As quantum technologies transition from the research laboratory into commercial development, the opportunities for students to begin their careers in this new quantum industry are increasing. With these new career pathways, more and more people are considering the best ways to educate students about quantum concepts and relevant skills. In particular, the quantum industry is looking for new employees with experimental skills, but the instructional labs, capstone projects, research experiences, and internships that provide experiences where students can learn these skills are often resource intensive and not available at all institutions. The quantum company, Infleqtion, recently made its online quantum matter machine, Oqtant, publicly available, so people around the world could send commands to create and manipulate Bose-Einstein condensates and receive back real experimental data. Making a complex quantum experiment accessible to anyone has the potential to extend the opportunity to work with quantum experiments to students at less-resourced institutions. As a first step in understanding the potential benefits of using such a platform in educational settings, we collected data from instructors and students who were interested in using, or had used, Oqtant. In this study, we investigate instructors’ views about reasons they would like to use Oqtant and the challenges they would face in doing so. We also provide a concrete example of how Oqtant was used in an upper-division undergraduate quantum mechanics course and the instructor’s perception of its benefits. We complement this with the student perspective, discussing student experiences interacting with Oqtant in their course or through think-aloud interviews outside of a course. This allows us to investigate the reasons students perceive Oqtant to be a real experiment even though they never physically interact with it, how Oqtant compares to their other experimental experiences, and what they enjoy about working with it. These results will help the community consider the potential value of creating more opportunities for students to access remote quantum experiments.

When learning physics, students need more than just an understanding of mathematical and physical concepts. Integrating the two fields is crucial, as research indicates that students often struggle even when they have a strong grasp of both. In this paper, we use the heat equation as an example from higher education. Given the importance of the gradient and the Laplacian in the heat equation, as well as fluency and flexibility in using multiple external representations, this study investigates students’ reasoning about the gradient and the Laplacian of a function within different function representations in mathematics and physics contexts. To do so, we designed isomorphic open-response questions, administered as paper-and-pencil tests to 190 first-year students who were taking calculus-based introductory physics courses and multivariable calculus courses during their second semester. These students were enrolled in physics, mathematics, engineering, and bioengineering programs. We found that students face conceptual challenges with both the gradient and the Laplacian. Student difficulties with interpreting the gradient may be related to an incomplete understanding of steepness in graphical representations of functions of two independent variables. Moreover, their understanding of the Laplacian is limited. While context did not significantly affect students’ reasoning in terms of the types of difficulties they encountered, the proportion of students facing these difficulties, and their tendency to link or discuss more than one aspect of a concept, we did find context-specific prevalence of graphical, algebraic-symbolic, or linguistic descriptions. Students used linguistic descriptions more frequently in a physics context. We observed varying abilities to express the meaning of concepts in different answer representations. Linguistic descriptions of concepts proved particularly challenging for both concepts and contexts. Our findings provide insight into students’ understanding of two concepts related to the 2D heat equation.

This study investigated how students reason about the partial derivative and the directional derivative of a multivariable function at a given point, using different graphical representations for the function in the problem statement. Questions were formulated to be as isomorphic as possible in both mathematics and physics contexts and were given as pen-and-paper tests to 190 mathematics, physics, engineering, and bioengineering students in their second semester. Our first research question asked how students reason about partial derivatives and directional derivatives with different function representations and in different contexts. Our second research question investigated whether a physics context hinders or improves students’ understanding of these concepts. Performance on partial derivative questions varied with both the representations students used in their answers and the function representations used in the question. Students performed better when they provided algebraic-symbolic answers and when they answered Cartesian graph questions. For directional derivatives, students struggled with correct interpretations, often misinterpreting steepness as average steepness between points rather than as steepness at a specific point. The context did not significantly affect overall performance, but it did influence the representations students used in their answers, with a tendency toward linguistic descriptions in physics.

