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.

The role of autonomy in the student experience in a large-enrollment undergraduate introductory physics course was studied from a self-determination theory perspective. A correlational study investigated whether certain aspects of the student experience correlated with how autonomy supportive (versus controlling) students perceived their instructors to be. An autonomy-supportive instructor acknowledges students’ perspectives and feelings and provides students with information and opportunities for choice while minimizing external pressures (e.g., incentives or deadlines). It was found that the degree to which students perceived their instructors as autonomy supportive was positively correlated with student interest and enjoyment in learning physics ($\beta ={0.31}^{***}$) and negatively correlated with student anxiety about taking physics ($\beta =-{0.23}^{**}$). It was also positively correlated with how autonomous (versus controlled) students’ reasons for studying physics became over the duration of the course (i.e., studying physics more because they wanted to versus had to; $\beta ={0.24}^{***}$). This change in autonomous reasons for studying physics was in turn positively correlated with student performance in the course ($\beta ={0.17}^{*}$). Additionally, the degree to which students perceived their instructors as autonomy supportive was directly correlated with performance for those students entering the course with relatively autonomous reasons for studying physics ($\beta ={0.25}^{**}$). In summary, students who perceived their instructors as more autonomy supportive tended to have a more favorable motivational, affective, and performance experience in the course. The findings of the present study are consistent with experimental studies in other contexts that argue for autonomy-supportive instructor behaviors as the cause of a more favorable student experience.

In this article we compare students’ understanding of vector concepts in problems with no physical context, and with three mechanics contexts: force, velocity, and work. Based on our “Test of Understanding of Vectors,” a multiple-choice test presented elsewhere, we designed two isomorphic shorter versions of 12 items each: a test with no physical context, and a test with mechanics contexts. For this study, we administered the items twice to students who were finishing an introductory mechanics course at a large private university in Mexico. The first time, we administered the two 12-item tests to 608 students. In the second, we only tested the items for which we had found differences in students’ performances that were difficult to explain, and in this case, we asked them to show their reasoning in written form. In the first administration, we detected no significant difference between the medians obtained in the tests; however, we did identify significant differences in some of the items. For each item we analyze the type of difference found between the tests in the selection of the correct answer, the most common error on each of the tests, and the differences in the selection of incorrect answers. We also investigate the causes of the different context effects. Based on these analyses, we establish specific recommendations for the instruction of vector concepts in an introductory mechanics course. In the Supplemental Material we include both tests for other researchers studying vector learning, and for physics teachers who teach this material.

This study assesses the Japanese translation of the Force and Motion Conceptual Evaluation (FMCE). Researchers are often interested in comparing the conceptual ideas of students with different cultural backgrounds. The FMCE has been useful in identifying the concepts of English-speaking students from different backgrounds. To identify effectively the conceptual ideas of Japanese students and to compare them to those of their English-speaking counterparts, more work is required. Because of differences between the Japanese and English languages, and between the Japanese and American educational systems, it is important to assess the Japanese translation of the FMCE, a conceptual evaluation originally developed in English for American students. To assess its appropriateness, we examined the performance of a large sample of students on the translated version of the FMCE and then compared the results to those of English-speaking students. The data comprise the pretest results of 1095 students, most of whom were first-year students at a midlevel engineering school between 2003 and 2012. Basic statistics and the classical test theory indices of the translated FMCE indicate that its reliability and discrimination are appropriate to assess Japanese students’ concepts about force and motion. In general, the preconcepts of Japanese students assessed with the Japanese translation of the FMCE are quite similar to those of American students assessed with the FMCE, thereby supporting the validity of the translated version. However, our findings do show (1) that only a small percentage of Japanese students grasped Newtonian concepts and (2) that the percentage of Japanese students who used two different concept models together to answer some questions seems to be higher than that of American students.

Classroom response systems are widely used in interactive teaching environments as a way to engage students by asking them questions. Previous research on the time taken by students to respond to conceptual questions has yielded insights on how students think and change conceptions. We measure the amount of time students take to respond to in-class, conceptual questions [ConcepTests (CTs)] in two introductory physics courses taught using Peer Instruction and use item response theory to determine the difficulty of the CTs. We examine response time differences between correct and incorrect answers both before and after the peer discussion for CTs of varying difficulty. We also determine the relationship between response time and student performance on a standardized test of incoming physics knowledge, precourse self-efficacy, and gender. Our data reveal three results of interest. First, response time for correct answers is significantly faster than for incorrect answers, both before and after peer discussion, especially for easy CTs. Second, students with greater incoming physics knowledge and higher self-efficacy respond faster in both rounds. Third, there is no gender difference in response rate after controlling for incoming physics knowledge scores, although males register significantly more attempts before committing to a final answer than do female students. These results provide insight into effective CT pacing during Peer Instruction. In particular, in order to maintain a pace that keeps everyone engaged, students should not be given too much time to respond. When around 80% of the answers are in, the ratio of correct to incorrect responses rapidly approaches levels indicating random guessing and instructors should close the poll.

