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 current study explores the preferences of primary school teachers on the characteristics of Information and Communication Technologies (ICT)-based teaching via Discrete Choice Models (DCM). These models analyze the preferences of teachers towards alternatives that are formed by different characteristics. In this study we examined the…

The Poisson distribution describes the probability of a certain number of events occurring in an interval of time when the occurrence of the individual events is independent of one another and the events occur with a fixed mean rate. Probably the best-known example of the Poisson distribution in the physics curriculum is the temporal distribution…

Chaotic phenomena are not part of standard curricula, although this subject offers several interesting aspects which can help students better understand basic features of science. A central observation is that even simple physical systems, if chaotic, are unpredictable, just like the weather. We present the principles applied when developing a…

Teaching quantum physics (QP) to high school (HS) students is gaining momentum, necessitating the exploration of various effective methods. Specifically, the research on quantitative teaching methods is still in its early stages. Understanding the power of Dirac notation (DN) in teaching is crucial for grasping the complexities of QP, as it…

Clear and rigorous quantum reasoning is needed to explain quantum physical phenomena. As pillars of true quantum physical explanations, we suggest specific quantum reasoning derived from quantum physical key ideas. An experiment is suggested to support such a quantum reasoning, in which a quantized radiation field interacts with an optical beam…

Quantum computers are at the forefront of computing; however, few people understand how they work and their capabilities. We present two versions of an interactive activity designed for high school students (ages 13 to 18) that introduce a core quantum concept--"entanglement." The first version illustrates a simple connection between two…

In this article, we use a simple lattice model to illustrate the concepts of entropy, free energy, and thermodynamic equilibrium from a microscopic perspective. These physical concepts are based on elementary knowledge of discrete probability distribution and weighted average. Calculations about this model involve basic algebra and counting, which…

Most likely a large number of students have heard of the Northern Lights (Aurora Borealis), and know that they are a phenomenon in the sky. Although they may not have seen the Northern Lights, most have probably seen other phenomena in the sky, such as a rainbow, shooting star, or super moon. These experiences provide an opportunity for students…

In quantum mechanics, probability amplitudes are complex numbers and the relative phases between the terms in superposition states have measurable effects. This article describes an investigation into sophomore- and junior-level students' reasoning patterns in relating relative phases and real-world quantum phenomena. The investigation involved…

Explanations of phenomena in chemistry are grounded in discussions of particulate-level behavior, but there are limitations to focusing on single particles, or as an extension, viewing a group of particles as displaying uniform behavior. More sophisticated models of physical processes evoke considerations related to the dynamic nature of bulk…

A central aim of physics education research is to understand the processes of learning and use that understanding to inform instruction. To this end, researchers often conduct studies to measure the effect of classroom interventions on student outcomes. Many of these intervention studies have provided an empirical foundation of reformed teaching…

The fruit fly ("Drosophila melanogaster") is an ideal subject for studying inheritance patterns, Mendel's laws, meiosis, Punnett squares, and other aspects of genetics. Much of what we know about genetics dates to evolutionary biologist Thomas Hunt Morgan's work with mutated fruit flies in the early 1900s. Many genetic laboratories…

Time dependence is of fundamental importance for the description of quantum systems, but is particularly difficult for students to master. We describe the development and evaluation of a combined simulation-tutorial to support the development of visual understanding of time dependence in quantum mechanics. The associated interactive simulation…

Bayesian Knowledge Tracing (BKT) is a commonly used approach for student modeling, and Long Short Term Memory (LSTM) is a versatile model that can be applied to a wide range of tasks, such as language translation. In this work, we directly compared three models: BKT, its variant Intervention-BKT (IBKT), and LSTM, on two types of student modeling…