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This research aims to design immersive virtual reality with cognitive conflict to support practical learning of quantum physics. This type of research is design research through the stages of needs analysis, product design, validity test, and practicality test. The needs analysis used questionnaire sheets distributed with Google Forms and obtained from 97 students. Immersive virtual reality design was developed by utilizing the Blender and Unity applications in the form of Android Package Kit (APK) format installed on virtual reality devices. The validity test involved six experts using validity instruments, and the practicality test involved nine students using practicality instruments. The validity test results on the learning and material indicators obtained a value of 0.89 in the valid category. A validity value of 0.95 was obtained in the valid category of the media aspect indicator. The average overall practicality score of the ease of use, display, design efficiency, and benefits indicators was 92 in the very practical category. The novelty of these research results is that they combine immersive virtual reality with cognitive conflict models applied to quantum physics learning that have been tested to be valid and practical.

In this article we offer a conceptual and practical contribution to the field of STEM education by investigating the concepts educators may include in Quantum Technologies (QT) outreach activities. We embed our approach in the discipline-culture (DC) framework, in which we consider the cultural nuances of QT as an important factor which must not be ignored in education efforts. To this end, a survey study by the pilot project Quantum Technologies Education For Everyone (QuTE4E), investigating key concepts for QT outreach, was conducted between December 2021 and June 2022. Here we present the results of the study, analysed through the DC framework, and consider the implications for designing QT outreach activities. The data hints at the perceived value of highlighting core concepts of Quantum Mechanics (QM), while also raising the question of whether QT sits as a discipline of Physics, Computer Science, or elsewhere. This calls for a reordering of the primacy of certain concepts (such as qubit and spin) for outreach purposes, where core concepts in QM might not be core concepts in QT, and vice versa. The results of this study provide valuable insights for those interested in learning more about this rapidly-evolving field.

Mathematical symbols, such as those embodying quantum concepts, are indispensable for conveying complex ideas and relationships in academic writing. However, some education researchers and students keep a distance from anything mathematical: algebraic equations, geometrical reasoning, or statistical symbols. How to lower the access threshold for this type of mathematical narrative and reveal the meanings of a range of quantum conceptions to modern educators thus becomes a real problem. Using the pendulum motion equation as a reference point, I argue in this article for the advantages of academic English or French writing genres that fuse a range of mathematical symbols of quantum concepts and conceptual change. Such writings help demonstrate how incorporating the idea of probability (a) refines the debate among conceptual, verbal, and mathematical academic writing; (b) allows new conceptions that draw on the insights from quantum cognition-supported theories; (c) helps explain students' understanding of mathematical symbols; and (d) offers a new taxonomy for categorizing academic writings.

The study investigates secondary students' understanding of "orbital" and "electron cloud" concepts in different quantum contexts (for values of the ?principal quantum number n = 1 and n = 2) on the basis of their verbal and pictorial representations, evaluating also their consistency. Participants, which were 192 12th-grade students from six urban secondary schools of Northern Greece, represented these two concepts through two corresponding tasks of a paper-and-pencil assessment tool, each of which comprised two parts for verbal and pictorial representations, respectively. Results provide evidence that although students struggle to express verbally the orbital and electron cloud concepts, their competences in the corresponding pictorial representations are relatively better, exhibiting inconsistencies between verbal and pictorial representations. Inconsistencies also exist between representations of the orbital and electron cloud concepts, since students appear to have verbally a better understanding of the electron cloud than the orbital, whereas the opposite holds true for their pictorial representations. Comparing verbal and pictorial representations, the pictorial ones appear to be more consistent tools, whereas a quantum context defined by n = 2 seems to be more challenging for students compared to that of n = 1. Furthermore, an analysis of student profiles leads to their categorization in four classes, providing additional relevant information. Implications for science education are also discussed.

We analyze here how pre-service teachers explicate their views about the wave-particle duality of photons and what role it plays in their arguments supporting the quantum nature of light. The data for the analysis is provided by 12 written reports about the double-slit experiment with feeble light. The analysis is based on constructing semantic networks corresponding to pre-service teachers' written texts. Contingency-like associative correlation between word-pairs is used to differentiate between word-pairs, where associations of two terms or words is systematic. Such associations indicate connections, which are significant for key term vocabularies in construction of inferences and arguments. Based on that information of the key vocabulary we then construct the structure of pre-service teachers' argument for the nature of the photon and its wave-particle duality, in the form of directed argument graphs (DAGs). The results show that argument structures in four to six out of 12 cases meet the goals set for pre-service teacher education. In these cases, experimental aspects and wave-particle duality play an important role in the pre-service teachers' argument and its structure.

Designing a relevant and engaging curriculum for biochemistry undergraduates can be challenging for topics which are at the periphery of the subject. We have used the framework of context-based learning as a means of assessing understanding of quantum theory in a group of students in their junior year. Our context, the role of retinol in skincare, provides a basis for the simple application of quantum mechanical principles to a biological context in an adaptation of the polyene in a box concept. As part of the learner journey, they gain experience of practical computational chemistry, which provided an in silico alternative to traditional laboratory work during the SARS-CoV-19 pandemic. Student feedback was overwhelmingly positive, and this approach is now firmly embedded in the undergraduate curriculum.

Quantum science is in the news daily and engages students' interest and curiosity. A fundamental quantum science concept that underpins medical imaging, quantum computing and many future technologies is quantum spin. Quantum spin can explain many physical phenomena that are in the lower secondary school curriculum, such as magnetism and light, making its inclusion a great motivator for students. Here we present an activity sequence for teaching quantum spin in the classroom using spinning tops and gyroscopes to highlight the common properties of classical angular momentum and quantum spin. These toys can provide an easily understood window to the quantum world for lower secondary school students. Students who have engaged in these activities reported enjoying the content and appreciating its relevance.

