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arXiv2025

Framing the Fundamental Theorem of Calculus Through Physics-Based Quantities

There is a substantial curricular overlap between calculus and physics, yet introductory physics students often struggle to connect the two. We introduce a quantity-based framing of the Fundamental Theorem of Calculus (FTC) to help unify learning across both disciplines. We propose a consistent approach to teaching definite integrals, including shared vocabulary and symbolism, to help students recognize how concepts like change, rate, and accumulation show up in both calculus and physics. We argue that the typical interpretation of the FTC in calculus, focusing on antiderivatives in closed form, doesn't align well with how physicists use or conceptualize integration. We advocate for an additional focus on Riemann sums and the underlying ideas of change, rate, products, and accumulation, which are fundamental in both fields. This approach can help students build a deeper, more coherent understanding of both mathematics and physics quantity. By aligning learning objectives across the disciplines, we argue that students can develop a stronger understanding of foundational mathematical principles.

physics.ed-ph↗

arXiv2025

Displacement current: examples that go beyond the beaten path

The Ampere-Maxwell's law and the displacement current constitute one of the most difficult aspects of electromagnetic theory for students in introductory electromagnetics courses. Here we present a set of examples that go beyond the classical ones usually discussed in introductory textbooks. In-depth analysis of these examples allows students to develop a deeper understanding of electromagnetic theory even in students who have not acquired the full mathematical toolkit of the more advanced courses.

physics.ed-ph↗

arXiv2025

Astronomy and Society: The Road Ahead

Astronomy, of all the sciences, is possibly the one with the most public appeal across all age groups. This is also evidenced by the existence of a large number of planetaria and amateur astronomy societies, which is unique to the field. Astronomy is known as a `gateway science', with an ability to attract students who then proceed to explore their interest in other STEM fields too. Astronomy's link to society is therefore substantive and diverse. In this white paper, six key areas are analysed, namely outreach and communication, astronomy education, history and heritage, astronomy for development, diversity, and hiring practices for outreach personnel. The current status of each of these areas is described, followed by an analysis of what is needed for the future. A set of recommendations for institutions, funding agencies, and individuals are evolved for each specific area. This work charts out the vision for how the astronomy-society connection should take shape in the future, and attempts to provide a road-map for the various stakeholders involved.

physics.ed-ph↗

arXiv2026

Inference uncertainty about an aircraft crash

Problem-based learning benefits from situations taken from real life, which usually stimulate student interest. In this paper, we examine the shooting down of the Rwandan president's aircraft on April 6th, 1994. We discuss methods to infer information about the location from which the missile was launched, its trajectory and type, where the aircraft was struck and its trajectory during the fall. To this end, we developed a physics-based analysis based on expert reports, witness statements, and other publicly available information, as interpreted by our calculations. The analysis is designed to be understandable using undergraduate-level physics. The uncertainty of each result is discussed and propagated to ensure a proper assessment of the hypotheses and a traceability of their consequences. Such approach encourages the students to exercise their critical mind and teaches inference methods that are routinely used in physics research. In addition, it illustrates the importance and limits of scientific expertise during a judiciary process.

physics.ed-ph↗

arXiv2025

Learning quantum properties with informationally redundant external representations: An eye-tracking study

Recent research indicates that the use of multiple external representations MERs has the potential to support learning, especially in complex scientific areas, such as quantum physics. In particular, the provision of informationally redundant external representations can have advantageous effects on learning outcomes. This is of special relevance for quantum education, where various external representations are available and their effective use is recognised as crucial to student learning. However, research on the effects of informationally redundant external representations in quantum learning is limited. The present study aims to contribute to the development of effective learning materials by investigating the effects of learning with informationally redundant external representations on students' learning of quantum physics. Using a between-subjects design, 113 students were randomly assigned to one of four learning conditions. The control group learnt with a traditional multimedia learning unit on the behaviour of a single photon in a Mach-Zehnder interferometer. The three intervention groups received redundant essential information in the Dirac formalism, the Bloch sphere, or both. The use of eye tracking enabled insight into the learning process depending on the external representations provided. While the results indicate no effect of the study condition on learning outcomes (content knowledge and cognitive load), the analysis of visual behaviour reveals decreased learning efficiency with the addition of the Bloch sphere to the multimedia learning unit. The results are discussed based on current insight in learning with MERs. The study emphasises the need for careful instructional design to balance the associated cognitive load when learning with informationally redundant external representations.

