Many physics faculty are aware of and interested in using research-based instructional strategies. However, knowledge and motivation are not sufficient to support successful and sustained adoption. To address this problem, we present a faculty online learning community (FOLC) model for educational change and describe its application (the New Faculty Workshop FOLC, NFW-FOLC) to provide a year of support to new faculty following attendance at the Physics and Astronomy New Faculty Workshop. FOLCs are an extension of the faculty learning community model. Here we present the theoretical underpinnings of the general FOLC model, the design principles of our particular NFW-FOLCs, and the learning objectives for NFW-FOLC participants. We demonstrate the efficacy of our NFW-FOLCs by analyzing postexperience interviews with participants from the first four NFW-FOLC cohorts. The primary motivation given by faculty for joining our FOLCs is to improve their teaching as they learn more about teaching strategies, get implementation help, and connect to a broader community. These motivations align with our NFW-FOLC design principles. Participants overwhelmingly report the experience was valuable and impacted them positively with the most commonly reported impacts of NFW-FOLC membership being changes in their implementation of teaching strategies, increased reflection about teaching, increased confidence as teachers, increased knowledge about teaching, benefits to their students, time saved, and gaining a resource. The reported impacts provide evidence that the NFW-FOLC is successfully meeting its goals. We argue that the reported impacts are uniquely supported by the FOLC model of professional development. We advance FOLCs as a generalizable model of professional development offering a number of advantages over traditional reform efforts as well as traditional Faculty Learning Communities.

Students’ difficulties in quantum mechanics may be the result of unproductive framing rather than a fundamental inability to solve the problems or misconceptions about physics content. Using the theoretical lens of epistemological framing, we applied previously developed frames to seek an underlying structure to the long lists of published difficulties that span many topics in quantum mechanics. Mapping descriptions of published difficulties into errors in epistemological framing and resource use, we analyzed descriptions of students’ problem solving to find their frames, and compared students’ framing to the framing (and frame shifting) required by problem statements. We found three categories of error: mismatches between students’ framing and problem statement framing inappropriate or absent shifting between frames and insufficient resource activation within an appropriate frame.

Historically, the implementation of research-based assessments (RBAs) has been a driver of educational change within physics and helped motivate adoption of interactive engagement pedagogies. Until recently, RBAs were given to students exclusively on paper and in class; however, this approach has important drawbacks including decentralized data collection and the need to sacrifice class time. Recently, some RBAs have been moved to online platforms to address these limitations. Yet, online RBAs present new concerns such as student participation rates, test security, and students’ use of outside resources. Here, we report on a study addressing these concerns in both upper-division and lower-division undergraduate physics courses. We gave RBAs to courses at five institutions; the RBAs were hosted online and featured embedded JavaScript code which collected information on students’ behaviors (e.g., copying text, printing). With these data, we examine the prevalence of these behaviors, and their correlation with students’ scores, to determine if online and paper-based RBAs are comparable. We find that browser loss of focus is the most common online behavior while copying and printing events were rarer. We found that correlations between these behaviors and student performance varied significantly between introductory and upper-division student populations, particularly with respect to the impact of students copying text in order to utilize internet resources. However, while the majority of students engaged in one or more of the targeted online behaviors, we found that, for our sample, none of these behaviors resulted in a significant change in the population’s average performance that would threaten our ability to interpret this performance or compare it to paper-based implementations of the RBA.

Undergraduate quantum mechanics (QM) uses a variety of notations, each with their own advantages and constraints, for representing quantum states and carrying out individual calculations. An example of this can be seen when calculating expectation values, which can be solved using several different methods. Analysis of written exam data given at three universities (teaching spins-first QM) showed students were more likely to use matrix or integral calculation in situations where it is much simpler to use a summation method. By adapting the structural features framework by Gire and Price, we are able to answer questions regarding how and why students use different methods. We analyze student responses to expectation value problems administered in interviews conducted at two universities in the middle and end of the semester to highlight specific areas of difficulty and features of the methods which led to students’ choices of one method over another.

