The purpose of this study is to examine how students may hold coexisting and competing conceptual ideas and how students’ uses of such ideas may evolve during the process of conceptual change by combining two complementary methods including model analysis and the conceptual framework model of knowledge integration. Conceptual change is fundamental to science learning, highlighting the processes of students’ transitions from predominantly relying on alternative views to using scientific ones. Recent studies suggest a growing consensus that alternative views and scientific conceptions coexist and compete in students’ learning. However, explicit research on how the states of coexistence and competition evolve during the process of conceptual change is underdeveloped. Building on existing research, the model analysis provides a quantitative framework to represent the different consistent and coexisting/competing states through probabilities of consistent and/or mixed (coexisting) use of incorrect and scientific ideas. Meanwhile, the conceptual framework model of knowledge integration provides content-specific, cognitive explanations for the developmental levels and processes of conceptual change from novice to expert. By combining these two methods, researchers can gain insights into how the coexistence and competition among different conceptual ideas may evolve as conceptual change progresses. To target the research goal, a model-based knowledge integration assessment of Newton’s third law is developed to measure students’ levels of knowledge integration and model states in a single test. Quantitative data were collected from Chinese high school students, supplemented by interviews with a subgroup from the same population. The model analysis results show the heterogeneity of conceptual development and the evolving competition across novice, intermediate, and expert students, as well as across different concept dimensions. The interviews provide cognitive explanations for the observed model states, framed from the lens of knowledge integration. These insights can inform the development of effective assessments and instructional strategies to facilitate favorable conceptual change in student learning.

Physics experts and students commonly use a variety of representations when working with partial derivatives, including symbols, graphs, and words. One especially powerful representation is the contour graph. In open-ended problem-solving interviews with nine upper-division physics students, we asked students to determine derivatives from contour graphs with electrostatic and thermodynamic contexts. Students undertook three overarching actions: (i) orienting to the given graph, (ii) finding one or more derivatives, and (iii) reflecting on the task. In general, students tended to have more difficulty with the thermodynamic task than the electrostatic one. Students made use of a variety of representational features throughout the interviews, namely by annotating the provided contour graphs in ways that highlighted what is held constant. We use these results to generalize the existing concept image framework for ordinary derivatives to create a framework useful for understanding student ideas about multivariable derivatives. In particular, we add a new layer to the framework—the change layer—that calls attention to how students do or do not attend to which variables are changing (or remaining constant) when finding a derivative. We view the change layer as a powerful central idea for both further research and the development of instructional tasks for physics students.

[This paper is part of the Focused Collection in Investigating and Improving Quantum Education through Research.] We discuss an investigation of student sensemaking and reasoning in the context of degenerate perturbation theory (DPT) in quantum mechanics. We find that advanced undergraduate and graduate students in quantum physics courses often struggled with expertlike sensemaking and reasoning to solve DPT problems. The sensemaking and reasoning were particularly challenging for students as they tried to integrate physical and mathematical concepts to solve DPT problems. Their sensemaking showed local coherence but lacked global consistency with different knowledge resources getting activated in different problem-solving tasks even if the same concepts were applicable. Depending upon the issues involved in the DPT problems, students were sometimes stuck in the “physics mode” or “math mode” and found it challenging to coordinate and integrate the physics and mathematics appropriately to solve quantum mechanics problems involving DPT. Their sensemaking shows the use of various reasoning primitives. It also shows that some advanced students struggled with self-monitoring and checking their answers to make sure they were consistent across different problems. Some also relied on memorized information, invoked authority, and did not make appropriate connections between their DPT problem solutions and the outcomes of experiments. Advanced students in quantum mechanics often displayed analogous patterns of challenges in sensemaking and reasoning as those that have been found in introductory physics. Student sensemaking and reasoning show that these advanced students are still developing expertise in this novel quantum physics domain as they learn to integrate physical and mathematical concepts.

