In order to investigate students’ misunderstandings of potential wells and tunneling, a conceptual knowledge test was administered to Dutch secondary school students after they were taught about quantum mechanics. A frequency analysis of responses to the multiple choice questions ($n=98$) and coding of the responses to the open-ended questions and explanations ($n=13$) shows that Dutch secondary school students experience difficulties similar to those reported for undergraduate students. The students’ underlying difficulties were analyzed using a typology of learning impediments. Results of this analysis show that students have difficulty connecting knowledge of potential wells and tunneling to their prior knowledge. Students mainly have creative and epistemological learning impediments, which cause eight incorrect synthetic models.

This paper presents the first results from draw-a-scientist tests (DASTs) over five years that were used to measure the effect of 8–10 week long astronomy clubs and week long summer camps on 3 rd–5 th grade elementary school students’ perceptions of scientists. We facilitated these DASTs prior to these clubs or camps, which provide a baseline for a student’s initial conception of scientists, and once at the end, to determine whether their conception changed, possibly as a result of their involvement. In total we analyze 89 pairs of DASTs using a numerical grading scheme designed to quantify the presence of various features in the drawn scientist and their activities. We find that there is a gender imbalance in both the pre- and postclub drawings, with only 32% and 35%, respectively, of students drawing female scientists. We also find that a third to a half of the scientists have a stereotypical appearance and/or are performing stereotypical activities. Although we find insignificant changes ($<5\%$) in most categories, we do find an 8% increase in the number of scientists that have a stereotypical appearance, which is worth following up, but a significant 12% decrease in the number of scientists who are performing stereotypical activities. In addition, we present some possible improvements to implementing DASTs and discuss other possible assessments that could provide a more direct method of gauging the effect of these astronomy clubs or camps.

Momentum is a foundational concept in physics. Although it is often taught in introductory mechanics courses, there are a limited number of studies on this topic in the literature. The results from these studies have consistently shown that students have difficulties in understanding momentum, especially the connections between net force, time, and change in momentum, which are signs of fragmented knowledge structure and poor knowledge integration. This study adopts the conceptual framework representation to model student understanding and guide the design of an assessment test on momentum. Informed by the previous work on knowledge integration, the conceptual framework maps out the key concepts and their connections within a student’s knowledge structure. Recent studies have shown that a conceptual framework can be used as a guide to create assessment items that follow different reasoning pathways, probing various misconceptions and student difficulties. In this study, an assessment of momentum was developed and tested among a large number of U.S. college freshmen and Chinese high school students. Based on testing and interview results, students’ understanding is separated into three progression levels of knowledge integration including novicelike, transitional, and expertlike. Furthermore, the comparison between the two countries’ curriculum and momentum test results indicates that an emphasis on the central idea of impulse-momentum theorem can be an essential instructional strategy to help students make the necessary connections within their knowledge structure, leading to a deeper conceptual understanding of momentum.

Instructional labs are being transformed to better reflect authentic scientific practice, often by removing aspects of pedagogical structure to support student agency and decision making. We explored how these changes impact men’s and women’s participation in group work associated with labs through clustering methods on the quantified behavior of students. We compared the group roles students take on in two different types of instructional settings: (i) highly structured traditional labs, and (ii) less structured inquiry-based labs. Students working in groups in the inquiry-based (less structured) labs assumed different roles within their groups, however men and women systematically took on different roles and men behaved differently when in single- versus mixed-gender groups. We found no such systematic differences in role division among male and female students in the traditional (highly structured) labs. Students in the inquiry-based labs were not overtly assigned these roles, indicating that the inequitable division of roles was not a result of explicit assignment. Our results highlight the importance of structuring equitable group dynamics in educational settings, as a gendered division of roles can emerge without active intervention. As the culture in physics evolves to remove systematic gender biases in the field, instructors in educational settings must not only remove explicitly biased aspects of curricula but also take active steps to ensure that potentially discriminatory aspects are not inadvertently reinforced.