Course syllabi are a required component of college and university courses. Syllabi present both broader course structuring practices, are a valuable “first impression” of what instructors want to offer their students, and are used as tools in course design. While best teaching practices suggest specific recommendations for syllabi development, there is little research evidence regarding their structure and use, especially in the context of introductory physics for life sciences (IPLS) courses. IPLS courses typically host students pursuing careers in the biological or health-related sciences, which are rapidly growing majors compared to other STEM degrees. Since few of these students have significant previous experience with physics, the course syllabus provides a first framing and establishment of expectations for them. In this paper, we analyzed how IPLS instructors write syllabi, how they use them in the course design process, and what experienced instructors recommend to be included in the syllabi. Furthermore, based on these analyses we compiled a set of 31 key components (organized in seven categories) for IPLS course syllabi supported by both widespread use and recommendations from experienced practitioners. We present these components and discuss implications for IPLS syllabus design. Specifically, we bring attention to the value of explicitly incorporating interdisciplinary language in syllabi narratives and learning objectives. This work provides guidance for IPLS course and syllabus design, and can also be relevant for modern interdisciplinary courses with features similar to IPLS courses.

Students in one discipline often receive their scientific training from faculty in other disciplines. As a result of tacit disciplinary differences, especially as implemented in courses at the introductory college level, such students can have difficulty in understanding the nature of the knowledge they are learning in a discipline that they do not identify as their own. We developed a course in introductory physics for life science (IPLS) students that attempts to help them cross disciplinary boundaries. By analyzing student reasoning during recitation sections and interviews, we identified three broad ways in which students in our course meaningfully crossed boundaries: (i) by unpacking biochemical heuristics in terms of underlying physical interactions, (ii) by locating both biochemical and physical concepts within a mathematical bridging expression, and (iii) by coordinating functional and mechanistic explanations for the same biological phenomenon. Drawing on episodes from case-study interviews and in-class problem-solving sessions, we illustrate how each of these types of boundary crossing involves the coordination of students’ conceptual and epistemological resources from physics, chemistry, and biology in distinct but complementary ways. Together, these boundary crossing categories form a theoretical framework for classifying student coherence seeking. We explore how the IPLS course helps our life science students fill in the gaps that exist between traditional introductory courses, by finding and exploring questions that might otherwise fall through disciplinary cracks. By identifying these types of explanatory coherence, we hope to suggest ways of inviting life science students to participate in physics and see physics as a tool for making sense of the living world.

Many studies have examined the structure and properties of the Force Concept Inventory (FCI); however, far less research has investigated the Force and Motion Conceptual Evaluation (FMCE). This study applied Multidimensional Item Response Theory (MIRT) to a sample of $N=4528$ FMCE post-test responses. Exploratory factor analysis showed that 5, 9, and 10-factor models optimized some fit statistics. The FMCE uses extensive blocking of items into groups with a common stem; these blocks factored together in most models. A confirmatory analysis, which constrained the MIRT models to a theoretical model constructed from expert solutions, produced a model requiring only 8 principles, fundamental reasoning steps. This was substantially fewer than the 19 principles identified in the FCI by a previous study. Correlation analysis also demonstrated that the two instruments were very dissimilar. The reduced number of principles and the repetition of items using a single principle allowed the extraction of eight single-principle subscales, seven with Cronbach’s alpha greater than the 0.7 required for acceptable internal consistency. The differences between the FCI and the FMCE suggest that the two instruments could provide complementary, but different, information about student understanding of Newton’s laws with the FCI measuring an integrated Newtonian force concept and the FMCE measuring details of that force concept.

In this work we study how different motivations of learners relate to their engagement in a massive open online course (MOOC). The research was conducted in a cohort-based astronomy MOOC “Astronomy: Exploring Time and Space” provided through the Coursera platform. In order to discern motivations of course participants, the Science Motivation Questionnaire II was administered as a first assignment of the course. The survey data were collected from December 2016 until December 2018 and responses from 3701 learners were acquired. In order to determine the relationship of motivation to course performance, four course engagement indicators are defined: course completion, use of video lectures, participation in the discussion forums, and participation in peer-grading assignments. Self-determination and self-efficacy are identified as the main motivational factors influencing all aspects of the course engagement except for the video usage. We show that both of these decrease with age, but increase with the number of previously taken science courses. The main reasons for signing up for the course which had an effect on course engagement were the goal of getting a certificate and perceived importance of the reputation of the instructor. There was no statistically significant difference in motivations between people who dropped after the first peer graded writing assignment and those who successfully completed the course, suggesting that after the first writing assignment learners quit from other reasons than lack of motivation. Unexpectedly, learners with high career, grade, and social motivation watched statistically significantly fewer instructional videos, and social motivation did not play a role in the forum usage.