Graphical representations of data are common in many disciplines. Previous research has found that physics students appear to have better graph comprehension skills than students from social science disciplines, regardless of the task context. However, the graph comprehension skills of physics students have not yet been compared with (veterinary) medicine students, both of which are disciplines that require multiple science, technology, engineering, and mathematics (STEM) courses. This study extends previous research on this subject by exploring whether physics majors possess superior graph comprehension skills due to their study discipline. Here, participants solved 24 graph comprehension tasks across various subjects, including mathematics, physics, and medicine; these tests were conducted at the beginning and end of their first semester. Graph comprehension gain was calculated based on the percentage of correct and incorrect answers in the pretest and the post-test. In addition to these comparisons, we replicated previous research that successfully distinguished correct and incorrect solvers based on their visual behavior by using a novel machine-learning method tailored to small datasets. Through this replication of statistical analyses, we aim to ensure the reliability of adaptive learning systems in the future, regardless of data size, using the same machine-learning method. Physics and medical students were found to exhibit relatively similar graph comprehension gain; this is in contrast to previous research comparing physics and non-STEM students. Our results also revealed that both physics and medical students use similar visual strategies to solve these tasks. However, correct and incorrect solvers could be distinguished via machine-learning methods regardless of their discipline. Our research suggests that visual behavior is a good predictor of graph comprehension skills.

[This paper is part of the Focused Collection in Investigating and Improving Quantum Education through Research.] It is beneficial for quantum mechanics students to have a unified understanding of eigentheory concepts, so they can recognize the shared structure of mathematized phenomena from the different quantum mechanical systems of spin, energy, or position and recognize those as instantiations of the same overarching concept. Quantum mechanics instructors should, therefore, provide opportunities for their class community to develop a shared unified understanding of eigentheory concepts. One such opportunity can arise by engaging students in analogizing eigentheory concepts in one context with those from another context. We investigate the pedagogical moves related to analogies that can be used by a quantum mechanics course instructor to support a class community in developing a shared unified understanding of eigenequations. We analyze classroom data to characterize an instructor’s pedagogical moves as he engaged students in analogical reasoning. Some moves include posing tasks conducive to analogizing; preparing, soliciting, and scaffolding students’ participation in analogical reasoning; using deictic gestures and inscriptions; juxtaposing symbols representing the analogized concepts; and explicitly highlighting the sameness of the analogized concepts. We exemplify these pedagogical moves with analytical descriptions of illustrative class episodes. We discuss how these pedagogical moves can support the class community’s expansion of their common ground by fostering the development of the class’s shared unified understanding of eigentheory concepts.

[This paper is part of the Focused Collection in Investigating and Improving Quantum Education through Research.] The teaching and learning of quantum physics has recently become a topic of increasing interest in physics education research. In particular, the study of two-state systems is gaining importance as a means of teaching quantum physics at various educational levels. Meanwhile, a number of approaches have been developed that are also suitable for high school students. It can be assumed that the different approaches have different degrees of effectiveness in teaching central quantum concepts. However, suitable evaluation instruments to test this are still lacking. Therefore, as a first step, a short questionnaire on quantum measurement, suitable for both research and classroom use, was developed in several steps. First, a questionnaire with open and closed items was created and piloted with a total of $N=120$ learners. The responses were evaluated qualitatively using a comprehensive coding manual, which provided insights into learners’ conceptions. These results led to the development of an eight-item questionnaire that could be adapted to different teaching approaches. This questionnaire was subjected to expert review and, finally, successfully tested for its psychometric properties with a sample of $N=201$ learners. Overall, our results provide initial empirical evidence that context (i.e., which two-state approach is used) does matter for student learning, but in general, two-state approaches appear to be particularly conducive to learning quantum concepts (specified in this article for quantum measurement) compared to traditional instruction.

[This paper is part of the Focused Collection in Investigating and Improving Quantum Education through Research.] Instruction in quantum mechanics is becoming increasingly important as the field is not only a key part of modern physics research but is also important for emerging technologies. However, many students regard quantum mechanics as a particularly challenging subject, in part because it is considered very mathematical and abstract. One potential way to help students understand and contextualize unintuitive quantum ideas is to provide them opportunities to work with physical apparatus demonstrating these phenomena. In order to understand how working with quantum experiments affects students’ reasoning, we performed think-aloud lab sessions with two pairs of students as they worked through a sequence of quantum optics experiments that demonstrated particle-wave duality of photons. Analyzing the in-the-moment student thinking allowed us to identify the resources students activated while reasoning through the experimental evidence of single-photon interference, as well as student ideas about what parts of the experiments were quantum versus classical. This work will aid instructors in helping their students construct an understanding of these topics from their own ideas and motivate future investigations into the use of hands-on opportunities to facilitate student learning about quantum mechanics.

