Polarization of light is one of the topics in the Croatian high school physics curriculum. It is taught in the final year of high school education. Twenty-seven Croatian high-school students (aged 18–19 years) were interviewed after regular instruction about their understanding of polarization of light and the model of light itself. This paper reports on the observed students’ reasoning strategies and conceptual difficulties. Some of the reported difficulties correspond with previously identified difficulties, but some new difficulties were also found. Students often based their explanations on the remembered but misinterpreted common schematic representations of polarization. Explanations seemed to be created on the spot, suggesting the absence of prior models of polarization.

We designed a rubric to assess free-response exam problems in order to compare thinking skills evidenced in exams in classes taught by different pedagogies. The rubric was designed based on Bloom’s taxonomy and then used to code exam problems. We have analyzed historical and recent exam problems in both algebra-based and calculus-based exams. In particular, we have examined cases where the same problem was administered on exams taught by different pedagogies. In some cases, we were able to compare different sections of the algebra-based physics course taught by the same instructor, sometimes during the same semester, one with inquiry-based instruction and the other in a more traditional lecture environment. We discuss the development of the instrument and present results. The inquiry-based students consistently demonstrated use of the thinking skills coded at least as often as the traditional students, and usually more often.

Introductory university astronomy courses have emerged as a powerful opportunity to improve science understanding, literacy, and appreciation of the scientific method to a wide range of future citizens and voters. Students in an introductory astronomy course were instructed to record and analyze their naked-eye astronomical observations over a semester (13 weeks). The effect this activity had on students’ learning of basic astronomy concepts and attitudes towards astronomy and science were measured using an astronomy concept diagnostic test and attitudes survey administered at the start and at the end of the semester, and compared with a similar introductory astronomy course that did not include the observing assignment. The results suggest that the observing diary is a positive learning experience for the majority of students, and that completing this assessment assists in developing students’ deeper engagement with astronomy and astronomy concepts. We recommend the use and assessment of observing diaries as an effective learning activity in introductory astronomy classes.

Introductory physics lab courses serve as the starting point for students to learn and experience experimental physics at the undergraduate level. They often focus on measurement uncertainty, an essential topic for practicing physicists and a foundation for more advanced lab learning. As such, measurement uncertainty has been a focus when studying and improving introductory physics lab courses. There is a need for a research-based assessment explicitly focused on measurement uncertainty that captures the breadth of learning related to the topic, and that has been developed and documented in an evidence-centered way. In this work, we present the first step in the development of such an assessment, with the goal of establishing the breadth and depth of the domain of measurement uncertainty in introductory physics labs. We conducted and analyzed interviews with introductory physics lab instructors across the US, identifying prevalent concepts and practices related to measurement uncertainty, and their level of emphasis in introductory physics labs. We find that instructors discuss a range of measurement uncertainty topics beyond basic statistical ideas like mean and standard deviation, including those connected to modeling, another lab learning goal. We describe how these findings will be used in the subsequent development of the assessment, called the Survey Of Physics Reasoning On Uncertainty Concepts In Experiments (SPRUCE).

The purpose of this study is to validate the physics affective characteristics scale (PACS) by investigating its psychometric properties. The PACS is a revised version of the affective characteristics scale (ACS), which was developed for Turkish students following introductory physics courses. The questionnaire includes 51 items in 11 subscales: situational interest in physics, personal interest in physics, relevance of physics to everyday life, relevance of physics to future career, relevance of physics to other courses, physics course anxiety, physics test anxiety, student motivation in physics, self-efficacy in physics, self-concept in physics, and physics achievement motivation. In this version, the relevance subscale—named as importance subscale in the previous version—was revised, and the aspiring extra activities related to physics subscale was removed. The PACS was administered to 240 nonphysics (biology and pharmacy) majors enrolled in an introductory physics course at a Flemish university. Confirmatory factor analysis was used to test the factor structure of the questionnaire. The results showed that the model fits well indicating that the revised questionnaire also has satisfactory psychometric properties, and supporting a multidimensional relevance construct. As expected, the indicators all showed significant positive factor loadings. The results of this study suggest that the Dutch version of the PACS is a useful instrument with sufficient reliability and validity to measure nonphysics majors’ affective characteristics.

