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Graphs are essential representations in the professions and education concerning the science, technology, engineering, and mathematics (STEM) disciplines. Beyond their academic relevance, graphs find extensive utility in everyday scenarios, ranging from news media to educational materials. This underscores the importance of people's being able to understand graphs. However, the ability to understand graphs is connected to the ability to create graphs. Therefore, in school education, particularly in STEM subjects, not only the understanding but also the skill of constructing graphs from numerical data is emphasized. Although constructing graphs is a skill that most people do not require in their everyday lives and professions, it is a well-established student activity that has been empirically studied several times. Therefore, since a synthesis of the research findings on this topic has not yet been conducted, a summary of the studies investigating graphing via various viewpoints and differing methods could be a valuable contribution. To provide an overview of the empirical literature on this important topic, our systematic review identifies how the construction of convention-based graphical representations of numerical data, referred to as graphing, has been studied in previous research, how effective graphing is, and which types of difficulties are encountered by students. Based on these aspects, we defined inclusion criteria that led to 50 peer-reviewed empirical studies on graphing in K-12 STEM education found in SCOPUS, ERIC, and PsychInfo. Graphing instruction seemed to be beneficial for student learning, not only improving graph construction but also graph interpretation skills. However, the students experienced various difficulties during graphing, both during graph construction and the interpretation and usage of data., Comment: 63 pages, 9 figures

Quantum cryptography is a central topic in the quantum technology field that is particularly important for secure communication. The training of qualified experts in this field is necessary for continuous development. However, the abstract and complex nature of quantum physics makes the topic difficult to understand. Augmented reality (AR) allows otherwise invisible abstract concepts to be visualized and enables interactive learning, offering significant potential for improving quantum physics education in university lab courses. In addition, personalized feedback on challenging concepts can facilitate learning, and large language models (LLMs) like ChatGPT can effectively deliver such feedback. This study combines these two aspects and explores the impact of an AR-based quantum cryptography experiment with integrated ChatGPT-based feedback on university students' learning outcomes and cognitive processes. The study involved 38 students in a physics laboratory course at a German university and used four open-ended questions to measure learning outcomes and gaze data as a learning process assessment. Statistical analysis was used to compare scores between feedback and non-feedback questions, and the effect of ChatGPT feedback on eye-tracking data was examined. The results show that ChatGPT feedback significantly improved learning outcomes and affected gaze data. While the feedback on conceptual questions tended to direct attention to the visualizations of the underlying model, the feedback on questions about experimental procedures increased visual attention to the real experimental materials. Overall, the results show that AI-based feedback draws visual attention towards task-relevant factors and increases learning performance in general.

With the advent and development of real-world quantum technology applications, a practically-focused quantum education including student quantum experiments are gaining increasing importance in physics curricula. In this paper, using the DeFT framework, we present an analysis of the representations in our AR-enhanced quantum cryptography student experiment, in order to assess their potential for promoting conceptual learning. We also discuss learner visual attention with respect to the provided multiple representations based on the eye gaze data we have obtained from a pilot study where N=38 students carried out the tasks in our AR-enhanced quantum cryptography student experiment.

In quantum physics (QP) education, the use of representations such as diagrams and visual aids that connect to mathematical concepts is crucial. Research in representation theory indicates that combining symbolic-mathematical elements (e.g. formulae) with visual-graphical representations enhances conceptual understanding more effectively than representations that merely depict phenomena. However, common representations vary widely, and existing categorisation systems do not adequately distinguish between them in QP. To address this, we developed a new set of differentiation criteria based on insights from representation research, QP education, and specific aspects of the quantum sciences. We created a comprehensive category system for evaluating visual QP representations for educational use, grounded in Ainsworths (2006) DeFT Framework. Twenty-one experts from four countries evaluated this category system using four qubit representations: the Bloch sphere, Circle Notation, Quantum Bead, and the pie chart (Qake) model. This evaluation enabled us to assess the discriminative power of our criteria and the effectiveness of each representation in supporting the learning of QP concepts. It evaluated how well each representation conveyed quantum concepts such as quantum state, measurement, superposition, entanglement, and quantum technologies (X-, Z-, and H-gates) across 16 criteria. The results showed significant differences in the effectiveness of these representations, particularly in conveying key concepts like superposition and measurement. Additionally, expert ratings indicated notable variations in the potential of each representation to induce misconceptions, linked to differences in shape, measurement behaviour, and requirements for understanding entanglement. We also discuss considerations for developing new representations and suggest directions for future empirical studies.