Most educational literature on conceptual change concerns the process by which introductory students acquire scientific knowledge. However, with modern developments in science and technology, the social significance of learning successive theories is steadily increasing, thus opening new areas of interest to discipline-based education research, e.g., quantum logic, quantum information, and communication. Here, we present an initial proposal for modeling the transition from the understanding of a theory to the understanding of its successor and explore its generative potential by applying it to a concrete case--the classical-quantum transition in physics. In pursue of such task, we make coordinated use of contributions from research not only on conceptual change in education, but also on the history and philosophy of science, on the teaching and learning of quantum mechanics, and on mathematics education. By means of analytical instruments developed for characterizing conceptual trajectories at different representational levels, we review empirical literature in the search for the connections between theory change and cognitive demands. The analysis shows a rich landscape of changes and new challenges that are absent in the traditionally considered cases of conceptual change. In order to fully disclose the educational potential of the analysis, we visualize categorical changes by means of dynamic frames, identifying recognizable patterns that answer to students' need of comparability between the older and the new paradigm. Finally, we show how the frame representation can be used to suggest pattern-dependent strategies to promote the understanding of the new content, and may work as a guide to curricular design.

This mixed-methods study examines how pre-service teachers select instructional videos on YouTube for physics teaching. The study focuses on the role of surface features that YouTube provides (e.g., likes, views, thumbnails) and the comments underneath the videos in the decision-making process using videos on quantum physics topics as an example. The study consists of two phases: In phase 1, N = 24 (pre-service) physics teachers were randomly assigned to one of three groups, each covering a different quantum topic (entanglement, quantum tunneling, or quantum computing, respectively). From eight options provided, they selected a suitable video for teaching while their eye movements were tracked using a stationary eye tracker in a laboratory setting, and think-aloud data was collected. In the subsequent phase 2, participants were allowed to freely choose one YouTube video on a second topic of the above-mentioned ones while thinking aloud. The results reveal a significant emphasis on video thumbnails during selection, with over one-third of the fixation time directed towards them. Think-aloud data confirms the importance of thumbnails in decision-making, e.g., as evidenced by a categorization of the study participants' arguments and thoughts voiced. A detailed analysis identifies that participants did not rely on (content-related) comments despite they have been found to be significantly correlated with the videos' explaining quality. Instead, decisions were influenced by surface features and pragmatic factors such as channel familiarity. Retrospective reflections through a questionnaire including rating scale items support these observations. Building on the existing empirical evidence, a decision tree is proposed to help teachers identify high-quality videos considering duration, likes, comments, and interactions. The decision tree can serve as a hypothesis for future research and needs to be evaluated in terms of how it can help systematize the process of selecting high-quality YouTube videos for science teaching.

Reasoning with mathematics plays an important role in university students' learning throughout their courses in the scientific disciplines, such as physics. In addition to understanding mathematical concepts and procedures, physics students often must mathematize physical constructs in terms of their associated mathematical structures and interpret mathematical entities in terms of the physical context. In this study, we investigate physics students' reasoning about mathematics in relation to physics content addressed in two quantum mechanics problems. Through qualitative analysis of interview data from twelve students, results show that 1) students use intricate, nonuniform problem-solving methods with reasoning that moves fluidly between structural (mathematizing and interpreting) and technical (conceptual and procedural) skills in quick succession, and 2) student reasoning about orthonormal bases, change of basis, inner products, and probability informed their flexibility in choosing problem-solving approaches. We illustrate the results with examples of student reasoning and discuss the inextricability of mathematics and physics in students' reasoning.

Large language models, such as ChatGPT, have great potential to enhance learning and support teachers, but they must be used with care to tackle limitations and biases. This paper presents two easy-to-implement examples of how ChatGPT can be used in physics classrooms to foster critical thinking skills at the secondary school level. A pilot study (n=53) examining the implementation of these examples found that the intervention had a positive impact on students' perceptions of ChatGPT, with an increase in agreement with statements related to its benefits and incorporation into their daily lives.

The research on students' perceptions after implementing a teaching style is recommended due to its potential to inform reformed education. The present study surveyed 319 students and revealed their perceptions of multimedia usage in teaching and learning quantum physics. Among these students, 156 were surveyed after learning quantum physics with a multimedia-aided method, while 163 were surveyed after learning with a lecture method. The piloting of the test used generated Cronbach alpha of 0.841 of internal consistency, and it contained quantitative Likert scale items and supporting qualitative items. The data were analyzed descriptively and inductively. Students taught by multimedia perceived quantum physics as easy, while those taught by lecture perceived it as difficult due to its abstractness and mathematics needs. Students preferred computer simulations, animations, and YouTube videos as interactive methods that fit quantum physics lessons. Students testified that a quantum physics course that uses visualization methods in some of its teachings is more interesting than a course taught without them. However, students in both classes concurred that their class was student-centered and full of demonstration. Recommendations related to teaching practices and future research foci were made.

Teaching and learning the language of science is an important part of science education. Learning the vocabulary of science plays a key role in learning the language of science. The meaning of abstract scientific terms builds on their connections with other terms and how they are used. In this research, we study pre-service physics teachers' physics-related vocabularies and investigate how rich a vocabulary they use and what similarities and differences there are in their vocabularies regarding electrons and photons. We investigate the connectedness of physics terms by categorizing them according to their role in explaining quantum physics and carry out a lexical network analysis for N=60 written reports. The analysis shows that vocabularies do not share much similarity and the reports reflect narrow images of photons and electrons. We conclude that science teacher education needs to pay attention to explicit teaching of the language of science for pre-service teachers.

