Metarepresentational competence (MRC) is a theoretical framework that is used to analyze how people create and interact with external representations. Within quantum mechanics, problems may be approached or perceived differently based on the notation used (such as Dirac, Matrix, or Spinor notation) in the problem statement or by the person working on the problem. Semistructured interviews were conducted to present physics students with change of basis content problems in the context of quantum mechanics. These content questions were paired with MRC-focused follow-up questions for the explicit purpose of asking students about MRC concepts directly. Student statements were coded to confirm previously identified MRC concepts and to identify MRC concepts that are novel in this data. Our analysis of three student interviews demonstrates an array of MRC concepts, the usefulness of asking direct questions about MRC concepts as part of an interview, and solidifies MRC as a useful lens for investigating student thinking.

Tablets and smartphones provide compact and relatively inexpensive tools for measuring many physical quantities, and numerous applications of these “mobile devices as experimental tools” (MDETs) have been published over the last decade, covering a broad range of topics. According to the literature, MDETs can offer educational benefits by creating authentic, real-life contexts for physics learning, enhancing student motivation through the use of familiar technology, and supporting cognitive processes by providing multiple representations (videos, tables, and graphs) of physical phenomena. On the other hand, serious concerns have been raised about potential distractions and cognitive overload. Regarding these conflicting perspectives, few empirical studies on the impact of MDETs in real classroom settings of regular, full-length physics courses are available, and—to the best of our knowledge—none focus on a nonspecialized high-school target group. The purpose of this contribution is to present a study of a mechanics course in such a setting, addressing the tight curricular, material, and practical constraints inherent to it. A quasiexperimental pre- and post-test design comparing a treatment group using MDETs and a control group without (same content, lesson plan, and teacher) was used. The 19-week teaching sequence focused on conceptual learning and motivational outcomes (e.g., interest, self-concept, and curiosity), controlled by several predictor variables. Findings reveal substantial pre- and post-test learning gains for both groups (Cohen’s $d=0.9$) and small gains for perceived relation to reality ($d=0.29$). However, no significant differences between treatments were found, indicating that the use of MDETs does not outperform conventional approaches under the given constraints. On the other hand, no evidence of negative effects such as distraction or cognitive overload was observed. Moreover, little to no interactions with predictors such as gender or prior knowledge were found. In conclusion, MDETs show considerable potential as a viable and effective option for integrating technology into physics teaching, offering learning outcomes comparable to those of successful conventional teaching, but not better. Furthermore, no evidence of negative effects from distraction or cognitive overload was found, nor of strong interactions with gender and other predictors. The MDETs approach thus appears suitable for both sexes and different kinds of learners. This leads to suggestions for future utilization of MDETs as a component of physics education, which are discussed as potential perspectives.

How students use mathematics in their physics classes has been studied extensively in the physics education literature. In addition to specific mathematical methods in specific physics contexts, possible effects of more general “cultural” differences between the two disciplines have also been explored. However, there has been little examination of students’ own awareness and interpretations of these differences. We explore the undergraduate student experience of these cultural contrasts, and how students think they affect their learning. Through a qualitative exploratory study, including surveys and interviews with students double majoring in mathematics and physics (or majoring in one and minoring in the other), we investigate students’ awareness of distinct pedagogical approaches, mathematical justifications, and organization of concepts in mathematics versus physics classes. We find that students do recognize and navigate these cultural differences, often employing specific coping strategies. We identify specific themes from our data and comment on how students feel that these themes impact their learning. We suggest that increased faculty and student awareness of the identified differences in educational practice could facilitate knowledge transfer between mathematics and physics.