[This paper is part of the Focused Collection in Investigating and Improving Quantum Education through Research.] Teaching quantum physics (QP) to high school (HS) students is gaining momentum, necessitating the exploration of various effective methods. Specifically, the research on quantitative teaching methods is still in its early stages. Understanding the power of Dirac notation (DN) in teaching is crucial for grasping the complexities of QP, as it provides a concise and powerful symbolic framework that facilitates both conceptual and computational understanding. This study investigates the proficiency of HS students in interpreting, producing, and manipulating DN within QP. Utilizing qualitative content analysis of student responses to various tasks, quizzes, and final tests, the study aims to uncover the sensemaking opportunities DN provides and the difficulties students encounter. The findings indicate that DN facilitates both conceptual understanding and quantitative problem solving in QP by enabling students to interpret and produce representations of quantum states. The results highlight the importance of extensive practice and well-structured teaching sequences in developing DN proficiency, reinforcing the role of DN as an effective tool for teaching QP at the HS level. The study contributes to the ongoing discourse on integrating mathematical modeling in physics education, emphasizing the potential of DN in enhancing students’ grasp of QP concepts and their application in problem solving.

Network analysis has become a well-recognized methodology in physics education research (PER), with study topics including student performance and persistence, faculty change, and the structure of conceptual networks. The social network analysis side of this work has focused on quantitative analysis of whole-network cases, such as the structure of networks in single classrooms. Egocentric or personal network approaches are largely unexplored, and qualitative methods are underdeveloped. In this paper, we outline theoretical and practical differences between two major network paradigms—whole-network and egocentric—and introduce theoretical frameworks and methodological considerations for egocentric studies. We also describe qualitative and mixed-methods approaches that are currently missing from the PER literature. We identify areas where these additional network methods may be of particular interest to physics education researchers and end by discussing example cases and implications for new PER studies.

[This paper is part of the Focused Collection in Investigating and Improving Quantum Education through Research.] When thinking about measurement uncertainty in a laboratory experiment that features quantum mechanical effects, it is important to consider both the physical principles of underlying quantum theory (e.g., the uncertainty due to quantum mechanical superposition states) as well as the limitations of the measurement (e.g., the spread in outcomes due to instrumental imperfections). Prior research has found student difficulties with these sources of uncertainty both individually and in students’ ability to distinguish between them. Additionally, students are less likely to access ideas related to experimental uncertainty in quantum mechanical contexts unless explicitly prompted. In this work, we have developed a simulation-homework activity focused on the Stern-Gerlach experiment to help students develop an understanding for the different ways that modifying the quantum state, improving the experimental setup, or collecting more data, will affect the resulting outcome distribution. The activity uses a purpose-built interactive simulation, coupled with homework questions grounded in the literature on student thinking about uncertainty. We analyze the effectiveness of the activity with students in junior-level undergraduate quantum mechanics courses using pre- and post-testing. The results indicate that the activity was successful in helping students distinguish between quantum mechanical uncertainty and uncertainty caused by instrumental imperfections, and in increasing the accessibility of instrumental limitations in this context. The activity can thus support student understanding of the core concept of quantum uncertainty, as well as link between the often abstract nature of quantum theory and laboratory experiments with their limitations.

