Quantum mechanics is a notoriously counterintuitive subject within physics and has been the subject of a number of studies at the undergraduate level, and a few pioneering studies at the graduate level. The sketching of wave functions in a confining well is in one sense one of the most basic activities in quantum mechanics. But in another sense, it may be viewed as a rather advanced skill, as it requires the coherent inclusion of a number of details of the wave function, such as wavelength, probability amplitude, and boundary conditions, among others. Although sketching a wave function is not a common activity at the graduate level, a great deal of graduate work is concerned with the aforementioned details, especially boundary conditions. Whether it is seen as a basic skill, or as linked to higher-level understanding, sketching a wave function is an ability that physics graduate students should have. Here, we report on graduate students’ ability to sketch wave functions in an asymmetric potential well. We find that the frequency of many errors is not significantly reduced from pretest to posttest, meaning that many errors persist through to the end of graduate quantum mechanics instruction. We find that only 5% of graduate students tested can sketch the 2nd excited state wave function without errors. We include quantitative and diagrammatic descriptions of student errors covering a broader range of misunderstandings than has previously been identified, and we include interview information that speaks to the persistence of some of the errors.

Mathematical reasoning with algebraic and geometric representations is essential for success in upper-division and graduate-level physics courses. Complex algebra requires student to fluently move between algebraic and geometric representations. By designing a task for middle-division physics students to translate a geometric representation to several algebraic representations, we identified students’ facilities and difficulties with complex number algebra. Students were successful when they isolated approaches, which was characterized by students’ use of circle trigonometry, triangle trigonometry, the Pythagorean theorem, and the square of the norm approaches. When students were not successful, they inappropriately mixed approaches to the problem, including failing to distinguish between triangle and circle trigonometry.

We present the design, statistical analysis, and validation of a questionnaire to assess students’ knowledge about basic aspects of quantum mechanics (QM). The QM evaluation (QME) is a true-false and multiple-choice mixed questionnaire that features 10 two-tier items spanning three relevant themes in quantum mechanics: wave behavior of matter, measurement, and atoms and electrons behavior. Its validity was assessed through a pilot administration to students and interviews with course instructors. We checked its internal consistency using both classic test theory and Rasch analysis to account for the different difficulty of each tier and for different scoring methods of the items. The questionnaire was administered to about 450 undergraduate physics students and high school physics teachers. Data show that it is a reliable instrument and all items have a good discriminatory power. Since the test does not require an advanced mathematical knowledge, it ideally lends itself to probe students’ knowledge about quantum mechanics in a variety of university courses, from the introductory ones to those more formal and mathematically oriented.

A considerable body of research shows that individuals who demonstrate a wide variety of metacognitive skills perform better on scientific problem solving. We developed a way of implementing homework in an undergraduate physics course to promote metacognitive skills. This novel homework design includes both an individual and a team phase and was implemented in a team-based learning environment. We developed a coding table to conduct both qualitative and quantitative analyses of students’ expressions of metacognitive thinking. Results indicate that students’ expressions of metacognitive thinking improved during the term. Data also show that team discussion helps improve metacognitive skills.

Introductory physics lab instruction is undergoing a transformation, with increasing emphasis on developing experimentation and critical thinking skills. These changes present a need for standardized assessment instruments to determine the degree to which students develop these skills through instructional labs. In this article, we present the development and validation of the physics lab inventory of critical thinking (PLIC). We define critical thinking as the ability to use data and evidence to decide what to trust and what to do. The PLIC is a 10-question, closed-response assessment that probes student critical thinking skills in the context of physics experimentation. Using interviews and data from 5584 students at 29 institutions, we demonstrate, through qualitative and quantitative means, the validity and reliability of the instrument at measuring student critical thinking skills. This establishes a valuable new assessment instrument for instructional labs.

In this paper, we present a case study of a pair of students as they use nondisciplinary communicative practices to mechanistically reason about binary star dynamics. To do so, we first review and bring together the theoretical perspectives of social semiotics and embodied cognition, therein developing a new methodological approach for analyzing student interactions during the learning of physics (particularly for those interactions involving students’ bodies). Through the use of our new approach, we are able to show how students combine a diverse range of meaning-making resources into complex, enacted analogies, thus forming explanatory models that are grounded in embodied intuition. We reflect on how meaning-making resources—even when not physically persistent—can act as coordinating hubs for other resources as well as how we might further nuance the academic conversation around the role of the body in physics learning.

