We examine how student aptitudes impact how much students learn from doing graded online and written homework in an introductory electricity and magnetism course. Our analysis examines the correlation between successful homework completion rates and exam performance as well as how changes in homework completion correlate with changes in exam scores for students with different physics aptitudes. On average, successfully completing many homework problems correlated to better exam scores only for students with high physics aptitude. On the other hand, all other students showed zero or even a negative correlation between successful homework completion and exam performance. Low- and medium-aptitude students who did more homework did no better and sometimes scored lower on exams than their low- and medium-aptitude peers who did less homework. Our work also shows that long-term changes in homework completion correlated to long-term changes in exam scores only for students with high physics aptitude, but not for students with medium or low aptitude. We offer several explanations for the disparity in homework learning gains, including cognitive load theory, ineffective homework strategies, and various mismatches between homework and exams. Several solutions are proposed to address these possible deficiencies in graded online and written homework.

Peer Instruction, a well-known student-centered teaching method, engages students during class through structured, frequent questioning and is often facilitated by classroom response systems. The central feature of any Peer Instruction class is a conceptual question designed to help resolve student misconceptions about subject matter. We provide students two opportunities to answer each question—once after a round of individual reflection and then again after a discussion round with a peer. The second round provides students the choice to “switch” their original response to a different answer. The percentage of right answers typically increases after peer discussion: most students who answer incorrectly in the individual round switch to the correct answer after the peer discussion. However, for any given question there are also students who switch their initially right answer to a wrong answer and students who switch their initially wrong answer to a different wrong answer. In this study, we analyze response switching over one semester of an introductory electricity and magnetism course taught using Peer Instruction at Harvard University. Two key features emerge from our analysis: First, response switching correlates with academic self-efficacy. Students with low self-efficacy switch their responses more than students with high self-efficacy. Second, switching also correlates with the difficulty of the question; students switch to incorrect responses more often when the question is difficult. These findings indicate that instructors may need to provide greater support for difficult questions, such as supplying cues during lectures, increasing times for discussions, or ensuring effective pairing (such as having a student with one right answer in the pair). Additionally, the connection between response switching and self-efficacy motivates interventions to increase student self-efficacy at the beginning of the semester by helping students develop early mastery or to reduce stressful experiences (i.e., high-stakes testing) early in the semester, in the hope that this will improve student learning in Peer Instruction classrooms.

Narrated animated solution videos were implemented in a clinical study that compared a mastery setting that employed repeated cycles of testing with instructional support to a group that had a single opportunity to experience the materials. The mastery setting students attempted sequential questions sets on a topic, with animated solutions between each set, until mastery was achieved, combining formative assessment with worked examples. Students showed significant improvement from their first to second tries on similar sets of problems, attributable to the feedback and solutions they were given after the first try. These improvements were shown in two topics, superposition and electric potential. The single try group was given one version of the questions and solutions, and while they were not required to watch the solutions to move forward, they chose to. On a post-test including near and far transfer questions, no significant difference was seen between the mastery group and the single try group, but both significantly outperformed a control group that received no instructional support, indicating that students successfully transferred the skills from the solutions to the post-test.

The impact of lecture instruction on student conceptual understanding in physics has been the subject of research for several decades. Most studies have reported disappointingly small improvements in student performance on conceptual questions despite direct instruction on the relevant topics. These results have spurred a number of attempts to improve learning in physics courses through new curricula and instructional techniques. This paper contributes to the research base through a retrospective analysis of 20 randomly selected qualitative questions on topics in kinematics, dynamics, electrostatics, waves, and physical optics that have been given in introductory calculus-based physics at the University of Washington over a period of 15 years. In some classes, questions were administered after relevant lecture instruction had been completed; in others, it had yet to begin. Simple statistical tests indicate that the average performance of the “after lecture” classes was significantly better than that of the “before lecture” classes for 11 questions, significantly worse for two questions, and indistinguishable for the remaining seven. However, the classes had not been randomly assigned to be tested before or after lecture instruction. Multiple linear regression was therefore conducted with variables (such as class size) that could plausibly lead to systematic differences in performance and thus obscure (or artificially enhance) the effect of lecture instruction. The regression models support the results of the simple tests for all but four questions. In those cases, the effect of lecture instruction was reduced to a nonsignificant level, or increased to a significant, negative level when other variables were considered. Thus the results provide robust evidence that instruction in lecture can increase student ability to give correct answers to conceptual questions but does not necessarily do so; in some cases it can even lead to a decrease.

