Developing expertise in physics requires appropriate integration and assimilation of physics and mathematics. Instructors and students often describe physics courses in terms of their emphasis on conceptual and quantitative problem-solving. For example, they may argue that a course emphasizes primarily conceptual over quantitative problem-solving or may emphasize equally on both depending on instructional context and assessment design. In this study, we investigated how students and instructors across different levels of physics instruction perceive the roles and development of conceptual and quantitative problem-solving in student learning and expertise development. Using departmental surveys administered at the beginning and end of each semester, we collected both Likert-scale and open-ended responses from students enrolled in introductory, upper-level undergraduate and graduate physics courses. These surveys assessed students' self-perceived skills, preferences and perceptions of instrucots and course emphasis. To complement student perspectives, we conducted interviews with instructors using parallel questions adapted to reflect instructional goals and expectations. Our findings highlight patterns in how students and instructos prioritize conceptual and quantitative problem-solving across course levels, as well as alignment and misalignment between student and instructor perspectives.

Compressible flow problems are characterized by highly nonlinear, implicit, and often transcendental governing equations. In undergraduate gas dynamics educa- tion, solving these equations traditionally relies on iterative numerical methods or extensive look-up tables, which can obscure the physical intuition of the solution space. This paper introduces a comprehensive framework using Deep Learning to generate high-fidelity surrogate models for five canonical problems: Rayleigh flow, Fanno flow, oblique shocks, convergent-divergent nozzles, and unsteady shock tubes. We detail the specific neural network architectures and physics-informed feature en- gineering strategies required for each problem, such as using logarithmic inputs for Fanno friction parameters or geometric anchors for oblique shocks. The resulting models achieve high accuracy and enable instantaneous visualization of complex design spaces, such as thermodynamic T s diagrams and unsteady x t wave interactions. This approach demonstrates how modern data-driven techniques can be integrated into the physics curriculum to enhance conceptual understanding.

"Computational experiments" use code and interactive visualizations to convey mathematical and physical concepts in an intuitive way, and are increasingly used to support ex cathedra lecturing in scientific and engineering disciplines. Jupyter notebooks are particularly well-suited to implement them, but involve large amounts of ancillary code to process data and generate illustrations, which can distract students from the core learning outcomes. For a more engaging learning experience that only exposes relevant code to students, allowing them to focus on the interplay between code, theory and physical insights, we developed scicode-widgets (released as scwidgets), a Python package to build Jupyter-based applications. The package facilitates the creation of interactive exercises and demonstrations for students in any discipline in science, technology and engineering. Students are asked to provide pedagogically meaningful contributions in terms of theoretical understanding, coding ability, and analytical skills. The library provides the tools to connect custom pre- and post-processing of students' code, which runs seamlessly "behind the scenes", with the ability to test and verify the solution, as well as to convert it into live interactive visualizations driven by Jupyter widgets.

Limited infrastructure, scarce educational resources, and unreliable internet access often hinder physics and photonics education in underdeveloped regions. These barriers create deep inequities in Science, Technology, Engineering, and Mathematics (STEM) education. This article explores how Small Language Models (SLMs)-compact, AI-powered tools that can run offline on low-power devices, offering a scalable solution. By acting as virtual tutors, enabling native-language instruction, and supporting interactive learning, SLMs can help address the shortage of trained educators and laboratory access. By narrowing the digital divide through targeted investment in AI technologies, SLMs present a scalable and inclusive solution to advance STEM education and foster scientific empowerment in marginalized communities.