Clear and rigorous quantum reasoning is needed to explain quantum physical phenomena. As pillars of true quantum physical explanations, we suggest specific quantum reasoning derived from quantum physical key ideas. An experiment is suggested to support such a quantum reasoning, in which a quantized radiation field interacts with an optical beam splitter, leading to experimental results conflicting with classical physical predictions. The results, however, can be explained consistently with a quantum reasoning based on the key ideas of probability, superposition, and interference (PSI). In this quantum optical key experiment the optical beam splitter prepares a superposition of single photon states and a Michelson interferometer is used to detect the superposition via controlled propagation phases. Although different single photon experimental setups (aimed at helping students to gain access to foundational issues in quantum physics) have been discussed in the past, the wave-particle dualism bound to classical physics maintains its predominance as an explanation pattern for the interpretation of these experiments. The study presented here investigates the effect of the quantum optical key experiment on the ability of students to use quantum reasoning based on the key ideas of PSI to overcome the naive wave-particle dualism. The current state of relevant studies that test student access to quantum physics can roughly be divided into two distinct areas: one tests how mathematical abilities help them to understand quantum physics and one tests how nonmathematical representations of a set of specific quantum theoretical traits ("Wesenszüge") lead to a deeper understanding of quantum physics. There is a lack of questionnaires that focus on the idea of developing quantum reasoning based on superposition, probability, and interference of quantum states combined with a real experiment using true quantum light. In the first part of the article, we describe the physical modeling and present the development of the questionnaire. The set of items has been constructed from newly developed items and combined with well-tested ones. The validation of the set addresses qualitative and quantitative methods. In the second part, we give a pre- and poststudy examination of the impact of the quantum optical key experiment on students' quantum reasoning. A significant increase in the number of students using quantum arguments is based on PSI reasoning for the explanation of an interference, such as the behavior of single photon states. Though the increase is significant, we found only minor changes in a particular issue to the students' reasoning when approaching quantum physics as illustrated by a sample of answers given in the second part of the article. The concept of quantum states and the principle of superposition still appear particularly difficult.

Physics education research on explanatory videos has experienced a boost in recent years. Due to the vast number of explanatory videos available online, e.g. on YouTube, finding videos of high explaining quality is a challenging task for learners, teachers, and lecturers alike. Prior research on the explaining quality of explanatory videos on classical mechanics topics has uncovered that the surface features provided by YouTube (e.g. number of views or likes) do not seem to be suitable indicators of the videos' explaining quality. Instead, the number of content-related comments was found to be statistically significantly correlated with the explaining quality. To date, these findings have only been observed in the context of explanatory videos on classical mechanics topics. The question arises whether similar correlations between the explaining quality and YouTube surface features can be found for videos on topics that are difficult to access visually and verbally, for example from quantum physics. Therefore, we conducted an exploratory study analyzing the explaining quality of N = 60 YouTube videos on quantum entanglement and tunnelling. To this end, we made use of a category-based measure of explanatory videos' explaining quality from the literature. We report correlations between the videos' explaining quality and the surface features provided by YouTube. On the one hand, our results substantiate earlier findings for mechanics topics. On other hand, partial correlations shed new light on the relationship between YouTube's surface features and explaining quality of explanatory videos.

Background: Haptic feedback has been shown to be an effective facilitator of the learning of scientific concepts in a series of studies. However, little is known about the underlying salient learning mechanisms, which are activated when learning from haptic feedback. Objectives: We investigate the learning mechanism in a higher chemistry education setting, in which the students learned about the abstract concept of potential energy in a quantum chemical context. Methods: In this work, we present a mixed-methods problem-solving prior to instruction (PS-I) study with chemistry bachelor students. In an interactive quantum chemistry learning environment, the students explored the energetic profiles of nucleophilic substitution reactions and the corresponding activation barriers experienced as repulsion and attraction. We measured cognitive and affective mechanisms which have been shown to be activated in PS-I designs, such as knowledge gap awareness, state curiosity, and positive affect as well as the learning outcome quantitatively and the learning trajectories qualitatively. Results and Conclusions: Planned contrasts revealed a small hindering effect of the haptic feedback on the learning outcome. Thematic analysis of the qualitative data lets us attribute this effect to the lack of scaffolding of the haptic feedback and the spontaneous atomic movements in the simulation, which may be interpreted as a visual representation of force in itself. This work highlights the importance of accurate mappings of the haptic feedback unto the target domain and further delivers insight into the prior conceptions of chemistry undergraduate students.

Students ability to build correct knowledge relies on their understanding of concepts. Students must understand the concept well before applying it in real-life situations. With the advent of technology, teaching and learning quantum physics has been made easier and more effective in enhancing students' critical thinking and conceptual understanding. A multimedia-based learning approach is one way to enhance conceptual understanding. With the help of the multimedia application, this study aims to assess its impact on students' conceptual understanding of quantum physics at the University of Rwanda College of Education (UR-CE). The study adopted a quasi-experimental pre-test--post-test design with control and treatment group. Three hundred eighty-five undergraduate students in the UR-CE were purposively selected and allocated into the treatment group (193 students) and the control group (192 students). Control group students were taught eight quantum physics topics for six weeks using the traditional teaching approach, while treatment group students were taught the same topics using animations, PhET simulations, and YouTube videos. The study resulted in a very high statistically significant difference (p < 0.001) between teaching interventions provided after post-testing in favor of students who learned with multimedia (with a large effect size of 0.694). The use of multimedia resulted in a statistically significant increase in the student's conceptual understanding of quantum physics. The study's findings suggest that multimedia tools are effective for learning because they can enhance students' conceptual understanding of quantum physics. However, interactions between teachers and students or student-to-student are essential to facilitate conceptual learning and help the students gain a valuable understanding of their learning.