In the rapidly evolving interdisciplinary field of quantum information science and technology, a big obstacle is the necessity of understanding high-level mathematics to solve complex problems. Visualizations like the (dimensional) circle notation enable us to visualize not only single-qubit but also complex multi-qubit states, entanglement, and quantum algorithms. Current findings in educational research suggest that incorporating visualizations in settings of problem solving can have beneficial effects on students' performance and cognitive load compared to solely relying on symbolic problem solving content. In this pilot study, we aim to take a first step to identify in which contexts students benefit from the presentation of visualizations of multi-qubit systems in addition to mathematical formalism. We compare students' performance, time taken, and cognitive load when solving problems using the mathematical-symbolic Dirac notation alone with using it accompanied by the circle notation or the dimensional circle notation in single- and multi-qubit systems. Although little overall differences in students' performance can be detected depending on the presented representations, we observe that problem-solving performance is student- and context-dependent. In addition, the results indicate reduced cognitive load when participants are presented with visualization. The results are discussed with respect to relevant design aspects for future studies., Comment: 32(+20) pages, 16(+6) figures

As distance learning becomes increasingly important and artificial intelligence tools continue to advance, automated systems for individual learning have attracted significant attention. However, the scarcity of open-source online tools that are capable of providing personalized feedback has restricted the widespread implementation of research-based feedback systems. In this work, we present RATsApp, an open-source automated feedback system (AFS) that incorporates research-based features such as formative feedback. The system focuses on core STEM competencies such as mathematical competence, representational competence, and data literacy. It also allows lecturers to monitor students' progress. We conducted a survey based on the technology acceptance model (TAM2) among a set of students (N=64). Our findings confirm the applicability of the TAM2 framework, revealing that factors such as the relevance of the studies, output quality, and ease of use significantly influence the perceived usefulness. We also found a linear relation between the perceived usefulness and the intention to use, which in turn is a significant predictor of the frequency of use. Moreover, the formative feedback feature of RATsApp received positive feedback, indicating its potential as an educational tool. Furthermore, as an open-source platform, RATsApp encourages public contributions to its ongoing development, fostering a collaborative approach to improve educational tools., Comment: 40 pages, 6 figures

The increased presence of large language models (LLMs) in educational settings has ignited debates concerning negative repercussions, including overreliance and inadequate task reflection. Our work advocates moderated usage of such models, designed in a way that supports students and encourages critical thinking. We developed two moderated interaction methods with ChatGPT: hint-based assistance and presenting multiple answer choices. In a study with students (N=40) answering physics questions, we compared the effects of our moderated models against two baseline settings: unmoderated ChatGPT access and internet searches. We analyzed the interaction strategies and found that the moderated versions exhibited less unreflected usage (e.g., copy \& paste) compared to the unmoderated condition. However, neither ChatGPT-supported condition could match the ratio of reflected usage present in internet searches. Our research highlights the potential benefits of moderating language models, showing a research direction toward designing effective AI-supported educational strategies., Comment: paper consists of 13 pages 6 figures; supplementary material 15 pages

Effectively supporting students in mastering all facets of self-regulated learning is a central aim of teachers and educational researchers. Prior research could demonstrate that formative feedback is an effective way to support students during self-regulated learning (SRL). However, for formative feedback to be effective, it needs to be tailored to the learners, requiring information about their learning progress. In this work, we introduce LEAP, a novel platform that utilizes advanced large language models (LLMs), such as ChatGPT, to provide formative feedback to students. LEAP empowers teachers with the ability to effectively pre-prompt and assign tasks to the LLM, thereby stimulating students' cognitive and metacognitive processes and promoting self-regulated learning. We demonstrate that a systematic prompt design based on theoretical principles can provide a wide range of types of scaffolds to students, including sense-making, elaboration, self-explanation, partial task-solution scaffolds, as well as metacognitive and motivational scaffolds. In this way, we emphasize the critical importance of synchronizing educational technological advances with empirical research and theoretical frameworks., Comment: 9 pages, 3 Figures, 1 Table