Traditional, template physics labs are often associated with student dissatisfaction and superficial applications, and are known to leave students with fragmented knowledge. An alternative known as labatorials, a conceptually driven approach to labs, has been proposed. In a number of studies, labatorials have been shown to work well. However, what has been missing is a study comparing labatorials to traditional labs. In this study, labatorials are compared with traditional labs in terms of students’ learning experience and the quality of their conceptual learning. Additionally, we identify the scaffolding mechanisms that impact these elements. In the context of Concordia University’s introductory experimental mechanics course, we collect data spanning semistructured student and teaching assistant (TA) interviews, class observations, TA surveys, post-test and final exam scores and responses, and student writing products. Upon analysis and triangulation, we find that due to the scaffolding present in labatorials, students typically exhibit a high degree of collaboration and engagement with the material in a low-pressure environment, which allows students to focus on the learning. This is attributed to three primary forms of scaffolding inherent to the design of labatorials: peer scaffolding, instructor scaffolding, and scaffolding by the activity worksheet. In contrast, students in traditional labs have a tendency to rely on step-by-step instructions and focus on avoiding errors, which may inhibit their conceptual learning. These conclusions are supported by the students’ differing performance and understanding exhibited in different types of questions; traditional lab students tend to perform better on questions involving standardized processes or simple, memorization-based calculations, while labatorial students tend to perform better on conceptual questions.

A performance gap between the genders has been observed on the Force Concept Inventory (FCI) almost since its introduction. Many studies have sought to characterize this gender gap, however, few have tested the consistency of the factor structure across the genders. This study fills in this gap by offering the first piece of evidence that the genders (male and female due to data constraints) are interacting with the FCI in similar manners. Using multigroup measurement invariance techniques, a preinstruction sample of 6238 males and 2874 females, and a postinstruction sample of 6338 males and 2955 females, the latent variable structure of the FCI was tested for consistency between the genders. As this technique is not often used by the physics education research community, significant time was spent explaining the methodology. It was found that the Eaton and Willoughby five-factor modified (EW5M) model of the FCI factor structure exhibited strict invariance between the genders. Additionally, a single-factor model showed strong invariance and partial strict invariance for the FCI. Latent means from the EW5M model revealed that females underperform compared to males across all of the factors of the FCI, but these gaps in performance decreased over the course of instruction, however, some differences are still large. The results of this study suggest observed performance differences on the FCI between the genders may not be due to gender specific factor structure differences. However, this result is sample dependent and should be verified by other studies using different, independent samples.

We show how learning can be improved, beyond that shown in actively taught classrooms, by also transforming the homework using the principles of deliberate practice. We measure the impact of transforming the homework on student learning in a course that had already implemented an active approach to teaching in class. We compare performance on the same final exam in equivalent cohorts of students over three semesters of an introductory physics course: the first taught with traditional lectures and traditional homework, the second taught with active instruction coupled with traditional homework, and the last taught with both active instruction and transformed homework. We find students in the semester where both active teaching and transformed homework are used scored significantly higher on the final exam than the students taught actively but with traditional homework. This learning gain achieved by transforming the homework is comparable to that achieved by replacing traditional lectures with active teaching strategies in class. We further show the positive effects of transforming the homework on student learning through a shorter, controlled experiment. When everything but the homework implementation is controlled, students scored 5%–10% higher on a test of learning following transformed homework compared with traditional homework. This significant improvement to learning occurs despite students spending a similar amount of time on task. This study represents an initial step towards understanding how deliberate practice can be extended to improve pedagogy beyond what happens in the classroom to the out-of-class homework.

Causal reasoning is a fundamental cognitive process that supports a wide range of learning activities such as making predictions and inferences, explaining phenomena, and drawing conclusions. In physics learning, causal reasoning plays an important role in developing conceptual understanding and problem-solving skills. This study builds off the existing work to investigate aspects of students’ causal reasoning in understanding Newton’s third law. Quantitative assessment is conducted to explicitly probe four attributes of causal reasoning including the causal relation between a pair of interaction forces, magnitudes of interaction forces, the time order of interaction forces, and the action-reaction language. Interviews are also conducted to identify details of students’ reasoning pathways. The subjects of this study include high school and college students from China. The results suggest that after instruction on Newton’s third law many students still hold a belief of causal relation between the pair of interaction forces. Further analysis on students’ response patterns and interviews suggests that students’ belief in causality is strongly associated with asymmetries in scenario contexts due to dominant features, the scenario timeline, and the action-reaction language. In addition, the results also demonstrate a progression of four developmental levels of causal reasoning that each reveals a set of unique thinking pathways for using the asymmetries in reasoning to determine causality. The findings of this study suggest that the lack of correct causal reasoning may cause students to develop fragmented conceptual understanding, which should be addressed in future research and instruction. Detailed analysis of the findings and educational implications on assessment and instruction are discussed.