As part of an effort to examine students' mathematical sensemaking (MSM) in a spins-first quantum mechanics course during the transition from discrete (spin) to continuous (position) systems, students were asked to construct an eigenvalue equation for a one-dimensional position operator. A subset of responses took the general form of an eigenvalue equation written in Dirac notation. Symbolic blending, a combination of symbolic forms and conceptual blending, as well as a categorical framework for MSM, were used in the analysis. The data suggest two different symbolic forms for an eigenvalue equation that share a symbol template but have distinct conceptual schemata: A transformation that reproduces the original and to operate is to act. These symbolic forms, when blended with two sets of contextual knowledge, form the basis of three different interpretations of eigenvalue equations modeled here as conceptual blends. The analysis in this study serves as a novel example of, and preliminary evidence for, student engagement in sensemaking activities in the transition from discrete to continuous systems in a spins-first quantum mechanics course.

Efforts to build the workforce in support of the second quantum revolution are growing, including the creation of education programs that will prepare students for jobs in this area. We surveyed 186 undergraduate students with majors across the science, technology, engineering, and math (STEM) disciplines and followed up with group interviews to understand their perspectives. The project was designed to understand what these STEM students know about quantum and quantum career opportunities and their level of interest in pursuing a career related to quantum. We found that most of the students know very little about quantum. Nevertheless, except for students in the life sciences, there was an interest in quantum careers. Across STEM majors, women were less likely to express interest in quantum careers than men, but this difference disappeared when we examined only physical and computer science majors. Of the few students who had knowledge of quantum concepts, most learned about this topic from online media, especially online videos. Some students reported learning about quantum in high school classes, where it was taught as an extension beyond the usual topics of the course. The undergraduate STEM students in our study identified multiple ways they would like to learn more about quantum, including short videos, seminars, courses, certificates, and degree programs.

Photovoice is a type of participatory action research in which individuals document their experiences through photography. Through the taking, captioning, and reflecting on photographs that they have taken, participants are able to affect change within their communities. Participants also take part in an interview or focus group about their photos at the end of the photovoice process in which they determine themes that appear in their photos, allowing them to participate in the research being done. We used the photovoice methodology in a small, project-based, upper-division, physics capstone course at the University of Colorado Boulder, in which students worked on an authentic industry project in partnership with a company in the quantum industry. As an example of the types of research results and benefits one could obtain using photovoice, we present a discussion of how we implemented the photovoice process within this course and present some of our results, including students' experiences with the photovoice process. Photovoice may be particularly useful in understanding new, unique courses, as it allows students to co-create research that highlights ideas about the course that researchers would not know to ask about in more traditional research methodologies such as reflection questions.

Driven in large part by the National Quantum Initiative Act of 2018, quantum information science (QIS) coursework and degree programs are rapidly spreading across U.S. institutions. Yet prior work suggests that access to quantum workforce education is unequally distributed, disproportionately benefiting students at private research-focused institutions whose student bodies are unrepresentative of U.S. higher education as a whole. We use regression analysis to analyze the distribution of QIS coursework across 456 institutions of higher learning as of Fall 2022, identifying statistically significant disparities across institutions in particular along the axes of institution classification, funding, and geographic distribution suggesting today's QIS education programs are largely failing to reach low-income and rural students. We also conduct a brief analysis of the distribution of emerging dedicated QIS degree programs, discovering much the same trends. We conclude with a discussion of implications for educators, policymakers, and education researchers including specific policy recommendations to direct investments in QIS education to schools serving low-income and rural students, leverage existing grassroots diversity and inclusion initiatives that have arisen within the quantum community, and update and modernize procedures for collecting QIS educational data to better track these trends.

Modelling roles of mathematics in physics has proved to be a difficult task, with previous models of the interplay between the two disciplines mainly focusing on mathematical modelling and problem solving. However, to convey a realistic view of physics as a field of science to our students, we need to do more than train them to become fluent in modelling and problem solving. In this article, we present a new characterisation of the roles mathematics plays in physics and physics education, taking as a premise that mathematics serves as a constitutive structure in physics analogous to language. In doing so, we aim to highlight how mathematics affects the way we conceptualise physical phenomena. To contextualise our characterisation, we examine some of the existing models and discuss aspects of the interplay between physics and mathematics that are missing in them. We then show how these aspects are incorporated in our characterisation in which mathematics serves as a foundation upon which physical theories are built, and on which we may build mathematical representations of physical information that in turn serve as a basis for further reasoning and modifications. Through reasoning processes mathematics also aids in generating new information and explanations. We have elucidated each of these roles with an example from the historical development of quantum physics. To conclude, we discuss how our new characterisation may aid the development of physics education and physics education research.

Physics education has been identified as one of the public sectors that are mostly influenced by technological developments. This paper adopted the quasi-experimental pre- and post-test design to assess the effects of multimedia-aided technologies (MAT) on undergraduate students' performance in quantum physics (QP) at the University of Rwanda College of Education (UR-CE). The researcher used purposive sampling to get 385 undergraduate students. Participants were randomly allocated into experimental (group A) and control (group B) groups. Group A (187 students) students were taught selected topics of quantum physics (blackbody radiation, photoelectric effect, Compton effect, wave aspects of particles, De Broglie's hypothesis, diffraction, interference and double-slit experiment, model of the atom, uncertainty relations, wave function, and Schrodinger equations) for 6 weeks using multimedia-aided technologies and engage, predict, observe, and explain (EPOE) method, whereas group B (187 students) was taught same topics during the same period with a lecture method. The results of ANCOVA revealed that the group's performance was the same (p > 0.05) before learning with no effect size (.000), while they diverged after learning with different teaching interventions. The significance was very high and statistically different (p < 0.001) with a large effect size (> 0.5). This implies that students taught with multimedia-aided technologies (experimental group) outperformed those students taught with lecture teaching methods (control group). Thus, the study recommends that educators should adapt teaching using MAT and EPOE strategy not only in QP but also in other domains of physics to improve active engagement, understanding levels, and academic achievement.

