Measurement claims carry high stakes, yet students and early-career professionals rarely receive explicit training in the reasoning chain that justifies them. Despite growing emphasis on transferable competence, measurement reasoning remains a blind spot: learners seldom map a measurand (the quantity of interest) to an estimand (the reported quantity inferred from data), anchor inference in an explicit noise or likelihood model, or report results with uncertainty and traceability. This fragmentation weakens rigor and communication across domains. We define cross-disciplinary measurement literacy as the ability to connect a measurand to an estimand, justify inference under explicit noise and likelihood models, and report results with uncertainty and traceability. We operationalized this construct through a unified $\mathrm{Encoding}\to \mathrm{Evolution}\to \mathrm{Readout}\to \mathrm{Estimation}$ schema integrated with metrological closure and implemented it in a $4\times 2\text{−}\mathrm{h}$ module. This multicohort descriptive evaluation includes five cohorts with verified pre- and postadministration records ($N=114$) and two undergraduate team-task cohorts. Cohort-level summaries showed immediate post-test means 34–54 points above pretest means and normalized gains of 0.642–0.782 on an intervention-aligned assessment. Team rubric summaries provided evidence of feasible group-level enactment of the schema, while uncertainty budgeting and traceability remained the principal difficulties. This study is designed as a bounded descriptive evaluation. It provides evidence for the schema’s teachability and its utility as a short-term organizer for measurement reasoning, specifically within the instructional context studied.

The controlled-not (cnot) gate is essential to algorithms in quantum computing for its ability to entangle qubits. As such, it is important to understand how students learning quantum computing reason around the function and use of this critical quantum gate. To investigate this, we conducted think-aloud interviews in which students solved problems involving the cnot gate to understand students’ “cnot toolbox”—the strategies and cognitive resources students use when reasoning about the effect of the cnot gate. We identify three cognitive resources related to the cnot gate: (1) the procedural resource of applying cnot to specific states, (2) a qualitative description of cnot’s effect on the target qubit given the control qubit, and (3) the idea that the control qubit is not changed when cnot is applied to computational basis states. We find that students’ use of the first resource is foundational to their understanding of the second and third, that the second and third resources can sometimes lead students to incorrect conclusions, and that students can use each of these resources separately or in tandem. We also explore how students use these resources in conjunction with Dirac notation, superposition states, and entanglement to reason both productively and unproductively about quantum computing problems.

Despite daily observations of the Sun, many students continue to struggle with the mechanisms explaining its apparent motion. Even after formal instruction, students often develop only fragmentary understandings and construct alternative mental models. This study investigates these models in depth to gain genuine insight into the knowledge structures students develop regarding the Sun’s apparent motion. We conducted individual task-based think-aloud interviews with 16–18-year-olds in which they articulated their mental models verbally, through drawings and by using three-dimensional materials. These explanations were then analyzed to determine whether the mental models included the essential elements, characteristics, and connections consistent with scientific understanding. The analysis showed that students often described individual aspects of the phenomenon correctly, but rarely provided adequate allocentric explanations. Missing components in their models were frequently supplemented with alternative ideas that clustered around five themes: cardinal directions, distance, orientation of Earth’s axis, lines of sight and sunrays, and the orientation of the Sun’s orbital plane. These themes, the variety within each, and the implications of our findings are discussed in detail.

Promoting students’ interest in physics is a key goal of physics education. Describing students’ types of interest provides a great opportunity to offer practical and gender-independent recommendations to teachers for designing interesting learning activities. We investigated students’ types of interest in physics and their association with different student characteristics in a cross-cohort study involving German-speaking students aged 14–16 years ($N=1219$). We assessed the students’ interest in a classical and a modern physics content area, namely, mechanics and particle physics, as well as different student characteristics, such as physics-related self-concept. The collected data on students’ interest was analyzed using mixed Rasch models to unveil qualitative differences in the assessed constructs between different groups of students. The study showed that the vast majority of students (71%) can be categorized into one single type of interest in both content areas. Students of this first interest type were only interested in physics content set in certain contexts, for example, the context “one’s own body.” The second type of interest was specific to the different content areas. Students of the second interest type had relatively high physics-related self-concept and were interested in physics content, even when set in scientific or technical contexts. Whether students belong to one or the other type of interest was best described with a model comprising their degree of physics-related self-concept and their sex. Finally, we introduced the hierarchy of students’ levels of interest in physics (HOLIP) to describe the relative interestingness of different contexts for the first type of interest (i.e., the vast majority of students). We recommend using the HOLIP as a guideline for designing learning activities that promote interest in physics.