Students experience many difficulties learning the fundamental relationships in Newtonian mechanics, partly due to preexisting mental models that originate from their everyday lives. These preconceptions often persist even after instruction in mechanics and lead to a supposed incompatibility between physics lessons in school and personal experiences. This article presents research that focuses on students’ concept knowledge and conceptual understanding in the field of Newtonian dynamics. Interventions are presented that discuss authentic experiments with friction using different software as a tool. Overall, the interventions lead to an increase in conceptual understanding with a large effect size. A hierarchical linear model (HLM) is used to identify factors that lead to a larger or smaller increase in conceptual understanding of the topic. With the HLM, we infer that the pretest score, the students’ interest in how physical properties interrelate (interest in “theoretical physics”), prior physics performance (in kinematics in this case, measured in the physics grade), and the (intrinsic and extraneous) cognitive load influence the post-test score. We discuss possible explanations as to why these factors influence students’ conceptual change.

The galvanic cell is a typical interdisciplinary topic, which is primarily taught in chemistry but its underpinning is closely related to physics. Student learning in galvanic cell has been extensively studied in chemistry education, which has revealed a large number of misconceptions that are difficult to change through traditional instruction. A source of the learning difficulties is that most students lack an explanatory framework to integrate the many complex phenomena and processes into a coherent knowledge system. As a result, students often rely on memorization of terms, laws, and equations in solving problems but without a meaningful understanding of their reasoning. To address the deficit in learning, this study aims to help students develop an explanatory framework for supporting an integrated knowledge structure. Specifically, a conceptual framework model for galvanic cell is developed based on the central idea from physics, which is used as the core concept for mechanistic explanations of the related chemistry concepts. Guided by the conceptual framework, an instrument is developed to assess the knowledge integration in student learning of galvanic cell. A combination of qualitative and quantitative measures was used to assess the levels of knowledge integration in learning galvanic cell with a large number of Chinese high school and college students. The assessment results show that the conceptual framework model can effectively represent the knowledge structures of students at different levels of knowledge integration. The galvanic cell conceptual framework and assessment results can provide useful resources for teachers to develop instruction for promoting knowledge integration.

Physics Education Research has a rich history of identifying common student ideas about specific physics topics. In the context of electric circuits, existing research on students’ ideas has primarily focused on misconceptions, misunderstandings, and difficulties. In this paper, we take a resource-oriented approach to identifying common student ideas about circuits by characterizing ideas we see as generative “seeds of science” that could form the basis of more sophisticated understandings. Based on our analysis of 1557 university physics student responses to five conceptual questions, we identify four common resources for understanding circuits.

The current dropout rate in physics studies in Germany is about 60%, with the majority of dropouts occurring in the first year. Consequently, the physics study entry phase poses a significant challenge for many students. Students’ stress perceptions can provide more profound insights into the processes and challenges during that period. In a panel study featuring 67 measuring points involving up to 128 participants at each point, we investigated students’ stress perceptions with the perceived stress questionnaire (PSQ), identified underlying sources of stress, and assessed self-estimated workloads across two different cohorts. This examination occurred almost every week during the first semester, and for one cohort also in the second semester, yielding a total of 3241 PSQ data points and 5823 stressors. The PSQ data indicate a consistent stress trajectory across all three groups studied that is characterized by significant dynamics between measuring points, spanning from $M=20.1,\mathrm{S}\mathrm{D}=15.9$ to $M=63.6,\mathrm{S}\mathrm{D}=13.4$ on a scale from 0 to 100. Stress levels rise in the first weeks of the lecture, followed by stable, elevated stress levels until the exams and a relaxation phase afterward during the lecture-free time and Christmas vacation. In the first half of the lecture period, students primarily indicated the weekly exercise sheets, the physics lab course, and math courses as stressors; later on, preparation for exams and the exams themselves emerged as the most important stressors. Together with the students’ self-estimated workloads that correlate with the PSQ scores, we can create a coherent picture of stress perceptions among first-year physics students, which builds the basis for supportive measures and interventions.