The main purpose of this study was to investigate the consistency of pictorial representations of the atomic structure drawn by students on the basis of particular quantum numbers' characteristics. Participants were 192 students of the 12th grade of secondary Greek schools. This study's instrument, a paper-and-pencil assessment tool, included four open-ended tasks. In each one of the four tasks, students were asked to draw representations of the atomic structure under two specific conditions concerning particular quantum numbers' values. Results indicated the existence of a consistency between pictorial representations, providing indications that this kind of representation could be used as a consistent tool in order to study students' understanding of the contribution of quantum number characteristics in the configuration of the atomic structure. Furthermore Latent Class Analysis revealed distinct student profiles indicating how this consistency is distributed across the sample and emerging student classes that have problems in conceptualizing the characteristics of the first and fourth quantum numbers. Implications for science education are discussed.

A poorly elaborated learner's understanding of models has been reported to be one of the major sources for learning difficulties in the quantum domain. To be able to provide physics education in schools with evidence as to how this problem can be tackled, a deeper theoretical understanding of the structure of learners' mental models in quantum physics seems essential. In this respect, previous research has proposed two dimensions in learners' mental models in the atomic hull context, labelled Fidelity of Gestalt and Functional Fidelity. In this article, we investigate whether this proposed two-factorial structure can be transferred to quantum concepts beyond the atomic hull context. To approach this, we surveyed the structure of students' mental models in the context of photons' properties and behavior. We conducted a questionnaire study: 170 secondary school students completed a survey instrument adapted from the literature. Using exploratory factor analysis, the two factors Fidelity of Gestalt and Functional Fidelity to describe the students' mental models could be replicated for the photon context. We provide a selection of results from physics education literature to reveal that our two-factor framework to describe the students' mental models seems to be a promising endeavor in the landscape of science education research in general.

We developed a Quantum Mechanics Conceptual Understanding Survey (QMCUS) in this study. The survey was conducted using a quantitative methodology. A multiple-choice survey of 35 questions was administered to 338 undergraduate students. Three experienced quantum mechanics instructors examined the validity of the survey. The reliability of our survey was measured using Cronbach's alpha, the Fergusson delta index, the discrimination index, and the point biserial correlation coefficient. These indices showed that the developed survey is reliable. The statistical analysis of the students' results using SPSS shows that the scores obtained by the students have a normal distribution, around the score of 7.14. The results of the t-test show that the students' scores are below the required threshold, which means that it is still difficult for the students to understand the concepts of quantum mechanics. The obtained results allow us to draw some conclusions. The students' difficulties in understanding the quantum concepts are due to the nature of these concepts; they are abstract and counterintuitive. In addition, the learners did not have frequent contact with the subatomic world, which led them to adopt misconceptions. Moreover, students find it difficult to imagine and conceptualize quantum concepts. Therefore, subatomic phenomena are still explained with classical paradigms. Another difficulty is the lack of prerequisites and the difficulties in using the mathematical formalism and its translation into Dirac notation.

The climate emergency mandates a refocusing of society and education on the relationship between humans and the more-than-human world. Emerging from decades of social constructionism that openly promoted climate science denial, social and educational theorising now engages with new materialist philosophies and the agency of matter. Physicist Karen Barad's book Meeting the Universe Halfway, cited over 13,000 times, offers an ontological foundation for new materialism based on her idiosyncratic application of quantum physics. While critically reviewing Barad, I found myself unexpectedly "sliding back down" into the terrain of my physicist pastime, rereading quantum mechanics in depth. I reflect here on how this "ontological detour" empowered me to "climb up a ladder" towards the theoretical foundation for my PhD project in climate change education. I argue that ontological grounding and cross-disciplinary engagement are vital for advancing research and gaining perspectives through lateral connections.

The aim of this study is to examine the different aspects of national articles and postgraduate theses on the quantum learning model conducted in Turkiye between 2010-2021. This study is a study conducted with content analysis and includes research on the quantum learning model, which can be accessed from the TR index and YOK Thesis Center databases. The data were analyzed in reference to the type of publication, year of publication, research model, research design, sample group, number of samples, data collection tools, data analysis method, and study subject. The results of the analyzed studies are indicated with graphs and tables. It is thought that this study will provide a general perspective to researchers who will study the quantum learning model.

Teaching and learning quantum mechanics is one of the most demanding educational and conceptual challenges, in particular in secondary schools where students do not possess an adequate mathematical background to effectively support the description of quantum behaviour. Educational research shows that traditional approaches, generally based on historical and narrative perspectives, are only partially effective. The reason is that they do not address in depth those basic quantum concepts that radically question the fundamentals of classical physics. A research-based educational program has been proposed to two final-year classes of an Italian scientific high school. In order to build the main concepts of quantum mechanics and their formal basic representation via real and simulated experiments, the program uses the light polarization as a context. A quantum game was then integrated in the educational program, to support students' learning. Their conceptual paths, monitored by means of tutorials and questionnaires, show significant student learning especially on the concept of state and on appropriating the formalism meaning, whereas students more frequently referred to the geometrical vector representation instead of the algebraic-analytic formula. The quantum game has emerged to support intuition and operative experience in distinguishing the foundational concepts of superposition and entanglement.

Teaching and learning of quantum physics at secondary level is an active field of research. One important challenge is finding ways to promote understanding of quantum concepts without the mathematical formalism that is embedded in quantum mechanics but unavailable on the secondary level. We investigated Norwegian secondary students' (N = 291) descriptions of the wave nature of quantum particles and the uncertainty principle, as expressed during work with learning resources using a sociocultural approach emphasizing history, philosophy, and nature of science aspects. Responses from university students (N = 40) given after a formalism-based course in quantum physics were included for comparison. Themes were identified using thematic analysis and analyzed from the perspective of pedagogical link-making, seeing different themes as representing different levels of explanations of the concepts (phenomenological, qualitative, mathematical). The most dominant theme in descriptions of particle wave nature was that particles exhibit wave behavior in experiments, while referring to the mathematical description of particles by wave functions was a less prominent theme, even among university students. Two uncertainty principle themes were found: uncertainty as inability to measure pairs of variables precisely, and uncertainty as innate blurriness in nature. Largely missing from descriptions of both concepts were meaningful links between different levels of explanations. Based on the results, we discuss ways forward for teaching particle wave nature and uncertainty in secondary education.

