This study investigated how students reason about the partial derivative and the directional derivative of a multivariable function at a given point, using different graphical representations for the function in the problem statement. Questions were formulated to be as isomorphic as possible in both mathematics and physics contexts and were given…

Physics experts and students commonly use a variety of representations when working with partial derivatives, including symbols, graphs, and words. One especially powerful representation is the contour graph. In open-ended problem-solving interviews with nine upper-division physics students, we asked students to determine derivatives from contour…

When learning physics, students need more than just an understanding of mathematical and physical concepts. Integrating the two fields is crucial, as research indicates that students often struggle even when they have a strong grasp of both. In this paper, we use the heat equation as an example from higher education. Given the importance of the…

Several studies compared three different types of questions (conceptual, algorithmic, and graphical) across various topics, however, few focused specifically on gifted students. This study addressed this gap. The aim of the study, hence, was to determine whether there were notable differences in gifted students' performance in the three types of…

Student difficulties with making sense of graphs in physics have been thoroughly reported. In the study of one-dimensional waves, the issue is even trickier since the amplitude is a function of two variables (position and time). In this work, we investigate students' reasoning and difficulties with interpreting the graphical representation of the…

It's not surprising that rainbows have received a great deal of attention: in textbooks, in magazines, and on the web. They are, after all, beautiful, fascinating, occasionally awe-inspiring, even a little mysterious. They are an almost perfect blend of natural beauty and simple physics. Has everything that can be said about rainbows already been…

Introductory physics students often express fears regarding graphical vector addition. To ameliorate student trepidation of possibly making a mistake when moving the second vector to its new position at the head of the first vector before being added, as is most often advised by physics teachers, an alternative method is detailed here. This subtly…

A significant goal when teaching at the secondary education level is to present the generality of the procedures that are being used to describe a wide range of different physical phenomena. However, this approach is abandoned by physics instructors in many cases since the general mathematical background needed to present the above generality is…

The study investigated the effects of a combination of Peer Discussion and Isomorphic Problems (PD-IPs) on high school students' graph understanding and conceptual learning. The study was conducted on kinematics and Newton's Laws of Motion with 67 high school students from two groups. The experimental group (EG) consisted of 34 students, while the…

Research has identified several students' misinterpretations of the principles of the photoelectric effect (PE). Students cannot interpret the formula using the graph's context despite the linear dependence inherited in it. Many studies pointed out that the graphical representation of kinetic energy of the ejected electrons versus frequency of…

The drag effect on a falling ball caused by air is a conventional subject in the most well-known textbooks of classical mechanics and fluid dynamics. Further, there are some papers that employ video analysis to track objects movements in the air making it possible to obtain position data as a function of time and its graphs. However, none of them…

This article describes the implementation of an activity with a Predict-Observe-Explain (POE) learning cycle to teach the concepts of velocity and acceleration to physics students aged 17-19. The study indicates how the instructor enacted the activity and provides sample student responses and group discussions. The description includes an example…

Two of the most fundamental skills that students acquire in introductory undergraduate physics laboratory courses are how to accurately plot data and interpret the physical meaning of linear graphs. We redesigned our graphing skills lab with an open-ended approach designed to promote inquiry in graphical analysis and to address specific areas of…

The lesson presented here provides a multifaceted inquiry-based opportunity to develop a deep grasp of Archimedes' principle. It was originally developed for high school teachers as part of their training in the basic structure of the Next Generation Science Standards. There are numerous demonstrations illustrating Archimedes' principle, many of…

Using multiple representations (MR) such as graphs, symbols, diagrams, and text, is central to teaching and learning in physics classrooms. While different studies have provided evidence of the positive impact of the use of MR on physics learning, a comprehensive overview of existing literature on the use of MR in physics education, especially at…