We report on an educational pilot program for low-cost physics experimentation run in Ecuador, South Africa, and the United States. The program was developed after having needs-based discussions with African educators, researchers, and leaders. It was determined that the need and desire for low-cost, skills-building, and active-learning tools is very high. From this, we developed a 3D-printable, Raspberry Pi-based multispectral camera (15 to 25 spectral channels in the visible and near-IR) for as little as $100. The program allows students to learn 3D modeling, 3D printing, feedback, control, image analysis, Python programming, systems integration and artificial intelligence as well as spectroscopy. After completing their cameras, the students in the program studied plant health, plant stress, post-harvest fruit ripeness, and polarization and spectral analysis of nanostructured insect wings, the latter of which won the ``best-applied research" award at a conference poster session and will be highlighted in this paper. Importantly, these cameras can be an integral part of any developing country's agricultural, recycling, medical, and pharmaceutical infrastructure. Thus, we believe this experiment can play an important role at the intersection of student training and developing countries' capacity building.

We present an experimental visualization of the Terrell effect, an optical phenomenon predicted in 1959 by Roger Penrose and James Terrell, which reveals that the Lorentz contraction of a moving object is not visible in a snapshot photograph. Using fs-laser pulses and a gated intensified camera that allows gating times as short as 300 ps, we achieve a virtual reduction of the speed of light to less than 2 m/s, enabling the visualisation of relativistically moving objects in real time. By capturing light reflected from deliberately Lorentz-contracted objects, our setup effectively reconstructs their visual appearance. This didactic visualization not only commemorates the centennial of Anton Lampa's seminal 1924 paper on relativistic length contraction but also provides the first experimental evidence of the Terrell effect in a laboratory setup. Our results comprise detailed relativistic illustrations, simulations and photographic snapshots of a sphere and a cube, which are animated to velocities close to the speed of light, revealing the apparent rotation effect and the distortion predicted by relativistic theory.

Modeling complex systems using standard neural ordinary differential equations (NODEs) often faces some essential challenges, including high computational costs and susceptibility to local optima. To address these challenges, we propose a simulation-free framework, called Fourier NODEs (FNODEs), that effectively trains NODEs by directly matching the target vector field based on Fourier analysis. Specifically, we employ the Fourier analysis to estimate temporal and potential high-order spatial gradients from noisy observational data. We then incorporate the estimated spatial gradients as additional inputs to a neural network. Furthermore, we utilize the estimated temporal gradient as the optimization objective for the output of the neural network. Later, the trained neural network generates more data points through an ODE solver without participating in the computational graph, facilitating more accurate estimations of gradients based on Fourier analysis. These two steps form a positive feedback loop, enabling accurate dynamics modeling in our framework. Consequently, our approach outperforms state-of-the-art methods in terms of training time, dynamics prediction, and robustness. Finally, we demonstrate the superior performance of our framework using a number of representative complex systems.

We present an intuitive, conceptual, but semi-rigorous introduction to the celebrated Markov Chain Monte Carlo method using a simple model of population dynamics as our motivation and focusing on a few elementary distributions. Conceptually, the population flow between cities closely resembles the random walk of a single walker in a state space. We start from two states, then three states, and finally the setup is fully generalized to many states of both discrete and continuous distributions. Despite the mathematical simplicity, the setup remarkably includes all the essential concepts of Markov Chain Monte Carlo without loss of generality, e.g., ergodicity, global balance and detailed balance, proposal or selection probability, acceptance probability, up to the underlying stochastic matrix, and error analysis. Our teaching experience suggests that most senior undergraduate students in physics can closely follow these materials without much difficulty.

The importance of science beliefs such as self-efficacy, interest, identity, sense of belonging, perceived recognition and effectiveness of peer interaction in science education has been increasingly recognized in recent years. Here, we use five years of data from a validated survey administered to non-majors during their first year, physics majors throughout their undergraduate education, and first-year physics Ph.D. students at a large research university in the US. We find that physics majors in the first-year responded to the survey prompts more positively than their non-physics major peers who were in the same introductory courses, with the largest differences in perceived recognition, interest, and physics identity and somewhat smaller differences in self-efficacy, perception of peer interaction, and sense of belonging. Further, the average survey responses of physics majors for each belief remain largely constant over time from their first-year of the undergraduate curriculum through the last year and comparable to the Ph.D. students. This suggests that students are adjusting their interpretation of the survey items to match the current level of expertise expected of them. One exception occurs in the second year, when peer interaction and sense of belonging reach a minimum. Moreover, physics identity dips to the lowest value in the fourth year when many students are contemplating continuing in physics beyond their undergraduate years or switching fields. We also find that perceived recognition is the best predictor of physics identity for physics majors throughout their entire physics education, pointing to the importance of instructors making a concerted effort to recognize and affirm their students throughout their education.

