The practice of learning physics contributes to the development of many transdisciplinary skills learners are able to exercise independent of the physics discipline. However, the standard practices of physics instruction do not explicitly include the monitoring or evaluation of these skills. In a competency-based (CB) learning model, the skills (competencies) are clearly defined and evaluated. We envisioned that a CB approach, where the underlying competencies are highlighted within the instructional process, would be more suitable to teaching physics to learners with diversified disciplinary interests. A model CB course curriculum was developed and practiced at Purdue University to teach introductory college physics to learners who were majoring in the technology disciplines. The experiment took place from the spring semester in 2015 until the spring semester in 2017. The practice provided a means to monitor and evaluate a set of developmental transdisciplinary competencies that underlie the learning of force and motion concepts in classical physics. Additionally, the CB practice contributed to produce substantial physics learning outcomes among learners who were underprepared to learn physics in college.

Representation use is a critical skill for learning, problem solving, and communicating in science, especially in physics where multiple representations often scaffold the understanding of a phenomenon. University Modeling Instruction, which is an active-learning, research-based introductory physics curriculum centered on students’ use of scientific models, has made representation use a primary learning goal with explicit class time devoted to introducing and coordinating representations as part of the model building process. However, because of the semester break, the second semester course, Modeling Instruction-Electricity and Magnetism (MI-EM), contains a mixture of students who are returning from the Modeling Instruction-mechanics course (to whom we refer to as “returning students”) and students who are new to Modeling Instruction with the MI-EM course (to whom we refer to as “new students”). In this study, we analyze the impact of MI-EM on students’ representation choices across the introductory physics content for these different groups of students by examining both what individual representations students choose and their average number of representations on a modified card-sort survey with a variety of mechanics and EM questions. Using Wilcoxon-signed-rank tests, Wilcoxon-Mann-Whitney tests, Cliff’s delta effect sizes, and box plots, we compare students’ representation choices from pre- to postsemester, from new and returning students, and from mechanics and EM content. We find that there is a significant difference between returning and new students’ representation choices, which serves as a baseline comparison between Modeling Instruction and traditional lecture-based physics classes. We also find that returning students maintain a high representation use across the MI-EM semester, while new students see significant growth in their representation use regardless of content.

As astronomers further develop an understanding of the fate of the Universe, it is essential to study students’ ideas on the fate of the Universe so that instructors can communicate the field’s current status more effectively. In this study, we examine undergraduate students’ preinstruction ideas of the fate of the Universe in ten semester-long introductory astronomy course sections (ASTRO 101) at three institutions. We also examine students’ postinstruction ideas about the fate of the Universe in ASTRO 101 over five semester-long course sections at one institution. The data include precourse surveys given during the first week of instruction ($N=264$), postinstruction exam questions ($N=59$), and interviews. We find that, preinstruction, more than a quarter of ASTRO 101 students either do not respond or respond with “I don’t know” when asked what the long-term fate of the Universe is. We also find that, though the term was not necessarily used, students tend to describe a “big chill” scenario in the preinstruction surveys, among a wide variety of other scenarios. A fraction of students describe the fate of smaller-scale systems, possibly due to confusion of the hierarchical nature of structure in the Universe. Preinstruction, students mention the Universe’s expansion when describing how astronomers know the fate of the Universe but do not discuss how we know the Universe is expanding or the relationship between expansion and the fate of the Universe. Postinstruction, students’ responses shift toward greater degrees of completeness and correctness.

