To a student in introductory physics, using vectors is at best an exercise in bookkeeping. A two-dimensional kinematics problem effectively doubles the number of equations that a student must know, and invites the student to memorize factoids: "The horizontal motion is constant," "Gravity is only in the y-direction," etc. Force…

Research identifies two domains by which mathematics allows learning physics concepts: a technical domain that includes algorithmic operations that lead to solving formulas for an unknown quantity and a structural domain that allows for applying mathematical knowledge for structuring physical phenomena. While the technical domain requires…

I present a novel way to introduce the lunar orbital eccentricity in introductory astronomy courses. The Moon is perhaps the clearest illustration of the general orbital elements such as inclination, ascending node, eccentricity, perigee, and so on. Furthermore, I like the students to discover astronomical phenomena for themselves, by means of a…

Electromagnetic induction is probably one of the most challenging subjects for students in the introductory physics sequence, especially in algebra-based courses. Yet it is at the heart of many of the devices we rely on today. To help students grasp and retain the concept, we have put together a simple and dramatic classroom demonstration that…

Technology such as Microsoft PowerPoint presentations, clickers, podcasting, and learning management suites is becoming prevalent in classrooms. Instructors are using these media in both large lecture hall settings and small classrooms with just a handful of students. Traditionally, each of these media is instructor driven. For instance,…

There is a growing consensus that introductory physics courses should help students develop general scientific reasoning abilities that transform them into lifelong learners, preparing them for careers and citizenship in a rapidly evolving world. Despite the sometimes daunting nature of this challenge, activities developed by various physics…

In 2007 many AAPT members received a booklet that is the first chapter of a physics textbook available on a CD. This book espouses the new educational philosophy of teaching special relativity as the first item in the topic of mechanics. Traditionally, special relativity is part of one or more modern physics chapters at the end of the text, and…

For more than a hundred years there has been a debate about the sequence in which high school science should be taught. Many advocates of "Physics First" support a more conceptual ninth-grade physics course followed by chemistry and then biology while supporters of mathematically rigorous physics favor a sequence of biology-chemistry-physics. This…

The requirement for a method of capturing problem solving on a whiteboard for later replay stems from my teaching load, which includes two classes of first-year university general physics, each with relatively large class sizes of approximately 80-100 students. Most university-level teachers value one-to-one interaction with the students and find…

A coin tossed onto a table often ends up rolling in such a way that the center of mass remains approximately stationary. Although this phenomenon has been studied for many years and is well-documented in the literature, it is perhaps not widely appreciated in the physics education community that the motion can be understood without the use of…

Newton's proof of the connection between elliptical orbits and inverse-square forces ranks among the "top ten" calculations in the history of science. This time-honored calculation is a highlight in an upper-level mechanics course. It would be worthwhile if students in introductory physics could prove the relation "elliptical orbit" [arrow right]…

Presents a technique that helps students concentrate more on the science and less on the mechanics of algebra while dealing with introductory physics formulas. Allows the teacher to do complex problems at a lower level and not be too concerned about the mathematical abilities of the students. (JRH)

When studying wave interference, one often wants to know the difference in path length for two waves arriving at a common point P but coming from adjacent sources. For example, in many contexts interference maxima occur where this path-length difference is an integer multiple of the wavelength. The standard approximation for the path-length…