Various active learning methods have been developed for introductory physics, and these methods are increasingly being adopted by instructors. However, instructors often do not implement these methods exactly as was originally intended by the developers, as they may face issues related to funding and institutional support for active learning and/or have different instructional contexts (e.g., student populations) and environments (e.g., physical classroom layouts) than the developers. Existing research does not sufficiently capture the range of variation in instructor implementation of established active learning methods, especially in comparison with high-fidelity implementations. In this study, we first identify the critical components (i.e., components without which the active learning method cannot be said to have been implemented) of three named active learning methods: Student-Centered Active Learning Environment with Upside-Down Pedagogies (SCALE-UP), Investigative Science Learning Environment (ISLE), and Tutorials. We then evaluate the fidelity with which 18 different introductory physics instructors implement these methods by analyzing classroom observations and comparing the extent to which these broader implementations use each critical component in their classroom to high-fidelity implementations. We find across all three active learning methods that broader implementations and high-fidelity implementations spend similar amounts of class time on critical components. At the same time, we observe substantial variation in the sequences of activities through which broader implementers operationalize these critical components (e.g., doing a few long activities versus many short activities). Finally, we find no clear relationship between fidelity of implementation (as measured by student and instructor behaviors during class) and student conceptual learning gains for our study’s sample of instructors.

The interplay between mathematics and physics mutually affects both disciplines and is the subject of ongoing research. Here, we study the interplay in the empirical context of an MSc program for practicing high-school physics teachers putting strong emphasis on advanced physics courses taught by active physicists, together with pedagogical content courses taught by physics education researchers. Which aspects of the interplay between mathematics and physics do teacher instructors wish to convey to the teachers? We held semi-structured interviews with the physics instructors of the program, focusing on their goals for their courses. Thematic analysis of the interviews exposed several aspects of the interplay that instructors reported on integrating in their teaching, resulting in a characterization consisting of three families. The first strengthens established aspects in the literature: coherence, a tool for calculation, and mathematical derivation of new physics results (extraction). The second highlights new facets of existing aspects: the universality of geometry in physics, limits of approximations as invitations to explore, and simulations as virtual experiments (representations). The third comprises aspects that are less prominent in the physics education literature: concretization of abstract mathematics in physics contexts, and conflict as a mechanism for discovery (e.g., the Lorentz force’s dependence on velocity conflicting with Galilean invariance). Our findings provide a framework bridging tertiary physics and teaching across all levels—aspects of the interplay between mathematics and physics that are manifest in advanced physics could inform curricular design for high school and beyond, and for teacher education.

Motivated by the question of how the design of online team-working activities affects learning experiences, we present an analysis of three such activities studied by advanced undergraduate and postgraduate distance learning students in astrophysics and space sciences. The activities incorporate periods of team-working ranging from 1 to 9 weeks and have varied assessment strategies. Our study focuses on participation rates, the nature of student interactions, and the reported student experience and is informed by the content of asynchronous discussion forums and interviews with students. We find that variation in student participation differs between the three activities, and we suggest reasons for this related to activity design. We identify major themes of student interaction, these being related to learning and development, group building, and team self-organization. The incidence of communications in these thematic areas appears similar across all three activities. Our analysis framework includes subcategories of these themes, and interactions indicative of peer learning are found to be a major component of student communications. Such interactions are enhanced at the times at which teams are required to make major decisions to progress their joint work. Interviews with students reveal anxieties about participation in team-work and unequal contributions to group outputs. They also present a range of views about the different assessment models used. Overall, interviewees from all three activities report having positive experiences in their teams and that they see the activities as valuable for their individual learning as well as being useful preparation for future employment.