We examined physics graduate teaching assistants’ views about introductory physics problem “types,” i.e., different ways of posing the same underlying physics problem, within the context of a semester-long teaching assistant (TA) professional development course. Here, we focus on TAs’ views about two types of broken-into-parts problems that involve the same underlying physics scenario. One of these problem types does not involve explicit calculation, while the other does. The TAs were asked to list the pros and cons of these two types of broken-into-parts problems, rank them compared to other problem types (e.g., traditional textbook problem not broken-into-parts, context-rich problem, and multiple-choice problem) with the same underlying scenario in terms of their instructional benefit and the level of challenge they might produce for their students, and describe when and how likely they would be to use these types of problems in their own classes in different instructional situations if they had complete control of teaching the class. TAs reported that they found the broken-into-parts problem type to be the most instructionally beneficial out of all the problem types because of the guidance such problems offer, and would use a broken-into-parts problem type often and in a variety of ways (e.g., homework assignments, exams, and quizzes). While providing guidance to students is an appropriate instructional approach, our findings from interviews suggest that many TAs may be motivated to assign broken-into-parts problems out of a desire to make the problem-solving process easy and/or less stressful for students, especially because they felt that introductory students may not be capable of breaking a problem into subproblems on their own. The instructional benefits of gradually removing the scaffolding support to help students develop self-reliance in solving problems appeared to be overlooked by most TAs. In particular, in written responses or in interviews, most TAs did not mention a long-term goal of helping students develop more independence in problem solving for which one may start with broken-into-parts problems and gradually transition to problems that are not broken into parts. While the study findings that provide a snapshot of TA views in the middle and at the end of a TA professional development course may only apply to graduate TAs at a similar large university, at those institutions, professional development of TAs should take into account these findings and help TAs reflect on the important role that removing scaffolding support gradually and providing adequate challenge can play in helping introductory students develop self-reliance and become independent, expertlike problem solvers.

A small group of interested upper secondary education students participated in a workshop where they created a particle-based physics engine and used the engine to implement a hanging cloth simulation and a two-dimensional heat diffusion model of their own creation. During the implementation of their models, learning opportunities present themselves in the form of opening up and exploring different dimensions of variation for the students. By varying aspects and discerning how these changes affect the program, students can construct meaning about the system. The students were video and audio recorded during the workshop and interviewed afterwards. Based on the transcripts, students use of programming was analyzed using social semiotics and variation theory of learning with a focus on the three aspects: coding, visualization, and interaction. The analysis identifies usages of programming such as a transductive link between semiotic systems, the ease of varying and iterating aspects, and the ability to enter into a loop of discovery and understanding.

We describe the development and in-class evaluation of a quantum interactive learning tutorial (QuILT) on quantum key distribution, a context which involves an exciting application of quantum mechanics. The protocol used in the QuILT described here uses single photons with nonorthogonal polarization states to generate a random shared key over a public channel for encrypting and decrypting information. The QuILT strives to help upper-level undergraduate students learn quantum mechanics using a simple two state system. It actively engages students in the learning process and helps them build links between the formalism and the conceptual aspects of quantum physics without compromising the technical content. The in-class evaluation suggests that the validated QuILT is helpful in improving students’ understanding of relevant concepts.

Writing is an integral part of the process of science. In the undergraduate physics curriculum, the most common place that students engage with scientific writing is in lab classes, typically through lab notebooks, reports, and proposals. There has not been much research on why and how we include writing in physics lab classes, and instructors may incorporate writing for a variety of reasons. Through a broader study of multiweek projects in advanced lab classes, we have developed a framework for thinking about and understanding the role of writing in lab classes. This framework defines and describes the breadth of goals for incorporating writing in lab classes, and is a tool we can use to begin to understand why, and subsequently how, we teach scientific writing in physics.