Diagnostic tests for placing students into appropriate courses are commonly used in higher education math and science departments. We found no physics education research examining the validity of such exams, how well they are placing students into appropriate courses, and what guidance these exams can give for better focusing instruction. In this study, we present criteria by which to evaluate the validity and value of a diagnostic test, and we then apply these to the test developed for physics course placement at Stanford University. We examine the data collected from the first year in which all students intending to enroll in an introductory physics course were required to take the test and received an email suggesting which course would best match their level of preparation based on their score. We found that most students followed this advice. We also found that the diagnostic test score was a good predictor of performance in both the introductory physics course for physics majors and the course targeting science and engineering majors. It was not a good predictor of performance in two other courses, likely due to lack of alignment between course objectives and diagnostic measures. We found many individual questions which were particularly discriminating in predicting performance in the various courses, suggesting specific topics on which instruction should focus. We found that 27 of the 38 questions were predictive of performance in at least one of the courses studied, and only 8 questions that were not predictive of course performance or did not show any difference between students enrolled in different courses. These results provide evidence for the validity and usefulness of our diagnostic test, and we offer it to instructors at other institutions who might find it of value.

This study examines students’ visual behaviors when they tackle two types of synthesis problems, sequential and simultaneous problems. Sequential synthesis tasks can be solved by applying pertinent concepts consecutively, whereas simultaneous synthesis tasks require concurrent application of multiple concepts. Twenty-two students from an introductory calculus-based physics course participated in the study. We used an eye-tracker to record the students’ eye movements when they silently reflected on how to solve the problems and subsequently when they talked aloud their problem-solving strategies. We found that the students made more gaze transitions between text and diagram for the simultaneous problems than for the sequential ones. However, they spent more time looking at the diagram and making within-diagram eye transitions in the sequential tasks than in the simultaneous tasks. Further, most students invoked two concepts to solve the sequential tasks but only one for the simultaneous tasks. These findings indicate that the students made less effort to link text and diagram in solving sequential problems but frequently attempted to integrate information within each diagram. The pattern for the simultaneous problems appeared to be reversed. Our results suggest that different types of synthesis (i.e., sequential and simultaneous) may differentially influence the ways students handle tasks. As suggested by the eye-tracker data and confirmed by the participants’ verbal explanations, students tend to divide the situation in sequential problems into subtasks but treat simultaneous problems as a single-step task.

The purpose of this study was to explore how students with high- and low-prior-knowledge employed multiple representations in argumentation evaluation and generation tasks. The argumentation performance and eye-movement behaviors of 96 college students in these tasks were investigated. The number of participants who proposed complex argumentation levels and the argumentation accuracy was higher in the high-prior-knowledge group than in the low-prior-knowledge group. Moreover, the high-prior-knowledge group demonstrated greater eye-movement transitions between representations compared with the low-prior-knowledge group. Both groups had greater transitions in the generation task than the evaluation tasks. The high-prior-knowledge group distributed attention to representations with more flexibility, revealing that they were more aware of the task requirements and more able to employ multiple representations for arguments. In the argumentation evaluation tasks, the high-prior-knowledge group performed referencing behaviors in the reading sequences between representation text and equation and between representation table and figure, whereas the low-prior-knowledge group was inclined to look back and forth between representation text and table. In the argumentation generation task, the two groups displayed similar reading sequences. It indicated that learners with higher knowledge may perceive the similarity between homogeneous representations and constrained interpretations of the complex representations by using easier representations, or further integrated representations to achieve deeper understanding, which then improved their argumentation performance. The implications of instructions for improving learners’ argumentation skills in a multirepresentational display are discussed.