We demonstrate how students’ use of modeling can be examined and assessed using student notebooks collected from an upper-division electronics lab course. The use of models is a ubiquitous practice in undergraduate physics education, but the process of constructing, testing, and refining these models is much less common. We focus our attention on a lab course that has been transformed to engage students in this modeling process during lab activities. The design of the lab activities was guided by a framework that captures the different components of model-based reasoning, called the Modeling Framework for Experimental Physics. We demonstrate how this framework can be used to assess students’ written work and to identify how students’ model-based reasoning differed from activity to activity. Broadly speaking, we were able to identify the different steps of students’ model-based reasoning and assess the completeness of their reasoning. Varying degrees of scaffolding present across the activities had an impact on how thoroughly students would engage in the full modeling process, with more scaffolded activities resulting in more thorough engagement with the process. Finally, we identified that the step in the process with which students had the most difficulty was the comparison between their interpreted data and their model prediction. Students did not use sufficiently sophisticated criteria in evaluating such comparisons, which had the effect of halting the modeling process. This may indicate that in order to engage students further in using model-based reasoning during lab activities, the instructor needs to provide further scaffolding for how students make these types of experimental comparisons. This is an important design consideration for other such courses attempting to incorporate modeling as a learning goal.

We examine changes in students’ rating behavior during a semester-long sequence of peer evaluation laboratory exercises in an introductory mechanics course. We perform a quantitative analysis of the ratings given by students to peers’ physics lab reports, and conduct interviews with students. We find that peers persistently assign higher ratings to lab reports than do experts, that peers begin the semester by giving high ratings most frequently and end the semester with frequent middle ratings, and that peers go through the semester without much change in the frequency of low ratings. We then use student interviews to develop a model for student engagement with peer assessment. This model is based on two competing influences which appear to shape peer evaluation behavior: a strong disinclination to give poor ratings with a complementary preference to give high ratings when in doubt, and an attempt to develop an expertlike criticality when assessing peers’ work.

Developing a better understanding of the measurement process and measurement uncertainty is one of the main goals of university physics laboratory courses. This study investigated the influence of graphical representation of data on student understanding and interpreting of measurement results. A sample of 101 undergraduate students (48 first year students and 53 third and fifth year students) from the Department of Physics, University of Zagreb were tested with a paper-and-pencil test consisting of eight multiple-choice test items about measurement uncertainties. One version of the test items included graphical representations of the measurement data. About half of the students solved that version of the test while the remaining students solved the same test without graphical representations. The results have shown that the students who had the graphical representation of data scored higher than their colleagues without graphical representation. In the second part of the study, measurements of eye movements were carried out on a sample of thirty undergraduate students from the Department of Physics, University of Zagreb while students were solving the same test on a computer screen. The results revealed that students who had the graphical representation of data spent considerably less time viewing the numerical data than the other group of students. These results indicate that graphical representation may be beneficial for data processing and data comparison. Graphical representation helps with visualization of data and therefore reduces the cognitive load on students while performing measurement data analysis, so students should be encouraged to use it.

We measured the personality type of the students in a large introductory physics course of mostly life science students using the True Colors instrument. We found large correlations of personality type with performance on the precourse Force Concept Inventory (FCI), both term tests, the postcourse FCI, and the final examination. We also saw correlations with the normalized gain on the FCI. The personality profile of the students in this course is very different from the profile of the physics faculty and graduate students, and also very different from the profile of students taking the introductory physics course intended for physics majors and specialists.

Although physics education researchers often use workshops to promote instructional change in higher education, little research has been done to investigate workshop design. Initial evidence suggests that many workshop sessions focus primarily on raising faculty’s awareness of research-based instructional strategies, a fairly straightforward goal that has been largely met. However, increasing faculty’s awareness of existing strategies alone has somewhat limited benefits. We argue that workshop leaders should also aim to cultivate faculty’s ability and motivation to engage in pedagogical sensemaking, i.e., the pursuit of robust pedagogical logic based on observations and interpretations of classroom events. This goal is likely more challenging to achieve, and thus presents a greater need for research. In this paper, we pursue in situ, qualitative analysis of two parallel workshop sessions that seem to have the potential to support ambitious outcomes. We demonstrate how faculty may engage in aspects of pedagogical sensemaking, such as using observations of student behavior to support their arguments. We also show how faculty may instead seem to engage in interactions reminiscent of students “doing school,” such as evaluating instruction based on “correctness” alone. We also show how differences in workshop facilitation seemed to contribute to faculty engaging in pedagogical sensemaking in one session only. These differences include (i) strictly enforcing session rules versus gently navigating faculty’s incoming expectations, (ii) highlighting the workshop leaders’ expertise versus working to minimize power differentials, and (iii) emphasizing the benefits of adoption of a prescribed strategy versus encouraging faculty to reason about possible adaptations. We consider the implications of this analysis for future research and workshop design.

