[This paper is part of the Focused Collection in Investigating and Improving Quantum Education through Research.] The present review intends to show the current state of teaching quantum-related content, to analyze and compare its learning efficiency, and to give a systemized overview of quantum-educational activities in the last years. We focus on teaching and learning elements, their innovative tools, and process-oriented studies that are empirically validated. In terms of content, we mainly concentrate on aspects of modern quantum technology. The final dataset for our analysis and synthesis included 50 studies published since 2017 and until the follow-up survey in February 2024. We have found that most of the teaching strategies described and investigated are in the field of quantum mechanics and are designed to provide an introduction to the rather broad and differentiated topic of quantum science. Studies specifically addressing mathematical concepts can exclusively be found for the target group of university students. Visualizing ideas or innovative social interventions to improve quantum learning is mainly found in schools while only a few approaches for further education show validated results. Tools most often examined in the studies reported were of digital nature, though some experiment-focused learning environments were also evaluated.

Faculty members play a crucial role as change agents in promoting cultural transformation within academic environments and empathy, a fundamental component of effective teaching, mentoring, and collegiality, is essential for fostering a student-centered and holistic approach. We present a theoretical model for empathy development and navigation in physics faculty as they engage with students and colleagues. Two pathways—cognitive and affective—are connected with previous work and explored. Cognitive empathy, a slower, intellectual process, is mediated through reflective witnessing, whereas affective empathy, a faster, emotional process, builds on shared or adjacent lived experiences. Understanding the nuances associated with the different pathways can inform efforts to increase participation and foster an inclusive environment, which often presumes a meaningful understanding of what best supports individual students.

[This paper is part of the Focused Collection in Investigating and Improving Quantum Education through Research.] Evidence from physics education research suggests that the introduction of a formalistic description of quantum phenomena can be beneficial to student learning, particularly in terms of helping students move away from naive realist views of quanta or space-time descriptions of quantum phenomena. However, the mathematical requirements for mastering quantum formalism are typically far beyond the scope of secondary school education. Therefore, in previous research, we have proposed a reduced Dirac notation tailored to the capabilities of secondary school students, which is included in a novel teaching-learning sequence. However, the cognitive processes of students when confronted with an introduction to quantum physics via a reduced Dirac notation have not been thoroughly investigated: In particular, it seems important to investigate whether this approach is actually beneficial to students’ learning and to explore the learning difficulties students are likely to encounter in such a setting. This paper contributes to this research gap by reporting the findings of an acceptance survey: $N=14$ learners participated in one-on-one interviews following a protocol consisting of four cyclical phases (information phase, acceptance evaluation, paraphrasing phase, and application phase). The findings of our study indicate that the instructional elements within our new teaching-learning sequence were generally well accepted by students but also revealed learning difficulties that students may encounter. Thus, on the one hand, the findings of this study pave the way for future research on students’ learning of quantum physics using Dirac notation. On the other hand, the in-depth findings reported here may guide teachers in designing learning environments that introduce Dirac notation at the upper secondary school and introductory university levels.

In this paper, we demonstrate the fruitfulness of a theoretical framework called Commognition, developed in the context of mathematics education research, for conceptualizing and analyzing a professional development (PD) process on measurement uncertainty for secondary physics teachers. Evaluating measurement uncertainty is an important learning goal in the physics lab and is key to determining the validity of an experiment. While research has mapped difficulties students face and teaching strategies to support them, teacher PD still requires attention, both in capturing teachers’ existing perceptions and in designing PD activities that address these perceptions and support teachers in adopting a more scientifically aligned discourse on measurement uncertainty. Commognition perceives learning as becoming a participant in the discourse of a specific professional community. A discourse consists of keywords, visual mediators, narratives, and routines—and metarules that govern their use. The appropriation of a new discourse involves reconciling conflicts between the metarules of learners’ existing discourse and the new discourse (i.e., commognitive conflicts). We adopted the commognitive framework in all phases of our PD design. First, we mapped the canonical discourse we intended our teachers to adopt versus the prevailing discourse of physics teachers in our national context. Following this mapping, we designed PD tasks intended to lead participants to acknowledge the limitations of their existing discourse on measurement uncertainty as a precursor to internalizing the canonical discourse. Finally, the commognitive framework served as an analytical lens to detect commognitive conflicts involved in collaborative sensemaking among the teachers and between them and the PD facilitators. We demonstrate this type of analysis in a case study, in which learners who hold different discursive metarules encounter implicit commognitive conflicts and discuss implications and untapped opportunities for physics teachers’ PD process on measurement uncertainty.