Introductory mechanics is an obligatory course for many disciplines outside of physics and the failure rate is often high. Even the students who pass the course often fail to achieve the main learning goal: The conceptual knowledge required for modeling situations with physics principles. In many cases, this is due to inefficient learning strategies. However, little work has been done on the integration of learning strategies into physics courses. Here we present a study where we integrated three established learning strategies into the teaching of an introductory mechanics course: elaborative encoding, retrieval practice, and self-explanation. We also developed three scaffolding tools to facilitate the integration of the strategies: elaborative encoding questions, a hierarchical principle structure, and a problem-solution structure with emphasis on physics modeling. The overarching aim of this study is to use students’ experience-based reflections to find ways to improve the integration of the learning strategies. To fulfill this aim, we seek answers to the following three interrelated research questions: (i) What are the students’ experiences and associated reflections with the learning strategies and tools? (ii) How do the students’ experiences and reflections align with established theory on the learning strategies? (iii) What main barriers to effective implementation of the learning strategies may be hypothesized? To answer these questions, we did semi-structured research interviews with 12 students. Through the thematic analysis, we found that retrieval practice was used extensively while self-explanation and elaborative encoding was partly or wholly ignored. The analysis, together with theoretical considerations, indicates that successful implementation of elaborative encoding is critical for maximizing the benefits from retrieval practice in physics. We also present some promising findings on two of the tools: (i) Students’ extensive use of the hierarchical principle structure and (ii) that some students started practicing physics modeling after exposure to the solution structure. Finally, we offer suggestions for how to overcome the barriers to effective implementation of each of the learning strategies.

Educators and researchers often use research-based assessments before and after instruction to measure the efficacy of courses. Limited resources exist for interpreting assessment results, particularly for attitudinal surveys. We present analyses and representations created with data from 192 introductory physics courses that educators and researchers can use to provide a context for interpreting results from the Colorado Learning Attitudes About Science Survey. The provided data came from the online Learning About STEM Student Outcomes platform and from the scientific literature. The representations include scatter plots of pretest and post-test scores and distributions of effect sizes. Educators and researchers can use these representations to show how courses compare to the larger database before and after instruction. Results almost always associated physics courses for nonscience majors with shifts to more expertlike attitudes, whereas this was the case for approximately one-third of introductory physics courses for science majors.

High attrition rates in science, technology, engineering, and mathematics disciplines are an ongoing problem. Graduate student attrition, in particular, is understudied. Most past studies have focused on students’ attributes, undergraduate preparation, and mentoring relationships. Emerging results from the implementation of the American Physical Society Bridge Program (APSBP) suggest that departmental support structures could lead to increased retention. However, there are no validated instruments to measure students’ experience of the departmental support structures. This paper describes the development and psychometric evaluation of the aspects of student experience scale (ASES). Items were developed based on prior literature and the APSBP recommendations, revised based on APSBP feedback, and subjected to psychometric evaluation. Principal components analysis of data from 397 students at 19 physics graduate programs (2 M.S. and 17 Ph.D.) across the U.S. resulted in four distinct factors: (a) mentoring and research experience, (b) professional development, (c) social and academic integration, and (d) financial support. ASES meets the standard criteria for divergent validity, discriminant validity, and internal consistency. Results of students’ ASES response ratings are discussed, along with comparisons between students enrolled at APSBP and non-APSBP affiliated graduate programs. On average, we find that physics graduate students experience adequate mentoring and financial support; however, they report experiencing limited social and academic integration and a lack of professional development. We also find that students in APSBP affiliated programs report better experiences on all four factors than students in non-APSBP affiliated programs, with higher differences in social and academic integration and financial support. This study is a starting point for the refinement process of this instrument.

Existing research identifying common student ideas about forces focuses on students’ misunderstandings, misconceptions, and difficulties. In this paper, we characterize student thinking in terms of resources, framing student thinking as continuous with formal physics. Based on our analysis of 2048 written responses to conceptual questions, we identify six common conceptual resources for understanding forces. We document context-sensitive patterns in resource activation, and we discuss limitations of our research based on the demographics of our sample.

