The Force Concept Inventory is one of the most popular and most analyzed multiple-choice concept tests used to investigate students’ understanding of Newtonian mechanics. The correct answers poll a set of underlying Newtonian concepts and the coherence of these underlying concepts has been found in the data. However, this inventory was constructed after several years of research into the common preconceptions held by students and using these preconceptions as distractors in the questions. Their sole purpose is to deflect non-Newtonian candidates away from the correct answer. Alternatively, one can argue that the responses could also be treated as polling these preconceptions. In this paper we shift the emphasis of the analysis away from the correlation structure of the correct answers and look at the latent traits underlying the incorrect responses. Our analysis models the data employing exploratory factor analysis, which uses regularities in the data to suggest the existence of underlying structures in the cognitive processing of the students. This analysis allows us to determine whether the data support the claim that there are alternate non-Newtonian worldviews on which students’ incorrect responses are based. The existence of such worldviews, and their coherence, could explain the resilience of non-Newtonian preconceptions and would have significant implications to the design of instruction methods. We find that there are indeed coherent alternate conceptions of the world which can be categorized using the results of the research that led to the construction of the Force Concept Inventory.

The resources framework provides a useful and generative model of student thinking and learning. In particular, it suggests various strategies for instruction such as priming resources and refining intuition that allow students to build on knowledge they already have. In this paper, we describe the affordances of the resources framework in guiding the design, assessment, and refinement of interventions on pressure in fluids. This perspective kept us alert for cognitive resources on which students could build a deeper understanding and encouraged us to model student thinking as complex and context dependent, even on this narrow topic. This framework also facilitated a focus on evidence of productivity in student work as an alternative assessment to conceptual pre- and post testing.

Research on student epistemologies in introductory courses has highlighted the importance of understanding physics as “a refinement of everyday thinking” [A. Einstein, J. Franklin Inst. 221, 349 (1936)]. That view is difficult to sustain in quantum mechanics, for students as for physicists. How might students manage the transition? In this article, we present a case study of a graduate student’s approaches and reflections on learning over two semesters of quantum mechanics, based on a series of nine interviews. We recount his explicit grappling with the shift in epistemology from classical to quantum, and we argue that his success in learning largely involved his framing mathematics as expressing physical meaning. At the same time, we show he was not entirely stable in these framings, shifting away from them in particular during his study of scattering. The case speaks to literature on students’ epistemologies, with respect to the roles of everyday thinking and mathematics. We discuss what this case suggests for further research, with possible implications for instruction.

Learning quantum mechanics is challenging, even for upper-level undergraduate and graduate students. Research-validated interactive tutorials that build on students’ prior knowledge can be useful tools to enhance student learning. We have been investigating student difficulties with quantum mechanics pertaining to the double-slit experiment in various situations that appear to be counterintuitive and contradict classical notions of particles and waves. For example, if we send single electrons through the slits, they may behave as a “wave” in part of the experiment and as a “particle” in another part of the same experiment. Here we discuss the development and evaluation of a research-validated Quantum Interactive Learning Tutorial (QuILT) which makes use of an interactive simulation to improve student understanding of the double-slit experiment and strives to help students develop a good grasp of foundational issues in quantum mechanics. We discuss common student difficulties identified during the development and evaluation of the QuILT and analyze the data from the pretest and post test administered to the upper-level undergraduate and first-year physics graduate students before and after they worked on the QuILT to assess its effectiveness. These data suggest that on average, the QuILT was effective in helping students develop a more robust understanding of foundational concepts in quantum mechanics that defy classical intuition using the context of the double-slit experiment. Moreover, upper-level undergraduates outperformed physics graduate students on the post test. One possible reason for this difference in performance may be the level of student engagement with the QuILT due to the grade incentive. In the undergraduate course, the post test was graded for correctness while in the graduate course, it was only graded for completeness.

We propose a framework for improving accuracy, fluency, and retention of basic skills essential for solving problems relevant to STEM introductory courses, and implement the framework for the case of basic vector math skills over several semesters in an introductory physics course. Using an iterative development process, the framework begins with a careful identification of target skills and the study of specific student difficulties with these skills. It then employs computer-based instruction, immediate feedback, mastery grading, and well-researched principles from cognitive psychology such as interleaved training sequences and distributed practice. We implemented this with more than 1500 students over 2 semesters. Students completed the mastery practice for an average of about $13\min /\mathrm{week}$, for a total of about 2–3 h for the whole semester. Results reveal large ($>1\mathrm{SD}$) pretest to post-test gains in accuracy in vector skills, even compared to a control group, and these gains were retained at least 2 months after practice. We also find evidence of improved fluency, student satisfaction, and that awarding regular course credit results in higher participation and higher learning gains than awarding extra credit. In all, we find that simple computer-based mastery practice is an effective and efficient way to improve a set of basic and essential skills for introductory physics.