Understanding the parallelism between electric and magnetic phenomena can be challenging for students in introductory physics courses. This study compares students’ understanding of electric and magnetic fields and forces using parallel multiple-choice questions. Most of the electricity items were drawn from our previously published Test of Understanding of Electric Field, Force, and Flux (TU-E3F), while the magnetism items were newly developed as parallel questions based on the results of our earlier studies. The participants in the present study were 232 engineering students enrolled in a calculus-based electricity and magnetism course at a private university in the northeast of Mexico. We administered a five-item electricity test and a parallel five-item magnetism test to two independent groups of 116 students each and analyzed item difficulty and response patterns using chi-square tests. In this article, we compare students’ performance on parallel items and identify significant differences in the selection of the correct answers and incorrect answers. We also analyze the items by level of difficulty and identify the most frequent incorrect answers. Analysis of incorrect-answer categories highlighted recurrent difficulties with field representations, superposition, and “larger implies larger” reasoning, as well as interference between electric and magnetic ideas. Based on these results, we provide specific recommendations for improving instruction on these concepts. The analyses and recommendations can serve as valuable resources for physics education researchers and instructors teaching these topics. This study offers insights into how context influences students’ conceptual understanding, with implications for enhancing electricity and magnetism education.

Quantum information science (QIS) is a vast, diverse, and abstract field. In consequence, learners face many challenges. Science, technology, engineering, and mathematics education research has found that visualizations are valuable for aiding learners in complex matters. The conditions under which visualizations pose benefits are largely unexplored in QIS education. In this eye-tracking study, we examine the conditions under which the visualization of multiqubit systems with the dimensional circle notation (DCN) in addition to the mathematical symbolic Dirac notation (DN) is associated with a benefit for solving problems on the ubiquitously used hadamard gate operation, in terms of performance, extraneous cognitive load (ECL) and intrinsic cognitive load (ICL). We find that DCN increases performance and reduces cognitive load for participants with little experience in quantum physics. In addition, representational competence predicts reductions in ECL with DCN, but not performance or ICL. Analysis of the eye-tracking results indicates that task solvers with more transitions between DN and DCN benefit less from the visualization. We discuss the generalizability of the results and practical implications.

Introductory physics instruction emphasizes fluency with routine problem-solving procedures. However, even when applying these procedures, students frequently encounter challenges. This paper investigates how students navigate such moments when answering qualitative electricity and magnetism problems in interviews. Students frequently noted they had partially forgotten a key equation on a problem involving RC circuits. We present focal cases that show how coherence-seeking approaches were employed to overcome this problem-solving challenge. In attempts to reconstruct these equations, participants identified and chained qualitative dependencies and sought coherence between qualitative and mathematical understanding of the physical system. These moments of forgetting and reconstructing equations are a useful site for studying broader physics learning goals. While prior work investigates the use of mathematical sensemaking by examining how students respond to explicit prompts, our cases illustrate how students can spontaneously use mathematical sensemaking strategies. We reflect on these cases to consider how such adaptive reasoning can be a target for instruction and assessment.

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 recognized 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 informationally redundant external representations on students’ learning of quantum physics. Using a between-subjects design, 113 students were randomly assigned to one of four conditions. The control group learnt with a traditional multimedia learning unit on the behavior 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 behavior reveals decreased learning efficiency with the addition of the Bloch sphere to the multimedia learning unit. The results are discussed based on current insights into learning with MERs. The study emphasizes the need for careful instructional design to balance the associated cognitive load when learning with informationally redundant external representations.

The current work aims to better understand student course experiences for those who reported negative perceptions in introductory physics. We conducted semistructured interviews with 24 students who reported negative perceptions of their class on a screening survey. Participants were asked to share general reflections on challenges and successes they experienced, as well as their reflections on specific aspects of the course (e.g., experiences with instructors and peers). Interview transcripts were then coded to identify the types of experiences students reported, whether they were experienced as positive or negative, as well as the themes and features associated with those experiences. Experiences with the classroom, course structure, instructors, and exams were most frequently reported as negative. Experiences with peers, help-seeking, course curriculum, and specific learning activities were the most positive, although only experiences with peers had more positive than negative reports. We then used a resources vs demands framework [M. D. Seery, The biopsychosocial model of challenge and threat: Using the heart to measure the mind, Soc. Pers. Psychol. Compass. 7, 637 (2013)] to interpret the common instructional, cognitive, and motivational themes and features reported across multiple contexts. We discuss the implications of the results for theory and practice.

