The topic of atomic spectra is part of university and secondary school curricula around the world. Relatively little research, however, has been done on the learning and teaching of this subject, despite the fact that it forms a foundation for advanced study in quantum mechanics, astronomy, and astrophysics. A systematic investigation into student understanding of the formation and structure of atomic spectra was conducted among more than 1000 science majors in physics courses at the University of Zagreb, Croatia and the University of Washington, USA. The research had two primary goals: (i) to probe the extent to which university students are able to relate the wavelength of spectral lines to the transition of electrons between energy levels in an atom, and (ii) to probe the extent to which students recognize the conditions under which discrete line spectra are (and are not) formed. This paper focuses on the latter aspect, in particular, student understanding of the experimental setup that is commonly used to illustrate the formation of discrete line spectra. Students were asked about how changes to a setup consisting of a light source, a mask with a slit, a prism (or diffraction grating), and a screen affect the spectra observed. The findings suggest that relatively few students recognize that the type of light source is critical for the formation of line spectra. Instead students often attribute the formation of line spectra to the slit, the prism (or diffraction grating), or even to the distance between the prism and screen.

The evaluation of hypotheses, and the ability to learn from critical reflection on experimental and theoretical tests of those hypotheses, is central to an authentic practice of physics. A large part of physics education therefore seeks to help students understand the significance of this kind of reflective practice and to develop the strategies required to accurately update their belief in the utility of various hypotheses and models. Prior work has introduced Bayesian updating activities as one potential means for cultivating such reflective practice within the context of introductory physics courses. These activities are not fixed pieces of curricular matter, but are better thought of as codified practices that are incorporated within lectures, labs, homework, and exams, and which are adaptable to a broad range of course formats. The Bayesian updating activities engage students in the use of hypothetico-deductive reasoning to test a hypothesis or model, followed by Bayesian updating at the conclusion of this test to update their subjective confidence in the hypothesis or model that was tested. Prior work has identified significant gains in pre- and post comparison of student scores on the Epistemological Beliefs Assessment for Physical Science (EBAPS) in introductory algebra-based courses. Here, we conduct a quasi-experimental study of the impact of Bayesian updating activities on student EBAPS scores in introductory calculus-based courses. Our analysis examines the impact to the overall EBAPS score, the subscores for each of the five original axes identified by the authors of the EBAPS, and the subscores for five alternative axes that were recently identified in other work via factor analysis of student responses [Johnson and Willoughby, Phys. Rev. Phys. Educ. Res. 14, 010135 (2018)]. The results of our analysis show meaningful and credible gains on the overall EBAPS scores as well as for a multitude of the subscores. These gains are noteworthy due to their strength and their ability to be achieved with activities that were implemented as relatively minor alterations to a traditional course structure.

Computation is becoming an increasingly important part of physics education. However, there are currently few theories of learning that can be used to help explain and predict the unique challenges and affordances associated with computation in physics. In this study, we adapt the existing theory of computational literacy, which posits that computational learning can be divided into material, cognitive, and social aspects, to the context of undergraduate physics. Based on an exploratory study of undergraduate physics computational literacy, using a newly developed teaching tool known as a computational essay, we have identified a variety of student practices, knowledge, and beliefs across these three aspects of computational literacy. We illustrate these categories with data collected from students who engaged in an initial implementation of computational essays in a 3rd-semester electricity and magnetism class. We conclude by arguing that this framework can be used to theoretically diagnose student difficulties with computation, distinguish educational approaches that focus on material vs cognitive aspects of computational literacy, and highlight the benefits and limitations of open-ended projects like computational essays to student learning.

