Mathematics plays many roles in physics and physics education. While these roles have previously been extensively discussed in the physics education research community, no systematic picture of the multifaceted considerations has yet been formed. To gain a comprehensive overview of the previous studies on the topic, we conducted a systematic literature review on 122 journal articles published between 2000 and 2023 that examine the role of mathematics in physics and physics learning. In the reviewed articles, we employed qualitative content analysis, coded each article for its characteristics, and used network maps for visualization. We identified eight thematic article categories, highlighting the complex integration of mathematics in, for example, physical reasoning, problem solving, modeling, and experiments. Additionally, the review examines theoretical frameworks and contexts, revealing an overemphasis on problem solving in mechanics and a limited exploration of advanced physics topics like quantum mechanics. A detailed inductive analysis further identified six overarching roles that mathematics plays in physics and physics education: (i) supporting learning and achievement, (ii) enabling mathematical manipulations, (iii) guiding reasoning and sensemaking, (iv) facilitating experiments and modeling, (v) serving as a language, and (vi) providing a structural foundation for physics as a science. Based on the analysis, we discuss how the roles assigned to mathematics have been conceptualized in the reviewed articles and provide an overall picture of the types and features of the reviewed corpus. Our findings suggest opportunities for future research, including deeper explorations of underrepresented physics contexts and targeted investigations into specific roles of mathematics in teaching and learning.

This research was a qualitative transcendental phenomenological exploration of astronomy identity formation among astronomy majors and physics majors engaged in astronomy research. Participants ($N=10$), all of whom identified with traditionally marginalized groups in astronomy, were recruited from two large universities in New York state at different stages in their undergraduate careers. Social cognitive career theory and several science, technology, engineering, and mathematics identity frameworks conceptually guided the analysis of astronomy identity for undergraduate majors and undergraduate astronomy researchers by exploring participants’ interest in, choice to study, and persistence in astronomy. Themes related to astronomy interest were popular culture and directly observing astronomical phenomena, while astronomy choice and persistence were facilitated by experiences in introductory coursework, recognition from faculty, and socializing with peers. The emergent astronomy identity framework was characterized by six distinct yet interrelated constructs: (1) interest in astronomy, typically rooted in observing naturally occurring phenomena and engaging with popular culture; (2) recognition from peers, experts, and families; (3) peer socialization about shared astronomy experiences; (4) competence or the belief one can do the work of an astronomer; (5) sense of belonging within the astronomical community; and (6) astronomy career expectations. Findings from this research provide insights on factors that influence undergraduates in four-year colleges to study astronomy, and how students’ past experiences may lead to a natural interest in astronomy that may be fostered in secondary and postsecondary contexts. Implications suggest departments and institutions may facilitate the accessibility of astronomy at the collegiate level by promoting a more inclusive astronomy community, fostering interactions with astronomy faculty and graduate students, providing opportunities for undergraduate research, and communicating expectancy for astronomy-related future careers.

Clustering methods are often used in physics education research (PER) to identify subgroups of individuals within a population who share similar response patterns or characteristics. Among these, $k$-means (or $k$-modes, for categorical data) is one of the most commonly used clustering methods in PER. This algorithm, however, is distance-based rather than model-based: it relies on algorithmic partitioning and assigns each individual to one subgroup through hard assignment. Researchers must also conduct post hoc analyses to relate subgroup membership to other variables. Mixture models are a model-based alternative that offers several statistical tools for choosing the optimal number of subgroups, accounts for classification errors by assigning individuals probabilities of belonging to each subgroup rather than hard assignment, and allows researchers to directly integrate subgroup membership into a broader latent variable framework. In this paper, we outline the theoretical similarities and differences between $k$-modes clustering and latent class analysis (one type of mixture model for categorical data). We also present parallel analyses using each method to address the same research questions in order to demonstrate these similarities and differences. We provide the data and r code to replicate the worked example presented in the paper for researchers interested in using mixture models.