Brewe, Bruun, and Bearden first applied network analysis to understand patterns of incorrect conceptual physics reasoning in multiple-choice instruments introducing the module analysis for multiple-choice responses (MAMCR) algorithm. Wells et al. proposed an extension to the algorithm which allowed the analysis of large datasets called modified module analysis (MMA). This method analyzed the network structure of the correlation matrix of the responses to a multiple-choice instrument. Both MAMCR and MMA could only be applied to networks of incorrect responses. In this study, an extension of MMA is explored which allows the analysis of networks involving both correct and incorrect responses. The extension analyzes the network structure of the partial correlation matrix instead of the correlation matrix. The new algorithm, called MMA-P, was applied to the FCI and recovered much of the structure identified by MMA. The algorithm also identified sets of correct answers requiring similar physical reasoning reported in previous studies. Beyond groups of all correct and all incorrect responses, some groups of responses which mixed correct and incorrect responses were also identified. Some of these mixed response groups were produced when a correct response was selected for incorrect reasons; some of the groups were related to the gender unfair items previously reported for the FCI.

We introduce a template to (i) scaffold the problem solving process for students in the physics 1 course, and (ii) serve as a generic rubric for measuring how expertlike students are in their problem solving. This template is based on empirical studies of the problem solving practices of expert scientists and engineers, unlike most existing templates which are based on prescriptive, theoretical descriptions of expert problem solving and are largely based on how experts solve textbook-style problems. However, there is still some overlap with existing problem solving templates. In study 1, we investigated the validity of the template for use in introductory physics in two ways, first, by analyzing the final exam solutions from a Physics 1 course, and second, by analyzing seven think-aloud cognitive interviews as successful introductory physics students worked to solve a challenging problem. The results show that use of the elements of the template is correlated with successful problem solving, the template follows successful students’ existing problem solving processes, and explicitly using the template in solving problems does not add additional cognitive load. In study 2, analysis of final exam solutions from a different introductory physics course shows that the relationship between template use and problem solving performance depends on the type and difficulty of the problem. In this work, we also identified some consistent difficulties of unsuccessful students in solving problems which suggests some ways to better teach physics problem solving.

In an effort to examine students’ understanding about the structure of boundary conditions in upper-division courses, think-aloud interviews were conducted in the context of both quantum mechanics and electricity and magnetism. In the quantum mechanics task, students were presented with a standard potential step scenario. In the electricity and magnetism task, students were given a classical question about electromagnetic waves at the boundary of two media. The analysis of the interviews was guided by the use of a symbolic forms perspective. In this paper, we report the symbolic forms identified in students’ work and provide examples of students’ reasoning. Generally speaking, students were able to generate the correct symbolic templates while having difficulties with the underlying conceptual ideas. We also discuss instructional implications from this study.

Investigating student learning and understanding of conceptual physics is a primary research area within physics education research. Multiple quantitative methods have been employed to analyze commonly used mechanics conceptual inventories: the Force Concept Inventory (FCI) and the Force and Motion Conceptual Evaluation (FMCE). Recently, researchers have applied network analytic techniques to explore the structure of the incorrect responses to the FCI identifying communities of incorrect responses which could be mapped on to common misconceptions. In this study, the method used to analyze the FCI, modified module analysis was applied to a large sample of FMCE pretest and post-test responses ($N_{\mathrm{pre}}=3956$, $N_{\mathrm{post}}=3719$). The communities of incorrect responses identified were consistent with the item groups described in previous works. As in the work with the FCI, the network was simplified by only retaining nodes selected by a substantial number of students. Retaining as nodes only those incorrect answer choices selected by at least 20% of the students produced communities associated with only four misconceptions. The incorrect response communities identified for men and women were substantially different, as was the change in these communities from pretest to post-test. The 20% threshold was far more restrictive than the 4% threshold applied to the FCI in the prior work that generated similar structures. Retaining nodes selected by 5% or 10% of students generated a large number of complex communities. The communities identified at the 10% threshold were generally associated with common misconceptions producing a far richer set of incorrect communities than the FCI; this may indicate that the FMCE is a superior instrument for characterizing the breadth of student misconceptions about Newtonian mechanics.

