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.

Prior research suggests that introductory physics students have difficulty with graphing and interpreting graphs. Here, we discuss an investigation of student difficulties in translating between mathematical and graphical representations for a problem in electrostatics and the effect of increasing levels of scaffolding on students’ representational consistency. Students in calculus-based introductory physics were given a typical problem that can be solved using Gauss’s law involving a spherically symmetric charge distribution in which they were asked to write a mathematical expression for the electric field in various regions and then plot the electric field. In study 1, we found that students had great difficulty in plotting the electric field as a function of the distance from the center of the sphere consistent with the mathematical expressions in various regions, and interviews with students suggested possible reasons which may account for this difficulty. Therefore, in study 2, we designed two scaffolding interventions with levels of support which built on each other (i.e., the second scaffolding level built on the first) in order to help students plot their expressions consistently and compared the performance of students provided with scaffolding with a comparison group which was not given any scaffolding support. Analysis of student performance with different levels of scaffolding reveals that scaffolding from an expert perspective beyond a certain level may sometimes hinder student performance and students may not even discern the relevance of the additional support. We provide possible interpretations for these findings based on in-depth, think-aloud student interviews.

Promoting positive attitudes about science among teachers has important implications for teachers’ classroom practice and for their relationship to science as a discipline. In this paper, we report positive shifts in teachers’ attitudes about science, as measured by the Colorado Learning Attitudes about Science (CLASS) survey, over the course of their participation in a professional development course that emphasized the flexible use of energy representations to understand real world scenarios. Our work contributes to the larger effort to make the case that professional development matters for teacher learning and attitudes.

Problem-solving strategies learned by physics undergraduates should prepare them for real-world contexts as they transition from students to professionals. Yet, graduate students in physics-intensive research face problems that go beyond problem sets they experienced as undergraduates and are solved by different strategies than are typically learned in undergraduate coursework. This paper expands the notion of problem solving by characterizing the breadth of problems and problem-solving processes carried out by graduate students in physics-intensive research. We conducted semi-structured interviews with ten graduate students to determine the routine, difficult, and important problems they engage in and problem-solving strategies they found useful in their research. A qualitative typological analysis resulted in the creation of a three-dimensional framework: context, activity, and feature (that made the problem challenging). Problem contexts extended beyond theory and mathematics to include interactions with lab equipment, data, software, and people. Important and difficult contexts blended social and technical skills. Routine problem activities were typically well defined (e.g., troubleshooting), while difficult and important ones were more open ended and had multiple solution paths (e.g., evaluating options). In addition to broadening our understanding of problems faced by graduate students, our findings explore problem-solving strategies (e.g., breaking down problems, evaluating options, using test cases or approximations) and characteristics of successful problem solvers (e.g., initiative, persistence, and motivation). Our research provides evidence of the influence that problems students are exposed to have on the strategies they use and learn. Using this evidence, we have developed a preliminary framework for exploring problems from the solver’s perspective. This framework will be examined and refined in future work. Understanding problems graduate students face and the strategies they use has implications for improving how we approach problem solving in undergraduate physics and physics education research.

A body of research on physics problem solving has focused on single-concept problems. In this study we use “synthesis problems” that involve multiple concepts typically taught in different chapters. We use two types of synthesis problems, sequential and simultaneous synthesis tasks. Sequential problems require a consecutive application of fundamental principles, and simultaneous problems require a concurrent application of pertinent concepts. We explore students’ conceptual performance when they solve quantitative synthesis problems with varying mathematical complexity. Conceptual performance refers to the identification, follow-up, and correct application of the pertinent concepts. Mathematical complexity is determined by the type and the number of equations to be manipulated concurrently due to the number of unknowns in each equation. Data were collected from written tasks and individual interviews administered to physics major students ($N=179$) enrolled in a second year mechanics course. The results indicate that mathematical complexity does not impact students’ conceptual performance on the sequential tasks. In contrast, for the simultaneous problems, mathematical complexity negatively influences the students’ conceptual performance. This difference may be explained by the students’ familiarity with and confidence in particular concepts coupled with cognitive load associated with manipulating complex quantitative equations. Another explanation pertains to the type of synthesis problems, either sequential or simultaneous task. The students split the situation presented in the sequential synthesis tasks into segments but treated the situation in the simultaneous synthesis tasks as a single event.

A two-tier instrument for representational competence in the field of kinematics (KiRC) is presented, designed for a standard (1st year) calculus-based introductory mechanics course. It comprises 11 multiple choice (MC) and 7 multiple true-false (MTF) questions involving multiple representational formats, such as graphs, pictures, and formal (mathematical) expressions (1st tier). Furthermore, students express their answer confidence for selected items, providing additional information (2nd tier). Measurement characteristics of KiRC were assessed in a validation sample (pre- and post-test, $N=83$ and $N=46$, respectively), including usefulness for measuring learning gain. Validity is checked by interviews and by benchmarking KiRC against related measures. Values for item difficulty, discrimination, and consistency are in the desired ranges; in particular, a good reliability was obtained ($\mathrm{KR}20=0.86$). Confidence intervals were computed and a replication study yielded values within the latter. For practical and research purposes, KiRC as a diagnostic tool goes beyond related extant instruments both for the representational formats (e.g., mathematical expressions) and for the scope of content covered (e.g., choice of coordinate systems). Together with the satisfactory psychometric properties it appears a versatile and reliable tool for assessing students’ representational competency in kinematics (and of its potential change). Confidence judgments add further information to the diagnostic potential of the test, in particular for representational misconceptions. Moreover, we present an analytic result for the question—arising from guessing correction or educational considerations—of how the total effect size (Cohen’s $d$) varies upon combination of two test components with known individual effect sizes, and then discuss the results in the case of KiRC (MC and MTF combination). The introduced method of test combination analysis can be applied to any test comprising two components for the purpose of finding effect size ranges.