We used student surveys to assess changes in proficiency with integral calculus, calculus self-efficacy, and physics self-efficacy in a second semester course of introductory physics focused on electricity and magnetism. In addition to tracking the fraction of quantitative problems solved correctly on the calculus proficiency survey, we also used principal component analysis and factor analysis of the data collected using all three surveys to evaluate changes in student proficiency and attitude. These analyses indicate that while all students demonstrated an increase in proficiency with integral calculus, including using integration in the context of physics, women displayed larger gains than men. Conversely, men showed larger gains in calculus self-efficacy. When combined, these data suggest that student identity modulates the correlation between a student’s calculus abilities and their perception or self-evaluation of those abilities. We further show that calculus self-efficacy and physics self-efficacy are more strongly correlated for women than for men. These data suggest that student identity affects the coupling between calculus self-efficacy and physics self-efficacy, which could be consistent with previously published work demonstrating that mathematics self-efficacy is modulated by student identity [A. C. Frenzel et al., Learn. Instr. 17, 478 (2007); A. C. Frenzel et al., Eur. J. Psychol. Educ. 22, 497 (2007); R. A. Louis and J. M. Mistele, Int. J. Sci. Math. Educ. 10, 1163 (2012)]. These results may thus also highlight a potential contributing factor to gender-related differences in physics self-efficacy [J. M. Nissen and J. T. Shemwell, Phys. Rev. Phys. Educ. Res. 12, 020105 (2016); E. M. Marshman et al., Phys. Rev. Phys. Educ. Res. 14, 020123 (2018); T. Espinosa et al., Phys. Rev. Phys. Educ. Res. 15, 010132 (2019)] as well as the complexity of addressing those differences.

As quantum technologies transition out of the research lab and into commercial applications, it becomes important to better prepare students to enter this new and evolving workforce. To work toward this goal of preparing physics students for a career in the quantum industry, a senior capstone course called “Quantum Forge” was created at the University of Colorado Boulder. This course aims to provide students with a hands-on quantum experience and prepare them to enter the quantum workforce directly after their undergraduate studies. Some of the course’s goals are to have students understand what comprises the quantum industry and have them feel confident they could enter the industry if desired. To understand to what extent these goals are achieved, we followed the first cohort of Quantum Forge students through their year in the course in order to understand their perceptions of the quantum industry, including what it is, whether they feel that they could be successful in it, and whether or not they want to participate in it. The results of this work can assist educators in optimizing the design of future quantum-industry-focused courses and programs to better prepare students to be a part of this burgeoning industry.

Recent advancements in large language models (LLMs) hold significant promise for improving physics education research that uses machine learning. In this study, we compare the application of various models for conducting a large-scale analysis of written text grounded in a physics education research classification problem: identifying skills in students’ typed lab notes through sentence-level labeling. Specifically, we use training data to fine-tune two different LLMs, BERT and LLaMA, and compare the performance of these models to both a traditional bag-of-words approach and a few-shot LLM (without fine-tuning). We evaluate the models based on their resource use, performance metrics, and research outcomes when identifying skills in lab notes. We find that higher-resource models often, but not necessarily, perform better than lower-resource models. We also find that all models report similar trends in research outcomes, although the absolute values of the estimated measurements are not always within uncertainties of each other. We use the results to discuss relevant considerations for education researchers seeking to select a model type for use as a classifier.

We use a validated conceptual multiple-choice survey instrument focusing on thermodynamic processes and the first and second laws of thermodynamics at the level of introductory physics to investigate the problem-property dependence of introductory and advanced student responses to introductory thermodynamics problems after traditional lecture-based instruction. The survey instrument has qualitative problems involving the same concepts across multiple problems related to internal energy, work, heat transfer, and entropy. The concepts for which we investigated problem-property dependence include, among others, (i) internal energy and entropy are state variables while work and heat transfer are path-dependent variables, (ii) internal energy is proportional to the absolute temperature for an ideal gas, (iii) work corresponds to the (signed) area under the curve on a PV (pressure-volume) diagram, and (iv) internal energy is constant but entropy increases in isolated systems undergoing spontaneous and irreversible processes. This study used survey data from over 1000 college students in introductory-level algebra-based and calculus-based physics courses as well as upper-level thermodynamics courses; the survey was administered after traditional instruction in relevant concepts for each group. Think-aloud interviews were carried out to gain additional insight into students’ thinking as they responded to the survey problems. For concepts related to internal energy, heat transfer, and work, student responses for different concepts investigated often showed strong problem-property dependence, but advanced students, as a group, generally performed better than introductory students across different problems. For entropy concepts, introductory students consistently performed poorly across problem types, reflecting a persistent belief in the constancy of entropy. By contrast, upper-level students struggled consistently in cases where entropy was not increasing (e.g., net entropy change in a cyclic process). Our systematic investigation of problem-property dependence of student responses is novel for thermodynamics, made possible by the use of a survey that includes multiple varied problem scenarios involving the same underlying concept. In addition to yielding many previously unreported results regarding problem-property dependence in thermodynamics, our work confirms and extends, to new problem settings and student groups, findings previously reported through the study of more limited problem settings and student groups.