Mathematical reasoning skills are a desired outcome of many introductory physics courses, particularly calculus-based physics courses. Novices can struggle to understand the many roles signed numbers play in physics contexts, and recent evidence shows that unresolved struggle can carry over to subsequent physics courses. Positive and negative quantities are ubiquitous in physics, and the sign carries important and varied meanings. The mathematics education research literature documents the cognitive challenge of conceptualizing negative numbers as mathematical objects—both for experts, historically, and for novices as they learn. We contribute to the small but growing body of research in physics contexts that examines student reasoning about signed quantities and reasoning about the use and interpretation of signs in mathematical models. In this paper we present a framework for categorizing various meanings and interpretations of the negative sign in physics contexts, inspired by established work in algebraic contexts from the mathematics education research community. Such a framework can support innovation that can catalyze deeper mathematical conceptualizations of signed quantities in the introductory courses and beyond.

Introductory physics is taught to several hundred thousand university students every year. It is seen as especially difficult by many and the failure rate is often high. A relevant question is whether one can increase the success rate among the weaker students? Retrieval practice is an established learning strategy with large benefits. However, as pointed out last year in this journal, hardly any systematic research has been done on retrieval practice in physics. Here we present a novel tool for retrieval practice in physics called the hierarchical principle structure for mechanics (HPSM). HPSM hierarchically organizes the essential principles, equations, and definitions for translational, rotational, and fluid mechanics, to emphasize meaningful connections. We investigated HPSM in a two-phase study. First, we present a randomized controlled experiment showing that 70 min of retrieval practice of HPSM had a very large effect on a declarative factual test compared to 70 min of problem study, $d=1.42$. In the second phase, which was carried out the following year, we implemented distributed retrieval practice of HPSM in the first 15 min of 16 lectures. Although difficult to disentangle the effect from the lectures it was embedded in, distributed retrieval practice of HPSM seems to promote factual knowledge ($r=0.44$) and better exam results for the weaker students (significant main and interaction effects).

The topic of women in graduate education has been central to many calls for action in increasing diversity and inclusion in science, technology, engineering, and mathematics. The field of physics has been particularly resistant to change in the significant overrepresentation of men, while also being similar to the field of astronomy which has a higher overall representation of women than many other physical sciences. Little research has been done in the field of astronomy to better understand how women can be supported in other physical sciences. This paper presents an analysis of five women students in a U.S. astronomy graduate program. The results indicate the women in this study relied on student-student collaboration to succeed through their coursework and exams, while faculty and post-doctorate support were critical for their research perseverance. Furthermore, the career goals of these successful students indicate the importance of considering multiple life goals in determining a student’s pathway, and potentially suggests that the way faculty careers progress needs to be reconsidered if the field wants more diverse faculty and role models.

Self-efficacy is an aspect of students’ motivation that has been shown to play a critical role in students’ engagement, participation, and retention in academic careers in science, technology, engineering, and mathematics (STEM). Since women are underrepresented in STEM domains such as physics, we studied female and male students’ self-efficacy and its relation to learning outcomes in physics that can be useful for creating equitable and inclusive learning environments. In a longitudinal study, we surveyed approximately 1400 students in calculus-based physics 2 courses to investigate students’ motivational beliefs in physics using a validated survey. We examined female and male students’ self-efficacy scores and the extent to which self-efficacy related to learning outcomes (students’ grades and conceptual post-test scores), especially the significant gender difference in conceptual post-test scores. To reveal the unique contribution of self-efficacy on outcomes, we controlled for several other variables including Physics 1 grades, SAT math scores, and conceptual pretest scores in physics. We found that the gender differences in conceptual post-test performance were mediated by the model variables. In particular, initial self-efficacy differences showed a direct effect on outcomes even when controlling for students’ prior physics knowledge and skill differences, and self-efficacy also had the strongest total gender effect on conceptual learning. Given these findings, future work should focus on better understanding the drivers of these self-efficacy differences including the role that societal stereotypes and biases play in these in order to mitigate these differences.