Providing appropriate support is important for helping students manage conceptual difficulties in physics. Established scaffolding methods, such as structured tiered support, can be effective but are often resource-intensive to develop and implement broadly. AI chatbots may offer a more easily scalable alternative, but their potential as learning support tools needs to be examined carefully and in direct comparison with established forms of support. As a first step, this study compares a custom-configured AI chatbot, a tiered support system, and traditional textbook-style textual support with respect to students’ perceived cognitive load and affective-motivational outcomes during physics problem solving. In a cluster randomized field study, 268 ninth-grade students in Germany worked individually on a buoyancy problem using one of the three support formats. We measured intrinsic and extraneous cognitive load and affective-motivational outcomes (enjoyment, hope, hopelessness, self-efficacy, and situational interest) via research-validated questionnaires. Results showed that the AI chatbot and the tiered support system were associated with significantly lower perceived intrinsic and extraneous cognitive load than textual support. Post-test comparisons showed that students in the chatbot condition reported more favorable affective-motivational outcomes than students in the textual-support condition, while differences between the chatbot and tiered-support conditions were not statistically significant. Overall, the findings suggest that interactive support formats may shape students’ short-term perceived cognitive and affective-motivational experiences during physics problem solving; future research should examine how these experiences relate to solution quality, conceptual learning, and longer-term outcomes.

This study examines the extent to which physics graduate teaching assistants (TAs) are aware of introductory physics student thinking and the types of challenges introductory students commonly have with energy and momentum concepts, which is important for implementing active learning methodologies and supporting diverse learners in physics courses. We present findings from a TA professional development course and discuss an approach to investigate TAs’ pedagogical content knowledge, specifically their ability to recognize introductory student conceptual difficulties. We investigated 70 first-year graduate TAs’ ability to identify common introductory physics student alternate conceptions on the Energy and Momentum Conceptual Survey (EMCS). The TAs participated in a professional development course that emphasized reflection on introductory student thinking patterns to promote evidence-based pedagogical practices. TAs predicted the most common incorrect answers introductory students would select after lecture-based instruction, then compared their predictions with actual data from introductory students followed by a class discussion. This reflection process can promote robust understanding of introductory student thinking patterns, which is essential for effective teaching that accounts for how introductory students make sense of physics concepts. Results reveal gaps between TAs’ perceptions and introductory student thinking, with TAs performing poorly on many of the analyzed questions. For example, TAs consistently overestimated that introductory physics students would use novice-like thinking in many situations posed in EMCS problems, i.e., they expected introductory physics students to make more novice-like errors than they actually did. These findings have important implications for effective instructional design, e.g., physics TAs who misunderstand introductory physics student capabilities may inadvertently create barriers to learning by spending valuable class time on either overscaffolding or underchallenging introductory physics learners and not spending time on pedagogical issues that are important to address.

There are few studies that compare several theoretical models concerning conceptual understanding. We hypothesize that different models can provide complementary perspectives. In this work, we analyze the video and audio data from an interview with one student (Mark) using three different theoretical models: framework theory (FWT), knowledge-in-pieces (KiP), and social semiotics (SS). The interview discusses distances and sizes in the local universe (Earth, Moon, and Sun) and observable astronomical phenomena: the apparent sizes of the Moon and Sun, solar eclipses, and lunar phases. The results suggest a misconception (from FWT), a localized p-prim (from KiP), and a transductive chain (from SS). However, much more than the individual contributions, the results suggest the complementary nature of the different models. We argue for more work that combines different models both to understand data in a more detailed and nuanced way and to advance theory.