There is considerable long-term interest in understanding the dynamics of collaboration networks, and how these networks form and evolve over time. Most of the work done on the dynamics of social networks focuses on well-established communities. Work examining emerging social networks is rarer, simply because data are difficult to obtain in real time. In this paper, we use thirty years of data from an emerging scientific community to look at that crucial early stage in the development of a social network. We show that when the field was very young, islands of individual researchers labored in relative isolation, and the coauthorship network was disconnected. Thirty years later, rather than a cluster of individuals, we find a true collaborative community, bound together by a robust collaboration network. However, this change did not take place gradually—the network remained a loose assortment of isolated individuals until the mid 2000s, when those smaller parts suddenly knit themselves together into a single whole. In the rest of this paper, we consider the role of three factors in these observed structural changes: growth, changes in social norms, and the introduction of institutions such as field-specific conferences and journals. We have data from the very earliest years of the field, a period which includes the introduction of two different institutions: the first field-specific conference, and the first field-specific journals. We also identify two relevant behavioral shifts: a discrete increase in coauthorship coincident with the first conference, and a shift among established authors away from collaborating with outsiders, towards collaborating with each other. The interaction of these factors gives us insight into the formation of collaboration networks more broadly.

At large research universities, physics graduate teaching assistants (TAs) are often responsible for grading in courses at all levels. However, few studies have focused on TAs’ grading practices in introductory and advanced physics courses. This study was designed to investigate whether physics graduate TAs grade students in introductory physics and quantum mechanics using different criteria and if so, why they may be inclined to do so. To investigate possible discrepancies in TAs’ grading approaches in courses at different levels, we implemented a sequence of instructional activities in a TA professional development course that asked TAs to grade student solutions of introductory physics and upper-level quantum mechanics problems and explain why, if at all, their grading approaches were different or similar in the two contexts. We analyzed the differences in TAs’ grading approaches in the two contexts and discuss the reasons they provided for the differences in their grading approaches in introductory physics and quantum mechanics in individual interviews, class discussions, and written responses. We find that a majority of the TAs graded solutions to quantum mechanics problems differently than solutions to introductory physics problems. In quantum mechanics, the TAs focused more on physics concepts and reasoning and penalized students for not showing evidence of understanding. The findings of the study have implications for TA professional development programs, e.g., the importance of helping TAs think about the difficulty of a problem from an introductory students’ perspective and reflecting on the benefits of formative assessment.

In this study, we explore the strategic self-regulatory and motivational characteristics of students in studio-mode physics courses at three universities with varying student populations and varying levels of success in their studio-mode courses. We survey students using questions compiled from several existing questionnaires designed to measure students’ study strategies, attitudes toward and motivations for learning physics, organization of scientific knowledge, experiences outside the classroom, and demographics. Using a person-centered approach, we utilize cluster analysis methods to group students into learning profiles based on their individual responses to better understand the strategies and motives of algebra-based studio physics students. Previous studies have identified five distinct learning profiles across several student populations using similar methods. We present results from first-semester and second-semester studio-mode introductory physics courses across three universities. We identify these five distinct learning profiles found in previous studies to be present within our population of introductory physics students. In addition, we investigate interactions between these learning profiles and student demographics. We find significant interactions between a student’s learning profile and their experience with high school physics, major, gender, grade expectation, and institution. Ultimately, we aim to use this method of analysis to take the characteristics of students into account in the investigation of successful strategies for using studio methods of physics instruction within and across institutions.

Reliable and validated assessments of introductory physics have been instrumental in driving curricular and pedagogical reforms that lead to improved student learning. As part of an effort to systematically improve our sophomore-level classical mechanics and math methods course (CM 1) at CU Boulder, we have developed a tool to assess student learning of CM 1 concepts in the upper division. The Colorado Classical Mechanics and Math Methods Instrument (CCMI) builds on faculty consensus learning goals and systematic observations of student difficulties. The result is a 9-question open-ended post test that probes student learning in the first half of a two-semester classical mechanics and math methods sequence. In this paper, we describe the design and development of this instrument, its validation, and measurements made in classes at CU Boulder and elsewhere.