A small number of studies have investigated student understanding of vector addition and subtraction in generic or introductory physics contexts, but in almost all cases the questions posed were in the vector arrow representation. In a series of experiments involving over 1000 students and several semesters, we investigated student understanding of vector addition and subtraction in both the arrow and algebraic notation (using $\widehat{i}$, $\widehat{j}$, $\widehat{k}$) in generic mathematical and physics contexts. First, we replicated a number of previous findings of student difficulties in the arrow format and discovered several additional difficulties, including the finding that different relative arrow orientations can prompt different solution paths and different kinds of mistakes, which suggests that students need to practice with a variety of relative orientations. Most importantly, we found that average performance in the $ijk$ format was typically excellent and often much better than performance in the arrow format in either the generic or physics contexts. Further, while we find that the arrow format tends to prompt students to a more physically intuitive solution path, we also find that, when prompted, student solutions in the $ijk$ format also display significant physical insights into the problem. We also find a hierarchy in correct answering between the two formats, with correct answering in the $ijk$ format being more fundamental than for the arrow format. Overall, the results suggest that many student difficulties with these simple vector problems lie with the arrow representation itself. For instruction, these results imply that introducing the $ijk$ notation (or some equivalent) with the arrow notation concurrently may be a very useful way to improve student performance as well as help students to learn physics concepts involving vector addition and subtraction.

This theoretical article problematizes the access to disciplinary knowledge that different physics representations have the possibility to provide; that is, their disciplinary affordances. It is argued that historically such access has become increasingly constrained for students as physics representations have been rationalized over time. Thus, the case is made that such rationalized representations, while powerful for communication from a disciplinary point of view, manifest as learning challenges for students. The proposal is illustrated using a vignette from a student discussion in the physics laboratory about circuit connections for an experimental investigation of the charging and discharging of a capacitor. It is concluded that in order for students to come to appreciate the disciplinary affordances of representations, more attention needs to be paid to their “unpacking.” Building on this conclusion, two questions are proposed that teachers can ask themselves in order to begin to unpack the representations that they use in their teaching. The paper ends by proposing directions for future research in this area.

The Colorado Learning Attitudes about Science Survey (CLASS) is a widely used instrument designed to measure student attitudes toward physics and learning physics. Previous research revealed a fairly complex factor structure. In this study, exploratory and confirmatory factor analyses were conducted on data from an undergraduate introductory physics course ($n=3844$) to determine whether a more parsimonious factor structure exists. Exploratory factor analysis results indicate that many of the items from the original CLASS have poor psychometric properties and could not be used in a revised factor structure. The cross validation showed acceptable fit statistics for a three factor model found in the exploratory factor analysis. This research suggests that a more optimum measurement of students’ attitudes about physics and learning physics is obtained with a 15-item instrument, which describes the factors of personal application, personal effort, and problem solving. The proposed revised version of the CLASS offers researchers the opportunity to test a shortened version of the instrument that may be able to provide information about students’ attitudes in the areas of personal application of physics, personal effort in a physics course, and approaches to problem solving.

This paper is the first part of a multiphase study examining students’ mental models about the quantization of physical observables—light, energy, and angular momentum. Thirty-one second-year physics and physics education college students who were taking a modern physics course participated in the study. The qualitative analysis of data revealed six variations in students’ mental models about the quantization of physical observables: scientific model, primitive scientific model, shredding model, alternating model, integrative model, and evolution model. These models were determined to be context dependent. In addition, some students are in a mixed-model state where they use multiple mental models in explaining a phenomenon and use these models inconsistently.

We report on research carried out to improve teaching and student engagement in the introductory astronomy course at the University of Cape Town. This course is taken by a diverse range of students, including many from educationally disadvantaged backgrounds. We describe the development of an instrument, the Introductory Astronomy Questionnaire (IAQ), which we administered as pre- and posttests to students enrolled in the course. The instrument comprised a small number of questions which probed three areas of interest: student motivation and expectations, astronomy content, and worldview. Amongst our findings were that learning gains were made in several conceptual areas, and that students appeared to develop a more nuanced view of the nature of astronomy. There was some evidence that the course had a positive impact on students’ worldviews, particularly their attitudes towards science. We also identified a promising predictor of course success that could in the future be used to identify students requiring special teaching intervention.