physics.ed-ph↗

arXiv2025

COOL Research DAO Whitepaper -- Towards community-owned astrophysics for everyone

Astrophysics forms a cornerstone of human curiosity and has revolutionised our understanding of the Universe. However, conventional academic structures often hinder collaboration, transparency, and discovery. We present COOL Research DAO, a next-generation framework for cosmic origins astrophysics research that uses decentralised autonomous organisation (DAO) principles to make astrophysics research globally accessible, economically fair, and intellectually open. COOL Research DAO is designed to address four key systemic problems and their manifestations in traditional academic research: general inaccessibility, hierarchical organisation, unfair economic structures, and inefficient knowledge transfer. We describe how these inefficiencies can be addressed using blockchain-based tools and token systems. By fostering bottom-up governance, open-access knowledge networks, and transparent rewards, COOL Research DAO reshapes economic, organisational, and educational paradigms in astrophysics research. Our approach leverages the data-rich and inherently international nature of astrophysics, ensuring a scalable, collaborative platform that welcomes contributions ranging from computational analyses to public outreach. In doing so, we highlight a path toward realising our vision of a truly open research ecosystem, driven by community ownership, intellectual freedom, and shared fascination with our cosmic origins.

astro-ph.IM↗

arXiv2025

The Role of Conceptual Problem Solving in Learning Physics: A Study in a General Relativity University Course

Effective physics learning, especially in complex topics, requires balancing mathematical formalism with conceptual understanding. Conceptual problem-solving involves connecting math to physical reality, and using an epistemological framework like problem framing helps students justify their mathematical decisions. This approach deepens students' understanding by linking theory to practice and enhancing their reasoning skills. This study explores the effectiveness of conceptual problem-solving in learning complex topics like general relativity (GR) through a pedagogical framework that emphasizes the integration of qualitative and quantitative reasoning. We present a case study conducted at the University of Cagliari in 2021 and 2022, examining how students construct problem frames and how this influences their conceptual understanding of GR. Findings indicate that students who effectively integrate conceptual reasoning with mathematical formalism demonstrate a deeper grasp of physical principles and enhanced problem-solving capabilities. The research underscores the importance of symbol sense and the iterative nature of problem framing, suggesting that an integrated approach - combining visual, symbolic, and natural language representations - can improve students' conceptual engagement. Furthermore, the methodology offers instructors valuable insights into students' thinking processes, supporting more effective and targeted feedback.

physics.ed-ph↗

arXiv2025

Revisiting the displacement current: Two key examples showing when and why it can be neglected

This work explores the role of the displacement current in systems beyond capacitors, focusing on coaxial cables and resistors with alternating currents. Although its contribution, compared to that of the conduction current, is negligible at low frequencies, the displacement current becomes essential for accurately describing electromagnetic fields in dynamic regimes. Introductory physics textbooks typically restrict the discussion of displacement currents to capacitor charging, which can limit the students' understanding of its broader relevance and the interdependence of Maxwell's equations. By analyzing two specific cases, we clarify the conditions under which the displacement current can be neglected, when simplified laws like Biot-Savart are valid, and where coupled electromagnetic equations are essential. This approach highlights the boundaries of common models and promotes a deeper understanding of dynamic field interactions.

physics.ed-ph↗

arXiv2025

From Staging to Insight: An Educational Path to Understanding Bell's Inequalities

Quantum Physics is a cornerstone of modern science and technology, yet a comprehensive approach to integrating it into school curricula and communicating its foundations to policymakers, industrial stakeholders, and the general public has yet to be established. In this paper, we discuss the rationale for introducing entanglement and Bell's inequalities to a non-expert audience, and how these topics have been presented in the exhibit "Dire l'indicibile" ("Speaking the Unspeakable"), as a part of the Italian Quantum Weeks project. This initiative aims to make quantum mechanics accessible to all, bridging the gap between complex scientific principles and public understanding. Our approach meets the challenge of simplifying quantum concepts without sacrificing their core meaning, specifically avoiding the risks of oversimplification and inaccuracy. Through interactive activities, including a card game demonstration and the staging of CHSH experiments, participants explore the fundamental differences between classical and quantum probabilistic predictions. They gain insights into the significance of Bell inequality verification experiments and the implications of the 2022 Nobel Prize in Physics. Preliminary results from both informal and formal assessment sessions are encouraging, suggesting the effectiveness of this approach.