Representations in physics possess both physical and conceptual aspects that are fundamentally intertwined and can interact to support or hinder sense making and computation. We use distributed cognition and the theory of conceptual blending with material anchors to interpret the roles of conceptual and material features of representations in students’ use of representations for computation. We focus on the vector-arrows representation of electric fields and describe this representation as a conceptual blend of electric field concepts, physical space, and the material features of the representation (i.e., the physical writing and the surface upon which it is drawn). In this representation, spatial extent (e.g., distance on paper) is used to represent both distances in coordinate space and magnitudes of electric field vectors. In conceptual blending theory, this conflation is described as a clash between the input spaces in the blend. We explore the benefits and drawbacks of this clash, as well as other features of this representation. This analysis is illustrated with examples from clinical problem-solving interviews with upper-division physics majors. We see that while these intermediate physics students make a variety of errors using this representation, they also use the geometric features of the representation to add electric field contributions and to organize the problem situation productively.

The Next Generation Science Standards (NGSS) require teachers to understand aspects of energy degradation and the second law of thermodynamics, including energy’s availability and usefulness, changes in energy concentration, and the tendency of energy to spread uniformly. In an effort to develop learning goals that support teachers in building robust understandings of energy from their existing knowledge, we studied teachers’ impromptu conversations about these topics during professional development courses about energy. Many of these teachers’ ideas appear to align with statements from the NGSS, including the intuition that energy can be present but inaccessible, that energy can change in its usefulness as it transforms within a system, and that energy can lose its usefulness as it disperses, often ending up as thermal energy. Some teachers’ ideas about energy degradation go beyond what is articulated in the NGSS, including the idea that thermal energy can be useful in some situations and the idea that energy’s usefulness depends on the objects included in a scenario. Based on these observations, we introduce learning goals for energy degradation and the second law of thermodynamics that (1) represent a sophisticated physics understanding of these concepts, (2) originate in ideas that teachers already use, and (3) align with the NGSS.

In our pilot studies, we found that many introductory physics textbook illustrations with supporting text for sound standing waves of air columns in open-open, open-closed, and closed-closed pipes inhibit student understanding of sound standing wave phenomena due to student misunderstanding of how air molecules move within these pipes. Based on the construct of meaningful learning from cognitive psychology and semiotics, a quasiexperimental study was conducted to investigate the comparative effectiveness of two alternative approaches to student understanding: a traditional textbook illustration approach versus a newly designed air molecule motion illustration approach. Thirty volunteer students from introductory physics classes were randomly assigned to two groups of 15 each. Both groups were administered a presurvey. Then, group A read the air molecule motion illustration handout, and group B read a traditional textbook illustration handout; both groups were administered postsurveys. Subsequently, the procedure was reversed: group B read the air molecule motion illustration handout and group A read the traditional textbook illustration handout. This was followed by a second postsurvey along with an exit research questionnaire. The study found that the majority of students experienced meaningful learning and stated that they understood sound standing wave phenomena significantly better using the air molecule motion illustration approach. This finding provides a method for physics education researchers to design illustrations for abstract sound standing wave concepts, for publishers to improve their illustrations with supporting text, and for instructors to facilitate deeper learning in their students on sound standing waves.

We have applied the heuristic-analytic theory of reasoning to interpret inconsistencies in student reasoning approaches to physics problems. This study was motivated by an emerging body of evidence that suggests that student conceptual and reasoning competence demonstrated on one task often fails to be exhibited on another. Indeed, even after instruction specifically designed to address student conceptual and reasoning difficulties identified by rigorous research, many undergraduate physics students fail to build reasoning chains from fundamental principles even though they possess the required knowledge and skills to do so. Instead, they often rely on a variety of intuitive reasoning strategies. In this study, we developed and employed a methodology that allowed for the disentanglement of student conceptual understanding and reasoning approaches through the use of sequences of related questions. We have shown that the heuristic-analytic theory of reasoning can be used to account for, in a mechanistic fashion, the observed inconsistencies in student responses. In particular, we found that students tended to apply their correct ideas in a selective manner that supported a specific and likely anticipated conclusion while neglecting to employ the same ideas to refute an erroneous intuitive conclusion. The observed reasoning patterns were consistent with the heuristic-analytic theory, according to which reasoners develop a “first-impression” mental model and then construct an argument in support of the answer suggested by this model. We discuss implications for instruction and argue that efforts to improve student metacognition, which serves to regulate the interaction between intuitive and analytical reasoning, is likely to lead to improved student reasoning.