Large language models (LLMs) have recently gained popularity. However, the impact of their general availability through ChatGPT on sensitive areas of everyday life, such as education, remains unclear. Nevertheless, the societal impact on established educational methods is already being experienced by both students and educators. Our work focuses on higher physics education and examines problem solving strategies. In a study, students with a background in physics were assigned to solve physics exercises, with one group having access to an internet search engine (N=12) and the other group being allowed to use ChatGPT (N=27). We evaluated their performance, strategies, and interaction with the provided tools. Our results showed that nearly half of the solutions provided with the support of ChatGPT were mistakenly assumed to be correct by the students, indicating that they overly trusted ChatGPT even in their field of expertise. Likewise, in 42% of cases, students used copy & paste to query ChatGPT -- an approach only used in 4% of search engine queries -- highlighting the stark differences in interaction behavior between the groups and indicating limited reflection when using ChatGPT. In our work, we demonstrated a need to (1) guide students on how to interact with LLMs and (2) create awareness of potential shortcomings for users., Comment: Pre-print currently under review

Generative AI technologies such as large language models show novel potentials to enhance educational research. For example, generative large language models were shown to be capable to solve quantitative reasoning tasks in physics and concept tests such as the Force Concept Inventory. Given the importance of such concept inventories for physics education research, and the challenges in developing them such as field testing with representative populations, this study seeks to examine to what extent a generative large language model could be utilized to generate a synthetic data set for the FCI that exhibits content-related variability in responses. We use the recently introduced ChatGPT based on the GPT 4 generative large language model and investigate to what extent ChatGPT could solve the FCI accurately (RQ1) and could be prompted to solve the FCI as-if it were a student belonging to a different cohort (RQ2). Furthermore, we study, to what extent ChatGPT could be prompted to solve the FCI as-if it were a student having a different force- and mechanics-related misconception (RQ3). In alignment with other research, we found the ChatGPT could accurately solve the FCI. We furthermore found that prompting ChatGPT to respond to the inventory as-if it belonged to a different cohort yielded no variance in responses, however, responding as-if it had a certain misconception introduced much variance in responses that approximate real human responses on the FCI in some regards., Comment: 13 pages, 3 figures, 2 tables

In the field of quantum information science and technology, the representation and visualization of quantum states and related processes are essential for both research and education. In this context, a focus especially lies on ensembles of few qubits. There exist many powerful representations for single-qubit and multi-qubit systems, such as the famous Bloch sphere and generalizations. Here, we utilize the dimensional circle notation as a representation of such ensembles, adapting the so-called circle notation of qubits and the idea of representing the n-particle system in an n-dimensional space. We show that the mathematical conditions for separability lead to symmetry conditions of the quantum state visualized, offering a new perspective on entanglement in few-qubit systems and therefore on various quantum algorithms. In this way, dimensional notations promise significant potential for conveying nontrivial quantum entanglement properties and processes in few-qubit systems to a broader audience, and could enhance understanding of these concepts as a bridge between intuitive quantum insight and formal mathematical descriptions., Comment: 22 pages, 20 figures

The recent advancement of large language models presents numerous opportunities for teaching and learning. Despite widespread public debate regarding the use of large language models, empirical research on their opportunities and risks in education remains limited. In this work, we demonstrate the qualities and shortcomings of using ChatGPT 3.5 for physics task development by prospective teachers. In a randomized controlled trial, 26 prospective physics teacher students were divided into two groups: the first group used ChatGPT 3.5 to develop text-based physics tasks for four different concepts in the field of kinematics for 10th grade high school students, while the second group used a classical textbook to create tasks for the same concepts and target group. The results indicate no difference in task correctness, but students using the textbook achieved a higher clarity and more frequently embedded their questions in a meaningful context. Both groups adapted the level of task difficulty easily to the target group but struggled strongly with sufficient task specificity, i.e., relevant information to solve the tasks were missing. Students using ChatGPT for problem posing rated high system usability but experienced difficulties with output quality. These results provide insights into the opportunities and pitfalls of using large language models in education., Comment: 10 pages, 3 figures, 3 tables