The completion of graduate-level coursework is an important milestone on the path to a doctoral degree in physics. Yet the structure and content of the graduate curricula remain largely undocumented. Here we provide the first national-scale analysis of the graduate-level quantum curriculum, drawing on catalogs from 184 institutions, 121 core quantum course syllabi, and 91 quantum field theory (QFT) course syllabi. Our results reveal the majority of graduate programs require two quantum courses (60.3%) and most commonly use Sakurai’s Modern Quantum Mechanics textbook (41.2%). Core quantum syllabi converged on four canonical topics: kinematics, angular momentum, approximations, and dynamics. While QFT may be considered advanced coursework that is not necessary for all research fields, it remains essential for describing relativistic and multiparticle systems, yet it is nearly absent from the physics education research (PER) literature. We found that 39% of graduate programs had no formal QFT course offering. Statistical analyses revealed that smaller graduate programs with less research activity were more likely not to offer a QFT course, raising concerns about equity and access. Among institutions that did offer QFT courses, a canonical set of topics emerged: interacting fields, Feynman diagrams, quantum electrodynamics, and radiative corrections. We provide comparisons to the undergraduate quantum curriculum, as well as recommendations to instructors and programs.

Initial physics teacher education frequently approaches kinematics problem solving as a procedural activity, with limited engagement in conceptual reasoning, argumentation, and metacognitive regulation. This study examines the effects of Socratic dialogue mediated by generative artificial intelligence (GAI), compared with teacher-guided Socratic dialogue alone, on discipline-specific critical thinking (CT) in one-dimensional kinematics. A concurrent mixed-methods, within-group preexperimental design was implemented with 18 preservice physics teachers working in small groups across two sequential phases using parallel kinematics problem sets. Because the instructional conditions were implemented in a fixed order, the observed differences cannot be disentangled from possible practice, learning, and carryover effects. In the first stage, students engaged in instructor-guided Socratic dialogue; in the second stage, the same structure was maintained while incorporating GAI-mediated Socratic support under instructor supervision. Critical thinking was assessed through an analytic rubric applied to written group solutions and complemented by Likert-scale surveys and open-ended responses. Rubric scores showed consistent improvement during the GAI-mediated phase across all groups, with no observed declines. Students also reported higher self-efficacy and intrinsic motivation, while cognitive load exhibited heterogeneous responses associated with the need for verification and epistemic control when interacting with GAI. These results suggest that integrating generative AI into a teacher-mediated Socratic framework can support critical thinking in kinematics, although the sequential preexperimental design requires cautious interpretation.

Project-based learning (PBL), recognized as an active learning strategy, has been linked to students’ self-efficacy in prior studies, including those within physics education research. Meanwhile, technological advancements have significantly facilitated the optimization of diverse learning modes, including online learning. However, comprehensive investigations addressing questions such as how students perceive PBL and their self-efficacy, what forms of PBL design they prefer, and what benefits and challenges they encounter during its implementation remain underexplored in existing literature. This work presents the results of 1- and 2-year pedagogical research on 10 students as preservice physics teachers in an online PBL physics class, focusing on its influence on their self-efficacy within a phenomenological study. Data were collected via semistructured, in-depth interviews. Social cognitive theory, Bandura’s self-efficacy theory, and a theoretical framework for the impact of project-based learning on educational outcomes were employed as guiding frameworks to shape the interpretation of students’ experiences and perspectives. Through interpretative phenomenological analysis, the researchers identified three primary themes representing the students’ experiences. There are (1) variety of unique learning experiences based on students’ perceptions about their character, (2) pivotal experiences as catalysts in the learning process, and (3) student self-awareness. The findings contribute novel insights for educators in implementing PBL, particularly in online contexts, by highlighting strategies to accommodate diverse student personality characteristics. Moreover, the latest findings in this study, compared with relevant research that has been done previously, are discussed. The study offers valuable references for research on the interplay between PBL and self-efficacy. Possible directions for further research are discussed.

