A deep understanding of mathematical equations and their physical meaning is an important skill for physicists and therefore a central learning goal in university physics education. However, many students approach mathematical expressions in physics in a purely procedural manner, using them as calculation tools without critically evaluating their physical plausibility. Making sense of equations, that is, being able to interpret and evaluate equations within a physical context, is essential for the development of expertlike reasoning in physics. Frequently employed strategies that assist in the sensemaking process are dimensional, covariational, special, and limiting case analysis. Despite their importance, these strategies are rarely taught or practiced explicitly in university physics courses. The present intervention study systematically implemented sensemaking strategies within a university course for first-year physics students covering topics of electro- and magnetostatics as well as electrodynamics. Traditional exercises were enriched with tasks requiring students to critically evaluate the plausibility of self-derived equations. The tasks were integrated into recitation sessions and homework assignments. A total of $N=67$ physics students participated in the study. A quasiexperimental pre-post design with two groups was employed to evaluate the effectiveness of the intervention approach. Results show that students highly valued all four strategies equally and reported an increased perceived competence in their application after the intervention. Significant improvements in performance were observed for dimensional ($d=0.67$) as well as for special case analysis ($d=0.50$). Students’ performance in analyzing covariations only showed a tendency favoring the intervention group. No intervention-related impact on the performance of limiting case analysis was found, suggesting that this strategy may require more extensive practice. The findings underscore the importance and usefulness of explicitly teaching strategies to support students’ sensemaking of physics equations.

A growing number of introductory physics instructors are implementing active learning methods in their classrooms, and they are modifying these methods to fit their local instructional contexts. However, we lack a detailed framework for describing the range of what these instructor adaptations of active learning methods look like in practice. Existing studies apply structured protocols to classroom observations and report descriptive statistics (e.g., the fraction of class time spent on each activity), but this approach overlooks the complex nature of instruction. In this study, we apply network analysis techniques to classroom observations to define a typology of active learning that considers the temporal and interactional nature of instructional practices. We analyze video data from 30 instructors at 27 institutions who implemented one of the following named active learning methods in their introductory physics or astronomy courses: Investigative Science Learning Environment (ISLE), Peer Instruction, Tutorials, and Student-Centered Active Learning Environment with Upside-down Pedagogies (SCALE-UP). We first create one classroom observation network per instructor that captures temporal sequences of activities measured using the Classroom Observation Protocol for Undergraduate STEM (COPUS). We then calculate the cosine similarity between all pairs of observation networks, create a similarity network where each instructor’s classroom observation network is a node and the edges represent cosine similarity, and apply the Infomap clustering algorithm to the similarity network to identify types of active learning instruction. We find five types of instruction: clicker lecture, dialogic clicker lecture, dialogic lecture with short groupwork activities, short groupwork activities, and long groupwork activities. We find no significant relationship between these instruction types and the named active learning methods; instead, implementations of each of the four methods are spread across different instruction types. This result prompts a shift in the way we discuss and study active learning: the names of developed active learning methods may not actually reflect classroom instruction. We also find that student conceptual learning does not vary across the identified instruction types, suggesting that instructors may be flexible in the style in which they implement these methods without sacrificing effectiveness. We discuss the implications of these results for both research and the professional development of college physics instructors.

The majority of previous studies of physics courses at the upper undergraduate level have been content-related or focused on the format of instruction, while detailed investigation of student performance patterns across various conceptual and quantitative measures in this context has been neglected, relatively speaking, in comparison to the substantial work that has been carried out in introductory courses. In this study, we used a sample of students in a traditional upper-level electricity and magnetism course at a large U.S. university to examine performance patterns and understand the extent to which, and the ways in which, conceptual and quantitative performance were related to each other. To this end, we used various measures of prior preparation (including standardized math scores and background in physics and mathematics in high school and college), in-course quantitative performance (homework, quizzes, and exams), and conceptual performance (scores on the Conceptual Survey of Electricity and Magnetism). Overall, our analysis revealed that prior preparation was a significant predictor of success in this course and that there were strong correlations between students’ conceptual and quantitative performance. In particular, grades in the most recent upper-level physics course (upper-level mechanics) were the strongest predictor of upper-level electricity and magnetism course performance, even after controlling for mathematical preparation. Although average normalized conceptual gains were relatively large and independent of preinstruction conceptual scores, threshold effects suggested that students entering with the lowest conceptual understanding were unable to achieve high postinstruction conceptual scores or overall course grades. Our findings suggest that better prior preparation through early development of mathematical skills, as well as instructional strategies that support learners in bridging physics and mathematics effectively, may be crucial for success in upper-level electricity and magnetism.