In quantum mechanics, probability amplitudes are complex numbers and the relative phases between the terms in superposition states have measurable effects. This article describes an investigation into sophomore- and junior-level students’ reasoning patterns in relating relative phases and real-world quantum phenomena. The investigation involved one observational experiment and three testing experiments, during which we formulated and tested three hypotheses that allow us to gain insights into why students have difficulty recognizing the measurable effects of relative phases. We found that, in both $\mathrm{spin}\text{−}1/2$ and infinite square well contexts, many students do not recognize that quantum states differing only by a relative phase are experimentally distinguishable. Moreover, student ability to recognize the measurable effects of relative phase does not improve when given (i) a task that specifically prompts students to compare the probabilities for a particular observable and (ii) a task that does not require taking inner products or changing basis. We also examined the extent to which lacking proficiency with complex numbers may have hindered student understanding of relative phase. The data indicate that most students are proficient with complex numbers. These findings suggest that many students do not, in fact, recognize the purpose of using complex numbers in superposition states. We discuss possible explanations for why students do not seem to recognize this purpose, and we also provide suggestions for future avenues of research.

Research has highlighted difficulties experienced by students when studying quantum physics in introductory courses. In this paper, we present a teaching and learning sequence (TLS) aiming at introducing a quantum model of emission and absorption of radiation and we assess its impact on the students’ learning about atomic spectra. The TLS has been designed based on the contributions from physics education research and it was implemented among high school seniors. A detailed description of the TLS is also presented accompanied by a description of how it is implemented. Based on a pre- and post-assessment questionnaire and student interviews, we conclude that students are able to successfully use the models to reason about relevant phenomena.

The number of physics bachelor’s degrees that are awarded in the United States annually is small compared to most other science, technology, engineering, and mathematics fields, and only about one-fifth of these degrees are awarded to women. Understanding the influence of students’ science and engineering experiences on career choices is critical in order to improve future efforts to increase the number of physics majors and the participation of women. In this work, we use a physics identity framework to examine the impact of out-of-class science and engineering activities on three identity dimensions and the relationship between these dimensions and physics career choice. Through structural equation modeling of survey data from 5541 college students, we find that out-of-class science and engineering activities have the largest influence on physics performance/competence beliefs, but the association of performance/competence beliefs to overall physics identity and physics career choice is primarily mediated through recognition beliefs and physics interests. Furthermore, out-of-class science and engineering activities have a larger effect on recognition beliefs for men than for women, which is a challenging finding in light of the fact that recognition beliefs are the most influential identity dimension for women. The results of this work begin to highlight the need for out-of-class science and engineering activities that focus on not only enhancing students’ performance/competence beliefs but also students’ interests, particularly those students not previously interested, and women’s recognition beliefs with respect to physics.

We investigate upper-division student difficulties with direct integration in multiple contexts involving the calculation of a potential from a continuous distribution (e.g., mass, charge, or current). Integration is a tool that has been historically studied at several different points in the curriculum including introductory and upper-division levels. We build off of these prior studies and contribute additional data around student difficulties with multivariable integration at two new points in the curriculum: middle-division classical mechanics and upper-division magnetostatics. To facilitate comparisons across prior studies as well as the current work, we utilize an analytical framework that focuses on how students activate, construct, execute, and reflect on mathematical tools during physics problem solving (i.e., the ACER framework). Using a mixed-methods approach involving coded exam solutions and student problem-solving interviews, we identify and compare students’ difficulties in these two different contexts and relate them to what has been found previously in other levels and contexts. We find that some of the observed student difficulties were persistent across all three contexts (e.g., identifying integration as the appropriate tool, and expressing the difference vector), while other difficulties seemed to fade as students advanced through the curriculum (e.g., expressing differential line, area, and volume elements). We also identified new difficulties that appear in different contexts (e.g., interpreting and expressing the current density). These findings represent one of the first cross-context looks at students’ difficulties with integration across multiple courses in the physic curriculum. These results can help instructors and researchers focus instruction and materials development on the aspects of integration that are most challenging in a particular context or persistent across multiple contexts.

The Force Concept Inventory (FCI) is widely used to investigate the effect of education level on conceptual understanding of Newtonian mechanics but has only recently been scrutinized for gender effects and retention. This study examines both the gender gap in first year physics undergraduates compared to the gap for nonphysicists and the FCI retention after three months. All participants were either studying or working at the University of Sheffield in the UK and had completed a similar compulsory level of secondary education. As expected the results show that a greater level of education in physics is associated with a larger average FCI score. However, further analysis shows that there exists a gender gap at all levels of education. The size of the effect of gender is quantified using Cohen’s $d$ and ranges from 0.84 to 1.17 which indicates a large effect due to gender for all levels of education. Despite the FCI having been used as a tool to measure learning gains immediately following instruction in Newtonian mechanics there has been little work to investigate whether this increase in FCI score remains after some time has elapsed. Here the increase in FCI scores is found to remain increased after a three month absence of mechanics-related teaching, and that this retention of FCI scores is independent of gender. Despite this, the gender gap still remains large and statistically significant after the three month delay.