[This paper is part of the Focused Collection in Investigating and Improving Quantum Education through Research.] The COVID-19 pandemic has increased the interest in the possible causes of the spread of science-based fake news. Indeed, such phenomenon can lead to a generalized distrust of science with serious consequences for our society, ranging from vaccine avoidance to climate change denial. Research in educational psychology has only recently begun to explore the psychological drivers and relationships between misinformation, conspiracy theories and pseudoscientific beliefs. However, existing studies have not focused on specific scientific domains and have involved samples with individuals of different age and sociocultural background. In this empirical study, we focus specifically on the pseudoscientific beliefs of high school students and teachers in a science area where fake news are spreading rapidly on websites and social media, namely, quantum mechanics (QM). To this end, we used a 21-item instrument specifically developed by our group in a previous study to measure pseudoscientific beliefs in QM. The cross-sectional sample included $N=1119$ high school students ($\text{female}\text{students}=52\%$) and $N=125$ high school teachers. The data collected were analyzed using the following methods: confirmatory factor analysis to establish the validity of the instrument; multiple correspondence analysis, to transform categorical variables measuring sociocultural background into continuous variables; repeated measures analysis of variance and linear regression to describe which factors most influence students’ and teachers’ pseudoscientific beliefs. The results show that, for students, endorsement of pseudoscientific beliefs in QM depends on the following factors: trust in public and science institutions, scientific content consumption, type of high school attended, and QM literacy. For teachers, endorsement of pseudoscientific beliefs in QM depends on the type of degree obtained, QM literacy, perceived usefulness of teaching QM, and confidence in teaching QM. Our study suggests that outreach and popularization interventions for high school students focused on QM, as well as teacher training courses on QM, should also incorporate elements of the nature of science, i.e., on how we develop scientific knowledge, to provide more effective tools to help teachers and students distinguish between correct claims and plausible but false claims, using both prebunking and debunking approaches.

[This paper is part of the Focused Collection in Artificial Intelligence Tools in Physics Teaching and Physics Education Research.] Using a high-stakes thermodynamics exam as the sample (252 students, four multipart problems), we investigate the viability of four workflows for AI-assisted grading of handwritten student solutions. We find that the greatest challenge lies in converting handwritten answers into a machine-readable format. The granularity of grading criteria also influences grading performance: employing a fine-grained rubric for entire problems often leads to errors and grading failures, as the model appears to be unable to keep track of scores for more than a handful of rubric items, while grading problems in parts is more reliable but tends to miss nuances. We also found that grading hand-drawn graphics, such as process diagrams, is less reliable than mathematical derivations due to the difficulty in differentiating essential details from extraneous information. Although the system is precise in identifying exams that meet passing criteria, exams with failing grades still require human grading. We conclude with recommendations to overcome some of the encountered challenges.

Curricular analytics (CA) is a quantitative method that analyzes the sequence of courses (curriculum) that students in an undergraduate academic program must complete to fulfill the requirements of the program. The main hypothesis of CA is that the less complex a curriculum is, the more likely it is that students complete the program. This study compares the curricular complexity of undergraduate physics programs at 60 institutions in the United States. The institutions were divided into three tiers based on national rankings of the physics graduate program, and the means of each tier were compared. No significant difference between the means of each tier was found, indicating that there is not a relationship between program curricular complexity and program ranking. Further analysis focused on the physics, chemistry, and mathematics courses, defined as the core courses of the curriculum. Significant differences in the number of required core courses and the complexity per core course were measured between the tiers; both were measured as large effects. Programs with the highest rankings required fewer core courses while having a higher complexity per core course. These institutions have more strict prerequisite requirements than lower ranking programs. This study also showed complexity was quantitatively related to curricular flexibility operationalized as the number of available eight-semester degree plans. The number of available degree plans exponentially decreased with increasing core complexity per course. Modifications to a curriculum at one institution were analyzed; a similar relationship between the number of available degree plans and increasing complexity per core course was found.

This research focuses on the experiences of seven undergraduate women who were majoring in physics in a medium-size physics department at a small liberal arts college. In the semistructured, empathetic interviews we conducted, the women discussed how they decided to major in physics, their interactions with their peers and instructors, and who supported them during their physics trajectory. We used Standpoint Theory and focused on the experiences of undergraduate women to get a holistic perspective of how they became interested in physics, how they have been supported in their physics journey, as well as identify any challenges that they faced in their undergraduate physics program due to their identity. Using the Domains of Power framework, we analyzed how those in the position of power, e.g., instructors, can play important roles in establishing and maintaining safe, equitable, and inclusive environments for students, which is especially important for historically marginalized students such as women and ethnic and racial minority students in physics.

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.