[This paper is part of the Focused Collection in Artificial Intelligence Tools in Physics Teaching and Physics Education Research.] This study examines the feasibility and potential advantages of using large language models, in particular GPT-4o, to perform partial credit grading of large numbers of student written responses to introductory level physics problems. Students were instructed to write down verbal explanations of their reasoning process when solving one conceptual and two numerical calculation problems on two exams. The explanations were then graded according to a three-item rubric with each item graded as binary (1 or 0). We first demonstrate that machine grading using GPT-4o with no examples or reference answers can reliably agree with human graders in 70%–80% of all cases, which is equal to or higher than the level at which two human graders agree with each other. Two methods are essential for achieving this level of accuracy: (i) Adding explanation language to each rubric item that targets the errors of initial machine grading. (ii) Running the grading process 5 times and taking the most frequent outcome. Next, we show that the variation in outcomes across five machine grading attempts can serve as a grading confidence index. The index allows a human expert to identify $\sim 40\%$ of all potentially incorrect gradings by reviewing just 10%–15% of all responses with the highest variation. Finally, we show that it is straightforward to use GPT-4o to write a clear and detailed explanation of the partial credit grading outcome. Those explanations can be used as feedback for students, which will allow students to understand their grades and raise different opinions when necessary. Almost all feedback messages generated were rated three or above on a five-point scale by two instructors who had taught the course multiple times. The entire grading and feedback generating process costs roughly $5 per 100 student answers, which shows immense promise for automating labor-intensive grading process through a combination of machine grading with human input and supervision.

[This paper is part of the Focused Collection in Investigating and Improving Quantum Education through Research.] One of the greatest weaknesses of physics education research is the paucity of research on graduate education. While there are a growing number of investigations of graduate student degree progress and admissions, there are very few investigations of learning at the graduate level. Additionally, existing studies of learning in physics graduate programs frequently focus on content knowledge rather than professional skills such as problem solving. Given that over 90% of physics Ph.D. graduates report solving technical problems regularly in the workplace, we sought to develop an assessment to measure how well graduate programs are training students to solve problems. Using a framework that characterizes expert-like problem-solving skills as a set of decisions to be made, we developed and validated such an assessment in graduate quantum mechanics (QM) following recently developed design frameworks for measuring problem solving and best practices for assessment validation. We collected validity evidence through think-aloud interviews with practicing physicists and physics graduate students, as well as written solutions provided by physics graduate and undergraduate students. The assessment shows strong potential in differentiating novice and expert problem solving in QM and showed reliability in repeated testing with similar populations. These results show the promise of measuring expert decision making in graduate QM and provide baseline measurements for future educational interventions to more effectively teach these skills.

Undergraduate physics and astronomy students are expected to engage with scientific literature as they begin their research careers, yet reading comprehension skills are rarely explicitly taught in major courses. We seek to determine the efficacy of a reading assignment designed to improve undergraduate astronomy (or related) majors’ perceived ability to engage with research literature by using accessible summaries of current research written by experts in the field. During the 2022–2023 academic year, faculty members from six institutions incorporated reading assignments using accessible summaries from Astrobites into their undergraduate astronomy major courses, surveyed their students before and after the activities, and participated in follow-up interviews with our research team. Quantitative and qualitative survey data from 52 students show that students’ perceptions of their abilities to understand jargon and identify the main takeaways of a paper significantly improved with the use of the tested assignment template. Additionally, students reported increased confidence in their abilities within astronomy after exposure to these assignments, and instructors having valued a ready-to-use resource for incorporating reading comprehension into their pedagogy. This exploratory case study, using Astrobites-based assignments, suggests that incorporating current research into the undergraduate classroom through accessible literature summaries may increase students’ confidence and ability to engage with research literature, thereby assisting in their preparation for participation in research careers.