This theoretical paper introduces a new way to view and characterize learning astronomy. It describes a framework, based on results from empirical data, analyzed through standard qualitative research methodology, in which a theoretical model for a vital competency of learning astronomy is proposed: reading the sky, a broad description under with various skills and competencies are included. This model takes into account not only disciplinary knowledge but also disciplinary discernment and extrapolating three dimensionality. Together, these constitute the foundation for the competency referred to as reading the sky. In this paper, these competencies are described and discussed and merged to form a new framework vital for learning astronomy to better match the challenges students face when entering the discipline of astronomy.

Self-efficacy represents an individual’s belief that he or she can perform a particular task in a given domain. It is a strong predictor for performance and persistence in STEM education. Research shows that there is a large and persistent gender gap in student self-efficacy in STEM academic disciplines. In some cases, active teaching strategies have been shown to positively affect physics self-efficacy but it is unclear how this impact differs between men and women. In this study, we investigate the impact of a physics class taught with active teaching strategies on students’ self-reported physics self-efficacy and how this impact varies across gender lines. We measured the change in physics self-efficacy over four different dimensions; conceptual understanding, problem-solving, lab and hands-on activities, and collaborative work. We report three main findings. First, the initial physics self-efficacy gender gap disappeared by the end of the semester. Second, female students’ self-efficacy improved significantly, whereas there was no significant change in the self-efficacy of the male students. Third, the gender gaps in the conceptual understanding and problem-solving dimensions in particular, were significantly reduced. This study represents an initial step towards understanding the influence of active teaching strategies can have on reducing the self-efficacy gender gap.

Over the last decade, the “gender gap” in physics conceptual inventory scores has been extensively studied by the physics education research community. Researchers have identified many factors that influence the overall differences in post-test scores between men and women. More recently, it has been shown that the Force Concept Inventory (FCI) contains eight items that are substantially unfair; six are unfair to women, two are unfair to men. The Force and Motion Conceptual Evaluation (FMCE) and the Conceptual Survey of Electricity and Magnetism (CSEM), however, contain fewer unfair items. In this work, results from prior studies are used to further explore the gender gap in five large samples of conceptual inventory data: the FCI ($N_1=3663$), the FMCE ($N_2=2551$, $N_3=3719$), and the CSEM ($N_4=1767$, $N_5=2439$). The gender gap in these samples is partitioned into four components: the gender gap resulting from the student’s academic performance, the gender gap resulting from prior preparation in physics, the gender gap resulting from instrumental fairness, and the gender gap of students with equal academic performance and physics preparation on the fair instrument. For all samples, very little of the gender gap was explained by differences in academic performance between men and women, measured by ACT or SAT math percentile scores or physics test average. The percentage of the gender gap resulting from instrumental fairness varied across samples from 30% in the FCI to 2% to 6% in the CSEM. A substantial part of the gender gap in four of the five samples (30%–40%) was explained by differences in prior physics preparation, measured by pretest scores on the conceptual inventories. Further correcting for conceptual physics prior preparation using the post-test score in the previous class reduced gender differences substantially.

Secondary school level quantum physics (QP) courses have recently been implemented in the national curricula of many countries. QP gives opportunities to acquaint students with more recent physics and its applications and to discuss aspects of the nature of science. Research has shown that QP is a challenging area for students. Because the inclusion of QP in national curricula is rather new in most countries, it is interesting to compare QP curricula from these countries to make the choices by curriculum designers visible. In this study, we provide a detailed overview of QP courses from fifteen countries. We collected and analyzed official curriculum documents to identify key items present in most curricula. Our inventory identifies a shared current core curriculum of QP which contains the following seven main categories: discrete atomic energy levels, interactions between light and matter, wave-particle duality, de Broglie wavelength, technical applications, Heisenberg’s uncertainty principle, and the probabilistic nature of QP. We also found differences in the focus of the listed topics of certain countries, which indicate different views on teaching QP and might inspire curriculum designers struggling with QP. For instance, challenging items like QP interpretations or epistemological aspects of QP are taught only in a few countries. Although research suggests that epistemological aspects help students to comprehend novel QP concepts, many countries do not explicitly include these in the curriculum. We provide reasons and suggestions for this.

The Next Generation Science Standards (NGSS) provide a succession of objectives for energy learning and set an expectation for teachers to assess learners’ representations of energy in a variety of science contexts. To support teachers in evaluating the extent to which representations of energy display NGSS objectives, we have (i) discerned the constituent ideas that comprise the NGSS model of energy in the physical sciences and (ii) developed a checklist for assessing the extent to which an energy diagram provides evidence of the NGSS energy model. This energy diagram checklist is representation independent (so that diverse diagrams in a course may all be evaluated) and scenario independent (so that it can be applied throughout the physical science curriculum). We demonstrate the use of the checklist for assessing both pedagogical energy diagrams and learner-invented energy diagrams, including measuring a class’s increased facility with energy diagrams.