We present a new secondary school teaching method of quantum uncertainties of two-state systems. Intending to be a material teachable in schools, only two-state systems described by real numbers can be considered. An elementary argumentation based on school statistics leads to the identification of the uncertainty of a physical quantity in such systems with the standard deviation of two random variables. We provide a qualitative picture on the state-dependence of the uncertainty, leading to a pictorial representation in the form of four petals of a flower. When considering the product of uncertainty of two essentially different physical quantities we conclude that the general feature: "if the measurement of one of the quantities is certain, the other remains uncertain", cannot be faithfully expressed by means of an inequality, the product has no lower bound different from zero. The application of techniques used by school materials for teaching quantum physics leads to an exact formula for the state-dependence of the uncertainty valid in any two-state system described by real numbers, in full harmony with the qualitative picture. We compare the two-state case with the celebrated Heisenberg position-momentum uncertainty relation and show that these are both specific facets, but only the Heisenberg relation can be expressed by an inequality. The latter hardly provides any hint on the uncertainties of physical quantities in two-state systems. We conclude that the two-state approach is worth teaching in schools also in relation to the uncertainty relation, even if the Heisenberg relation is not part of the curriculum.

Quantum physics is an essential field of science education research, which reflects the high relevance of research on quantum physics and its technologies all around the globe. In this paper, we report on a bibliometric analysis of the science education research community's scientific output in the area of quantum physics in the period from 2000 to 2021. A total of 1520 articles published in peer-reviewed physics and science education journals were retrieved from Web of Science and Scopus databases to conduct bibliometric analysis. This study aims to provide an overview of quantum physics education research in terms of scientific production, preferred publication venues, most involved researchers and countries (including collaborations), and research topics. The main findings point to a continuous increase in research output in the field of quantum physics education over the last two decades. Furthermore, they indicate a shift regarding the research foci. While formerly mainly papers on the teaching of quantum physics content were published, recently, an increase in the relevancy of empirical studies on the teaching and learning of quantum physics can be observed.

This article reports the development and validation of a test instrument to assess secondary school students' declarative quantum optics knowledge. With that, we respond to modern developments from physics education research: Numerous researchers propose quantum optics-based introductory courses in quantum physics, focusing on experiments with heralded photons. Our test instrument's development is based on test development standards from the literature, and we follow a contemporary conception of validity. We present results from three studies to test various assumptions that, taken together, justify a valid test score interpretation, and we provide a psychometric characterization of the instrument. The instrument is shown to enable a reliable ([alpha] = 0.78) and valid survey of declarative knowledge of quantum optics focusing on experiments with heralded photons with three empirically separable subscales.

The purpose of this study is to investigate physicists' views about the possible impacts of recent developments in quantum physics on educational implementations, particularly on science learning. Throughout the research a mixed-methods strategy was used. The data were collected from the physicists working at the European Organization for Nuclear Research (CERN). The qualitative and quantitative results were compared to portray the consistency between the two cohorts. The results indicated that the physicists' experiences could provide valuable contributions to educational practices, and both teachers and students could benefit from the knowledge exchange between the field specialists. The implications for, and potential contributions to educational practices are discussed, taking into account the three most pertinent subfields, namely curriculum, learning, and teaching methods.

Background: Knowledge of quantum computing is arguably inaccessible to many, with knowledge of the complex mathematics involving a particular barrier to entry, creating difficulty in terms of teaching and inclusive learning for those without a high level of mathematics. Meanwhile, it is increasingly important that the knowledge of quantum technologies is accessible to those who work with real-world applications and is taught to the younger generation. Purpose: Resulting from collaborative dialogue between physicists, computer scientists, educationalists, and industrial end users, we propose the concept of quantum literacy as one means of addressing the need for transdisciplinary research in response to the complex problems that we see at the heart of issues around global sustainability. In this way, quantum literacy can contribute to UN Sustainable Development Goal 4, Quality Education. Methods: We introduce a specific puzzle visualization learning tool through which to achieve the pedagogic ends we set out with respect to quantum literacy. Visualization through puzzles can enable non-specialists to develop an intuitive, but still rigorous, understanding of universal quantum computation and provide a facility for non-specialists to discover increasingly complex and new quantum algorithms. Using the Hong-Ou-Mandel optical effect from quantum mechanics, we demonstrate how visual methods such as those made possible through the puzzle visualization tool can be very useful for understanding underlying complex processes in quantum physics and beyond and therefore support the aims of quantum literacy. Conclusion: We argue that quantum literacy, as defined here, addresses the challenges of learning within a highly bounded discipline and of access to the kind of powerful knowledge that should be more accessible to a wide group of learners. We therefore argue for the importance of addressing pedagogic issues when powerful knowledge consists of dense concepts, as well as complex and hierarchical relations between concepts, in addition to presenting a strong barrier to entry in the form of mathematics.

With the increasing industrial relevance of new quantum technologies, a well-educated quantum workforce becomes increasingly crucial. The foreseeable lack of workforce raises important questions. What are the expectations regarding the future relevance of second-generation quantum technologies? What are the requirements for the workforce in the coming quantum industry? Which competences, knowledge, and skills should future employees have? In this paper, we report the results of our study that were aimed at mapping requirements and forecasts for the future quantum workforce. Our study consisted of three consecutive survey rounds. In total, we gathered 188 responses from industry and academic experts across Europe. Our study results served as an input for the development of the European Competence Framework for Quantum Technologies, delivered by the project QTEdu CSA for the European Quantum Flagship. In addition, we will discuss predictions from experts related to the future quantum workforce, including the expected industrial relevance of the main areas of quantum technologies, the need for educational efforts, and the expected influence of quantum technologies on everyday life.