We compare open- and closed-response versions of two questions that measure students’ reasoning on the Physics Measurement Questionnaire, same mean different spread (SMDS), and different mean same spread (DMSS). We conducted an experiment in one class ($N=248$) to test if asking students for their reasoning on an open-response question changes their answer to the closed-response question. To test whether answering the open-response question alters students’ closed-response answers, we prompted half of the students to explain their reasoning before seeing the closed-response options, while the other half went straight to the closed-response reasoning options. We find no effect of asking students their reasoning in an open-response question on their subsequent closed-response answers. Additionally, we investigated whether we measure students’ reasoning differently on the closed-response versus open-response versions of the question by evaluating the consistency between the students’ open-response and closed-response answers. Although we measure similarities in students’ reasoning across the two methods, the differences indicate that the open-response and closed-response questions provide different information. The results inform the need for critical judgment when deciding between open- and closed-response assessment formats.

Large language models (LLMs) often face challenges in generating accurate and coherent explanations when solving physics questions. Prompt engineering serves as an effective strategy for human-artificial intelligence communication, guiding LLMs to generate precise and contextually relevant responses with well-designed instructions. The study utilized prompt engineering on the Coze platform to construct two types of instructional agents: a teacher-centered agent and a student-centered agent. They were designed to respond to students’ questions in accordance with their respective roles and communication styles. Specifically, the teacher-centered agent tended to provide authoritative, professionally grounded, and content-focused responses, whereas the student-centered agent was designed to be more attentive to students’ prior knowledge and learning needs, offering adaptive and supportive guidance. The study compared the effects of these two agents on students’ learning performance, cognitive load, flow experience, and empathy perception. The results revealed differential effects between the two prompt-engineered agent conditions. Compared with the teacher-centered agent, students interacting with the student-centered agent condition showed higher learning performance, lower extraneous cognitive load, stronger germane cognitive engagement, greater flow experience, and higher empathy perception.

Physics students, teachers, and preservice teachers (PSTs) struggle with the abstract nature of quantum mechanics (QM), which has led to calls for a more conceptual approach to QM teaching and learning. In response, this study uses a novel analogy between Kundt’s tube and the infinite quantum well to elicit discussion of ontological issues. We investigated PSTs’ use of ontologies, including their interpretation of the wave function. Nine PSTs participated in the analogy lesson; dialogues were recorded, transcribed, and thematically analyzed. We identified five different ontologies: one classical and four quantum ontologies. The importance of probabilities in PSTs’ quantum ontologies stood out. Three ontologies (probabilistic particle, particle-wave, and probabilistic wave) expand the particle-wave duality, while the fourth (wave collapse) added a dynamic element to this axis. PSTs often used a single ontology in response to one aspect of the analogy but switched flexibly between ontologies across aspects of the analogy that they discussed. Concerning the wave function, we found both realist and formalist stances, revealing a diversity of interpretations that contrasts with the uniformity of the formalist QM courses PSTs had attended. We conclude that explicit attention to ontological issues in QM, supported by classical-quantum analogies, provides insight into PSTs’ ontological reasoning and offers a conceptual approach to teaching and learning QM. We present recommendations for PST training and implications for QM teaching reform.

The physics education research (PER) literature on quantum mechanics (QM) often acknowledges and minimizes what we refer to as the enigma of QM, viewing these aspects of QM as a challenge to overcome, rather than an inherent feature to be leveraged for learning. Using the overlapping theories of knowledge-in-pieces and resource theory as connected to an epistemological framing perspective, we focus on students’ descriptions of the enigma of QM and the epistemological frames that students view as relevant when approaching QM. Data comes from interviews with 10 undergraduate physics students who had learned quantum physics topics across different courses in the curriculum, ranging from sophomore-level modern physics to an advanced undergraduate-level QM course. To elicit students’ ideas on QM, the interview protocol emphasized their perspectives and empowerment when possible. Iterative rounds of qualitative analysis coded the data for how students described enigmatic aspects of QM, along with three epistemological frames students identified as their reasoning strategies: reasoning about scale, reasoning about the connections between QM and mathematics, and reasoning about the connections between QM and classical mechanics. The results document that students are aware that something about QM is unexplainable, an enigma to acknowledge. We argue that acknowledgment of the enigma of QM is a key part of what we refer to as thinking quantumly. Additionally, the epistemological frame of reasoning about scale has not been widely discussed in the QM-PER literature, which students use to distinguish QM from classical mechanics and to explain why mathematical models are needed. These results are important for amplifying students’ voices in how they approach enigmatic aspects of QM. Thus, our results begin to move the QM-PER literature beyond viewing enigmatic aspects of QM as obstacles to be corrected through refined instruction, toward an asset-based orientation as a source of meaningful insights for the learning process.

