Dynamic geometry software (DGS) has long been studied in mathematics education as a way for students to explore and interact with geometric objects and figures. Recent advances in Augmented Reality (AR) technologies that allow dynamic three-dimensional mathematical objects to appear in students' environment as holograms have changed the nature of…

This study investigated evidence of how students' mental models of fundamental kinematic relations evolved (i.e., developed cognitively over time) as observed during an introductory course in calculus-based classical mechanics. The core of the curriculum is based on a claim known as Galileo's principle of relativity. The course material comprised…

The magnetic field of Earth, B[subscript e], is an intriguing topic in the introductory physics curriculum that engages students' curiosity and inspires numerous speculations about the nature of this phenomenon. There are several methods for measuring Earth's magnetic field. Probably, the most widespread and visual method of measuring the field in…

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…

The cases of constant and quadratic damping of free oscillations are missing from standard textbooks, even at college and university level. The case most examined is that of linear damping, the reason being that the student can work out a closed form which describes all stages of motion. The case of constant damping is straightforward to be…

Around the world, musical engagement frequently involves movement. Most adults easily clap or sway to a wide range of tempos, even without formal musical training. The link between movement and music emerges early--young infants move more rhythmically to music than speech, but do not reliably align their movements to the beat. Laboratory work…

As places of learning, schools inevitably foreground cognition. Neglected in schools and in the literature is the body, often an inconvenience or barrier to learning rather than a site of perception and understanding. Where the body is considered, it is primarily concerned with pedagogy and children rather than analysing the broad range of…

In high school, and also in introductory physics courses in higher levels of schooling, the law of universal gravitation of planets is introduced by postulating Johannes Kepler's three laws, and later Isaac Newton's law of the inverse of the square of the distance to the Sun. The justification of the laws is only achieved in advanced courses in…

Experimental results are presented concerning the motion of a ball that bounces up an incline a few times then bounces back down again. The number of bounces up the incline is typically small since the speed of the ball in a direction parallel to the incline decreases rapidly, not only during each bounce but also while the ball is in the air. The…

It is widely accepted that nonverbal communication is crucial for learning, but the exact functions of interpersonal coordination between instructors and learners remain unclear. Specifically, it is unknown what role instructional approaches play in the coupling of physical motion between instructors and learners, and crucially, how such…

Recent studies have identified an incomplete student understanding of how elastic rebound causes earthquakes. We hypothesized that realistic imaging of spatial patterns in ground motions over the course of the earthquake cycle would improve student understanding. Incorporating spatial change information in the form of both motion vectors and…

Virtual reality (VR) can provide access to otherwise inaccessible aspects of the world and thus promote science learning. We developed a VR learning tool about the water cycle, with 11 lessons for classroom teaching at the primary level. We assessed prior knowledge before a four-week intervention and learning outcomes directly after the…

This paper has a didactic aim. Indeed, starting from the well-known principle of free fall discovered by Galileo Galilei, we want to make some reflections that we consider useful for secondary school students. Being the acceleration invariant with respect to Galilei's transformations, it is useful to underline that the free fall in a gravitational…

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…

In our first-semester introductory physics laboratory, we have an exercise on rotational dynamics. We have recently upgraded the equipment that we use in that exercise without changing the actual exercise. The new equipment has performed well so far, and we wanted to share what we did with others who may be looking for a relatively inexpensive way…