In the context of quantum mechanics, students are often asked to use delta functions to solve problems. Here, we investigate three typical problem-solving processes using delta functions: a delta function potential well problem, a position space delta function problem, and a momentum space delta function problem. We studied students'solutions in written exams and conducted think-aloud interviews. We use the activation, construction, execution, and reflection framework for our analysis. We find that students encountered various difficulties in solving quantum mechanics problems using delta functions. Common challenges included difficulty with establishing expressions of delta functions for position eigenstates, difficulty with expressing the orthonormality of eigenfunctions with continuous spectra using delta functions, difficulty with boundary conditions for delta function potentials, and difficulty with calculating integrals involved delta functions. In particular, students rarely used effective reflective methods to gain confidence in their solutions. We commonly observed this challenge for students in all questions we investigated. In addition, we compare the similarities and differences in the use of delta functions in electrostatics and in quantum mechanics, and discuss possible explanations for the reasoning mechanisms that cause these difficulties. Finally, we discuss the potential pedagogical implications of our findings.

Broadly speaking, many physicists value intuition in their work, and many instructors hope their students develop intuition (while possibly being wary of their initial, unrefined intuitions). These considerations are especially relevant in quantum mechanics, a subject many see as counterintuitive because it is removed from classical everyday experience. Do students consider quantum mechanics intuitive, how does this affect their approach to the subject, and what does "intuitive" mean to them? We investigate these questions through a mixed-methods approach within the context of one upper-division quantum mechanics class at an R1 university. We find that most students in this population expect to have little intuition for quantum mechanics, so many consider it more unintuitive than counterintuitive. We also find that students use the word intuitive to refer to a number of distinct ideas. Overall, students have a diverse set of perspectives on intuition and its role in studying quantum mechanics. This study lays groundwork for additional research into students' views on intuition in physics and informs how we can address intuition as educators. Quantum instructors should be aware of their students' perspectives on intuition, and can integrate the different ways students perceive intuition into their lessons.

As quantum information science and technology (QIST) is becoming more prevalent and occurring not only in research labs but also in industry, many educators are considering how best to incorporate learning about quantum mechanics into various levels of education. Although much of the focus has been on quantum concepts in nonlab courses, current work in QIST has a substantial experimental component. Many instructors of undergraduate lab courses want to provide their students the opportunity to work with quantum experiments. One common way this is done is through a sequence of quantum optics experiments often referred to as the "single-photon experiments." These experiments demonstrate fundamental quantum phenomena with equipment common to research labs; however, they are resource intensive and cannot be afforded by all institutions. It is therefore imperative to know what unique affordances these experiments provide to students. As a starting point, we surveyed and interviewed instructors who use the single-photon experiments in undergraduate courses, asking how and why they use the experiments. We describe the most commonly used experiments in both quantum and beyond-first-year lab courses, the prevalence of actions the students perform, and the learning goals, ranging from conceptual knowledge to lab skills to student affect. Finally, we present some strategies from these data demonstrating how instructors have addressed the common challenges of preparing students to work with conceptually and technically complex experiments and balancing the practice of technical skills with the completion of the experiments.

Background: Quantum physics has found its way into upper secondary school physics curricula worldwide. This trend coincides with increased attention for conceptual understanding in physics education in general and quantum physics education in particular. Students' conceptual difficulties of learning quantum physics are regularly reported. Little systematic attention has been paid to the opportunities and challenges teachers and students experience for teaching and learning quantum physics. Purpose: The opportunities and challenges secondary school teachers and their students experience were examined to gain insights into their perspectives teaching and learning quantum physics. These insights inform improvements in teaching and learning quantum physics at the secondary school level. Sample: Three teachers and five of each teacher's students participated in this study. Design & Methods: A context analysis was conducted to explore the experiences of the teachers and students. Teachers were individually interviewed; students were interviewed in a focus group session. The semi-structured interviews were analysed resulting in three case reports. These case reports were used to conduct a cross-case analysis to find common opportunities and challenges among teachers' and students' experiences. Results: Teachers and students felt that teachers had an important role in supporting students' understanding of quantum physics. Teachers were challenged to enthuse their students for quantum physics as they struggled to convey the relevance of the subject to their students. Freely available digital materials were considered as an opportunity to support students' conceptual understanding as they have the potential to engage students and benefit their conceptual development. Conclusion: Several implications are discussed to improve teaching and learning of quantum physics, such as opportunities for teacher professional development as well as ways to effectively use freely available digital materials.

Quantum mechanics is a field often considered very mathematical, abstract, and unintuitive. One way some instructors are hoping to help familiarize their students with these complex topics is to have the students see quantum effects in experiments in undergraduate instructional labs. Here, we present results from an interview study about what it means to both instructors and students to see quantum effects in experiments. We focus on a popular set of quantum optics experiments and find that students believe they are observing quantum effects and achieving related learning goals by working with these experiments. Although it is not possible to see the quantum phenomena directly with their eyes, students point out different aspects of the experiments that contribute to them observing quantum effects. This often includes seeing the experimental results, sometimes in conjunction with interacting with or understanding part of the experiment. There is additional variation across student achievement of the various related learning goals, ranging from many of the students being excited about these experiments and making a connection between the mathematical theory and the experiments to only some of the students seeing a connection between these experiments and quantum technologies. This work can help instructors consider the importance and framing of quantum experiments and raises questions about when and how in the curriculum quantum experiments can be best utilized and how to make related learning goals available to all students. [This paper is part of the Focused Collection on Instructional labs: Improving traditions and new directions.]