Efforts to improve the number and quality of the high school physics teaching workforce have taken several forms, including those sponsored by professional organizations. Using a series of large-scale teacher demographic data sets from the National Center for Education Statistics (NCES), this study sought to investigate trends in teacher quality at the national level in the two and a half decades between 1987 and 2012. Specifically, we investigated (i) details about the degree backgrounds, main teaching assignments, and experience levels of those assigned to teach physics; (ii) whether the proportion of those with certifications in physics as a fraction of the entire physics teaching workforce had changed; and (iii) if workforce diversity (with respect to race and gender) had changed over time. Our data indicate that trends in these domains have generally been positive, but still fall short of having a highly qualified physics teacher in each classroom. Additionally, the population of physics teachers has more novices and fewer veterans than it did 10 years ago, although veteran physics teachers are not as rare as those in other branches of high school STEM fields. We also analyzed trends in physics teacher race and gender diversity and found them to lag behind other STEM and non-STEM teacher communities. High school physics is still mostly taught by white males with backgrounds from outside of physics. Implications for future policy decisions at the local and national levels are discussed, including attending to the specific needs of degree-holding and non-degree-holding physics teachers separately and localizing teacher recruitment and preparation efforts in regional centers.

We present the Electricity and Magnetism Conceptual Assessment (EMCA), a new assessment aligned with second-semester introductory physics courses. Topics covered include electrostatics, electric fields, circuits, magnetism, and induction. We have two motives for writing a new assessment. First, we find other assessments such as the Brief Electricity and Magnetism Assessment and the Conceptual Survey on Electricity and Magnetism not well aligned with the topics and content depth of our courses. We want to test introductory physics content at a level appropriate for our students. Second, we want the assessment to yield scores and gains comparable to the widely used Force Concept Inventory (FCI). After five testing and revision cycles, the assessment was finalized in early 2015 and is available online. We present performance results for a cohort of 225 students at Siena College who were enrolled in our algebra- and calculus-based physics courses during the spring 2015 and 2016 semesters. We provide pretest, post-test, and gain analyses, as well as individual question and whole test statistics to quantify difficulty and reliability. In addition, we compare EMCA and FCI scores and gains, and we find that students’ FCI scores are strongly correlated with their performance on the EMCA. Finally, the assessment was piloted in an algebra-based physics course at George Washington University (GWU). We present performance results for a cohort of 130 GWU students and we find that their EMCA scores are comparable to the scores of students in our calculus-based physics course.

We examine students’ mathematical performance on quantitative “synthesis problems” with varying mathematical complexity. Synthesis problems are tasks comprising multiple concepts typically taught in different chapters. Mathematical performance refers to the formulation, combination, and simplification of equations. Generally speaking, formulation and combination of equations require conceptual reasoning; simplification of equations requires manipulation of equations as computational tools. Mathematical complexity is operationally defined by the number and the type of equations to be manipulated concurrently due to the number of unknowns in each equation. We use two types of synthesis problems, namely, sequential and simultaneous tasks. Sequential synthesis tasks require a chronological application of pertinent concepts, and simultaneous synthesis tasks require a concurrent application of the pertinent concepts. A total of 179 physics major students from a second year mechanics course participated in the study. Data were collected from written tasks and individual interviews. Results show that mathematical complexity negatively influences the students’ mathematical performance on both types of synthesis problems. However, for the sequential synthesis tasks, it interferes only with the students’ simplification of equations. For the simultaneous synthesis tasks, mathematical complexity additionally impedes the students’ formulation and combination of equations. Several reasons may explain this difference, including the students’ different approaches to the two types of synthesis problems, cognitive load, and the variation of mathematical complexity within each synthesis type.