Light interference is an essential topic for understanding the wavelike nature of light, however, there are limited studies on modeling and assessing students’ misconceptions and learning difficulties in this area. Based on the knowledge integration modeling approach, a conceptual framework for light interference is developed and used to model student understanding and guide the development of an assessment tool on light interference. The conceptual framework provides a representation of students’ reasoning pathways to clearly show their connections through different conceptual components and contextual features of problem-solving settings. This type of representation focuses on showing students’ knowledge structures regarding the features of integration and fragmentation. Experts’ reasoning pathways always flow through a central idea of a concept with well-established connections to a wide range of contextual features and conditions. These connections form an integrated knowledge structure, which demonstrates deep understanding. In contrast, novices often focus on surface details without linking the central idea, forming fragmented local connections that link directly between contextual features and task outcomes. As a result, novice students’ problem solving often relies on memorization of formula and solutions without any deep understanding. Through testing and interviews at a large Chinese university, a light interference test (LIT) has been developed and validated. Assessment results also demonstrate that students with a strong conceptual understanding of the central idea are able to apply expertlike reasoning to familiar and novel questions regardless of the contextual details. Meanwhile, students with weaker or nonexistent understanding of the central idea often struggle when novel situations are presented. LIT provides a useful tool to measure students’ conceptual understanding on light interference and probe thought pathways of students’ reasoning that can further indicate students’ knowledge structure and levels of deep understanding.

While numerous studies have analyzed the conceptions probed by the Force Concept Inventory (FCI), assessments dedicated to electricity and magnetism lack similar analyses. This paper investigated the conceptions explored by the Brief Electricity and Magnetism Assessment (BEMA) and the Conceptual Survey of Electricity and Magnetism (CSEM) using exploratory factor analysis techniques. Exploratory factor analysis (EFA) was performed on both assessments using 5368 and 4941 postinstruction student responses for the BEMA and CSEM, respectively. A 6-factor EFA generated model was found for the CSEM, and was fit against another sample of 4964 student responses using confirmatory factor analysis to supply evidence for the possible generalizability of the model. The 5-factor EFA generated model for the BEMA could not be fit against another sample when trying to check for generalizability. The EFA generated factor models for the BEMA and CSEM were then compared and found to be similar in conceptual content, with the exception of one or two factors. Thus, from a factor analysis perspective, the BEMA and CSEM were found to be similar in conceptual content as revealed by student responses. With a better understanding of these electricity and magnetism assessments, future research into this domain of physics will then be able to make stronger conclusions based on students’ results within these assessments.

Understanding perceptions of graduate admissions from multiple stakeholders can cultivate an improved understanding about the process of graduate induction, the role that admissions plays in restricting diversity in physics, and contribute to more informed practices for all involved. Prior studies in graduate admissions have reported on how certain admission criteria weigh in the consideration of applicants primarily from faculty perspectives. Motivated by the concept of multivocal knowledge, in this article, we report on prospective students’ perspectives of the importance of the same admission criteria—a stakeholder group that is critical but underempowered in the admissions process. We identify a substantial agreement between students and faculty regarding the importance of recommendation letters, undergraduate math or physics GPA, and standardized exam scores (GRE). On the other hand, students rated several criteria, including personal statements, prior research experiences, publications, and familiarity with department as significantly more important than did faculty. A perceived “overimportance” of criteria may be detrimental to students’ admissions-related decision making and reduce their chances of success, so these results emphasize the importance of taking students’ perspectives into account in the admissions process.

We investigated the influence of context on students’ understanding of cross products of vectors using three isomorphic multiple-choice tests asking for the direction of a cross product in different geometrical settings. One version of the test involved the Lorentz force, the second version involved the torque on an electric dipole, and the third version was without physics context. We administered the tests to 216 first-year pre-med students at a Belgian (Flemish) university. We found that students perform significantly better in the context of the Lorentz force. Students more often chose the incorrect alternative corresponding to the vector sum in the test versions involving an electric dipole or without physics context when the vectors are not orthogonal. For orthogonal vectors, a sign error—i.e., inverting the direction of the resulting vector—was the most common mistake in both tests with physics context, while without physics context selecting the alternative corresponding to the sum remained the most common mistake. Prior familiarity with a right-hand rule in a specific context seems to be able to explain improved scores in the test version concerning the Lorentz force. Instructors and curriculum developers can benefit from adopting an integrated approach in which the mathematical aspects of the cross product are treated together with multiple examples in physics, allowing students to transition from using specific rules to determine a cross product, to a more integrated understanding of it.