Research-validated multiple-choice questions comprise an easy-to-implement instructional tool that serves to scaffold student learning and formatively assess students' knowledge. We present findings from the implementation, in consecutive years, of a research-validated multiple-choice question sequence [referred to in this study as a clicker question sequence (CQS)] on quantum measurement as it applies to two-state quantum systems. This study was conducted in an advanced undergraduate quantum mechanics course, in both online and in-person learning environments across three years. Student learning was assessed after traditional lecture-based instruction in relevant concepts, and their performance was compared with that on a similar assessment given after engaging with the CQS. We analyze, compare, and discuss the trends observed in the three implementations.

Collaborative learning with peers can lead to students learning from each other and solving physics problems correctly not only in situations in which one student knows how to solve the problems but also when none of the students can solve the problems alone. We define the rate of construction as the percentage of groups collaborating on problem solving that solve the problem correctly out of all groups having at least one member who answered correctly and one incorrectly while solving the same problem individually first. We define the rate of co-construction on each problem as the percentage of collaborating groups that answered it correctly if no student in the group individually answered it correctly before the collaborative work. In this study, we investigated student learning measured by student performance on a validated quantum mechanics survey and rates of construction and co-construction of knowledge when students first worked individually after lecture-based instruction in relevant concepts and then worked with peers during class without receiving any feedback from the course instructor. We find that construction of knowledge consistently occurred at a high rate during peer collaboration. However, rates of co-construction were more varied. High rates of co-construction were generally achieved when approximately half of the students knew the correct answers initially. We also conducted an analysis of some of the survey questions that correlate with high rates of co-construction to gain some insight into what students converged on after peer interaction and what types of difficulties were reduced. Our findings can be valuable for instructors who want to provide in-class and out-of-class opportunities for peer collaboration in their physics courses.

Measurement uncertainty is an important topic in the undergraduate laboratory curriculum. Previous research on student thinking about experimental measurement uncertainty has focused primarily on introductory-level students' procedural reasoning about data collection and interpretation. In this paper, we extended this prior work to study upper-level students' thinking about sources of measurement uncertainty across experimental contexts, with a particular focus on classical and quantum mechanics contexts. We developed a survey to probe students' thinking in the generic question "What comes to mind when you think about measurement uncertainty in [classical/quantum] mechanics?" as well as in a range of specific experimental scenarios and interpreted student responses through the lens of availability and accessibility of knowledge pieces. We found that limitations of the experimental setup were most accessible to students in classical mechanics while principles of the underlying physics theory were most accessible to students in quantum mechanics, even in a context in which this theory was not relevant. We recommend that future research probe which sources of uncertainty experts believe are relevant in which contexts and how instruction in both classical and quantum contexts can help students draw on appropriate sources of uncertainty in classical and quantum experiments.

In the Italian education system, secondary students (ages 14-19) are confronted with the foundations of quantum physics during the final term of scientific high school (pre-university year). The Italian Ministry of Education, University and Research (acronym MIUR) has remarked its importance in the syllabus to address the high school exit examination (30% of the 5th year physics course) but, due to limited learning time and intrinsic difficulty, this branch of physics is neither assimilated nor appreciated as it should. We wish to illustrate six didactic suggestions focused on learning motivation, emerged during a 17-year long teaching experience, which could help to tackle the main problems found. The key references are two peer-reviewed talks given, respectively, in 2018 at the 6th Annual International Conference on Physics by the Athens Institute for Education and Research and in 2013 at the 2nd Rome workshop "Science Perception" by the Roma Tre University together with a concise and evocative poster outlining the history of quanta (Figure 1). Other useful resources are a 2015 conceptual diagram (Figure 2) and four invited lectures held in the years 2010-2017.

Learning the wave-particle dualism of electrons and photons plays a central role in understanding quantum physics. Teaching it requires that the teacher is fluent in using abstract and uncommon terms. We inspect the lexical structures of pre-service teachers' declarative knowledge about the wave-particle dualism of electrons and photons in the context of double-slit interference. The declarative knowledge is analyzed in the form of a lexical network of terms. We focus on lexical structures because, in teaching and learning, knowledge is communicated mostly through lexical structures, i.e., by speaking and writing. Using the lexical networks, we construct the lexicons used by pre-service teachers to express their knowledge of electrons and photons in the context of double-slit interference. The lexicons consist of eight different key terms, each representing a set of closely-related or synonymous terms. The lexicons by 14 pre-service teachers reveal remarkable variation and differences, and are strongly context-dependent. We also analyzed lexicons corresponding to two didactically-oriented research articles on the same topic and found that they also differ. Lexicons paralleling both texts are found among the pre-service teachers' lexicons. However, only some of the pre-service teachers use such rich vocabulary as would indicate multi-faceted understanding of quantum entities.

Studying quantum physics in upper secondary school is now a standard practice (Stadermann et al., 2019). But given the context of science education, with low recruitment numbers in higher education and poor attitudes towards science, it remains a question whether students find the learning of quantum physics relevant. In this study, we explore how students perceive the importance of quantum physics and technology and whether their perception changes after an intervention, namely the "Quantum Rules!" visit. We also aim to understand if they overall feel that learning quantum is relevant or not. In order to answer these questions, we followed a mixed-methods approach, combining both questionnaires and interviews. The quantitative analysis showed that the 'Quantum Rules!' intervention has a positive effect on students' perception of the relevance of quantum physics and technology, especially regarding how important they feel quantum science is for society. Nevertheless, the qualitative information revealed that although students may find quantum physics and technology important for society, that does not necessarily mean that they find learning quantum physics relevant. We found that students believe the latter is relevant to them only if they find it interesting. We therefore rediscover the common expression "important, but not for me", and we further propose that this perception derives from students not seeing the societal relevance of learning quantum physics.