Collaborative mathematical modeling of real-world problems requires learners not only to engage in multiple epistemic practices but also to remain aligned around shared physical models as assumptions and solution paths evolve. However, few empirical studies have traced how such coordination unfolds moment by moment during authentic work. This study examined the in vivo discourse of a group of preservice physics teachers solving an ill-structured mechanics problem by tracking their collaborative reasoning turn by turn. We analyzed the group’s work by coding their epistemic modeling phases and the operational physical models in use, alongside a time-resolved measure of discourse model coherence (DMC) that indexes alignment around shared model assumptions. By combining turn-level qualitative coding with time-resolved quantitative visualizations, we traced how the group’s shared problem space evolved over time and identified moments of convergence and divergence. The analysis revealed that the group progressed through six epistemic phases of modeling while iterating across multiple operational physics models of increasing complexity. Periods of heightened complexity were marked by slower progression and frequent fluctuations between epistemic phases. Cross-model comparisons functioned as a key evaluative resource, in which simpler models served as benchmarks for judging more complex ones. Instructor prompts played a significant role: moves that narrowed the modeling scope tended to stabilize coherence, whereas prompts that reopened assumptions often increased epistemic uncertainty and temporarily disrupted alignment that produced measurable drops in DMC. These findings provide a time-resolved account of collaborative modeling dynamics and offer methodological and instructional insights for supporting modeling-rich physics learning.

This study compares conceptual understanding, as well as the prevalence and consistency of student ideas regarding simple dc circuits, between two distinct groups: high school students after initial instruction ($N=1274$) and undergraduate students in physics-related degree programs before attending university lectures ($N=423$). To investigate student ideas, we employed the 2T-SEC test, a two-tier multiple-choice instrument. Results show a significantly higher conceptual understanding among undergraduates (Cohen’s $d=0.96$). However, the overall prevalence of specific student ideas appears to be similar across both groups: of the 13 student ideas examined, 5 occur equally often, 4 are more frequent among high school students, and 4 among undergraduates. Notably, certain ideas well documented in the literature, such as “sequential reasoning” and “current consumption,” are significantly more prevalent among undergraduates. Consistency analyses reveal generally low levels across both groups, with few significant group differences. Moreover, these findings suggest that everyday experiences and language may reinforce certain student ideas over time.

In this paper, we use the action, process, object, schema theoretical framework to validate a hypothetical learning trajectory of the 2D heat equation based on a preliminary genetic decomposition that stresses the conceptual understanding of its mathematical formulation. We design questions to probe specific mental constructions of the preliminary genetic decomposition. We interviewed eight second-year B.Sc. students enrolled in engineering, physics, or twin (mathematics and physics) majors. Our findings indicate that students engage with many predicted mental constructions. In particular, the coordination and encapsulation of two process conceptions of the Laplacian of temperature improve understanding, although doing so is challenging. Other parts of the genetic decomposition require refinements. These include mental constructions related to the temperature distribution function, heat flow, and temperature gradient.

We report on a department-wide initiative, implemented beginning in 2018, aimed at making computational methods a routine and integrated part of the undergraduate physics curriculum. Using survey data collected from undergraduate physics students across multiple years, we examined how students’ attitudes toward computation and their self-efficacy with computational skills change as they progress through the program. The survey includes attitudinal items and self-efficacy ratings for a range of computational tools and methods, as well as retrospective assessments of students’ initial skill levels. An exploratory factor analysis was conducted for both parts of the survey, and each part produced reliable, two-factor structures. Our analyses of student attitudes and self-efficacy throughout the program show that, at the program level, students generally report more positive views of computation and higher computational self-efficacy at later stages. However, these changes are not evenly distributed across the curriculum, with larger shifts concentrated in particular semesters. Together, these results show that our department-wide effort to integrate computational methods into the undergraduate curriculum supports growth in student attitudes and self-efficacy, but that this growth may be driven by specific experiences in the program rather than by progression alone. We also find that conclusions about growth in computational self-efficacy depend on how growth is measured. For some skills, growth based on present self-efficacy closely matches growth estimates that incorporate retrospective initial ratings, while for others, the two approaches differ substantially. Importantly, these differences are not uniform across skills but align with the underlying factor structure of the survey. Skills associated with specific computational tools or languages show relatively little response-shift effect, whereas skills associated with applied computational methods exhibit larger differences in growth estimates when retrospective measures are included. These findings suggest that retrospective pretest survey designs may be particularly important for assessing growth in methods-based computational skills. On the whole, this study highlights the importance of considering both curricular structure and measurement approach when evaluating our curriculum-wide initiative to integrate computation into undergraduate physics programs.