Quantitative reasoning is an essential learning objective of physics instruction. The Physics Inventory for Quantitative Literacy (PIQL) is an assessment tool that has been developed for calculus-based physics courses to help instructors evaluate whether their students learn to reason this way (White Brahmia, et al., 2019). However, the PIQL is not appropriate for the large population of students taking physics who are not enrolled in, or have not completed, calculus. To address this need, we have developed the General Equation-based Reasoning inventory of QuaNtity (GERQN). The GERQN is an algebra-based version of the PIQL and is appropriate for most physics students; the only requirement is that students have taken algebra so they are familiar with the use of variable, negative quantities, and linear functions. In this paper we present the development and validation of the GERQN, and a short discussion on how the GERQN can be used by instructors to help their students learn.

Network analysis has become a well-recognized methodology in physics education research (PER), with study topics including student performance and persistence, faculty change, and the structure of conceptual networks. The social network analysis side of this work has focused on quantitative analysis of whole-network cases, such as the structure of networks in single classrooms. Egocentric or personal network approaches are largely unexplored, and qualitative methods are underdeveloped. In this paper, we outline theoretical and practical differences between two major network paradigms--whole-network and egocentric--and introduce theoretical frameworks and methodological considerations for egocentric studies. We also describe qualitative and mixed-methods approaches that are currently missing from the PER literature. We identify areas where these additional network methods may be of particular interest to physics education researchers, and end by discussing example cases and implications for new PER studies.

Relating two quantities to describe a physical system or process is at the heart of "doing physics" for novices and experts alike. In this paper, we explore the ways in which experts use covariational reasoning when solving introductory physics graphing problems. Here, graduate students are considered experts for the introductory level material, as they often take the role of instructor at large research universities. Drawing on work from Research in Undergraduate Mathematics Education (RUME), we replicated a study of mathematics experts' covariational reasoning done by Hobson and Moore with physics experts [N. L. F. Hobson and K. C. Moore, in RUME Conference Proceedings, pp. 664-672 (2017)]. We conducted think-aloud interviews with 10 physics graduate students using tasks minimally adapted from the mathematics study. Adaptations were made solely for the purpose of participant understanding of the question, and validated by preliminary interviews. Preliminary findings suggest physics experts approach covariational reasoning problems significantly differently than mathematics experts. In particular, two behaviors are identified in the reasoning of expert physicists that were not seen in the mathematics study. We introduce these two behaviors, which we call Using Compiled Relationships and Neighborhood Analysis, and articulate their differences from the behaviors articulated by Hobson and Moore. Finally, we share implications for instruction and questions for further research.

This study is a pioneering endeavor to investigate the capabilities of Large Language Models (LLMs) in addressing conceptual questions within the domain of mechanical engineering with a focus on mechanics. Our examination involves a manually crafted exam encompassing 126 multiple-choice questions, spanning various aspects of mechanics courses, including Fluid Mechanics, Mechanical Vibration, Engineering Statics and Dynamics, Mechanics of Materials, Theory of Elasticity, and Continuum Mechanics. Three LLMs, including ChatGPT (GPT-3.5), ChatGPT (GPT-4), and Claude (Claude-2.1), were subjected to evaluation against engineering faculties and students with or without mechanical engineering background. The findings reveal GPT-4's superior performance over the other two LLMs and human cohorts in answering questions across various mechanics topics, except for Continuum Mechanics. This signals the potential future improvements for GPT models in handling symbolic calculations and tensor analyses. The performances of LLMs were all significantly improved with explanations prompted prior to direct responses, underscoring the crucial role of prompt engineering. Interestingly, GPT-3.5 demonstrates improved performance with prompts covering a broader domain, while GPT-4 excels with prompts focusing on specific subjects. Finally, GPT-4 exhibits notable advancements in mitigating input bias, as evidenced by guessing preferences for humans. This study unveils the substantial potential of LLMs as highly knowledgeable assistants in both mechanical pedagogy and scientific research.