In a recent study, Caballero and colleagues conducted a large-scale evaluation using the Force Concept Inventory (FCI) to compare student learning outcomes between two introductory physics curricula: the Matter and Interactions (M&I) mechanics course and a pedagogically-reformed-traditional-content (PRTC) mechanics course. Using a conventional approach to detect between-curriculum differences, the researchers found that students in the PRTC course outperformed their M&I peers on nearly all the FCI items. However, this conventional approach does not control for the levels of student mastery of the tested concepts, and hence falls short of revealing deep information about the key differences between the two curricula. To this end, we use a stratum-specific method, common for detecting differential item functioning, to analyze a subset of the empirical data in the study of Caballero et al. By comparing students of equal mastery levels measured by the FCI (stratum-specific analysis), we find that the M&I students in fact demonstrate an advantage on the questions regarding Newton’s first and second laws. In addition, the previously reported underperformance of the M&I students on kinematics diminishes in our stratum-specific analysis. Results from this study show better alignment with students’ exposure to relevant topics in their respective courses. Both our findings and methodological approach provide useful implications for research on effective curriculum evaluation.

Free-response research-based assessments, like the Colorado Upper-division Electrostatics Diagnostic (CUE), provide rich, fine-grained information about students’ reasoning. However, because of the difficulties inherent in scoring these assessments, the majority of the large-scale conceptual assessments in physics are multiple choice. To increase the scalability and usability of the CUE, we set out to create a new version of the assessment that preserves the insights afforded by a free-response format while exploiting the logistical advantages of a multiple-choice assessment. We used our extensive database of responses to the free-response CUE to construct distractors for a new version where students can select multiple responses and receive partial credit based on the accuracy and consistency of their selections. Here, we describe the development of this modified CUE format, which we call coupled multiple response (CMR), and present data from direct comparisons of both versions. We find that the two formats have the same average score and perform similarly on multiple measures of validity and reliability, suggesting that the new version is a potentially viable alternative to the original CUE for the purpose of large-scale research-based assessment. We also compare the details of student responses on each of the two versions. While the CMR version does not capture the full scope of potential student responses, nearly three-quarters of our students’ responses to the free-response version contained one or more elements that matched options provided on the CMR version.

We report on efforts to design the “Collaborative Workshop Physics” (CWP) instructional strategy to deliver the first interactive engagement (IE) physics course at Khalifa University of Science, Technology and Research (KU), United Arab Emirates (UAE). To our knowledge, this work reports the first calculus-based, introductory mechanics course on the Arabian Peninsula using physics education research (PER)-based instruction. A brief history and present context of general university and STEM teaching in the UAE is given. We present this secondary implementation (SI) as a case study of a novel context and use it to determine if PER-based instruction can be successfully implemented far from the cultural context of the primary developer and, if so, how might such SIs differ from SIs within the United States (U.S.) in terms of criteria for and risks to their success. With these questions in view, a prereform baseline comprised of Maryland Physics Expectations in Physics survey, Force Concept Inventory (FCI), course exam grades, and English language proficiency data are used to design a hybrid implementation of Cooperative Group Problem Solving. We find that for students with high English proficiency, normalized gain on FCI improves substantially, from $⟨g⟩=0.16\pm 0.10$ prereform to $⟨g⟩=0.47\pm 0.08$ in the CWP pilot (standard errors), indicating a successful SI. However, we also find evidence that normalized gains on FCI are strongly modulated by language proficiency and discuss likely causes. Regardless of language ability, problem-solving skill is also substantially improved and course drop-fail-withdrawal rates are cut from 50% to 24%. In particular, we find evidence in postreform student interviews that prior classroom experiences, and not broader cultural expectations about education, are the more significant cause of expectations that are at odds with the classroom norms of well-functioning PER-based instruction. We present this result as evidence that PER-based innovations can be implemented across great changes in cultural context, provided that the method is thoughtfully adapted in anticipation of context and culture-specific student expectations. This case study should be valuable for future reforms at KU, the broader Gulf region, and other institutions facing similar challenges involving SI of PER-based instruction outside the U.S.