Investigating students’ thinking in classroom tasks, particularly in science and engineering, is essential for improving educational practices and advancing student learning. In this context, the notion of Ways of Thinking (WoT) has gained traction in STEM education, offering a framework to explore how students approach and solve interdisciplinary problems. Building on our earlier studies and contributing to ongoing discussions on WoT frameworks, this paper introduces a new WoT framework—Ways of Thinking in Engineering Design-based Physics (WoT4EDP). WoT4EDP integrates five key elements—design, science, mathematics, metacognitive reflection, and computational thinking—within an undergraduate introductory physics laboratory. This novel framework highlights how these interconnected elements foster deeper learning and holistic problem solving in ED-based projects. A key takeaway is that this framework serves as a practical tool for educators and researchers to design, implement, and analyze interdisciplinary STEM activities in physics classrooms. We describe the development of WoT4EDP, situate it within undergraduate STEM education, and characterize its components in detail. Additionally, we compare WoT4EDP with two contemporary frameworks—Dalal et al. (2021) and English (2023)—to glean insights that enhance its application and promote interdisciplinary thinking. This paper is the first of a two-part series. In the upcoming second part, we will demonstrate the application of the WoT4EDP framework, showcasing how it can be used to analyze student thinking in real-world, ED-based physics projects.

We conducted two studies to investigate the extent to which brief, spaced, mastery practice on skills relevant to introductory physics affects student performance. The first study investigated the effect of practice of “specific” physics skills, each one relevant to only one or a few items on the course exam. This study employed a quasiexperimental design with 766 students assigned to “intervention” or “control” conditions by lecture section sharing common exams. Results of the first study indicate significant improvement in the performance for only some of the exam items relevant to the specific skills practiced. We also observed between-section performance differences on other exam items not relevant to training, which may be due to specific prior quiz items from individual instructors. The second study investigated the effect of practice on the “general” skill of algebra relevant to introductory physics, a skill which was relevant to most of the exam items. This study employed a similar quasiexperimental design with 363 students assigned to treatment or control conditions, and we also administered a reliable pre- and post-test assessment of the algebra skills that was iteratively developed for this project. Results from the second study indicate that 75% of students had high accuracy on the algebra pretest. Students in the control condition who scored low on the pretest gained about 0.7 standard deviations on the post-test, presumably from engagement with the course alone, and students in the algebra practice condition had statistically similar gains, indicating no observed effect of algebra practice on algebra pre- to post-test gains. In contrast, we find some potential evidence that the algebra practice improved final exam performance for students with high pretest scores and did not benefit students with low pretest scores, although this result is inconclusive: the point estimate of the effect size was 0.24 for high pretest scoring students, but the 95% confidence interval [$-0.01$, 0.48] slightly overlapped with zero. Further, we find a statistically significant positive effect of algebra practice on exam items that have higher algebraic complexity and no effect for items with low complexity. One possible explanation for the added benefit of algebra practice for high-scoring students is fluency in algebra skills may have improved. Overall, our observations provide some evidence that spaced, mastery practice is beneficial for exam performance for specific and general skills, and that students who are better prepared in algebra may be especially benefitting from mastery practice in relevant algebra skills in terms of improved final exam performance.

Electricity and magnetism are fundamentally interconnected, as represented by the symmetry in Maxwell’s equations. Much of the research on Gauss’s and Ampere’s laws has focused on their application in calculating electric or magnetic fields. However, there remains a significant gap in the literature in exploring these laws in a broader context—particularly in understanding electric flux and magnetic circulation as distinct yet related concepts through the lens of the superposition principle. This study will fill this gap by examining students’ comprehension of electric flux and magnetic circulation. It focuses on their role in Gauss’s and Ampere’s laws beyond their typical use for computing other physical quantities. The study involved 322 engineering students completing a course on electricity and magnetism. The students were given two open-ended questionnaires of parallel problems: half answered questions addressing the electricity context, and the other half responded to questions addressing magnetism. Our phenomenographic analysis revealed significant conceptual confusion between electric field and electric flux, as well as between magnetic field and magnetic circulation, which affected their ability to apply the superposition principle. Additionally, some students incorrectly assigned physical reality to Gaussian surfaces and Amperian loops, further hindering their understanding of the superposition principle due to a blocking effect. We identify several factors that may contribute to these difficulties and suggest implications for teaching to address the conceptual difficulties identified in this study.

