In a typical first physics class, homework consists of problems in which numerical values for physical quantities are given and the desired answer is a number with appropriate units. In contrast, most calculations in upper-division undergraduate physics are entirely symbolic. Despite the need to learn symbolic manipulation, students are often…

Students in introductory college physics often have wide ranges of preparation, making it challenging to deliver effective instruction for all. While numerous educational products and strategies have been shown to be broadly effective, there is a need for research-based online materials that support personalized learning and focus specifically on…

The law of conservation of momentum is a fundamental law of nature. It states that the momentum of an isolated system is conserved. In high school or introductory-level physics courses, for simplicity, teachers and textbooks always use collisions in one dimension as the examples to introduce the concept of conservation of momentum. To solve simple…

A common homework problem in many introductory physics courses is similar to the following. "A car drives at constant speed over a hill on a road in the shape of a vertical circular arc. What is the maximum speed the car can have and not lose contact with the road at the crest of the hill?" Unfortunately this problem is flawed, because…

For years there has been an acknowledged interest in having students assess the rationality of their solutions to physics problems. In fact, many textbooks now routinely include end-of-problem assessments as part of the authors' detailed solutions to examples. Over the past two decades, I have experimented with various forms of end-of-problem…

When teaching a general education introductory astronomy course that includes a mathematics prerequisite, it is important to convey that formulas and equations physically represent properties of actual objects and processes that occur that can actually be observed. Students with varying comfort levels with mathematics often need to be convinced…

Students in the physical sciences--physics and chemistry--often take multiple-choice exams for introductory courses. Some students will write a lot on their exams, while others write very little. Does the student doing more scratch work on their exam perform better than one who does not write as much? We analyzed multiple-choice exams in physics…

Most physics instructors believe that adequate sleep is important in order for students to perform well on problem solving, and many instructors advise students to get plenty of sleep the night before an exam. After years of giving such advice to students at Loyola Marymount University (LMU), one of us decided to find out how many hours students…

Analysis of collisions is standardly included in the introductory physics course. In one dimension (1D), there do not seem to be any unusual issues: Typically, the initial velocities of the two colliding objects are specified, and the problem is to find the final velocities. In 1D there are therefore two unknown variables. One can write the…

Over the past several years, we have contributed several articles to "TPT" that focused on a forensics-style reexamination of historical events. In each article, we presented a case study as a pedagogy for teaching topics from introductory-level physics courses. Recently, we assembled our prior work into a series of…

Many introductory physics courses begin with the teaching of motion and kinematics. This naturally leads to the use of constant acceleration equations to solve various problems involving common motions (free fall being a notable example). Students can sometimes get the impression that these equations are the only thing they need to remember in…

The goal of this paper is to illustrate different ways that cardsorting activities (or "card stacks") can be implemented in the introductory physics classroom, along with various tips and resources for getting started. My first attempt at developing a card stack came about from simply wanting to try out a fun way to change student…

Introductory physics courses can be a challenge for some college students, especially those that have not taken Advanced Placement (AP) physics courses in high school. Even some classical mechanics concepts, such as energy, power, or the laws of Newton, can be non-intuitive and hard to grasp. When it comes to evaluating the learning outcome of our…

The use of systems in many introductory courses is limited and often implicit. Modeling two or more objects as a system and tracking the center of mass of that system is usually not included. Thinking in terms of the center of mass facilitates problem solving while exposing the importance of using conservation laws. We present below three…

The velocity selector is a classic first-year physics problem that demonstrates the influence of perpendicular electric and magnetic fields on a charged particle. Traditionally textbooks introduce this problem in the context of balanced forces, often asking for field strengths that would allow a charged particle, with a specific target velocity,…