[This paper is part of the Focused Collection in Investigating and Improving Quantum Education through Research.] With the current growth in quantum information science and technology (QIST), there is an increasing need to prepare precollege students for postsecondary QIST study and careers. This mixed methods, explanatory sequential research focused on students’ affective outcomes from a one-week, 25-h summer program for U.S. high school students in grades 10–12. The workshop structure was based upon psychosocial theories of self-determination and planned behavior, where QIST aspirations may be facilitated and viewed as achievable choices if students acquire disciplinary knowledge, self-efficacy, normative expectancy of their capacity in the field, and awareness of vocational roles. The program featured lectures, demonstrations, and hands-on experiences in classical and quantum physics and quantum computing. Students’ attitudes toward QIST ($N=77$)—including self-efficacy, self-concept, relevance, career aspirations, and perceptions of quantitative fluency—showed improvement with a medium effect size, even though treatment students entered the program with more positive QIST attitudes when compared with a control group of high school physics students ($N=65$). Postprogram interviews with $n=12$ participants identified several explanatory themes: (i) Students tended to comprehend classical and quantum topics taught through multiple representations, regardless of whether they had taken physics previously; (ii) students experienced some challenges with mathematics and science concepts that support quantum understanding, yet they revealed a willingness to learn new concepts outside of their comfort zone; (iii) students expressed motivation for pursuing science, technology, engineering, and mathematics and/or quantum-related careers in the future, as well as increased QIST self-concept, largely through understanding the relevance of QIST in solving technological problems; and (iv) students reported increased self-efficacy in understanding QIST topics and performing related tasks. This informal summer program showed promise in promoting positive student attitudes toward QIST, a critical emerging field in advancing technological solutions for global challenges.

The Survey of Physics Reasoning on Uncertainty Concepts in Experiments (SPRUCE) was designed to measure students’ proficiency with measurement uncertainty concepts and practices across ten different assessment objectives to help facilitate the improvement of laboratory instruction focused on this important topic. To ensure the reliability and validity of this assessment, we conducted a comprehensive statistical analysis using classical test theory. This analysis includes an evaluation of the test as a whole, as well as an in-depth examination of individual items and assessment objectives. We make use of a previously reported on scoring scheme involving pairing items with assessment objectives, creating a new unit for statistical analysis referred to as a “couplet.” The findings from our analysis provide evidence for the reliability and validity of SPRUCE as an assessment tool for undergraduate physics labs. This increases both instructors’ and researchers’ confidence in using SPRUCE for measuring students’ proficiency with measurement uncertainty concepts and practices to ultimately improve laboratory instruction. Additionally, our results using couplets and assessment objectives demonstrate how these can be used with traditional classic test theory analysis.

Little research in physics education focuses on graduate student experiences related to structural elements of their programs. This departmental case study examines the impact and perceptions of written qualifying exams (QEs) from a student perspective, following recent research which questions the role and utility of such exams. We conducted semistructured interviews with two physics doctoral students at a large research university before and after taking their QEs, capturing their expectations, preparedness levels, and apprehensions regarding the exam. We also conducted a survey of the rest of their student cohort one month before and one month after their exams to understand further variation in the students’ perspectives. The students’ experiences reflected substantial frustration with the nature and transparency of the QE process, as well as substantial negative emotional and mental impacts of the exams. The students’ experiences with the QEs are consistent with psychological responses to traumatic events. The responses further indicate that building trust and establishing transparency around the QE process, as well as creating emotionally and academically safe spaces that allow students to fail on exams and in coursework without the threat of punitive action, are important trauma-informed pedagogical strategies that faculty can use to support students through this process and help them build resilience. While we do not suggest that the current QE process in this department follows best practices for assessment, the students and faculty in this department do agree on the need for some kind of assessment indicating research readiness early in the graduate program; this provides a common perspective from which departmental change can begin.