In physics education research it has been common to interpret student errors on conceptual questions in topic-specific ways, rather than in terms of general perceptual or reasoning difficulties. This paper examines two alternative accounts for responses to questions related to the concept of center of mass. In one account, difficulties are said to be perceptual in nature; in the other, difficulties are said to be tightly linked to the concepts in question. Hypotheses derived from the former perspective are tested in studies conducted among university students in introductory physics courses. The results do not provide strong support for the perceptual hypothesis; in fact, there is evidence that performance on perception tasks may be influenced by subjects’ ideas about the physical scenario. While the results do not provide general support for one perspective versus the other, the paper serves as an illustration of the type of investigation needed to develop the kind of rich representation of student thinking that will allow instructional resources to be most effectively targeted.

Language ambiguities in concept meanings can exacerbate student learning difficulties and conceptual understanding of physics concepts. This is especially true for the concept of “weight,” which has multiple meanings in both scientific and everyday usage. The term weight has been defined in several different ways, with nuances, but in textbooks and teaching the term is almost always defined in one of two ways: operationally either as the contact force between an object and a measuring scale or as the gravitational force on an object due to some other body such as Earth. The use of the same name for different concepts leads to much confusion, especially in accelerating situations, and to conflicting notions of “weightlessness” in free fall situations. In the present paper, we share an innovative approach that initially avoids the term weight entirely while teaching the physics of each situation, and then teaches the language ambiguities explicitly. We developed an instructional module with this approach and implemented it over two terms in three sections of an introductory physics course for preservice elementary teachers. Learning gains for content understanding were assessed using pretests and post-tests. Participants achieved remarkably high gains for both static and accelerating situations. Surveys pre- and postinstruction showed substantially improved appreciation of language issues and ambiguities associated with weight, weightlessness, and free fall. Interviews with instructors teaching the module provided additional insight into the advantages and teaching demands of the new approach.

Instructional labs are widely seen as a unique, albeit expensive, way to teach scientific content. We measured the effectiveness of introductory lab courses at achieving this educational goal across nine different lab courses at three very different institutions. These institutions and courses encompassed a broad range of student populations and instructional styles. The nine courses studied had two key things in common: the labs aimed to reinforce the content presented in lectures, and the labs were optional. By comparing the performance of students who did and did not take the labs (with careful normalization for selection effects), we found universally and precisely no added value to learning course content from taking the labs as measured by course exam performance. This work should motivate institutions and departments to reexamine the goals and conduct of their lab courses, given their resource-intensive nature. We show why these results make sense when looking at the comparative mental processes of students involved in research and instructional labs, and offer alternative goals and instructional approaches that would make lab courses more educationally valuable.

This study examines the causal reasoning that university students use to explain how dc circuits work. We analyze how students use the concepts of electric field and potential difference in their explanatory models of dc circuits, and what kinds of reasoning they use at the macroscopic and microscopic levels in their explanations. This knowledge is essential to help instructors design and implement new teaching approaches that encourage students to articulate the macroscopic and microscopic levels of description. A questionnaire with an emphasis on explanations was used to analyze students’ reasoning. In this analysis of students’ reasoning in the microscopic and macroscopic modeling processes in a dc circuit, we refer to epistemological studies of scientific explanations. We conclude that the student explanations fall into three main categories of reasoning. The vast majority of students employ an explanatory model based on simple or linear causality and on relational reasoning. Moreover, around a third of students use a relational reasoning that relates two magnitudes current and resistance or conductivity of the material, which is included in a macroscopic explanatory model based on Ohm’s law and the conservation of the current. In addition, few students situate the explanations at the microscopic level (charges or electrons) with unidirectional cause-effect reasoning. This study looks at a number of aspects that have been little mentioned in previous research at the university level, about the reasoning types students use when establishing macro-micro relationships and some possible difficulties with complex reasoning.

As research-based, self-paced electronic learning tools become increasingly available, a critical issue educators encounter is implementing strategies to ensure that all students engage with them as intended. Here, we first discuss the effectiveness of electronic learning tutorials as self-paced learning tools in large enrollment brick and mortar introductory physics courses and then propose a framework for helping students engage effectively with the learning tools. The tutorials were developed via research in physics education and were found to be effective for a diverse group of introductory physics students in one-on-one implementation. Instructors encouraged the use of these tools in a self-paced learning environment by telling students that they would be helpful for solving the assigned homework problems and that the underlying physics principles in the tutorial problems would be similar to those in the in-class quizzes (which we call paired problems). We find that many students in the courses in which these interactive electronic learning tutorials were assigned as a self-study tool performed poorly on the paired problems. In contrast, a majority of student volunteers in one-on-one implementation greatly benefited from the tutorials and performed well on the paired problems. The significantly lower overall performance on paired problems administered as an in-class quiz compared to the performance of student volunteers who used the research-based tutorials in one-on-one implementation suggests that many students enrolled in introductory physics courses did not effectively engage with the tutorials outside of class and may have only used them superficially. The findings suggest that many students in need of out-of-class remediation via self-paced learning tools may have difficulty motivating themselves and may lack the self-regulation and time-management skills to engage effectively with tools specially designed to help them learn at their own pace. We conclude by proposing a theoretical framework to help students with diverse prior preparations engage effectively with self-paced learning tools.