In order to support physics students in their future careers, there is a need to understand the relationship between undergraduate education and professional practice in physics-related fields. This study investigated high-level goal driven mathematical problem-solving activities that are found within two disciplinary cultures: physical science research labs in academia and photonics workplaces in industry. We conducted semistructured interviews with 10 Ph.D. students and 22 engineers and technicians. Math use in professional workplaces was characterized through an adaptation of epistemic games framework, which revealed six common epistemic games in these workplaces: conceptual math modeling, analytical-numerical math modeling, design-oriented math modeling, fabrication, improving processes, and making meaning out of data games. The workplace-specific epistemic games capture the goals, starting and ending conditions, constraints and contextual features, moves, tools, and representations. The games involve a broad spectrum of math that ranges from arithmetic to computational modeling. The games reveal how goals and particular contextual features impact approaches to mathematical problem solving. The findings extend prior work on mathematical problem solving in physics to a new population of professional researchers, engineers, and technicians in their workplaces. The research may guide new approaches for developing problems and explicitly teaching problem solving in diverse physics contexts, which may additionally benefit undergraduate students’ preparation for their future careers.

This paper aims to provide a contribution to the research in physics education regarding the interplay between mathematics and physics in teaching and learning physics at the university level. The argument is developed through a study focused on the historical case study of the blackbody that led Planck to make one of the most significant scientific breakthroughs in physics: the introduction of discreteness and quantization into physical processes. The study is methodologically guided by the model that Udhen, Karam, Pietrocola, and Pospiech elaborated to highlight the interplay between physics and mathematics within teaching and learning practices [O. Uhden, R. Karam, M. Pietrocola, and G. Pospiech, Modelling mathematical reasoning in physics education, Sci. Educ. Netherlands 21, 485 (2012).]. The model emphasizes the distinction between the technical and structural roles of mathematics in physics, with the latter role being argued to correspond to processes of mathematization and interpretation. We used this model to analyze Planck’s original papers and to reconstruct the reasoning that, thanks to the structural role played by mathematics, paved the way for the quantistic scientific breakthrough. The results of the analysis led us to design a teaching tutorial that we implemented with mathematics and physics university students. Students’ reactions are reported to discuss the educational potential of the approach beyond the specific case and to argue for its potential general application to other similar physics topics.

Over the course of instruction, not only does most introductory physics students’ content knowledge evolve but their attitudes and approaches to problem solving are also likely to evolve. This change may depend on many factors including the curricula and pedagogies used, the degree to which instruction actively engages students in the learning process, as well as the gender of the students. While changes in epistemology and beliefs about physics have been examined in the literature, how students’ attitudes and approaches to problem solving change from the beginning to the end of instruction in introductory physics and how method of instruction or gender of the student impact them remain largely unexplored. To examine the potential changes in attitudes and approaches to problem solving over a semester, we administered a previously validated attitudes and approaches to problem solving (AAPS) survey both at the beginning (pre) and at the end of instruction (post) in eight large enrollment calculus-based introductory physics classes at a large research university in the United States. At both points in time (beginning and end of a semester of instruction), each class was also given surveys measuring students’ conceptual understanding: the Force Concept Inventory (FCI) or the Conceptual Survey of Electricity and Magnetism (CSEM), depending upon whether it was the first or second semester course. In addition, final exam scores, gender of students, and descriptions of the instructional methods used for each class were collected. The AAPS survey was used to measure students’ attitudes and approaches to problem solving, and the conceptual surveys and exam scores were used to measure the degree to which each course helped students learn physics concepts. We examined students’ performance on the AAPS survey, FCI or CSEM, and final exams, and compared the results for different instructional methods, and gender of students. Moreover, we examined whether or not there were correlations between the expertlike response on the AAPS survey and the performance on FCI or CSEM or final exams. We found that all classes exhibited a decline in score on the AAPS survey suggesting worse attitudes related to problem solving after instruction. Furthermore, controlling for the initial scores, classes which involved significant use of evidence-based active engagement methods exhibited statistically significantly better scores on the AAPS survey at the end of the course compared to classes which were taught primarily using a traditional lecture-based approach. Equally importantly, unlike broader epistemological surveys, female students were found to exhibit less of a decline in AAPS scores than did their male counterparts in all classes and the AAPS scores were always higher for female students at the end of the course. Future research should contemplate how this novel finding may be effectively exploited to develop and implement curricula and pedagogies to reduce the gender gap in performance often observed in introductory physics.