This case study used individual interviews to investigate graduate students’ sensemaking in upper-level electrostatics in the context of problems that can be efficiently solved for the electric potential using Laplace’s equation. Although there are many technical mathematical issues involved in solving Laplace’s equation, the focus of this research is not on those issues. Instead, the focus is on structural issues such as whether students recognize when solving Laplace’s equation would be an effective approach to finding the potential and set up the problems correctly, and whether they can draw the electric field lines and equipotential surfaces in a given situation. Although many prior investigations have shed light on student sensemaking in introductory physics contexts, very few investigations have focused on graduate student sensemaking while solving advanced physics problems. We present the findings of our research, which was conducted through the lens of the epistemic game framework proposed by Tuminaro and Redish. We observe different nested epistemic games played by students.

Examining teaching practices in university physics is crucial for addressing the lack of student achievement in and engagement with the subject. Research-based instructional strategies (RBIS) offer evidence-based methods to enhance student engagement and learning outcomes, but face adoption challenges due to institutional, contextual, and individual barriers, particularly in higher-year courses. This case study investigates how second-year physics instructors at a research-intensive university within a trimester system engaged with RBIS, using the EPIC-implementation model to guide analysis. A case-study approach, using semistructured interviews and secondary data (e.g., course evaluations and materials), explored instructors’ decision making through the EPIC-implementation model (exposure, persuasion, identification, commitment, and implementation). The study reveals how individual motivation, peer influence, institutional constraints, and discipline-specific challenges shape RBIS adoption. While some instructors maintained commitment, others reverted to traditional methods due to systemic barriers. Co-teaching dynamics played a key role in influencing adoption, yielding mixed results. The findings contribute to the growing literature on instructional change by highlighting the importance of institutional support, peer mentorship, and alignment with teaching philosophies in sustaining RBIS adoption in major courses beyond the first year. They highlight the need for supportive institutional frameworks, discipline-specific strategies, and the alignment of teaching methods with instructors’ values. This study provides practical insights for educators, institutional leaders, and policymakers to encourage innovative teaching practices in higher education.

Physics teacher identity encompasses teachers’ beliefs and views toward being a physics teacher. Physics teacher identity is influenced by teachers’ perspectives on physics teaching and learning. Previous studies on teacher identity in general suggest that the construct is complex and malleable. Studies further suggest that it influences instructional methods, student engagement, and classroom environment. However, within physics education, there has yet to be an examination of how physics teacher identity influences “equitable” teaching approaches. This qualitative study sought to identify various dimensions of physics teacher identity and its implications for physics education research. We interviewed secondary and postsecondary physics teachers ($n=10$) from different regions of the country with varying years of experience. We searched for consistent themes regarding the influence of physics teacher identity on equitable instruction using a conceptual framework that examines conceptions of self, others, knowledge, and pedagogy. Findings showed that teachers held a variety of conceptions of self and others, while many struggled to describe their conceptions of knowledge and pedagogy. Our findings are significant for physics teachers, educators, and researchers aiming to employ equitable teaching strategies. Ultimately, this study fostered a deeper understanding of the relationship between physics teacher identity and equitable instruction.

Enhancing students’ conceptual understanding is one of the primary goals of science education. Existing literature suggests that the degree of knowledge integration among students can reflect their level of conceptual understanding. This study focuses on the concept of friction force, constructing a cognitive structure model of friction force to depict the cognitive structure features of students with different levels of conceptual understanding. Additionally, a cognitive diagnostic test tool for friction force was developed. Based on this tool, 827 Chinese high school students were tested. The results demonstrate that the cognitive structure model of friction force is reasonable and can effectively characterize the knowledge structures of students with varying levels of conceptual understanding. Furthermore, analysis revealed multiple viable pathways for cognitive development. Based on empirical data, we identified the progression pathway optimally aligned with students’ cognitive schemata. The findings of this study provide a novel approach for mapping the cognitive development process of students and offer valuable information for personalized instructional guidance.