The ideal gas law is a fundamental concept in physics, yet students often struggle to develop a deep understanding of its principles. Despite its central role in secondary school physics and introductory college thermodynamics, research indicates that, even after instruction, students frequently retain fragmented knowledge structures and fail to achieve deep conceptual understanding. To address these challenges, this study develops a conceptual framework to model features of knowledge integration in students’ learning of the ideal gas law. The conceptual framework identifies essential concepts and their interrelationships, which are used to guide the development of a diagnostic tool that targets knowledge integration and deep learning. Administered to cohorts of Chinese high school and college students, the assessment revealed four distinct knowledge integration levels, including novice, lower-intermediate, upper-intermediate, and expertlike, through a combination of quantitative test results and qualitative interview data. Findings indicate that the conceptual framework can effectively capture features of integration in students’ knowledge structures, which can provide valuable insights for developing educational interventions that help students to establish critical connections within their knowledge structures and thereby deepen their understanding of the ideal gas law.

Analyzing and understanding the differences between novices and experts in domains such as physics has been proven to be important for enhancing competence acquisition in that field. This study investigates these differences through an expert-novice comparison by analyzing visual attention, cognitive strategies, and behavior during scientific diagram interpretation. A total of 23 participants (11 novices and 12 experts) completed 10 diagram-based tasks, while their eye movements and verbalizations were recorded. Experts outperformed novices across several dimensions: higher task success (86% vs 70%), significantly greater visual efficiency (23% vs 17%), and longer dwell times in task-relevant areas. Their shorter, more structured scan paths reflected goal-directed, conceptually driven strategies. In contrast, novices showed disoriented gaze behavior, frequent shifts between the diagram and task text, and relied on surface-level reverse-matching strategies, indicating higher extraneous cognitive load. Think-aloud data revealed qualitative reasoning differences: experts used precise, technical language and referenced diagrams accurately, while novices were vague, hesitant, and uncertain. Emotional expressions in novice protocols aligned with signs of cognitive overload. These findings support cognitive load theory, suggesting experts draw on schemas to manage intrinsic load, while novices struggle with element interactivity. Unexpectedly, some experts in the study showed novicelike behavior, whereas some novices exhibited patterns typically associated with expert performance. Novicelike experts often lacked recent exposure to diagram-related coursework. Conversely, some novices demonstrated efficient gaze patterns and structured scanning but still made conceptual errors. To contextualize human performance, two large language models (ChatGPT-4 and DeepSeek-R1) were tested on the same tasks. ChatGPT-4 reached an overall success rate of 50%, handling simple extractions but failing with visual relationships. DeepSeek-R1 performed poorly (10%), revealing current AI limitations in visual interpretation. These results underscore the uniquely human capacity for visual reasoning, schema activation, and metacognitive monitoring, which AI still lacks. The findings emphasize the critical role of graph literacy, representational competence, and cognitive strategy use in diagram interpretation. They highlight the need for explicit instructional interventions to help novices develop expertlike visual attention patterns and reasoning skills.

We investigated sustained departmental change catalyzed by three Departmental Action Teams (DATs) that worked on change projects independently following an initial period of external facilitation. Using qualitative analysis of interview data, we documented four main categories of change catalyzed by DATs, three categories of supports for change, and four categories of constraints on change. DATs accomplished a wide variety of sustained changes, and DAT members frequently leveraged their individual learning to benefit the work in departmental groups outside of their DAT. Change was documented at the levels of the individual, the group, and the organization (i.e., department or university), suggesting that the DAT model is capable of supporting organizational learning at all of these levels. Additionally, DATs successfully used levers of project prioritization and positional power to generate sustained change. DATs did not rely heavily on support outside of their departments to accomplish sustained change. This study provides insight into the mechanisms by which departmentally based change teams accomplish change in departmental cultures, practices, and processes influencing science, technology, engineering, and mathematics education.