physics.ed-ph↗

arXiv2025

Code in Motion: Integrating Computational Thinking with Kinematics Exploration

Although physics has become increasingly computational, with computing even being considered the third pillar of physics, it is still not well integrated into physics education. Research suggests that integrating Computational Thinking (CT) into physics enhances conceptual understanding and strengthens students' ability to model and analyze phenomena. Building on this, we designed a didactic sequence for K9 students to foster specific CT practices while reinforcing fundamental kinematics concepts. The activity revealed students' ability to apply CT skills and is well suited for use in introductory kinematics courses.

physics.ed-ph↗

arXiv2025

Applying a STEM Ways of Thinking Framework for Student-generated Engineering Design-based Physics Problems

This second paper in a multi-part series builds on the first, which introduced the Ways of Thinking for Engineering Design-based Physics (WoT4EDP) framework for STEM education in an introductory undergraduate physics course. Here, we apply the framework to analyze transcripts of group discussions and written reports from 14 student teams as they engaged in a self-generated engineering design (ED) problem in an introductory physics laboratory. We qualitatively examine: (i) the aspects students address in their problem statements; (ii) how they engage in design-based, science-based, and mathematics-based thinking, as well as metacognitive reflection, while developing solutions; and (iii) how they incorporate computational thinking through Python coding. Key findings highlight the need for: (i) increased guidance for iterative problem framing; (ii) structured support for assessing design limitations, engaging in a feasibility study, adopting a systematic approach to applying physics and mathematics in their iterations, and making specific metacognitive reflections; and (iii) integration of Python-based activities into laboratory tasks with appropriate scaffolding. We present our findings through a detailed qualitative analysis, drawing extensively from the qualitative methods literature. We outline our analytical approach, present coding charts, and employ qualitative methods such as thematic analysis and thick description to convey our findings. In doing so, we contribute to ongoing efforts to enhance the rigor of qualitative analysis in physics education research (PER). Based on our analysis, we provide valuable insight for educators and researchers in designing physics-based engineering design tasks and promoting interdisciplinary problem-solving in STEM education.

physics.ed-ph↗

arXiv2025

Schematic Representation Method for Quantum Circuits: An Intuitive Approach to Quantum Gate Effects

In quantum circuits, qubits and the quantum gates acting on them have traditionally been analysed using matrix algebra and Dirac notation. While powerful, these can be unintuitive for conceptual understanding and rapid problem solving. In this work, a new schematic representation method is developed that visualizes the effects of quantum gates on qubits without relying on complex mathematical operations. In the new notation, quantum bits (qubits) are represented using black (0) and white (1) circles. When a quantum gate is applied to a qubit, the circle representing the qubit is visually modified. For example, a Hadamard gate transforms a solid black or white circle into a half-black and half-white circle representing superposition. The work shows how this method simplifies the visualization of quantum algorithms, entanglement, and multi-qubit operations. Thus, the effects of quantum circuits can be analysed with simple schematic representations without having to go into complex mathematical operations.

physics.ed-ph↗

arXiv2025

Combining physics education and machine learning research to measure evidence of students' mechanistic sensemaking

Advances in machine learning (ML) offer new possibilities for science education research. We report on early progress in the design of an ML-based tool to analyze students' mechanistic sensemaking, working from a coding scheme that is aligned with previous work in physics education research (PER) and amenable to recently developed ML classification strategies using language encoders. We describe pilot tests of the tool, in three versions with different language encoders, to analyze sensemaking evident in college students' written responses to brief conceptual questions. The results show, first, that the tool's measurements of sensemaking can achieve useful agreement with a human coder, and, second, that encoder design choices entail a tradeoff between accuracy and computational expense. We discuss the promise and limitations of this approach, providing examples as to how this measurement scheme may serve PER in the future. We conclude with reflections on the use of ML to support PER research, with cautious optimism for strategies of co-design between PER and ML.

physics.ed-ph↗

arXiv2025

Birds of a Feather Undermine Equity: A Strategy to Align Intent and Outcome in Team-Based Learning in Higher Education