In this yearlong, naturalistic case study in a high school physics classroom, we examine the different dimensions of politicized care displayed by Sarah, an African American teacher teaching physics to working-class students of color traditionally underserved in science. Through extended field observations and a series of interviews with the teacher, we identified the various forms of care, social, epistemic, and academic, that Sarah expressed for her students throughout her teaching. We recognized that these forms of care are manifestations of Sarah’s politicized care. As we traced Sarah’s care along these different forms, we identified tensions and synergies among these expressions of care, differentially shaping opportunities for students’ disciplinary learning. More broadly, our findings call for conceptualizing politicized care as an essential aspect of effective physics teaching, especially for minoritized students. This care involves careful acts of balancing disciplinary and teaching demands, mindful of wider societal and institutional inequities while honoring children as social, academic, and epistemic beings. Such care for her students can be understood as an intentional act of resistance to current oppressive educational and wider societal systems.

This study investigates the cognitive processes of novice students in science learning, with a specific focus on how inhibitory control is employed to overcome a common student misconception about the buoyant force in liquid, which leads to the belief that “the greater the depth an object is in a liquid, the greater the buoyant force it experiences.” Utilizing a negative priming paradigm integrated with eye-tracking technology, the research examines the role of inhibitory control in facilitating conceptual change among novice learners. The findings reveal that successful problem- solving in novices is contingent not only on the acquisition of scientific knowledge but also on the effective activation of inhibitory control over misconceptions. A repeated measures analysis of variance (ANOVA) demonstrated significant effects of student expertise levels and experimental conditions on reaction times, with novices exhibiting significantly longer reaction times compared to experts, indicative of lower inhibitory control ability. However, following targeted intervention, novices’ average reaction times progressively decreased, approaching those of experts, suggesting an improvement in inhibitory control. Additionally, eye movement data analysis revealed distinct differences in information processing strategies between novice and expert students. Novices frequently engaged in reviewing and comparing information across multiple areas during problem solving, whereas experts exhibited more efficient information processing, rapidly identifying and suppressing misconceptions. The eye-tracking data provided further insights into the cognitive processes and behavioral patterns of novices across different intervention phases, highlighting the dynamic interplay between inhibitory control and conceptual learning. These findings underscore the critical role of inhibitory control in overcoming misconceptions and offer implications for the design of targeted instructional interventions.

[This paper is part of the Focused Collection in Artificial Intelligence Tools in Physics Teaching and Physics Education Research.] Generative AI tools, including the popular ChatGPT, have had a significant impact on discourses about future work and educational practices. Previous research in science education has highlighted the potential of generative AI in various education-related areas, including generating valuable discussion material, solving physics problems, and acting as a tutor. However, little research has been conducted on the role of generative AI tools in laboratory work, an essential part of science education, and physics education specifically. Here, we show various ways in which high school students use ChatGPT during a physics laboratory session and discuss the relevance of using generative AI tools to investigate acoustic levitation and the speed of sound in air. Additionally, employing variation theory as a theoretical lens in the analysis, we identify how generative AI can be used to further develop students’ problem-solving skills in the physics laboratory. However, although our study shows that generative AI tools may handle some relevant questions and problems during laboratory work, the teacher still plays a crucial role in identifying students’ needs and capabilities of understanding the potential and limitations of generative AI. Finally, this study serves as an important point of discussion regarding the ways in which students need support and training to efficiently utilize generative AI to further their learning of physics.

When describing motion in physics, the selection of a frame of reference is crucial. The graph of a moving object can look quite different based on the frame of reference. In recent years, various tests have been developed to assess the interpretation of kinematic graphs, but none of these tests have specifically addressed differences in reference frames. Moreover, existing tests that explore differences in reference frame typically focus on the equivalence principle through written answers, interviews, or simple calculations and vector addition; however, none of these tests evaluate position-time graphs. To address this gap in the research, we developed and evaluated the Inventory of Galilean Transformation of uniform linear motion in position-time graphs (IGT). The IGT consists of 15 multiple-choice items that systematically use position-time graphs of linear uniform motion to assess the understanding of 3 types of Galilean transformations: the identity transformation, the transformation between two (opposing) stationary displaced frames of reference, and the transformation from a stationary into a uniformly moving frame of reference. Herein, we presented the development and validation of the IGT. A total of 532 upper secondary school students in the advanced track participated in the multistage development process. We evaluated the psychometric properties via classical test theory and item response theory. The degree of item discrimination and reliability were within the desired range. The IGT demonstrated good internal consistency ($\omega =0.88$), and confirmatory factor analysis supported the intended structure of the test. Rasch analysis revealed that the item difficulties were consistent with the increasing complexity of the three different transformations. The IGT also revealed several alternative student conceptions about frames of references, such as confusion between two scenarios of cars crossing versus overtaking, as well as misunderstandings regarding the changing shape of a graph when a uniformly moving object is transformed into a moving frame of reference. In its current form, the IGT serves as a new instrument for assessing students’ ability to interpret position-time graphs under the influence of the Galilean transformation, making it suitable for formative or summative assessment in advanced upper secondary education.