Integrating problem-posing activities into instruction fosters students’ critical and creative thinking while deepening their understanding of problem solving. However, complementing the problem-solving process with direct mental processes such as recalling memorized information will make a limited contribution to meaningful learning. In this context, having students construct their own problems and use metacognitive strategies while doing so will increase their cognitive awareness in the problem-solving process. Drawing on this perspective, the present study investigates the processes through which preservice physics teachers pose nonroutine physics problems, focusing on the metacognitive strategies they employ and the pedagogical beliefs they hold during these processes. The study was conducted with 20 volunteer preservice physics teachers from different grade levels at a public university. Data were collected through a five-item problem-posing task, a metacognition-oriented reflection form, and a process-based opinion form, and were analyzed qualitatively. The findings indicated that nonroutine problem-posing performance generally increased with grade level and that preservice physics teachers actively used metacognitive strategies such as ease of learning, decision making about learning, experiencing a sense of knowing, and confidence in the answer during the problem-posing process. Nevertheless, participants faced difficulties, particularly in evaluating alternative solutions and engaging in creative thinking. Despite these challenges, they maintained a positive attitude toward problem-posing activities, highlighting the potential of nonroutine problem posing as an effective pedagogical tool in physics teacher education.

Learners often struggle to develop expandable mental models of polarization due to its abstract nature and the multitude of models used to describe it. A closer examination of the structure of mental models for linear polarization is therefore worthwhile in order to gain insight into mental abstraction processes. Existing research has largely documented misconceptions, leaving the underlying cognitive structures of mental models insufficiently explored. To address this gap, we employed the Fidelities Model of Conceptual Development (FMCD) to investigate learners’ cognitions of linear polarization. The framework, distinguishes two dimensions of students’ mental models: Gestalt, which refers to visual and structural representations, and Functionality, which captures how well a model explains underlying processes. The degrees to which these dimensions align with reality allow for a typification of learners’ reasoning patterns. We developed a test instrument based on established students’ mental models and validated it through expert review and think-aloud studies. In a cross-sectional survey with $N=178$ German secondary school and university students, confirmatory factor analysis confirmed a robust two-factor structure ($\mathrm{CFI}=0.96$, $\mathrm{RMSEA}=0.03$, $\mathrm{SRMR}=0.07$) with solid factor-reliability (${\omega }_{\text{FF}}=0.71$, ${\omega }_{\text{FG}}=0.81$). Descriptive results showed developmental trends: while secondary students often exhibited “dual” models combining both FG and FF, university students increasingly relied on functionally oriented reasoning. The findings validate the FMCD in the domain of polarization and provide a diagnostic tool that informs instructional design for supporting students’ conceptual development in optics.

Understanding the mechanisms of student sensemaking while navigating the physics problem-solving process can play an important role in developing approaches to helping students become proficient problem solvers. Since most prior studies on student sensemaking in physics have focused on introductory physics, this study sheds light on a relatively unexplored research area involving advanced physics students’ sensemaking. We conducted individual interviews with graduate students to investigate their sensemaking while solving upper-level undergraduate electrostatics problems in the context of the method of images. Analysis through the lens of the epistemic game framework proposed by Tuminaro and Redish shows that the central part of student sensemaking can be mapped onto the Pictorial Analysis game, with other epistemic games also playing a role, but the ontological components of some games require refinement. The study involves an in-depth comparison of sensemaking on related but distinct problems for individual graduate students and a comparison between multiple students solving the same problems. It provides insights into how graduate students transfer and translate strategies between different problems while sensemaking. Graduate students showed persistence in activating different knowledge resources and consistent use of reasoning primitives across different problems, such as a “balancing” primitive multiple times while sensemaking. The study investigated the impact of small nudging and scaffolding that resulted in significant improvements in graduate students’ problem-solving approaches. Another novel finding is that graduate students’ problem-solving approaches significantly improved with successive attempts and multiple drawings for the same problem and across problems. Often, graduate students initially drew more three-dimensional figures with conducting planes given in the problem statement to visualize and understand the problem; they also drew diagrams from different viewing angles, which helped in improving their physical understanding and comprehension of the symmetry of the underlying problem.