We present three versions of a pendulum lab activity to explore how theoretical commitments, motivations, and aspirations are reflected in curriculum design. In earlier work, Boudreaux and Elby [How curriculum developers’ cognitive theories influence curriculum development, Phys. Rev. Phys. Educ. Res. 16, 020144 (2020)] discussed how different theoretical perspectives led them to different designs of tutorials. Here, we discuss our finding that even starting from the same theoretical perspective and having similar goals for students can lead to differences in design. We give three interacting reasons why our labs diverge: We have different expectations of students at our respective institutions; we have different ancillary goals; and we draw different implications from our shared theoretical commitments. Our account demonstrates the complexity of the relationship between theory, goals, and curriculum design. In this way, it adds to prior arguments for the importance of designers’ articulating the reasoning for their choices as well as for the possible value of instructors’ responsive adaptations to curricula.

Since 2022, artificial intelligence (AI) tools have become publicly available, thereby enabling physics teachers to employ them in a multitude of ways. The aim of this research is to evaluate the potential of AI in assisting physics teachers in lesson planning. The objective is to identify which cognitive demands of lesson planning can be carried out by the AI, therefore reducing the workload for teachers. To compare teachers with different backgrounds, we examine three groups: prospective, out-of-field, and experienced physics teachers. The participants planned a lesson on Newton’s third law using an AI tool. To analyze the participants’ lesson planning process, we employed evaluative qualitative content analysis. Each of the groups presented a different approach to lesson planning using AI. For example, out-of-field physics teachers focused on the physics content, while experienced physics teachers were more prone to asking how to adapt the learning materials to the students’ cognitive level. One of the key findings was that the AI tools considered the clarity of the learning objectives and phasing of the lessons without necessarily being prompted, in all three groups. Moreover, in general, the experienced physics teachers were more critical about using AI for lesson planning than the other two groups. The findings of this study might inform teacher professional development courses focused on the use of AI in physics education.

Upper-secondary education has been identified as a critical period for understanding young people’s (non)continuation in physics, as well as their broader trajectories into science, technology, engineering, and mathematics (STEM). This paper illuminates the longitudinal identity negotiations within upper secondary school physics and mathematics by focusing on two students, Kristi and Svea, who embody a paradox: Despite entering upper secondary school with strong science and mathematics identities and pursuing advanced coursework in both disciplines, they consistently refrained from considering futures in STEM. Central to our analysis is the concept of disciplinary and celebrated identities, which we integrate with perspectives from narrative psychology. This study draws on three rounds of semistructured narrative interviews with each student ($n=6$). The analysis was carried out by applying an in-depth reflexive thematic approach, focusing on how gendered identities and power dynamics shaped the young women’s negotiations within these masculine fields. The analysis showed how the two young women were presented with challenges in (i) aligning their interests and identity work with the disciplines’ norms and practices, and that facing such narrative disturbances was a gendered experience; (ii) bonding with the teachers enabled recognition, even though it involved applying narrow masculine strategies; and (iii) having to submit themselves to a “sink or swim” culture amplified their sense of inadequacy and unfitness for evolving strong disciplinary identities. Our findings show that these factors together discouraged the young women from maintaining sustainable narratives and negotiating positive choice considerations for a future in STEM. From a diversity perspective, our findings illustrate that inclusion is not only about access to participation but also about whose interests and ways of meaning-making are valued and legitimized within disciplinary practices. In doing so, this study advances research on diversity and inclusion in STEM by showing how disciplinary identities are shaped through sedimented practices of recognition over time. The implications call for rethinking participation to embrace and foster gender-inclusive teaching and learning environments, for example, through reforms in teacher training. Finally, we argue for moving away from deficit framings that describe young women as lacking confidence in physics and mathematics. Instead, feelings of not being “clever enough” should be understood as a product of the field itself, shaped by disciplinary practices in school physics and mathematics.

