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.

In this article, we present several modifications to the Test of Understanding Graphs in Kinematics. The most significant changes are (i) the addition and removal of items to achieve parallelism in the objectives (dimensions) of the test, thus allowing comparisons of students’ performance that were not possible with the original version, and (ii) changes to the distractors of some of the original items that represent the most frequent alternative conceptions. The final modified version (after an iterative process involving four administrations of test variations over two years) was administered to 471 students of an introductory university physics course at a large private university in Mexico. When analyzing the final modified version of the test it was found that the added items satisfied the statistical tests of difficulty, discriminatory power, and reliability; also, that the great majority of the modified distractors were effective in terms of their frequency selection and discriminatory power; and, that the final modified version of the test satisfied the reliability and discriminatory power criteria as well as the original test. Here, we also show the use of the new version of the test, presenting a new analysis of students’ understanding not possible to do before with the original version of the test, specifically regarding the objectives and items that in the new version meet parallelisms. Finally, in the PhysPort project (physport.org), we present the final modified version of the test. It can be used by teachers and researchers to assess students’ understanding of graphs in kinematics, as well as their learning about them.

The physics community explores and explains the physical world through a blend of theoretical and experimental studies. The future of physics as a discipline depends on training of students in both the theoretical and experimental aspects of the field. However, while student learning within lecture courses has been the subject of extensive research, lab courses remain relatively under-studied. In particular, there is little, if any, data available that address the effectiveness of physics lab courses at encouraging students to recognize the nature and importance of experimental physics within the discipline as a whole. To address this gap, we present the first large-scale, national study ($N_{\text{institutions}}=75$ and $N_{\text{students}}=7167$) of undergraduate physics lab courses through analysis of students’ responses to a research-validated assessment designed to investigate students’ beliefs about the nature of experimental physics. We find that students often enter and leave physics lab courses with ideas about experimental physics as practiced in their courses that are inconsistent with the views of practicing experimental physicists, and this trend holds at both the introductory and upper-division levels. Despite this inconsistency, we find that both introductory and upper-division students are able to accurately predict the expertlike response even in cases where their views about experimentation in their lab courses disagree. These finding have implications for the recruitment, retention, and adequate preparation of students in physics.

The ability to switch between various representations is an invaluable problem-solving skill in physics. In addition, research has shown that using multiple representations can greatly enhance a person’s understanding of mathematical and physical concepts. This paper describes a study of student difficulties regarding interpreting, constructing, and switching between representations of vector fields, using both qualitative and quantitative methods. We first identified to what extent students are fluent with the use of field vector plots, field line diagrams, and symbolic expressions of vector fields by conducting individual student interviews and analyzing in-class student activities. Based on those findings, we designed the Vector Field Representations test, a free response assessment tool that has been given to 196 second- and third-year physics, mathematics, and engineering students from four different universities. From the obtained results we gained a comprehensive overview of typical errors that students make when switching between vector field representations. In addition, the study allowed us to determine the relative prevalence of the observed difficulties. Although the results varied greatly between institutions, a general trend revealed that many students struggle with vector addition, fail to recognize the field line density as an indication of the magnitude of the field, confuse characteristics of field lines and equipotential lines, and do not choose the appropriate coordinate system when writing out mathematical expressions of vector fields.

Students’ difficulties in quantum mechanics may be the result of unproductive framing and not a fundamental inability to solve the problems or misconceptions about physics content. We observed groups of students solving quantum mechanics problems in an upper-division physics course. Using the lens of epistemological framing, we investigated four frames in our observational data: algorithmic math, conceptual math, algorithmic physics, and conceptual physics. We discuss the characteristics of each frame as well as causes for transitions between different frames, arguing that productive problem solving may occur in any frame as long as students transition appropriately between frames. Our work extends epistemological framing theory on how students frame discussions in upper-division physics courses.

The work of physics learners at all levels revolves around problems. Physics education research has inspired attention to the forms of these problems, whether conceptual or algorithmic, closed or open response, well or ill structured. Meanwhile, it has been the work of curriculum developers and instructors to develop these problems. Physics education research has supported these efforts with studies of students problem solving and the effects of different kinds of problems on learning. In this article we argue, first, that developing problems is central to the discipline of physics. It involves noticing a gap of understanding, identifying and articulating its precise nature, and motivating a community of its existence and significance. We refer to this activity as problematizing, and we show its importance by drawing from writings in physics and philosophy of science. Second, we argue that students, from elementary age to adults, can problematize as part of their engaging in scientific inquiry. We present four cases, drawing from episodes vetted by a panel of collaborating faculty in science departments as clear instances of students doing science. Although neither we nor the scientists had problematizing in mind when screening cases, we found it across the episodes. We close with implications for instruction, including the value of helping students recognize and manage the situation of being confused but not yet having a clear question, and implications for research, including the need to build problematizing into our models of learning.

This study focuses on student development of two important laboratory skills in the context of introductory college-level physics. The first skill, which we call model making, is the ability to analyze a phenomenon in a way that produces a quantitative multimodal model. The second skill, which we call model breaking, is the ability to critically evaluate if the behavior of a system is consistent with a given model. This study involved 116 introductory physics students in four different sections, each taught by a different instructor. All of the students within a given class section participated in the same instruction (including labs) with the exception of five activities performed throughout the semester. For those five activities, each class section was split into two groups; one group was scaffolded to focus on model-making skills and the other was scaffolded to focus on model-breaking skills. Both conditions involved direct measurement videos. In some cases, students could vary important experimental parameters within the video like mass, frequency, and tension. Data collected at the end of the semester indicate that students in the model-making treatment group significantly outperformed the other group on the model-making skill despite the fact that both groups shared a common physical lab experience. Likewise, the model-breaking treatment group significantly outperformed the other group on the model-breaking skill. This is important because it shows that direct measurement video-based instruction can help students acquire science-process skills, which are critical for scientists, and which are a key part of current science education approaches such as the Next Generation Science Standards and the Advanced Placement Physics 1 course.

Our field has long valued the goal of teaching students not just the facts of physics, but also the thinking and reasoning skills of professional physicists. The complexity inherent in scientific reasoning demands that we think carefully about how we conceptualize for ourselves, enact in our classes, and encourage in our students the relationship between the multifaceted practices of professional science. The current study draws on existing research in the philosophy of science and psychology to advocate for intertwining two important aspects of scientific reasoning: using evidence from experimentation and modeling. We present a case from an undergraduate physics course to illustrate how these aspects can be intertwined productively and describe specific ways in which these aspects of reasoning can mutually reinforce one another in student learning. We end by discussing implications for this work for instruction in introductory physics courses and for research on scientific reasoning at the undergraduate level.

In this paper, we investigate some of the ways in which students, when given the opportunity and an appropriate learning environment, spontaneously engage in collaborative inquiry. We studied small groups of high school students interacting around and with an interactive whiteboard equipped with Algodoo software, as they investigated orbital motion. Using multimodal discourse analysis, we found that in their discussions the students relied heavily on nonverbal meaning-making resources, most notably hand gestures and resources in the surrounding environment (items displayed on the interactive whiteboard). They juxtaposed talk with gestures and resources in the environment to communicate ideas that they initially were not able to express using words alone. By spontaneously recruiting and combining a diverse set of meaning-making resources, the students were able to express relatively fluently complex ideas on a novel physics topic, and to engage in practices that resemble a scientific approach to exploration of new phenomena.