Many science, technology, engineering, and math degrees require passing an introductory physics course. Physics courses often have high failure rates that disproportionately harm students who are historically and continually marginalized by racism, sexism, and classism. We examined the associations between learning assistant (LA) supported courses and equity in nonpassing grades [i.e., drop, fail, or withdrawal (DFW)] in introductory physics courses. The data used in the study came from 2312 students in 41 sections of introductory physics courses at a regional Hispanic serving institution. We developed hierarchical generalized linear models of student DFW rates that accounted for gender, race, first-generation status, and LA-supported instruction. We used a quantitative critical race theory (QuantCrit) perspective focused on the role of hegemonic power structures in perpetuating inequitable student outcomes. Our QuantCrit perspective informed our research questions, methods, and interpretations of findings. The models associated LAs with overall decreases in DFW rates and larger decreases in DFW rates for Black, Indigenous, and people of color than their White peers. While the inequities in DFW rates were lower in LA-supported courses, they were still present.

Systematic research on physics teacher education (PTE) programs in the United States is rare, owing both to the great variety of practices and structures enacted by U.S. PTE programs and to the lack of measurement tools available to measure what successful PTE programs do. To help meet the need for a specific, objective, and reliable guide for research on PTE programs, the Physics Teacher Education Coalition developed the Physics Teacher Education Program Analysis (PTEPA) rubric, which characterizes the practices and structures observed at “thriving” PTE programs (defined as programs in the U.S. that frequently graduate five or more physics teachers per year). Initial research based on the PTEPA rubric suggests that thriving programs are strong in multiple areas (especially institutional commitment, leadership, and collaboration among partners in education and physics), and that several areas of strength align with those indicated by the existing PTE literature. However, thriving programs are not necessarily strong in all areas, instead reflecting local conditions at the institutional and state level. Such findings illustrate the opportunity for measurement and hypothesis testing about the most important features that PTE programs should have.

Given the insufficient number of well-qualified future physics teachers in the U.S., physics programs often seek guidance for how to address this national need. Measurement tools can provide such guidance, by both defining excellence in physics teacher education (PTE) and providing a means to measure progress towards excellence. This paper describes the development of such a measurement tool—the Physics Teacher Education Program Analysis rubric. The rubric was developed by identifying common features and practices at 8 “thriving” PTE programs, defined as large U.S. programs consistently graduating 5 or more future physics teachers in a year. The rubric consists of 89 items, each with 3 levels of achievement (developing, benchmark, exemplary), plus a not present level, which are organized into 6 standards. The rubric has demonstrated a variety of forms of validity, including a strong theoretical basis, empirical validation through program visits, and expert review. The rubric and its associated supporting materials are intended to help program leaders in using a process of continuous improvement and assessment to strengthen existing PTE programs or to establish new pathways for student licensure. The rubric also provides substantive opportunities for research, through further validation and development of the rubric, and by using rubric results to learn more about effective practices in physics teacher education.

In recent years, there has been an increased interest in conceptual blending in physics and mathematics education research as a theoretical framework to study student reasoning. In this paper, we adapt the conceptual blending framework to construct a blending diagram that not only captures the product but also the process of student reasoning when they interpret a mathematical description of a physical system. We describe how to construct a dynamic blending diagram (DBD) and illustrate this using two cases from an interview study. In the interview, we asked pairs of undergraduate physics and mathematics students about the physical meaning of boundary conditions for the heat equation. The selected examples show different aspects of the DBD as an analysis method. We show that by using a DBD, we can judge the degree to which students integrate their understandings of mathematics and physics. The DBD also enables the reader to follow the line of reasoning of the students. Moreover, a DBD can be used to diagnose difficulties in student reasoning.