Physics education research (PER) has used quantitative modeling techniques to explore learning, affect, and other aspects of physics education. However, these studies have rarely examined the predictive output of the models, instead focusing on the inferences or causal relationships observed in various data sets. This research introduces a modern predictive modeling approach to the PER community using transcript data for students declaring physics majors at Michigan State University. Using a machine learning model, this analysis demonstrates that students who switch from a physics degree program to an engineering degree program do not take the third semester course in thermodynamics and modern physics, and may take engineering courses while registered as a physics major. Performance in introductory physics and calculus courses, measured by grade as well as a students’ declared gender and ethnicity play a much smaller role relative to the other features included in the model. These results are used to compare traditional statistical analysis to a more modern modeling approach.

The mindset literature is a longstanding area of psychological research focused on beliefs about intelligence, response to challenge, and goals for learning. However, the mindset literature’s applicability to the context of college physics has not been widely studied. In this paper we narrow our focus toward students’ descriptions of their responses to challenge in college physics. We ask the research question, “can we see responses to challenge in college physics that resemble that of the mindset literature?” In addressing this question, it is also necessary to ask, “how do students express evidence of challenge?” and “to what extent is this evidence similar or different to the mindset literature?” To answer these questions, we developed a novel coding scheme for interview dialogue around college physics challenge and students’ responses to it. In this paper we present the development process of our coding scheme. We find that it is possible to see student descriptions of their responses to challenge that resemble the mindset literature’s characterizations. However, college physics challenges are frequently different than those studied in the mindset literature. We show that, in the landscape of college physics challenges, mindset beliefs cannot always be considered to be the dominant factor in how students respond to challenge. Broadly, our coding scheme helps the field move beyond broad Likert-scale survey measures of students’ mindset beliefs.

The coordination of multiple external representations is important for learning, but yet a difficult task for students, requiring instructional support. The subject in this study covers a typical relation in physics between abstract mathematical equations (definitions of divergence and curl) and a visual representation (vector field plot). To support the connection across both representations, two instructions with written explanations, equations, and visual representations (differing only in the presence of visual cues) were designed and their impact on students’ performance was tested. We captured students’ eye movements while they processed the written instruction and solved subsequent coordination tasks. The results show that students instructed with visual cues (VC students) performed better, responded with higher confidence, experienced less mental effort, and rated the instructional quality better than students instructed without cues. Advanced eye-tracking data analysis methods reveal that cognitive integration processes appear in both groups at the same point in time but they are significantly more pronounced for VC students, reflecting a greater attempt to construct a coherent mental representation during the learning process. Furthermore, visual cues increase the fixation count and total fixation duration on relevant information. During problem solving, the saccadic eye movement pattern of VC students is similar to experts in this domain. The outcomes imply that visual cues can be beneficial in coordination tasks, even for students with high domain knowledge. The study strongly confirms an important multimedia design principle in instruction, that is, that highlighting conceptually relevant information shifts attention to relevant information and thus promotes learning and problem solving. Even more, visual cues can positively influence students’ perception of course materials.

We present an analysis of the in situ support provided to preservice physics teachers (PPTs) enrolled in a Methods for Teaching Physics course ($N=28$) at a research university, while working on the design of 20 lessons in mechanics and waves they taught later in the course. The PPTs submitted 4 evolving plans for each lesson, and received guidance and support in two consecutive consultation meetings on each lesson plan (30 min each), as well as written feedback via the course website. Using grounded theory methods, the analysis examines the interactions between instructors and preservice teachers over the evolving lesson plans as captured in the videos of the consultation meetings and written correspondence. We analyze the PPT-initiated and instructor-initiated concerns, guidance, and support to infer and unpack tacit professional knowledge, practices, and beliefs. The emergent categorization articulates the knowledge, practices, and beliefs that inform and guide the design of physics lessons that offer in-depth treatment of concepts, procedures, practices, and epistemological aspects of physics in an engaging and meaningful way for students, and foster active learning. The extent to which these categories are grounded in the discipline is discussed.