Large language models (LLMs) can now generate physics practice problems in real time, yet the educational value of these items hinges on rapid, reliable postgeneration vetting. In this exploratory study, we investigated which automated checks are both technically feasible and pedagogically meaningful when exercises are produced on demand within a chatbot interface. A cohort of 34 introductory-physics students generated and attempted 543 practice problems during exam preparation. Each item was labeled by an expert on a wide range of quality attributes and presented to the learners in pairs to record their preference. We then (i) benchmarked three commodity LLMs as “judges” against the expert labels, (ii) quantified which attributes predict student choice via random-forest models, and (iii) triangulated these results with free-form exit surveys. Only a small subset of the original metric items proved necessary to reliably address student preferences either directly or by proxy. The study demonstrates that scalable formative assessment does not require exhaustive scoring: a carefully curated core of structural and learner-visible checks is sufficient to ensure both technical soundness and user appeal. The findings provide a practical blueprint for deploying real-time, AI-generated practice in physics and other quantitative disciplines.

Diagnosing students’ mastery of physics concepts alongside their misconceptions is important for guiding effective physics instruction. Prior studies have analyzed distractor choices to identify misconceptions, and recent research has applied cognitive diagnostic modeling to obtain more fine-grained insights into student understanding. Building on this progress, we first proposed the two-stage multiple-choice deterministic inputs, noisy “and” gate with hierarchy (TS-MC-DINA-H) model, which estimates the probabilities of both conceptual mastery and misconceptions through option-level response coding. On the basis of this model, we developed a cognitive diagnostic assessment tool for forces and motion. An analysis of data from 492 high school students validated the assessment tool. Moreover, the diagnostic results revealed that students with identical total scores often exhibited different mastery-misconception profiles, thus suggesting that diagnostic information can complement traditional score-based evaluation. The key goal of this study is to provide a new approach for simultaneously diagnosing concept mastery and a wide range of misconceptions at the individual level. This dual diagnostic perspective provides a more comprehensive picture of student learning and offers practical implications for targeted instruction and personalized remediation.

Education literature recommends many different strategies for structuring student group work in labs. Many of these strategies, however, have not been sufficiently evaluated for their effects on student outcomes. One prior study suggested that sharing roles, rather than splitting roles, in lab groups can boost students’ physics interest and self-efficacy. Here, we expand upon this literature by evaluating the effects of a broader range of role distributions across several student outcomes in a large sample at two different institutions. We developed a survey item to probe the ways in which students distribute their roles in lab groups. The item asks for the percent of time in lab that students spent working together on lab roles (sharing), working alone on roles but rotating each session (rotating), and working alone in the same role throughout the semester (splitting). We employed hierarchical linear modeling to measure the effects of these role distributions on student critical thinking, self-efficacy, perceived agency, sense of belonging, and recognition based on survey items specific to physics lab contexts. We found that role distributions did not differentially impact student critical thinking. We also found that sharing roles tended to have a positive impact on student attitudes; splitting had a negative effect on attitudes; and rotating fell in between. Statistical significance varied across these attitudinal outcomes. Our findings invite further research and controlled studies to better understand the apparent benefits of sharing, rotating, and splitting roles in introductory physics labs.

We report on a profession-oriented course we offered at the University of Vienna, aimed at physics education teacher students. The course on theoretical classical mechanics was conceived and designed from the outset with the explicit goal of bridging the gap between the abstract, mathematical notions employed in theoretical physics and the concrete future needs of prospective teachers in their profession. We aimed to counter both the negative attitudes of students toward theoretical physics and the interrelated skepticism of professors regarding the students’ mathematical proficiency. Our main findings are that these goals can indeed be achieved through a careful selection of course material and the associated mathematical tools, through closely interwoven lecture topics and exercises, and through thorough planning according to principles for high-school teaching known from science education research. Establishing close connections between the material taught in the course and the students’ future occupation as high-school teachers has proven to be of utmost importance. This is possible without any sacrifice of mathematical rigor or the quality of physics presented.

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.