunately, implementing a simulation from scratch often requires users to think about programming issues that are not relevant to the simulation itself. We have developed a Python package called…

Research has shown that the types of tasks assigned to students affect their learning. Various authors have described desirable features of mathematical tasks or of the activity they initiate. Others have suggested task taxonomies that might be used in classifying mathematical tasks. Drawing on this literature, we propose a set of task types that…

This article illustrates ways that dynamic software using some sophisticated techniques in Excel can be used to demonstrate fundamental ideas related to regression and correlation analysis to increase student understanding of the concepts and methods in elementary statistics courses and in courses at the college algebra/precalculus level that…

When students of the of the physical sciences transition from school to university, they discover that knowledge of calculus is as vital as arithmetic, and that there is precious little useful information written without calculus. However, the lack of calculus in pre-university physics studies persists, especially in its application to the…

Numerical simulations are playing an increasingly important role in modern science. In this work it is suggested to use a numerical study of the famous perihelion motion of the planet Mercury (one of the prime observables supporting Einsteins general relativity) as a test case to teach numerical simulations to high school students. The paper…

Early exposure to data science skills, such as relational databases, is essential for students in statistics as well as many other disciplines in an increasingly data driven society. The goal of the presented pedagogy is to introduce undergraduate students to fundamental database concepts and to illuminate the connection between these database…

Students sometimes struggle with visualizing the three-dimensional solids encountered in certain integral problems in a calculus class. We present a project in which students create solids of revolution with clay on a pottery wheel and estimate the volumes of these objects using Riemann sums. In addition to giving students an opportunity for…

Calculus, perhaps more than other areas of mathematics, has a reputation for being steeped with procedures. In fact, through the years, it has been noticed of many students getting caught in the trap of trying to memorize algorithms and rules without developing associated concept knowledge. Specifically, students often struggle with the…

It is surprising to students to learn that a natural combination of simple functions, the function sin(1/x), exhibits behaviour that is a great challenge to visualize. When x is large the function is relatively easy to draw; as x gets smaller the function begins to behave in an increasingly wild manner. The sin(1/x) function can serve as one of…

In this paper we introduce a new collaborative technique in teaching and learning the epsilon-delta definition of a continuous function at the point from its domain, which connects mathematical logic, combinatorics and calculus. This collaborative approach provides an opportunity for mathematical high school students to engage in mathematical…

A hands-on activity can help multivariable calculus students visualize surfaces and understand volume estimation. This activity can be extended to include the concepts of Fubini's Theorem and the visualization of the curves resulting from cross-sections of the surface. This activity uses students as pillars and a sheet or tablecloth for the…

The concept of definite integral is almost always introduced as the Riemann integral, which is defined in terms of the Riemann sum, and its geometric interpretation. This definition is hard to understand for high school students. With the aid of mathematical software for visualisation and computation of approximate integrals, the notion of…