Single photon experiments involving a Mach-Zehnder interferometer can illustrate the fundamental principles of quantum mechanics, e.g., the wave-particle duality of a single photon, single photon interference, and the probabilistic nature of quantum measurement involving single photons. These experiments explicitly make the connection between the abstract quantum theory and concrete laboratory settings and have the potential to help students develop a solid grasp of the foundational issues in quantum mechanics. Here we describe students’ conceptual difficulties with these topics in the context of Mach-Zehnder interferometer experiments with single photons and how the difficulties found in written surveys and individual interviews were used as a guide in the development of a Quantum Interactive Learning Tutorial (QuILT). The QuILT uses an inquiry-based approach to learning and takes into account the conceptual difficulties found via research to help upper-level undergraduate and graduate students learn about foundational quantum mechanics concepts using the concrete quantum optics context. It strives to help students learn the basics of quantum mechanics in the context of single photon experiment, develop the ability to apply fundamental quantum principles to experimental situations in quantum optics, and explore the differences between classical and quantum ideas in a concrete context. We discuss the findings from in-class evaluations suggesting that the QuILT was effective in helping students learn these abstract concepts.

Developing critical thinking skills is a common goal of an undergraduate physics curriculum. How do students make sense of evidence and what do they do with it? In this study, we evaluated students’ critical thinking behaviors through their written notebooks in an introductory physics laboratory course. We compared student behaviors in the Structured Quantitative Inquiry Labs (SQILabs) curriculum to a control group and evaluated the fragility of these behaviors through procedural cueing. We found that the SQILabs were generally effective at improving the quality of students’ reasoning about data and making decisions from data. These improvements in reasoning and sensemaking were thwarted, however, by a procedural cue. We describe these changes in behavior through the lens of epistemological frames and task orientation, invoked by the instructional moves.

The kinematics concept test (KCT) is a multiple-choice test designed to evaluate students’ conceptual understanding of kinematics at the high school level. The test comprises 49 multiple-choice items about velocity and acceleration, which are based on seven kinematic concepts and which make use of three different representations. In the first part of this article we describe the development and the validation process of the KCT. We applied the KCT to 338 Swiss high school students who attended traditional teaching in kinematics. We analyzed the response data to provide the psychometric properties of the test. In the second part we present the results of a structural analysis of the test. An exploratory factor analysis of 664 student answers finally uncovered the seven kinematics concepts as factors. However, the analysis revealed a hierarchical structure of concepts. At the higher level, mathematical concepts group together, and then split up into physics concepts at the lower level. Furthermore, students who seem to understand a concept in one representation have difficulties transferring the concept to similar problems in another representation. Both results have implications for teaching kinematics. First, teaching mathematical concepts beforehand might be beneficial for learning kinematics. Second, instructions have to be designed to teach students the change between different representations.

This study analyzes the types of peer discussion that occur during lecture-based tutorial sessions. It focuses in particular on whether discussions of this kind have certain characteristics that might indicate success in the post-testing phase. The data were collected during an introductory physics course. The main data set was gathered with the aid of audio recordings. Data-driven content analysis was applied in the analysis to facilitate the placement of students’ discussions in particular categories related to different types of discussions. Four major discussion types were found: discussions related to the content knowledge, metalevel discussions including metaconceptual and metacognitive elements, discussions related to practical issues, and creating a base for discussion, seen here in the order of their prevalence. These categories were found to possess individual substructures that involved, for example, asking and answering questions, participating in a dialogue, or disagreeing with a peer. Analyzing the substructures of the categories revealed that there were evident differences between the groups, some of them related to the group size. With regard to the characteristics of discussions considered to be connected to a better learning outcome, it was observed that a great number of lines uttered related to the physics content or metalevel discussions seemed to have a direct bearing on success in the post test at the group level. For individual students, answering content-related questions posed by their peers might also indicate success in the post test. We would encourage researchers to continue this type of research in order to discover the essential characteristics of students’ discussions that facilitate learning.

Increasing student retention (successfully finishing a particular course) and persistence (continuing through a sequence of courses or the major area of study) is currently a major challenge for universities. While students’ academic and social integration into an institution seems to be vital for student retention, research into the effect of interpersonal interactions is rare. We use network analysis as an approach to investigate academic and social experiences of students in the classroom. In particular, centrality measures identify patterns of interaction that contribute to integration into the university. Using these measures, we analyze how position within a social network in a Modeling Instruction (MI) course—an introductory physics course that strongly emphasizes interactive learning—predicts their persistence in taking a subsequent physics course. Students with higher centrality at the end of the first semester of MI are more likely to enroll in a second semester of MI. Moreover, we found that chances of successfully predicting individual student’s persistence based on centrality measures are fairly high—up to 75%, making the centrality a good predictor of persistence. These findings suggest that increasing student social integration may help in improving persistence in science, technology, engineering, and mathematics fields.

