The ability to relate physical concepts and phenomena to multiple mathematical representations--and to move fluidly between these representations--is a critical outcome expected of physics instruction. In upper-division quantum mechanics, students must work with multiple symbolic notations, including some that they have not previously encountered.…

The most famous equation in physics, E = mc[superscript 2], is rarely introduced in middle school physics curricula. Recent research has shown that teaching Einsteinian concepts at the middle school level is feasible and beneficial. This paper analyses an Einsteinian energy teaching module for Year 8 students (13-14 years old), which encompasses…

This article presents a simple, fast, and equally accurate technique for measuring the area of a circle and of an ellipse without using geometric formulas. This therefore, together with the known radius of the circle and the semi-major and semi-minor axes of the ellipse, allows for the calculation of [pi]. The experiment is easy, thrilling, and…

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…

The article describes a new version of a demonstration experiment for the Maxwell distribution. In the first part students analyse the applicability of the Gaussian distribution to the projection of the particle velocities in the suggested experiment. Further, students observe two-dimensional distribution of particles by the modulus of velocity in…

In this paper we derive and discuss the time it takes for a force to turn a velocity. More precisely, we derive the formula for the time t it takes a constant force that makes an angle a with the initial velocity v(0) to have v(Tau) get within an angle ? < a of the force. We then show how the addition of a viscous force decreases Tau…

Error analysis consumes much of the focus in introductory physics labs. Catastrophic cancellation is a spike in error that occurs when subtracting two measurements of roughly equal magnitude. Often termed "loss of significance" or "subtractive cancellation," this effect can easily relegate experimental results to utter…

In this work, we have developed an alternative device composed by an Arduino board and an INA219 sensor to experimentally obtain the mathematical formulas describing the charge and discharge of the capacitor for educational proposes. We have obtained excellent agreement between theoretical prediction and experimental measurements. The INA219 DC…

The private company SpaceX regularly launches satellites into geostationary orbits. SpaceX posts videos of these flights with telemetry data displaying the time from launch, altitude, and rocket speed in real time. In this paper this telemetry information is used to determine the velocity boost of the rocket as it leaves its circular parking orbit…

The use and understanding of mathematics is a crucial component of the physical sciences. Much work has been done in physics education research and science education more broadly to determine persistent difficulties with mathematics. This work has led to the development of numerous problem solving strategies aimed at helping learners approach…

Costume jewelry beads are employed to demonstrate how a beam of beads are able to transform into a simple pendulum (single bead) where the pendulum length remains constant throughout. These beads are common and inexpensive for instructors, as well as attractive and exciting for students. Beads are removed from the top, keeping the same pendulum…

Analysing graphs, formulating covariational relationships, and hypothesizing systems' behaviour have emerged as frequent objectives of contemporary research in physics education. As such, these studies aim to help students achieve these objectives. While a consensus has been reached on the cognitive benefits of emphasizing the structural domain of…

This article integrated inquiry behaviors and a guided learning map (gMap) into a mobile app called Ubiquitous-Physics (U-Physics), which helps students to explore inclined plane phenomena in authentic contexts. The article investigated inquiry behaviors such as interpreting graphs, applying formulas, drawing conclusions, and peer collaboration,…

The study of students' use of representations is one of the main topics of physics education research and is guided by the overarching field of semiotics. In this paper we compare two semiotic frameworks, one coming from didactics of mathematics and one from physics education research; "the theory of registers of semiotic…

In many introductory-level physics textbooks, the derivation of the formula for the speed of transverse waves in a string is either omitted altogether or presented under physically overly idealized assumptions about the shape of the considered wave pulse and the related velocity and acceleration distributions. In this paper, we derive the named…