Employing scientific practices to obtain and use information is one of the central facets of next generation science standards. Especially in quantum technology education, the ability to employ such practices is an essential skill to foster both academic success and technological development. In order to help educators design effective instructions, the comparison between novices' and experts' eye movements allows the identification of efficient information extraction and integration strategies. In this work, we compare the gaze behavior of experts and novices while solving problems in quantum physics using an interactive simulation tool, Quantum Composer, which displays information via multiple external representations (numerical values, equations, graphs). During two reasoning tasks, we found that metarepresentational competences were crucial for successful engagement with the simulation tool. The analysis of the gaze behavior revealed that visual attention on a graph plays a major role and redundant numerical information is ignored. Furthermore, the total dwell time on relevant and irrelevant areas is predictive for the score in the second task. Therefore, the results demonstrate which difficulties novices encounter when using simulation tools and provides insights for how to design effective instructions in quantum technology education guided by experts' gaze behavior., Comment: 14 pages, 8 Figures, 3 Tables

Optics is a core field in the curricula of secondary physics education. In this study, we present the development and validation of a test instrument in the field of optics, the Converging Lenses Concept Inventory (CLCI). It can be used as a formative or a summative assessment of middle school students' conceptual understanding of image formation by converging lenses. The CLCI assesses: (1) the overall understanding of fundamental concepts related to converging lenses, (2) the understanding of specific concepts, and (3) students' propensity for difficulties within this topic. The initial CLCI consists of 16 multiple-choice items; however, one item was removed based on various quality checks. We validated the CLCI thoroughly with distractor analyses, classical test theory, item response theory, structural analyses, and analyses of students' total scores at different measurement points as quantitative approaches, as well as student interviews and an expert survey as qualitative approaches. The quantitative analyses are mostly based on a dataset of N = 318 middle school students who took the CLCI as a posttest. The student interviews were conducted with seven middle school students after they were taught the concepts of converging lenses. The expert survey included five experts who evaluated both individual items and the test as a whole. The analyses showed good to excellent results for the test instrument, corroborating the 15-item CLCI's validity and its compliance with the three foci outlined above.

The COVID-19 pandemic has significantly affected the education system worldwide that was responding with a sudden shift to distance learning. Various physics courses such as lectures, tutorials, and the laboratories had to be transferred into online formats rapidly, resulting in a variety of simultaneous, asynchronous, and mixed activities. To investigate how physics students perceived the sudden shift to online learning, we developed a questionnaire and gathered data from N = 578 physics students from five universities in Germany, Austria, and Croatia. In this article, we report how the problem-solving sessions (recitations) and laboratories were adapted, how students' judge different formats of the courses and how useful and effective they perceive them. The results are correlated to the students' self-efficacy ratings and other behavioral measures (such as self-regulated learning skills) and demographics. In a related article, we focus on the online physics lectures and compare simultaneous vs. asynchronous teaching and learning methods (n.n.). We find that good communication abilities and self-organization skills are positively correlated for perceived learning achievement. Furthermore, the previous duration of studies had a significant impact on the students' perceived overall learning achievement, on the students' acquisition of experimental skills during the physics laboratories, and on their assessment of the recitations' effectiveness. That is, students in their first academic year show consistently lower scores than more progressed students. For the physics laboratories, it was found that gathering real data was crucial to the acquisition of experimental skills and the reinforcement of content. For the physics recitations, handing in own solutions for feedback was correlated with perceived effectiveness. We draw conclusions and implications for future online classes., Comment: 11 pages, 5 figures, Appendix with instrument (questions)

This study used eye-tracking to capture the students' visual attention while taking the test of understanding graphs in kinematics (TUG-K). A total of N = 115 upper-secondary-level students from Germany and Switzerland took the 26-item multiple-choice instrument after learning about kinematics graphs in the regular classroom. Besides choosing the correct alternative among research-based distractors, the students were required to judge their response confidence for each question. The items were presented sequentially on a computer screen equipped with a remote eye tracker, resulting in a set of approx. 3000 paired responses (accuracy and confidence) and about 40 hours of eye movementdata (approx. 500.000 fixations). The analysis of students' visual attention related to the item stems (questions) and the item options reveal that high response confidence is correlated with shorter visit duration on both elements of the items. While the students' response accuracy and their response confidence are highly correlated on the score level, r(115) = 0.63, p < 0.001, the eye-tracking measures do not sufficiently discriminate between correct and incorrect responses. However, a more fine-grained analysis of visual attention based on different answer options reveals a significant discrimination between correct and incorrect answers in terms of an interaction effect: Incorrect responses are associated with longer visit durations on strong distractors and less time spent on correct options while correct responses show the opposite trend. Outcomes of this study provide new insights into the validation of concept inventories based on students' behavioural level.