The viability of using complexity science in physics education research (PER) is exemplified by (1) situating central tenets of student persistence research in complexity science and (2) drawing on the methods that become available from this to illustrate analyzing the structural aspects of students’ networked interactions as an important dynamic in student persistence. By drawing on the most cited characterizations of student persistence, we theorize that university environments are made up of social and academic systems, which PER work on student persistence has largely ignored. These systems are interpreted as being constituted from rules of interaction that affect the structural aspects of students’ social and academic network interactions from a complexity science perspective. To illustrate this empirically, an exploration of the nature of the social and academic networks of university-level physics students is undertaken. This is done by combining complexity science with social network analysis to characterize structural similarities and differences of the social and academic networks of students in two courses. It is posited that framing a social network analysis within a complexity science perspective offers a new and powerful applicability across a broad range of PER topics.

Constructed-response (CR) questions are a mainstay of introductory physics textbooks and exams. However, because of the time, cost, and scoring reliability constraints associated with this format, CR questions are being increasingly replaced by multiple-choice (MC) questions in formal exams. The integrated testlet (IT) is a recently developed question structure designed to provide a proxy of the pedagogical advantages of CR questions while procedurally functioning as set of MC questions. ITs utilize an answer-until-correct response format that provides immediate confirmatory or corrective feedback, and they thus allow not only for the granting of partial credit in cases of initially incorrect reasoning, but, furthermore, the ability to build cumulative question structures. Here, we report on a study that directly compares the functionality of ITs and CR questions in introductory physics exams. To do this, CR questions were converted to concept-equivalent ITs, and both sets of questions were deployed in midterm and final exams. We find that both question types provide adequate discrimination between stronger and weaker students, with CR questions discriminating slightly better than the ITs. There is some indication that any difference in discriminatory power may result from the baseline score for guessing that is inherent in MC testing. Meanwhile, an analysis of interrater scoring of the CR questions raises serious concerns about the reliability of the granting of partial credit when this traditional assessment technique is used in a realistic (but nonoptimized) setting. Furthermore, we show evidence that partial credit is granted in a valid manner in the ITs. Thus, together with consideration of the vastly reduced costs of administering IT-based examinations compared to CR-based examinations, our findings indicate that ITs are viable replacements for CR questions in formal examinations where it is desirable both to assess concept integration and to reward partial knowledge, while efficiently scoring examinations.

This paper presents a comprehensive synthesis of physics education research at the undergraduate level. It is based on work originally commissioned by the National Academies. Six topical areas are covered: (1) conceptual understanding, (2) problem solving, (3) curriculum and instruction, (4) assessment, (5) cognitive psychology, and (6) attitudes and beliefs about teaching and learning. Each topical section includes sample research questions, theoretical frameworks, common research methodologies, a summary of key findings, strengths and limitations of the research, and areas for future study. Supplemental material proposes promising future directions in physics education research.

Aiming at a deep understanding of some basic concepts of electric circuits in lower secondary schools, this work introduces an analogy between the behavior of children playing in a school yard with a central lake, subject to different conditions, rules, and stimuli, and Drude’s free electron model of metals. Using this analogy from the first school contacts with electric phenomena, one can promote students’ understanding of concepts such as electric current, the role of generators, potential difference effects, energy transfer, open and closed circuits, resistances, and their combinations in series and parallel. One believes that through this analogy well-known previous misconceptions of young students about electric circuit behaviors can be overcome. Furthermore, students’ understanding will enable them to predict, and justify with self-constructed arguments, the behavior of different elementary circuits. The students’ predictions can be verified—as a challenge of self-produced understanding schemes—using laboratory experiments. At a preliminary stage, our previsions were confirmed through a pilot study with three classrooms of 9th level Portuguese students.

Through in-class observations of teaching assistants (TAs) and students in the lab sections of a large introductory physics course, we study which TA behaviors can be used to predict student engagement and, in turn, how this engagement relates to learning. For the TAs, we record data to determine how they adhere to and deliver the lesson plan and how they interact with students during the lab. For the students, we use observations to record the level of student engagement and pretests and post-tests of lab skills to measure learning. We find that the frequency of TA–student interactions, especially those initiated by the TAs, is a positive and significant predictor of student engagement. Interestingly, the length of interactions is not significantly correlated with student engagement. In addition, we find that student engagement was a better predictor of post-test performance than pretest scores. These results shed light on the manner in which students learn how to conduct inquiry and suggest that, by proactively engaging students, TAs may have a positive effect on student engagement, and therefore learning, in the lab.