Learning assistants (LAs) play a pivotal role in transforming traditional physics instruction toward a more inquiry-oriented approach. While empirical evidence supports the effectiveness of LA-involved physics instruction, there is a research gap regarding the specific competencies of LAs that contribute to improved conceptual understanding. One conjectured reason is LAs’ inquiry-oriented pedagogical skills, like questioning, which engender more effective interactions with students at points of instructional needs. This study addresses the gap by constructing a model delineating the contribution of LAs’ competencies of questioning, referred to as pedagogical content knowledge in questioning (PCK-Q), to students’ conceptual learning in introductory classical mechanics and electromagnetism. The participants included an instructional team comprising instructors, graduate teaching assistants, and LAs, and students from two sections over two semesters. PCK-Q was measured using a prevalidated instrument of free-response questions from our previous study, which could predict LAs’ questioning practices. Employing a pre-post design, students’ learning gain in conceptual understanding and critical thinking was assessed, and separate models were constructed to explore the relationship between LAs’ PCK-Q and students’ learning gain. Findings suggest that LAs’ PCK-Q has a significant but slight impact on students’ conceptual learning, with little impact on critical thinking. Furthermore, we developed Likert-scale questions, derived equations to quantify PCK-Q from Likert-scale ratings, verified the feasibility of this streamlined approach in measuring LAs’ PCK-Q, and discussed its limitations. The implications of the research findings are discussed in the context of physics instruction and LA preparation.

Misconceptions coexisting with scientific understanding pose significant challenges in physics education. Inhibitory control may enable individuals to overcome interference from misconceptions. However, discerning the role of inhibitory control becomes intricate when the saliency of scientific- and misconception-related features varies in a problem. This study investigates the role of inhibitory control in overcoming such misconceptions when scientific and misconception-related features are similarly salient, particularly focusing on the range-time (range determines flight time) misconception. We adopted a negative priming (NP) paradigm with the eye-tracking technique in the study. Thirty-six college physics majors participated in the experiment. In the NP paradigm, the participants first compared the flight times in a neutral (same range) or incongruent (longer range, less flight time) primes and then completed the same task in a congruent (longer range, more flight time) probe. Results revealed longer reaction times for incongruent primes compared to neutral primes and longer reaction times to respond to congruent probes following incongruent primes than when neutral primes were present beforehand, suggesting that the inhibitory control may be involved in overcoming the interference from the range-time misconception. Moreover, the eye-tracking analysis highlighted an early overt attention to the salient misconception-related feature (longer range) during primes, along with additional attentional investment necessary to inhibit the range-time misconception. During probes, an early shift of attention away from the salient misconception-related feature and a greater investment of attention on processing the congruent probes after the incongruent primes than that after the neutral primes were observed, indicating a possible effect of the previous inhibitory control in the primes on the subsequent cognitive process on the probes. These findings contribute to a deeper understanding of the cognitive process underlying physics conceptual change and provide insights into physics education.

Historically, physics has been a predominantly male field, with previous literature showing that there is little diversity among U.S. physics students at the undergraduate and graduate levels or among physicists within the work force. Recent research indicates that the lack of diversity in physics is partially due to an unwelcoming climate within physics departments, as well as differential experiences during college. Most physics education research that addresses the lack of underrepresented identities within the field has focused on the identities of women and people of color. There has been little research to investigate people with multiple underrepresented identities, including those such as socioeconomic status, first-generation college students, or learning disabilities. Furthermore, there has been even less research conducted to better understand the impacts of the intersection of these underrepresented identities and how it relates to experiences when pursuing a physics major. In order to address this gap in the literature, our research project has investigated undergraduate physics students’ experiences to better understand what factors affect their experiences and how these may differ by the intersection of one’s underrepresented identities. In particular, we explored how these identities impact their experiences as a physics major. To achieve this goal, we conducted a series of in-depth interviews with physics majors at one university to learn more about their college experiences regarding physics. Our findings suggest that there is a disproportionate number of obstacles when pursuing a physics major faced by those with a greater number of underrepresented identities. We conclude that there is a need for more equitable pedagogical practices and departmental policies within the undergraduate physics experience, in addition to a more “human” approach to mentorship, in order to foster an environment in which students with underrepresented identities can feel supported and thrive academically and professionally. In particular, we believe that dedicated formal pedagogical trainings that teach diverse teaching skills to accommodate students with different learning styles would be useful to many university physics instructors. This type of formal training would include annual workshops designed to educate faculty on how curriculum, pedagogy, and departmental practices can be altered to be more inclusive with the intent to ensure a more equitable and welcoming experience for all students. Additionally, incorporating mentorship programs that focus on a more individualized and natural support system would likely benefit all students, especially those with underrepresented identities, by creating a more welcoming and inclusive space within physics departments.