Using molecular dynamics simulation, we study the plastic zone created during nanoindentation of a large CuZr glass system. The plastic zone consists of a core region, in which virtually every atom undergoes plastic rearrangement, and a tail, where the density distribution of the plastically active atoms decays to zero. Compared to crystalline substrates, the plastic zone in metallic glasses is significantly smaller than in crystals. The so-called plastic-zone size factor, which relates the radius of the plastic zone to the contact radius of the indenter with the substrate, assumes values around 1, while in crystals -- depending on the crystal structure -- values of 2--3 are common. The small plastic zone in metallic glasses is caused by the essentially homogeneous deformation in the amorphous matrix, while in crystals heterogeneous dislocations prevail, whose growth leads to a marked extension of the plastic zone., Comment: 5 pages, 4 figures

Tribological properties of materials play an important role in engineering applications. Up to now, a number of experimental studies have identified correlations between tribological parameters and the mechanical response. Using molecular dynamics simulations, we study abrasive wear behavior via nanoscratching of a Cu$_{64.5}$Zr$_{35.5}$ metallic glass. The evolution of the normal and transverse forces and hardness values follows the behavior well known for crystalline substrates. In particular, the generation of the frontal pileup weakens the response of the material to the scratching tip and leads to a decrease of the transverse hardness as compared to the normal hardness. However, metallic glasses soften with increasing temperature, particularly above the glass transition temperature thus showing a higher tendency to structurally relax an applied stress. This plastic response is analyzed focusing on local regions of atoms which underwent strong von-Mises strains, since these are the basis of shear-transformation zones and shear bands. The volume occupied by these atoms increases with temperature, but large increases are only observed above the glass transition temperature. We quantify the generation of plasticity by the concept of plastic efficiency, which relates the generation of plastic volume inside the sample with the formation of external damage, viz. the scratch groove. In comparison to nanoindentation, the generation rate of the plastic volume during nanoscratching is significantly temperature dependent making the glass inside more damage-tolerant at lower temperature but more damage-susceptible at elevated temperatures., Comment: 14 pages, 13 figures

The concepts of the Coriolis and the centrifugal force are essential in various scientific fields and they are standard components of introductory physics lectures. In this paper we explore how students understand and apply concepts of rotating frames of reference in the context of an exemplary lecture demonstration experiment. We found in a $Predict-Observe-Explain$-setting, that after predicting the outcome prior to the demonstration, only one out of five physics students correctly reported the observation of the trajectory of a sphere rolling over a rotating disc. Despite this low score, a detailed analysis of distractors revealed significant conceptual learning during the observation of the experiment. In this context, we identified three main misconceptions and learning difficulties. First, the centrifugal force is only required to describe the trajectory if the object is coupled to the rotating system. Second, inertial forces cause a reaction of an object on which they act. And third, students systematically mix-up the trajectories in the stationary and the rotating frame of reference. Furthermore, we captured students' eye movements during the $Predict$ task and found that physics students with low confidence ratings focused longer on relevant task areas than confident students despite having a comparable score. Consequently, this metric is a helpful tool for the identification of misconceptions using eye tracking. Overall, the results help to understand the complexity of concept learning from demonstration experiments and provide important implications for instructional design of introductions to rotating frames of reference., Comment: 12 pages

Studying the primary {\alpha}- and secondary {\beta}-relaxation process has contributed significantly to the understanding of the structure and rheology of metallic glasses. In this letter, we report on a third relaxation mechanism indicated by a maximum in the loss modulus at low temperatures, which we term {\gamma}-relaxation. Contrary to the {\alpha}- and {\beta}-relaxation mechanisms, this irreversible, low energy excitation causes a macroscopic rejuvenation, which we assign to non-affine atomic rearrangements in the matrix that are driven by thermal stresses during cooling. Observed in three different glassy alloys, the low temperature relaxation is identified as a general process in metallic glasses., Comment: 15 pages including supplementary material, 4 figures (main text) and 3 additional figures (supplementary material)