Traditionally, multiple choice assessments are graded in a dichotomous manner, where selecting the correct option for a question awards 1 point and the selection of an incorrect option awards 0 points. As a result of this grading scheme, all incorrect response options are treated as being equally incorrect regardless of potential differences in their relative correctness, intentional or otherwise. We propose a partial credit grading model for the Force Concept Inventory (FCI) that allots points to the incorrect responses. This was done using slope parameters from the two-parameter logistics nominal response model (2PLNRM), a model from polytomous item response theory (PIRT). The resulting scores from the partial credit model represent student growth towards a proper Newtonian mindset, as measured by the FCI. Observations indicate that this model accounts for student progression through prominent misconceptions (i.e., impetus) as their world views become more Newtonian. As expected, we find that student total scores increase as a result of the model, but the average overall gains on the assessment are essentially unchanged. The data used in this analysis were maintained and organized by PhysPort and included about 20 000 responses from first semester introductory physics courses at multiple universities. Ultimately, this partial credit model allows instructors to more accurately gauge the growth of their students over the course of instruction. Additionally, as a result of these partial credit scores, we are able to identify potentially malfunctioning questions on the FCI that may be sources of error in measuring student abilities.

Theories developed by Tinto and Nora identify academic performance, learning gains, and involvement in learning communities as significant facets of student engagement that, in turn, support student persistence. Collaborative learning environments, such as those employed in the Modeling Instruction introductory physics course, provide structure for student engagement by encouraging peer-to-peer interactions. Because of the inherently social nature of collaborative learning, we examine student interactions in the classroom using network analysis. We use centrality—a family of measures that quantify how connected or “central” a particular student is within the classroom network—to study student engagement longitudinally. Bootstrapped linear regression modeling shows that students’ centrality predicts future academic performance over and above prior GPA for three out of four centrality measures tested. In particular, we find that closeness centrality explains 28 % more of the variance than prior GPA alone. These results confirm that student engagement in the classroom is critical to supporting academic performance. Furthermore, we find that this relationship for social interactions does not emerge until the second half of the semester, suggesting that classroom community develops over time in a meaningful way.

In physics education research (PER), concept inventories (CIs) have become standard instruments for assessing students’ learning throughout instruction. To promote widespread use of concept inventories, previous studies have developed an approach to split a full length CI into short versions of CIs. This research extends the existing method to fully utilize the item response theory framework in equating and linking between the short CIs and the full length CIs. Three quantitative studies have been conducted: First, the extended algorithm is applied to divide the Brief Electricity and Magnetism Assessment (BEMA) into two half-length BEMAs (HBEMAs). Through a series of test-equating and validation analysis, the HBEMAs are confirmed to measure the same latent constructs of student understanding of electricity and magnetism to that of the original BEMA at a similar level of reliability. The second study establishes equivalent score conversions among the three versions of BEMA using the Stocking-Lord method, which has the best performance on equating error reduction among several methods explored. It is also confirmed that the equivalent statistical characteristics of the three versions of BEMA are equity and population invariant. In the third study, the extended algorithm is applied to link and compare the BEMA and the Conceptual Survey of Electricity and Magnetism (CSEM). After linking the BEMA and CSEM assessment scales, it becomes possible to directly convert and compare students’ performances on the two CIs. It is found that the scales of BEMA and CSEM are almost identical after scale transformation. Based on these studies, it can be suggested that all short and long versions of BEMA and CSEM can be used interchangeably after scale transformation.

Gender differences in students’ physics identity in introductory physics courses can influence students’ interest in science, technology, engineering, and mathematics and their career decisions. Exploring the components that influence these identities is critical to developing a better understanding of the underrepresentation of women in physics courses and physics-related majors. We used a revised version of the physics identity framework developed by Hazari et al. [J. Res. Sci. Teach. 47, 978 (2010)] to investigate whether the relation between gender and physics identity was mediated by motivational factors, such as competency belief, interest, and perceived recognition by others. We surveyed approximately 500 students in introductory level calculus-based physics courses in which 30% of the students are women. Analysis revealed that the relation between gender and physics identity was mediated by students’ self-reported motivation at the end of the semester. The model showed that perceived recognition by others played a major role in students’ endorsement of physics identity with female students less likely to endorse statements that others perceived them as a “physics person.”

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.