Efforts to promote equity in higher education often rely on shared intent among instructors and students. Yet, as demonstrated in this study, when students form their own teams for Team-Based Learning (TBL) tasks, they unintentionally cluster with peers of similar socio-economic backgrounds, ultimately undermining equity. This study introduces a simple strategy to facilitate equitable team formation through a quantitative reflection of students' socio-economic backgrounds and their self-perceived preparedness. When applied, the strategy yielded balanced teams and improved performance. In its absence, team compositions became skewed and class performance declined. These findings highlight a behavioural gap between intent and outcome and underscore the need for structural supports to translate equity goals into practice.

cs.CY↗

arXiv2026

The Quantum Technology Job Market: Data Driven Analysis of 3641 Job Posts

The rapid advancement of Quantum Technology (QT) has created a growing demand for a specialized workforce, spanning across academia and industry. This study presents a quantitative analysis of the QT job market by systematically extracting and classifying 3641 job postings worldwide. The classification pipeline leverages large language models (LLMs) whilst incorporating a "human-in-the-loop" validation process to ensure reliability. The research identifies key trends in regional job distribution, degree and skill requirements, and the evolving demand for QT-related roles. Findings reveal a strong presence of the QT job market in the United States and Europe, with increasing corporate demand for engineers, software developers, and PhD-level researchers. Despite growing industry applications, the sector remains in its early stages, dominated by large technology firms. However, there are signs that change may be forthcoming, indicated by a strong presence of Bachelor's and Master's graduates in the workforce.

physics.ed-ph↗

arXiv2025

Motivating reflection in problem solving: homework corrections in upper-division physics courses

Despite the recognition that reflection is an essential part of problem solving, it is often not emphasized in upper-division physics courses. In this paper, we discuss homework corrections (HWCs) as a pedagogical tool to motivate reflection on homework assignments. We focus on gaining a qualitative understanding of how students may engage with the process of homework corrections, considering potential impacts on content understanding, metacognitive skills, and affect. To do so, we present three comparative case studies to elucidate different aspects of student engagement with HWCs; we also present descriptive statistics of participation in HWCs. We find that HWCs can be a useful pedagogical tool, but more scaffolding may be necessary to support students in identifying and learning from their mistakes, even in upper-division courses.

physics.ed-ph↗

arXiv2025

Directed Self Guided Learning of Blended Math-Science Sensemaking for Historically Marginalized STEM Learners

Blended math science sensemaking (MSS) is reflected in a student ability to integrate math and science knowledge to develop mathematical descriptions of observations. While an important component of scientific thinking, there is little research on teaching MSS. Students from backgrounds historically marginalized in STEM often lack prior learning opportunities needed to succeed in STEM. Supporting them in developing MSS could help them build quantitative understanding and improve STEM performance. Fostering MSS calls for supporting transferable, lifelong skills. We designed and tested a self-guided learning model grounded in simulations and a cognitive framework to achieve transferable MSS. We tested the activities grounded in the framework with 27 students from backgrounds historically marginalized in STEM attending minority serving 2- and 4-year US colleges. We evaluated long and short-term MSS transfer by asking student to complete transfer tasks immediately following and at least 1 week post activity. Most students started at the lowest and progressed to the highest MSS level and demonstrated considerable short and long-term transfer after completing just one activity, suggesting the effectiveness of this approach for fostering transferable MSS.

physics.ed-ph↗

arXiv2025

The role of natural language in understanding the universe: a teaching-learning sequence for high school students

Introducing gravitational physics at high school provides educational means for bridging the gap between the image of science held by students and science itself. Natural language is fundamental in this learning. It engages students in constructing an understanding of a concept or a notion, establishing new relations between previous and new elements of knowledge. We present a teaching/learning sequence (TLS) aimed to contextualize gravitational physics along the lines of the Einstein Telescope educational program in Sardinia devoted to upper secondary school students. We focused on the role of debates and controversy in the evolution of science, proposing science-reflexive meta discourses to present physics as a unified knowledge textbook. We discuss our design and present results by analyzing students' semiotic registers to recap their learning during the activity. Finally, we discuss the potentiality of our TLS in orientating students towards STEM.

physics.ed-ph↗