In this paper, we report on an experimental activity for discussing the concepts of speed, instantaneous speed and acceleration, generally introduced in first year university courses of calculus or physics. Rather than developing the ideas of calculus and using them to explain these basic concepts for the study of motion, we led 82 first year…

Density functional theory (DFT) is a type of electronic structure calculation that has rapidly gained popularity. In this article, we provide a step-by-step demonstration of a DFT calculation by hand on the helium atom using Slater's X-Alpha exchange functional on a single Gaussian-type orbital to represent the atomic wave function. This DFT…

We introduce a new open source (free) software package that provides a simple, highly interactive interface for carrying out certain mathematical tasks that are commonly encountered in physics. These tasks include plotting and animating functions, solving systems of coupled algebraic equations, and basic calculus (differentiating and integrating…

The refraction problem, well-known in calculus and physics, continues to reveal new insights. This paper presents a geometric solution in which the trammel of Archimedes plays the prominent role. When properly configured, the trammel generates an ellipse and its family of normal lines. One normal line in particular intersects the boundary…

This article is a project that takes students through the process of forming a mathematical model of bicycle dynamics. Beginning with basic ideas from Newtonian mechanics (forces and torques), students use techniques from calculus and differential equations to develop the equations of rotational motion for a bicycle-rider system as it tips from…

This paper deals with a brief introduction to major remarkable discoveries of the "soliton" and the "inverse scattering transform" in the 1960s. The discovery of the soliton (or the solitary waves) began with the famous physical experiments of the Scottish Engineer and Naval Architect John Scott Russell in the Glasgow-Edinburgh…

The purpose of this study was to examine the effect on student understanding of Newton's Third Law in an introductory calculus-based physics class when a new graphical representational tool called a system schema was used throughout instruction to help visualize objects and interactions between them explicitly. The system schema serves as an…

Describes a simple experiment that uses a CCD video camera, a display monitor, and a laser-printed bar pattern to illustrate signal sampling problems that produce aliasing or moiri fringes in images. Uses the Fourier transform to provide an appropriate and elegant means to explain the sampling theorem and the aliasing phenomenon in CCD-based…

The wave equation is a classic partial differential equation that one encounters in an introductory course on boundary value problems or mathematical physics, which can be used to describe the vertical displacement of a vibrating string. Using a video camera and Wave-in-Motion software to record displacement data from a vibrating string or spring,…

At some point in their education, pre-engineering students will take physics and/or calculus. For many freshmen who aren't certain about their career paths, taking these courses is a litmus test to determine whether they have the aptitude or desire to pursue an engineering degree. Therein lies the challenge for many students in the U.S. Science,…

Presents examples of experiments designed for high school students with the help of a microcomputer-based laboratory called Explorer. Argues that these tools enable students to investigate many principles of physics that were not feasible in the past. (DDR)

Presents several types of functions which fit a given set of data and create opportunities for classroom discussion comparing different kinds of functions and identifying some of the potential hazards associated with extrapolation from best-fit functions. (DDR)

The widespread deployment and use of Information Technologies (IT) has paved the way for change in many fields of our societies. The Internet, mobile computing, social networks and many other advances in human communications have become essential to promote and boost education, technology and industry. On the education side, the new challenges…

This volume of the 27th International Group for the Psychology of Mathematics Education Conference presents papers from: plenary panels; research forums; working sessions; discussion groups; short oral communications; and poster sessions from the meeting. Plenary lectures included: (1) Studying and Capturing the Complexity of Practice: The Case of…