Homework in introductory physics represents an important part of a student’s learning experience; therefore, choosing the manner in which homework is presented merits investigation. We performed three rounds of clinical trials comparing the effects of mastery-style homework vs traditional-style homework with students in both algebra-based and calculus-based introductory mechanics. Results indicate a benefit from mastery-style over traditional-style homework, principally for weaker students who are less familiar with the material being covered and on questions that are nearer transfer to the study materials.

Students’ categorization of physics problems reflects their expertise in problem solving. We conducted a pseudolongitudinal study to investigate the development of students’ categorization ability. Over 250 Chinese students from grade 10 to grade 12 were asked to categorize 20 problems of kinematics and mechanics into suitable categories based on the similarity of solutions. We compared the categories made by the students in different grades and found that, although students in all three grades performed as novices, their expertise in categorization gradually developed. The results also suggested that the training in problem solving may affect students’ categorization, especially for those in grade 12.

We address previous hypotheses about possible factors influencing the gender gap in attainment in physics. Specifically, previous studies claim that scaffolding may preferentially benefit female students, and we present some alternative conclusions surrounding this hypothesis. By taking both student attainment level and the degree of question scaffolding into account, we identify questions that exhibit real bias in favor of male students. We find that both multidimensional context and use of diagrams are common elements of such questions.

Developing students’ ability to troubleshoot is an important learning outcome for many undergraduate physics lab courses, especially electronics courses. In other work, metacognition has been identified as an important feature of troubleshooting. However, that work has focused primarily on individual students’ metacognitive processes or troubleshooting abilities. In contrast, electronics courses often require students to work in pairs, and hence students’ in-class experiences likely have significant social dimensions that are not well understood. In this work, we use an existing framework for socially mediated metacognition to analyze audiovisual data from think-aloud activities in which eight pairs of students from two institutions attempted to diagnose and repair a malfunctioning electric circuit. In doing so, we provide insight into some of the social metacognitive dynamics that arise during collaborative troubleshooting. We find that students engaged in socially mediated metacognition at multiple key transitions during the troubleshooting process. Reciprocated metacognitive dialogue arose when students were collectively strategizing about which measurements to perform, or reaching a shared understanding of the circuit’s behavior. Our research demonstrates the value of the framework of socially mediated metacognition in providing insight into the nature of collaborative student troubleshooting in the context of electronics. As such, this framework may be a useful resource for future efforts to examine and support the development of student troubleshooting skills in other upper-division laboratory courses.

Laboratory courses represent a unique and potentially important component of the undergraduate physics curriculum, which can be designed to allow students to authentically engage with the process of experimental physics. Among other possible benefits, participation in these courses throughout the undergraduate physics curriculum presents an opportunity to develop students’ understanding of the nature and importance of experimental physics within the discipline as a whole. Here, we present and compare both a longitudinal and pseudolongitudinal analysis of students’ responses to a research-based assessment targeting students’ views about experimental physics—the Colorado Learning Attitudes about Science Survey for Experimental Physics (E-CLASS)—across multiple, required lab courses at a single institution. We find that, while pseudolongitudinal averages showed increases in students’ E-CLASS scores in each consecutive course, analysis of longitudinal data indicates that this increase was not driven by a cumulative impact of laboratory instruction. Rather, the increase was driven by a selection effect in which students who persisted into higher-level lab courses already had more expertlike beliefs, attitudes, and expectations than their peers when they started the lower-level courses.

Research suggests that introductory physics students often have difficulty using a concept in contexts different from the ones in which they learned it without explicit guidance to help them make the connection between the different contexts. We have been investigating advanced students’ learning of quantum mechanics concepts and have developed interactive tutorials which strive to help students learn these concepts. Two such tutorials, focused on the Mach-Zehnder interferometer (MZI) and the double-slit experiment (DSE), help students learn how to use the concept of “which-path” information to reason about the presence or absence of interference in these two experiments in different situations. After working on a pretest that asked students to predict interference in the MZI with single photons and polarizers of various orientations placed in one or both paths of the MZI, students worked on the MZI tutorial which, among other things, guided them to reason in terms of which-path information in order to predict interference in similar situations. We investigated the extent to which students were able to use reasoning related to which-path information learned in the MZI tutorial to answer analogous questions on the DSE (before working on the DSE tutorial). After students worked on the DSE pretest they worked on a DSE tutorial in which they learned to use the concept of which-path information to answer questions about interference in the DSE with single particles with mass sent through the two slits and a monochromatic lamp placed between the slits and the screen. We investigated if this additional exposure to the concept of which-path information promoted improved learning and performance on the DSE questions with single photons and polarizers placed after one or both slits. We find evidence that both tutorials promoted which-path information reasoning and helped students use this reasoning appropriately in contexts different from the ones in which they had learned it.