Embedding physics problems in real-world settings—here termed contextualized physics problems (CPPs)—is widely believed to foster students’ interest, motivation, and learning. However, firm evidence for this claim remains scarce. To explore this issue, we surveyed 868 secondary students and 154 teachers to examine their attitudes toward CPP and investigate whether students and teachers perceive these problems as promoting student interest and motivation in learning physics. The findings reveal a divergence between teacher and student perspectives. While most teachers view CPP as essential for enhancing interest and motivation, student responses tell a different story. Contextualized problems appear to boost interest and motivation only among 8th graders who are newly introduced to the subject. From 9th to 11th grade, students expressed a clear preference for decontextualized physics problems and generally disagreed that CPP increased their interest in physics. Gender differences were also observed among younger students, with boys showing a moderately stronger preference for CPP than girls. These results provide valuable insights for educators in designing course materials and creating effective test and exercise questions. The discrepancy between teacher and student perceptions, as highlighted by the surveys and interviews, underscores the need to address this gap through targeted teacher training and professional development.

Large language models (LLMs) are now widely accessible, reaching learners across all educational levels. This development has raised concerns that their use may circumvent essential learning processes and compromise the integrity of established assessment formats. In physics education, where problem solving plays a central role in both instruction and assessment, it is therefore essential to understand the physics-specific problem-solving capabilities of LLMs. Such understanding is key to informing responsible and pedagogically sound approaches to integrating LLMs into instruction and assessment. This study therefore compares the problem-solving performance of a general-purpose LLM ($GPT\text{−}4o$, using varying prompting techniques) and a reasoning-optimized model ($o1$-preview) with that of participants in the German Physics Olympiad, based on a set of well-defined Olympiad problems. In addition to evaluating the correctness of the generated solutions, the study analyzes the characteristic strengths and limitations of LLM-generated solutions. The results of this study indicate that both tested LLMs ($GPT\text{−}4o$ and $o1$-preview) demonstrate advanced problem-solving capabilities on Olympiad-type physics problems, on average outperforming the human participants. Prompting techniques had little effect on $GPT\text{−}4o$’s performance, and $o1$-preview almost consistently outperformed both $GPT\text{−}4o$ and the human benchmark. The main implications of these findings are twofold: LLMs pose a challenge for summative assessment in unsupervised settings, as they can solve advanced physics problems at a level that exceeds top-performing students, making it difficult to ensure the authenticity of student work. At the same time, their problem-solving capabilities offer potential for formative assessment, where LLMs can support students in evaluating their own solutions to problems.

One expected outcome of physics instruction is that students develop quantitative reasoning skills, including strategies for evaluating solutions to problems. Examples of well-known “canonical” evaluation strategies include special case analysis, unit analysis, and checking for reasonable numbers. We report on responses from three tasks in different physics contexts prompting students in an introductory calculus-based physics sequence to evaluate expressions for various quantities: the velocity of a block at the bottom of an incline with friction, the final velocities of two masses involved in an elastic collision, and the electric field due to three point charges. Responses from written ($\mathit{N}=580$) and interview ($\mathit{N}=18$) data were analyzed using modified grounded theory and phenomenology. We also employed the analytical framework of epistemic frames. Students’ evaluation strategies were classified into three broad categories: consulting external sources, checking through computation, and comparing to the physical world. Some of the evaluation strategies observed in our data, including canonical as well as noncanonical strategies, have been reported in prior research on evaluation, albeit sometimes with different names and with varying levels of generalizability. We note four major, general observations prompted by our results. First, most students did not evaluate solutions to physics problems using an approach that an expert would consider an evaluation strategy. Second, many students used evaluation strategies that emphasized computation. Third, many students used evaluation strategies that are not canonical but are nonetheless useful. Fourth, the relative prevalence of different strategies was highly dependent on the task context. We conclude with remarks including implications for classroom instruction.