The ontologies students use—their conceptions about the nature of entities—impact the way they learn physics and reason through physics problems. We investigate students’ capacities for flexible use of ontologies in a modern physics context, focusing on students’ reasoning around two quantum entities (photons and electrons) for three canonical topics in introductory quantum physics (double slit experiment, Mach-Zehnder interferometer, and quantum tunneling). We present a description of a full framework to describe and distinguish between different kinds of dynamic ontologies. The framework identifies possible ontological structures in individual reasoning episodes, three of which we identify in our data set: unitary (applying a single stable ontology), parallel (switching back and forth between multiple ontologies), and blended (constructing a novel ontology by blending two or more input ontologies). These different ontological structures are applied to the specific ontologies used (e.g., wave or particle) for the specific entity (e.g., photon or electron). We demonstrate the utility of the framework by coding individual responses from a representative sample of an introductory modern physics course to an array of written and multiple-choice questions on homework, exams, and pre- and postsurveys. We present and explore the patterns of use of ontologies across the three topical contexts and these various modalities. We demonstrate that students use a variety of ontologies and ontological structures across entities and topic areas, even when not explicitly prompted to do so. In addition to providing evidence of students’ capacities for flexible use of ontologies, we find that the wording and framing of the question prompts impact students’ use of ontologies. Expanding on the aggregate data, we engage in analysis of a few notable examples to demonstrate how the wording, framing, and content of prompts can intersect to collectively impact students’ use of ontologies and ontological structures.

Implementing targeted instructional techniques requires an understanding of the initial alternative world views students possess. These alternative world views can be measured using validated conceptual inventories combined with factor analysis methodologies. Using exploratory factor analysis and network module analysis, Scott and Schumayer and Brewe, Bruun, and Bearden identified the most prevalent and “rigid” of these world views which remained in the postinstruction student responses to the Force Concept Inventory. This paper seeks to identify the alternative world views that exist for students before and after instruction through the use of factor analysis applied to pre- and postinstruction responses from 19 727 matched, student responses. Using the distractor taxonomy proposed by Hestenes, Wells, and Swackhamer, the prevalent alternative world views of these students are characterized and analyzed. We find that the pre-instruction and postinstruction coherent alternative world views are similar, suggesting they are learned by the students prior to instruction. Using a modified version of item response curves, it was found that the active force misconception is the most rigid of the misconceptions found pre- and postinstruction, and shows minor growth in these response rates at the end of instruction. The results of this study are consistent with what experienced instructors observe when determining what physics preconceptions incoming students have. This study’s agreement, combined with the results of Scott and Schumayer and Brewe, Bruun, and Bearden, strengthens the physics education research community’s suggestions for improving physics instruction when using only anecdotal or qualitative evidence.

Standardized concept inventories (CIs) have been widely used in science, technology, engineering, and mathematics education for assessment of student learning. In practice, there have been concerns regarding the length of the test and possible test-retest memory effect. To address these issues, a recent study developed a method to split a CI into two equivalent short CIs, which have been shown to provide equivalent mean score measures. However, the previous approach does not fully examine common requirements of test equating. This study extends the existing method with test equating analysis to form a revised algorithm for developing and validating equivalent short CIs. The method is applied to split the Conceptual Survey of Electricity and Magnetism (CSEM) into two half-length CSEMs (HCSEMs). Through a series of test-equating and validation analysis, the HCSEMs are confirmed to measure the same content clusters and the same construct of students’ understanding as that of the original CSEM at a similar level of reliability regarding their question design features. Furthermore, a best performing equating function to convert scores among the two HCSEMs and the CSEM is identified through comparisons of four commonly used equating functions. The conversions are further validated using the existing data sets as well as a data set collected from an empirical study using randomized testing. The results confirm that the three CIs can provide equivalent measures in different subpopulations. Overall, the results from this study have shown that the revised algorithm can provide a more complete framework in developing and validating equivalent short CIs. In addition, this method can also be applied to develop and validate parallel CIs in general.

Sexual harassment occurs more frequently in male-dominated fields and physics is a more male-dominated field than most other science, technology, engineering, and mathematics (STEM) fields. Thus, it is important to examine the occurrence and impact of sexual harassment on women in physics. A survey of undergraduate women, who attended a conference for undergraduate women in physics, revealed that approximately three quarters (74.3%; $338/455$) of survey respondents experienced at least one type of sexual harassment. This sample was recruited from a large fraction of undergraduate women in physics in the United States. We find that certain types of sexual harassment predict a negative sense of belonging and exacerbate the imposter phenomenon. The types of sexual harassment that predict these outcomes, both forms of gender harassment, while seemingly less severe types of harassment, have been found to have substantially negative personal and professional consequences. These findings are important since prior work has found that sense of belonging and the imposter phenomenon are related to students’ persistence in STEM fields. Our results have implications for understanding and improving persistence in physics by informing the community about the occurrence of sexual harassment and its effects so that we can begin to work towards reducing its occurrence and mitigating its effects.