Students and educators often face time constraints, making it essential to develop interventions that are both easy to implement and have a substantial impact on learning and performance. One promising strategy is retrieval practice, particularly in the context of physics education, where many students struggle with basic knowledge. Prior research has shown that retrieval practice improves self-explanation and problem-solving performance, yet many students avoid it, even when resources are provided. To address this, we introduced a mandatory retrieval test with a minimum benchmark of 50% to encourage greater engagement with retrieval practice. The primary aim of this study was to explore students’ experiences with the test and its impact on their use of retrieval practice. A secondary aim was to examine whether increased retrieval practice effort correlated with improved performance on factual, conceptual, and problem-solving exams. Interviews with 13 students revealed that about half crammed for the test, while the other half spaced their practice throughout the semester. Several students noted that the test motivated them to both memorize and understand the principles, with no complaints about the mandatory test. Of the 463 students, 179 achieved a perfect score, suggesting substantial engagement. Effect sizes on factual, conceptual, and problem-solving performance tests ranged from negligible to large, indicating substantial potential benefits with minimal risk. In conclusion, the mandatory retrieval test is an effective, low-effort intervention for educators, promoting greater student adoption of retrieval practice and yielding both qualitative and quantitative evidence of enhanced learning and performance.

Reform documents advocate for innovative pedagogical strategies to enhance student learning. A key innovation is the integration of science and engineering practices through engineering design (ED)-based physics laboratory tasks, where students tackle engineering design problems by applying physics principles. While this approach has its benefits, research shows that students do not always effectively apply scientific concepts, but instead rely on trial-and-error approaches, and end up gadgeteering their way to a solution. This leads to what is commonly referred to as the design-science gap—that students do not always consciously apply science concepts while solving a design problem. However, as obvious as the notion of a gap may appear, there seems to exist no consensus on the definitions of design and science, further complicating the understanding of this gap. This qualitative study addresses the notion of the design-science gap by examining student groups’ discussions and written lab reports from a multiweek ED-based undergraduate introductory physics laboratory task. Building on our earlier studies, we developed and employed a nuanced, multilayered coding scheme inspired by the Gioia Framework to characterize design thinking and science thinking. We discuss how student groups engage in various aspects of design and how they apply physics concepts and principles to solve the problem. In the process, we demonstrate the interconnectedness of students’ design thinking and science thinking. We advocate for the usage of the term design-science connection as opposed to design-science gap to deepen both design and science thinking. Our findings offer valuable insights for educators in design-based science education.

Video instruction has been widely studied and is generally considered as effective as live instruction for teaching scientific concepts and procedures. However, there is limited research on the effectiveness of prerecorded videos for teaching more challenging content. This study conducted a controlled experiment on over 300 high school students to compare the effectiveness of live instruction versus recorded video in teaching physics problem solving, a representative example of challenging content. Our results indicate that for simpler problems, there is no significant difference in student learning outcomes between live and video instruction, corroborating previous research. However, as problem complexity increases, live instruction significantly outperforms video instruction, potentially highlighting the importance of real-time adaptability, engagement, and sustained attention in face-to-face settings. We found a negative correlation between the effectiveness of video instruction and the difficulty level of the content. This study is the first to empirically investigate the use of video instruction for complex problem solving, making a significant contribution to the current body of literature. Additionally, the findings offer practical insights for school administrators or department heads, suggesting that while video instruction can effectively substitute for live teaching in simpler scenarios, live instruction remains crucial for more complex material, impacting decisions related to human resource allocation and instructional planning.

This study uses an initial attitudinal survey and a subsequent follow-up survey to assess which qualities are correlated with the persistence of women in physics. The initial survey was given to participants at the Conference for Undergraduate Women and Gender Minorities in Physics, and the follow-up survey was given years later, after they graduated; 478 matched surveys were used in this work. Using these surveys, we study how attitudes correlate with retention. First, we examine whether affective factors, mainly situated in identity theory, have any clear correlation with persistence in physics. Then, we study individual questions of the survey, such as a student’s interest in research specifically, to determine more fine-grained correlations with retention. Both of these were examined using analyses of variance (ANOVAs) with post hoc Tukey tests. From studying the overarching factors, we find that respondents who remained in physics after completing their bachelor’s degree reported higher interest than respondents who left physics at earlier points, with a medium effect size. We also find small evidence of associations between sense of belonging and correlation; respondents who leave physics before obtaining a bachelor’s degree tend to have a higher sense of belonging than other groups, while respondents who stay in physics until graduating, then leave for another science, technology, engineering, and mathematics field tend to have a lower sense of belonging. This association, however, shows a small effect size and should be examined more carefully to draw definitive conclusions. We find that identity, perceived recognition, performance competence, success mindset, and sense of community show no significant correlation with long-term persistence. When examining individual questions, we find that people who remain in physics tend to have a higher interest specifically in research, as well as career aspirations of going to graduate school and becoming a professor in physics.