This study reports an analysis of the Force Concept Inventory (FCI) using item response curves (IRC)—the fraction of students selecting each response to an item as a function of their total score. Three large samples ($N=9606$, 4360, and 1439) of calculus-based physics students were analyzed. These were drawn from three land-grant institutions with very different average FCI post-test scores. A significant number of the response curves for incorrect responses have a maximum at some intermediate value of the total score on the FCI. To analyze the incorrect responses (rather than just the correct response as is typically done), we used Bock’s nominal response model (NRM), primarily because it can fit these intermediate maximum curves. The one-dimensional NRM latent ability dimension was strongly correlated ($r=0.99$) with the latent ability determined by two-parameter logistic (2PL) item response theory applied with correct or incorrect grading even though the correct responses were not identified for the NRM. To understand the relation of Newtonian and non-Newtonian thinking, higher dimensional models were fit. The two-dimensional NRM model produced one ability dimension which could be rotated to be highly correlated with the 2PL latent ability ($r\ge 0.98$) and a second dimension which was most strongly related to misconceptions involving Newton’s third law. Cluster analysis was applied to the two latent ability dimensions producing a three-cluster solution where the cluster centroids were very similar for each of the three institutions. The clusters represented three groups of students: Newtonian thinkers still retaining some misconceptions, non-Newtonian thinkers strongly applying Newton’s third law misconceptions, and non-Newtonian thinkers weakly applying those misconceptions. The differences between overall FCI scores at the three institutions could be explained by the relative populations of the three clusters.

Traditionally, scholars in physics education research have focused on students solving well-structured learning activities at the university. However, due to their constrained nature, these problems hinder collaboration and idea generation. In order to encourage student collaboration and decision making demands among undergraduate students in an introductory physics course, we utilized a real-world problem where groups were asked to compose a well-structured physics problem for younger learners. In this study we explored how they collaborated in composing physics problems. Data collection consisted of audio recording of the group discussions while they were collaborating to develop their physics problems and their respective problem solutions. Through interviews, we accessed participants’ perceptions of the task and related challenges. Results suggest that composing problems is an opportunity for participants to propose ideas and make decisions regarding the goals of the problem, concepts and procedures, contextual details, and magnitudes and units to introduce in their activities. Further, participants valued the open-ended nature of the task and recognized its benefits in utilizing physics ideas into context, which in turn enabled collaboration in a way not experienced by them with traditional well-structured problems. These findings shed light on the nature of composing physics problems in undergraduate courses, where participants assume a different role by facing a real-world activity that encourages expertise through physics-related communication and writing.

Omitted variable bias occurs in most statistical models. Whenever a confounding variable that is correlated with both dependent and independent variables is omitted from a statistical model, estimated effects of included variables are likely to be biased due to omitted variables. This issue is particularly problematic in physics education research where many research studies are quasiexperimental or observational in nature due to ethical and logistical limitations. In this paper, we illustrate the mechanisms behind omitted variable bias in explanatory modeling using authentic data and analytical solutions. We demonstrate that omitting confounding variables that are strongly correlated with included variables and have large effects on the dependent variable can significantly bias estimated effects for included variables. We also find that controlling for variables that are uncorrelated with other variables or have no effect on the dependent variable does not appreciably bias estimated effects and may or may not affect the precision of those estimates. These results suggest that removing from explanatory models variables that are not “statistically significant” can have unintended consequences on model and variable interpretations. Our results underscore the importance of carefully considering why or why not to include a variable in a model, informed by both data and theory.

The test of understanding graphs in kinematics (TUG-K) has widely been used to assess students’ understanding of this subject. The TUG-K poses different objectives to the test takers such as (1) the selection of a graph from a textual description, (2) the selection of corresponding graphs, and (3) the selection of a textual description from a graph. Whether test takers follow these task requirements is usually inferred from evaluating the test scores as correct or incorrect, yet the process of how students actually interact with the different tasks remains unknown. Recent studies have shown that eye tracking can provide rich insight into student’s interaction with multiple-choice tasks. In the current work, we analyzed the eye movement patterns of $N=115$ high school students while solving the TUG-K. Each question was divided into a question area (Q) and an option area (O), then gaze transitions between Q and O and between different options were calculated. A cluster analysis using the transition metrics revealed three item groups, containing the aforementioned objectives of the items. The clusters remain stable for different subsamples of our dataset, for instance, considering only the correct or only the incorrect responses, or considering high- or low-confidence responses. We conclude that eye movements can reflect task demands on a procedural level well beyond the classical methods of evaluating test scores, eventually making eye tracking an additional method for item analysis that can be utilized to confirm or explore test and item structures.