Africa has amazing potential due to natural (such as dark sky) and human resources for scientific research in astronomy and space science. At the same time, the continent is still facing many difficulties, and its countries are now recognising the importance of astronomy, space science and satellite technologies for improving some of their principal socio-economic challenges. The development of astronomy in Africa (including Ethiopia) has grown significantly over the past few years, and never before it was more possible to use astronomy for education, outreach, and development as it is now. However, much still remains to be done. This paper will summarise the recent developments in astronomy research and education in Africa and Ethiopia and will focus on how working together on the development of science and education can we fight poverty in the long term and increase our possibilities of attaining the United Nations Sustainable Development Goals in future for benefit of all.

In this paper we numerically solve the time dependent Schrödinger equation for scenarios using wave packets. These examples include the free wave packet, which we use to show the difference between group and phase velocities, the packet in a harmonic oscillator potential with non-trivial initial conditions in one and two dimensions, which is compared with their classical analogs to show how Ehrenfest theorem holds. We also include simulations of the diffraction through the single and double slit potentials, the refraction with a step potential and the dispersion by a central potential. The aim of this paper is to illustrate with simulations, nowadays easy to implement, scenarios that can help explaining the basics of the wave-particle duality.

This paper introduces a theory about the role of language in learning physics. The theory is developed in the context of physics students' and physicists' talking and writing about the subject of quantum mechanics. We found that physicists' language encodes different varieties of analogical models through the use of grammar and conceptual metaphor. We hypothesize that students categorize concepts into ontological categories based on the grammatical structure of physicists' language. We also hypothesize that students over-extend and misapply conceptual metaphors in physicists' speech and writing. Using our theory, we will show how, in some cases, we can explain student difficulties in quantum mechanics as difficulties with language.

This study introduces an experimental teaching method that employs optic fiber interferometry (OFI) to investigate forced vibration phenomena. It is designed for undergraduate physics majors with foundational mechanics and optics training and optics-focused graduate students. This approach aims to deepen students' understanding of forced vibration theory and interferometric measurement principles while fostering skills in experimental design, data analysis, and problem solving. Leveraging OFI's high-precision displacement measurement capabilities, the experiment enabled accurate tracking of frequency and displacement variations. By scanning the driving force frequency, students obtained amplitude frequency curves to determine the system's natural frequency, which closely aligned with theoretical predictions. This method may bridge theoretical concepts and practical applications, offering insights into teaching vibration theory and precision measurement techniques and equipping students with integrated knowledge for real-world challenges.

The looping pendulum is a simple physical system consisting of two masses connected by a string that passes over a rod. We derive equations of motion for the looping pendulum using Newtonian mechanics, and show that these equations can be solved numerically to give a good description of the system's dynamics. The numerical solution captures complex aspects of the looping pendulum's behavior, and is in good agreement with the experimental results.

This work presents a structured systematic process for undergraduate capstone research projects embodying computational thinking (CT) practices. Students learn to conduct research with a decision support system utilizing CT. The system is demonstrated through a case study of a capstone research project course. The course is a 3rd year single semester capstone in an aviation program. CT was integrated over a decade, through 21 semesters of coordinating and delivering the course. The CT practices evolved and were utilized for more aspects over time. The CT system facilitated a significant reduction in staff workload by eliminating the need for direct one-on-one supervision and enabling the streamlining of marking. This resulted in fairer marking by eliminating supervisor bias. Student feedback shows a high degree of satisfaction, with comments highlighting choice and learning.