This study analyzed the relation between self-efficacy (SE) and sense of belonging (BL) in introductory physics courses by measuring these variables at two time points, early in the semester and midsemester. The study was performed in the introductory, calculus-based mechanics class at a large university in the United States and includes 1373 complete records. An extensive set of Observed Prior Causes (OPCs), including Force and Motion Conceptual Evaluation pretest scores, college and high school preparation variables, high school physics and math variables, personality variables, and demographics, were found to be predictive of SE or BL. Early in the semester, SE and BL were highly correlated ($r=0.56$); after controlling for OPCs, $r=0.37$ of this correlation remained. SE fully explained the relation of BL to midsemester test average, while OPCs fully explained the relation of SE to test average. Changes to SE and BL in response to course feedback in the form of test averages were also explored. Test average explained little of the relation between early and midsemester SE or BL. The analysis supported a model where test average predicted midsemester SE, which in turn predicted midsemester BL. Mediation analysis found both directed and correlational paths were important in explaining the complex relation of these variables. Some moderation effects were detected, but were generally small.

This paper presents a social network analysis of the professional support networks of 100 LGBTQ+ and/or women Ph.D. physicists, comparing the networks based on the career sectors of academia, industry, and government/nonprofit. The methods for constructing and analyzing the ego networks, which are novel in many ways, are explained in greater detail in an earlier publication (C. Hatcher et al. Phys. Rev. Phys. Educ. Res. 21, 020603 (2025)). We describe the networks of the whole group and use statistical tests of independence to explore differences between sectors in terms of whole network metrics, network composition based on alter (network member) characteristics, and support. We find that alters associated with groups (like affinity groups and personal and professional interest groups) are more likely to provide identity-based and community-building support, participants in academia have fewer personal friends in their networks, while those in industry have more; participants in government report less instrumental support, and those in academia report less material support. These results and others lead to suggestions for employers in these sectors on how to better support these physicists, including continuing to promote participation in affinity and interest groups, providing more material support and/or personal time in the academic sector, and more instrumental support in the form of professional development or training in the government sector.

This study examines the pedagogical quality and instructional adequacy of analogies included in high school physics textbooks (grades 9–12) in Türkiye. The analogies extracted systematically from 15 physics textbooks revealed a significant imbalance in their use across grade levels. The vast majority of the analogies were concentrated in the 10th grade textbooks, while their occurrence in other grades remained quite limited. A similar imbalance was also observed in subject focus: most of the analogies were allocated to the conceptually challenging and highly abstract topic of electricity, while other fundamental physics topics were largely neglected. In terms of pedagogical quality, all of the analogies were classified as either moderate or good according to Glynn’s teaching-with-analogies model. However, most of the analogies reviewed lacked a step for identifying their limitations, thereby increasing the risk of misalignment and the development of misconceptions. The analogies were also predominantly of the concrete-abstract type, which helps students connect abstract physics concepts to concrete examples from daily life, and were largely based on functional similarity, meaning they focus on how the concept works rather than its structural features. Furthermore, the increased emphasis on the relevance of analogies to learners’ backgrounds reflects a positive trend toward enhancing the contextual richness of analogies. To address the quantitative insufficiency of analogies and the imbalance across subject areas, it is essential that curriculum developers position analogical thinking as a required pedagogical tool for textbook authors.