The “gender gap” on various physics conceptual evaluations has been extensively studied. Men’s average pretest scores on the Force Concept Inventory and Force and Motion Conceptual Evaluation are 13% higher than women’s, and post-test scores are on average 12% higher than women’s. This study analyzed the gender differences within the Conceptual Survey of Electricity and Magnetism (CSEM) in which the gender gap has been less well studied and is less consistent. In the current study, data collected from 1407 students (77% men, 23% women) in a calculus-based physics course over ten semesters showed that male students outperformed female students on the CSEM pretest (5%) and post-test (6%). Separate analyses were conducted for qualitative and quantitative problems on lab quizzes and course exams and showed that male students outperformed female students by 3% on qualitative quiz and exam problems. Male and female students performed equally on the quantitative course exam problems. The gender gaps within CSEM post-test scores, qualitative lab quiz scores, and qualitative exam scores were insignificant for students with a CSEM pretest score of 25% or less but grew as pretest scores increased. Structural equation modeling demonstrated that a latent variable, called Conceptual Physics Performance/Non-Quantitative (CPP/NonQnt), orthogonal to quantitative test performance was useful in explaining the differences observed in qualitative performance; this variable was most strongly related to CSEM post-test scores. The CPP/NonQnt of male students was 0.44 standard deviations higher than female students. The CSEM pretest measured CPP/NonQnt much less accurately for women ($R^2=4\%$) than for men ($R^2=17\%$). The failure to detect a gender gap for students scoring 25% or less on the pretest suggests that the CSEM instrument itself is not gender biased. The failure to find a performance difference in quantitative test performance while detecting a gap in qualitative performance suggests the qualitative differences do not result from psychological factors such as science anxiety or stereotype threat.

As part of ongoing investigations into student learning in advanced undergraduate courses, we have developed a conceptual assessment tool for upper-division electrodynamics (E&M II): the Colorado UppeR-division ElectrodyNamics Test (CURrENT). This is a free response, postinstruction diagnostic with 6 multipart questions, an optional 3-question preinstruction test, and accompanying grading rubrics. The instrument’s development was guided by faculty-consensus learning goals and research into common student difficulties. It can be used to gauge the effectiveness of transformed pedagogy, and to gain insights into student thinking in the covered topic areas. We present baseline data representing 500 students across 9 institutions, along with validity, reliability, and discrimination measures of the instrument and scoring rubric.

The ability to solve physics problems that require multiple concepts from across the physics curriculum—“synthesis” problems—is often a goal of physics instruction. Three experiments were designed to evaluate the effectiveness of two instructional methods employing worked examples on student performance with synthesis problems; these instructional techniques, analogical comparison and self-explanation, have previously been studied primarily in the context of single-concept problems. Across three experiments with students from introductory calculus-based physics courses, both self-explanation and certain kinds of analogical comparison of worked examples significantly improved student performance on a target synthesis problem, with distinct improvements in recognition of the relevant concepts. More specifically, analogical comparison significantly improved student performance when the comparisons were invoked between worked synthesis examples. In contrast, similar comparisons between corresponding pairs of worked single-concept examples did not significantly improve performance. On a more complicated synthesis problem, self-explanation was significantly more effective than analogical comparison, potentially due to differences in how successfully students encoded the full structure of the worked examples. Finally, we find that the two techniques can be combined for additional benefit, with the trade-off of slightly more time on task.