Electromagnetic induction is an important, yet complex, physics topic that is a part of Croatian high school curriculum. Nine Croatian high school students of different abilities in physics were interviewed using six demonstration experiments from electromagnetism (three of them concerned the topic of electromagnetic induction). Students were asked to observe, describe, and explain the experiments. The analysis of students’ explanations indicated the existence of many conceptual and reasoning difficulties with the basic concepts of electromagnetism, and especially with recognizing and explaining the phenomenon of electromagnetic induction. Three student mental models of electromagnetic induction, formed during the interviews, which reoccurred among students, are described and analyzed within the knowledge-in-pieces framework.

Understanding the mechanisms of increasing the number of physics teachers educated per year at institutions with thriving physics teacher preparation programs may inspire and support other institutions in building thriving programs of their own. The Physics Teacher Education Coalition (PhysTEC), led by the American Physical Society (APS) and the American Association of Physics Teachers (AAPT), has supported transformation of physics teacher preparation programs at a number of institutions around the country for over a decade. In 2012–2013, PhysTEC supported an independent study on the sustainability of its sites after project funding ends. The study sought to measure the extent to which programs have been sustained and to identify what features should be prioritized for building sustainable physics teacher preparation programs. Most of the studied sites have sustained increases in the number of physics teachers educated per year as well as funding for physics teacher preparation. About half of the programs are thriving, in that in the post-award period, they have further increased both the number of physics teachers educated per year and funding for physics teacher preparation. All studied sites that sustained increases in the number of physics teachers educated per year have two features in common: a champion of physics teacher education and institutional commitment. The thriving physics teacher preparation programs in this study implemented different elements of physics teacher preparation according to diverse local priorities and opportunities, including the unique expertise of local personnel.

Previous research on problem diagrams suggested that including a supportive diagram, one that does not provide necessary problem solving information, may bring little, or even negative, benefit to students’ problem solving success. We tested the usefulness of problem diagrams on 12 different physics problems (6A/B experiments) in our massive open online course. By analyzing over 8000 student responses in total, we found that including a problem diagram that contains no significant additional information only slightly improves the first attempt correct rate for the few most spatially complex problems, and has little impact on either the final correct percentage or the time spent on solving the problem. On the other hand, in half of the cases, removing the diagram significantly increased the fraction of students’ drawing their own diagrams during problem solving. The increase in drawing behavior is largely independent of students’ physics abilities. In summary, our results suggest that for many physics problems, the benefit of a diagram is exceedingly small and may not justify the effort of creating one.

This study presents a review of the current state of research on teaching quantum mechanics in secondary and lower undergraduate education. A conceptual approach to quantum mechanics is being implemented in more and more introductory physics courses around the world. Because of the differences between the conceptual nature of quantum mechanics and classical physics, research on misconceptions, testing, and teaching strategies for introductory quantum mechanics is needed. For this review, 74 articles were selected and analyzed for the misconceptions, research tools, teaching strategies, and multimedia applications investigated. Outcomes were categorized according to their contribution to the various subtopics of quantum mechanics. Analysis shows that students have difficulty relating quantum physics to physical reality. It also shows that the teaching of complex quantum behavior, such as time dependence, superposition, and the measurement problem, has barely been investigated for the secondary and lower undergraduate level. At the secondary school level, this article shows a need to investigate student difficulties concerning wave functions and potential wells. Investigation of research tools shows the necessity for the development of assessment tools for secondary and lower undergraduate education, which cover all major topics and are suitable for statistical analysis. Furthermore, this article shows the existence of very diverse ideas concerning teaching strategies for quantum mechanics and a lack of research into which strategies promote understanding. This article underlines the need for more empirical research into student difficulties, teaching strategies, activities, and research tools intended for a conceptual approach for quantum mechanics.

Physics laboratory courses have been generally acknowledged as an important component of the undergraduate curriculum, particularly with respect to developing students’ interest in, and understanding of, experimental physics. There are a number of possible learning goals for these courses including reinforcing physics concepts, developing laboratory skills, and promoting expertlike beliefs about the nature of experimental physics. However, there is little consensus among instructors and researchers interested in the laboratory learning environment as to the relative importance of these various learning goals. Here, we contribute data to this debate through the analysis of students’ responses to the laboratory-focused assessment known as the Colorado Learning Attitudes about Science Survey for Experimental Physics (E-CLASS). Using a large, national data set of students’ responses, we compare students’ E-CLASS performance in classes in which the instructor self-reported focusing on developing skills, reinforcing concepts, or both. As the classification of courses was based on instructor self-report, we also provide additional description of these courses with respect to how often students engage in particular activities in the lab. We find that courses that focus specifically on developing lab skills have more expertlike postinstruction E-CLASS responses than courses that focus either on reinforcing physics concepts or on both goals. Within first-year courses, this effect is larger for women. Moreover, these findings hold when controlling for the variance in postinstruction scores that is associated with preinstruction E-CLASS scores, student major, and student gender.