Generative artificial intelligence (GenAI) offers strong potential to transform teaching practices; however, empirical research on its classroom effectiveness remains limited. This study explores how GenAI can be integrated into preservice physics teacher training by replacing two traditional instructor roles in an instructional design course: providing evaluative feedback and facilitating collaboration. A GenAI-based assistant was developed to assess instructional designs according to predefined criteria and to provide personalized feedback. A total of 110 preservice physics teachers received feedback from one of the three sources: a teaching expert, a teaching assistant, or GenAI to revise their instructional designs. They subsequently collaborated with GenAI for further refinement. Results indicate that GenAI evaluations closely aligned with those of human experts and teaching assistants. In blinded evaluations, preservice physics teachers rated GenAI feedback as comparable to human feedback. Furthermore, collaboration with GenAI resulted in significant improvements in the overall quality of instructional design. This progress was particularly most evident in the structured, content-expandable components. While these findings demonstrate GenAI’s feasibility from a functional perspective, challenges related to preservice teachers’ perceptions also emerged. Although design quality improved through collaboration with GenAI, independent design skills, measured by a final paper-and-pencil test, showed no similar improvement. Preservice physics teachers acknowledged the need to filter and revise GenAI-generated content, but often directly adopted its suggestions due to the convenience of GenAI. Notably, feedback was rated lower once participants realized it was AI-generated, even if the actual source was not, revealing trust-related concerns. This study moves beyond technical evaluations of GenAI, offering insights into the pedagogical challenges and limitations that arise when GenAI assumes the roles that are traditionally performed by human educators.

In the world of science, technology, engineering, and mathematics education practice, alternative grading strategies have been implemented and disseminated with the goal of reinforcing student outcomes like productive reasoning, motivation to learn, and sense of identity. However, while PER has successfully improved these outcomes through reformed instructional strategies, much less work has investigated how grading practices influence these outcomes. This dearth leaves PER without a framework readily available to formulate or interpret studies of alternative grading practices. To help address this gap, we surveyed $\mathit{N}=94$ students from introductory algebra-based and calculus-based physics courses, asking free-response questions about their experiences with and perspectives on grading in physics. We thematically coded their responses to identify themes in what they said grades represent (such as their effort invested in the course or their mastery of course content) and what effects they said grades produce (such as stress or an adversarial relationship with the instructor). We conducted focus groups to member-check these themes with the students. For themes about what they said grades represent, we further identify whether the student framed this representation positively (“Grades should represent my effort”), negatively (“Grades should not represent the features of a particular assignment”), or neutrally or in mixed terms. We particularly attend to whether students indicated that grades produce an adversarial relationship with their instructor, finding that a greater percentage of these students positively spoke of grades as representing improvement in their performance than among students who did not mention an adversarial relationship. We discuss how these themes offer insights into how we might further research alternative grading strategies, how students’ perspectives on grades might influence the broader goals of PER, and implications for physics instruction.