In 2003, Bailey and Slater [A review of astronomy education research, Astron. Educ. Rev. 2, 20 (2003)] published a review of astronomy education research (AER) to survey the field, identify areas of robust coverage, and uncover gaps in the research to help guide future researchers. While our review is not intended as a direct comparison to their original work, we aim to update the field’s progress since that time. After initially considering more than 450 works, primarily peer-reviewed publications, we focused on research conducted in undergraduate settings or related to non-K-12-teaching adults, such as planetarium professionals, participants in massive open online courses, and citizen scientists. We identified seven broad categories of research, continuing several categories from the original study, such as student understanding and efficacy of instructional strategies, while also introducing new topics, such as authentic research experiences. These findings demonstrate the evolution of AER over the past two decades. The largest body of research remains focused on the efficacy and implementation of instructional strategies. Progress has also been made in exploring technology use (e.g., simulations) in introductory astronomy classrooms and integrating active learning into fully online courses. Notably, course-based undergraduate research experiences have emerged as a new focus in AER. Moving forward, future research should better incorporate educational theory (e.g., mechanisms of learning) and explore the unique educational opportunities offered within astronomy.

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

Understanding particle motion in force fields (PMFF), which encompasses the nature of forces and the relationship between force and motion, is fundamental to mastering mechanics and electromagnetism. Effectively solving PMFF-related problems requires advanced reasoning skills and the ability to apply knowledge across diverse contexts. Despite evidence that students often encounter significant challenges with these concepts, comprehensive assessment tools to reliably evaluate their understanding remain limited. In high school and introductory college physics courses, the most commonly studied force fields include those generated by a point mass or a point charge, as well as uniform gravitational, electric, and magnetic fields. The basic types of motion observed in these fields include uniform linear motion, uniformly accelerated rectilinear motion, uniformly accelerated curvilinear motion, and uniform circular motion. This study developed a nine-item multiple-choice test designed to assess students’ understanding of PMFF concepts. Data were collected from 34 college physics majors using test scores, interviews, and eye-tracking technology. The analysis revealed several alternative conceptions that varied depending on the specific force field context. Students performed relatively well in uniform force field scenarios but faced significant difficulties with fields generated by a point mass or a point charge, as well as uniform magnetic fields. In fields of a point mass or point charge, common misconceptions centered on uniformly accelerated motion. In the uniform magnetic field context, students often struggled to differentiate between uniform linear motion and uniformly accelerated curvilinear motion. Eye-tracking data provided additional insights, revealing attention patterns that corroborated the observed difficulties. These findings highlight critical areas where students face challenges in understanding PMFF. The results can guide future research efforts to develop targeted educational interventions aimed at addressing these specific learning difficulties, ultimately improving student comprehension of PMFF concepts.

This research investigated how freshman students’ epistemological beliefs in physics are impacted by gender and academic performance in a general physics course. Data were collected from 1220 university freshman students from 22 different programs in Türkiye. In this causal-comparative research, the well-known Colorado Learning Attitudes about Science Survey (CLASS) was used to assess students’ beliefs about physics and learning physics. A Turkish version of the CLASS, consisting of 20 items measuring problem-solving effort, conceptual understanding, and personal interest and real-world connection, was employed. Additionally, demographic data such as gender, cumulative grade point average (CGPA), and previous academic performance in the General Physics I Course were collected. Cronbach’s alpha coefficient for the reliability analysis of the whole scale was calculated as 0.844. The two-way between-groups multivariate analysis of covariance (two-way MANCOVA) test was used to answer the research question. The results indicated that gender and achievement level in the general physics course independently had significant effects on students’ scores on three CLASS survey subscales when their CGPAs were controlled. An inspection of the mean scores indicated that males showed higher scores in the three CLASS subscale scores than females. Additionally, high-achieving groups were found to have higher scores in the three subscale scores than medium-achieving and low-achieving groups. The results were discussed and suggested how the results could be applied to improve physics education.