Research indicates that students learn effectively when they actively engage in planning, monitoring, and reflecting on their learning—a process known as self-regulated learning (SRL). This mixed-methods study examined the impact of a semester-long SRL intervention in an undergraduate physics course. In the first year, the instructor taught the course under standard conditions. The following year, after brief training sessions, the same instructor added digital prompts targeting various aspects of SRL to their course assignments. Results showed that students in this intervention group performed better on the final exam after controlling for preexisting self-efficacy, metacognitive awareness, and GPA. However, SRL outcomes did not increase in the intervention condition. Analysis of the prompts revealed that the instructor disproportionally focused on content- and management-related prompts and underutilized motivation, metacognition, and cognitive strategy prompts. Interview with the faculty indicated that the intervention was straightforward to implement, contributed to humanizing the course, and that additional training would have been desirable to help design prompts. Provided appropriate training and support structures are available, these findings show that integrating SRL strategies through digital prompts can be a practical and effective approach for supporting instructors in fostering students’ SRL.

The interplay of mathematics within physics—termed here as physmatics—presents unique cognitive challenges for students, requiring coordination between mathematical reasoning and physical sensemaking. While previous studies have documented common physmatic difficulties, capturing these challenges as they emerge in classroom instruction is rare. This study analyzed 273 teacher–student interactions from 23 video-recorded physics lessons taught across a diverse range of classrooms, aiming to identify and categorize physmatic difficulties as they naturally arose during instruction. Twenty-four codes of difficulties were identified through content analysis and grouped into five overarching clusters: (i) questions about model components, (ii) questions about the model, (iii) difficulties applying mathematics in a physical context, (iv) interrepresentational fluency, and (v) unit-related difficulties. A key finding of this study was the identification of systematic associations between the modeling skills teachers aimed to develop (i.e., mathematization, manipulation, interpretation, and validation) and the corresponding student difficulties. These findings underscore the centrality of modeling as a pedagogical framework for physics instruction and suggest that teachers who are aware of the links between skills and difficulties may be better prepared to anticipate student struggles, respond to them in real time, and even leverage them as part of their instructional practice.

Think-aloud interviews were used to investigate college students’ cross-disciplinary understanding of energy concepts. Interview subjects were enrolled in a set of four science content courses (physics, biology, geology, and chemistry) for preservice K-8 teachers. These courses, built around the common theme of the flow of energy and matter through interacting systems, use similar vocabulary, modeling tools, and pedagogy to teach energy concepts. The interview tasks were designed to probe how students apply energy concepts originally learned in the physics course in less familiar contexts in geology, biology, and chemistry. Transcripts were analyzed using a coding scheme based on conceptual resources. Thematic analysis was then conducted to identify common patterns in students’ cross-disciplinary reasoning, particularly with regard to potential energy. The constructs of disciplinary and situated productivity were used to guide the development of themes. We find that students engage in productive reasoning about energy across disciplines. Students activate ideas related to energy forms and the objects to which these forms are attached with relatively high frequency, and ideas related to physical indicators and mechanisms for energy transfers and transformations with relatively lower frequency. Students apply potential energy concepts across disciplines, but often struggle to identify the physical manifestations of potential energy changes in less familiar contexts. While this study was conducted in a set of courses for preservice teachers, the findings have broader implications for introductory physics courses that serve as prerequisites for other disciplinary coursework.

This study examines how the Minnesota Assessment of Problem-Solving rubric can be used to diagnose learning needs in secondary physics education. In total, 51 students (grades 9 and 11) from 5 German secondary schools solved a physics problem-solving task and completed an energy concept test. Rubric-guided analysis of their written problem solutions revealed seven characteristic performance patterns, ranging from expertlike reasoning to incomplete or failed approaches. While students generally managed descriptions and basic calculations, many struggled to apply the conservation principle and to structure their reasoning coherently. The combination of rubric scores with conceptual test results highlighted whether difficulties stemmed from missing knowledge or from challenges in applying it. These findings demonstrate that this combination of assessment tools, adapted to the secondary level, offers a practical approach for formative assessment and targeted support in physics problem solving. However, difficulties arise when students submit incomplete problem solutions. Future developments could focus on atomized approaches or the integration of AI technologies for automatic assessment.