The Force Concept Inventory was designed to poll the Newtonian conception of force. While there are many in-depth studies analyzing response data that look at the structure of the correct answers, we believe that the incorrect answers also carry revealing information about the students’ worldview. The inventory was originally designed so that the “distractors” in each question reflected commonly held misconceptions, and thus the rate at which students guess the correct answer is very low. Students select incorrect answers that correspond to the misconception that they hold and there are very few responses which appear obviously wrong to students. A side effect of this approach is that the incorrect responses reflect the non-Newtonian worldviews held by students. These non-Newtonian worldviews are coherent and robust, and this, at least in part, helps to explain why these misconceptions are so resistant to instruction. In this study we focus once more on the misconception data in Force Concept Inventory responses, particularly on the linkages between these misconceptions. We hypothesize that there are distinct groupings of distractor items formed by the strength of the association between these items. The two largest groupings are associated with the “impetus” world view in which the motion of an object is determined by the quantity of impetus which that object contains. We find that certain central items hold particularly important places in these groupings and also that individual groupings may be connected to each other by “connector” items. We finally suggest that, on the basis of this study, that these non-Newtonian worldviews might best be dismantled by addressing these key central and connector items.

In the context of introductory physics, we study student conceptual understanding of differentials, differential products, and integrals and possible pathways to understanding these quantities. We developed a multiple choice conceptual assessment employing a variety of physical contexts probing physical understanding of these three quantities and administered the instrument to over 1000 students in first and second semester introductory physics courses. Using a regression-based mediation analysis with conceptual understanding of integration as the dependent variable, we found evidence consistent with a simple mediation model: the relationship between differentials scores and integral scores may be mediated by the understanding of differential products. The indirect effect (a quantifiable metric of mediation) was estimated as $ab=0.29$, 95% CI [0.25, 0.33] for $N=1102$ Physics 1 students, and $ab=0.27$, 95% CI [0.14, 0.48] for $N=65$ Physics 2 students. We also find evidence that the physical context of the questions can be an important factor. These results imply that for introductory physics courses, instructional emphasis first on differentials then on differential products in a variety of contexts may in turn promote better integral understanding.

In the context of a generic harmonic oscillator, we investigated students’ accuracy in determining the period, frequency, and angular frequency from mathematical and graphical representations. In a series of studies including interviews, free response tests, and multiple choice tests developed in an iterative process, we assessed students in both algebra-based and calculus-based, traditionally instructed university-level introductory physics courses. Using the results, we categorized nine skills necessary for proficiency in determining period, frequency, and angular frequency. Overall results reveal that, postinstruction, proficiency is quite low: only about 20%–40% of students mastered most of the nine skills. Next, we used a semiquantitative, intuitive method to investigate the hierarchical structure of the nine skills. We also employed the more formal item tree analysis method to verify this structure and found that the skills form a multilevel, nonlinear hierarchy, with mastery of some skills being prerequisite for mastery in other skills. Finally, we implemented a targeted, 30-min group-work activity to improve proficiency in these skills and found a 1 standard deviation gain in accuracy. Overall, the results suggest that many students currently lack these essential skills, targeted practice may lead to required mastery, and that the observed hierarchical structure in the skills suggests that instruction should especially attend to the skills lower in the hierarchy.

Research on the test structure of the Force Concept Inventory (FCI) has largely ignored gender, and research on FCI gender effects (often reported as “gender gaps”) has seldom interrogated the structure of the test. These rarely crossed streams of research leave open the possibility that the FCI may not be structurally valid across genders, particularly since many reported results come from calculus-based courses where 75% or more of the students are men. We examine the FCI considering both psychometrics and gender disaggregation (while acknowledging this as a binary simplification), and find several problematic questions whose removal decreases the apparent gender gap. We analyze three samples (total $N_{\mathrm{pre}}=5391$, $N_{\mathrm{post}}=5769$) looking for gender asymmetries using classical test theory, item response theory, and differential item functioning. The combination of these methods highlights six items that appear substantially unfair to women and two items biased in favor of women. No single physical concept or prior experience unifies these questions, but they are broadly consistent with problematic items identified in previous research. Removing all significantly gender-unfair items halves the gender gap in the main sample in this study. We recommend that instructors using the FCI report the reduced-instrument score as well as the 30-item score, and that credit or other benefits to students not be assigned using the biased items.

We describe the construction, validation, and testing of a concept inventory for an Introduction to Physics of Semiconductors course offered by the department of physics to undergraduate engineering students. By design, this inventory addresses both content knowledge and the ability to interpret content via different cognitive processes outlined in Bloom’s revised taxonomy. The primary challenge comes from the low number of test takers. We describe the Rasch modeling analysis for this concept inventory, and the results of the calibration on a small sample size, with the intention of providing a useful blueprint to other instructors. Our study involved 101 students from Oklahoma State University and fourteen faculty teaching or doing research in the field of semiconductors at seven universities. The items were written in four-option multiple-choice format. It was possible to calibrate a 30-item unidimensional scale precisely enough to characterize the student population enrolled each semester and, therefore, to allow the tailoring of the learning activities of each class. We show that this scale can be employed as an item bank from which instructors could extract short testlets and where we can add new items fitting the existing calibration.

Group work is becoming increasingly common in introductory physics classrooms. Understanding how students engage in these group learning environments is important for designing and facilitating productive learning opportunities for students. We conducted a study in which we collected video of groups of students working on conceptual electricity and magnetism problems in an introductory physics course. In this setting, students needed to negotiate a common understanding and coordinate group decisions in order to complete the activity successfully. We observed students interacting in several distinct ways while solving these problems. Analysis of these observations focused on identifying the different ways students interacted and articulating what defines and distinguishes them, resulting in the development of the modes of collaboration framework. The modes of collaboration framework defines student interactions along three dimensions: social, discursive, and disciplinary content. This multidimensional approach offers a unique lens through which to consider group work and provides a flexibility that could allow the framework to be adapted for a variety of contexts. We present the framework and several examples of its application here.

Graduate admissions play a critical gatekeeping role in the physics community not only because they select students who are allowed to begin their graduate studies, but also because they influence how students perceive graduate school, and in some cases whether or not they will even choose to apply. In conjunction with the APS Bridge Program, we conducted a national survey of graduate directors (and related faculty) of physics Ph.D. programs in the United States to explore graduate admissions practices. Our focus was on criteria used in determining admissions, mechanisms through which graduate applicants are handled, and how student representation considerations are incorporated into admissions (if at all). We report here on existing graduate admission practices in physics departments and highlight some critical issues for understanding barriers for diversifying graduate physics, including the use of GRE scores (and the relative importance placed on them). We find that the use of a minimum GRE score for admission, a practice in opposition to recommendations made by the tests designers, is reported to be used in many departments (more than one in three). We also find letters of recommendation to be highly valued in admissions decisions. Our data describe various initiatives at the institutional or individual level to increase gender diversity in admissions. A sizable number of departments also express a latent demand for greater numbers of students from traditionally marginalized racial or ethnic groups, but simultaneously report a lack of such applicants.

Mathematical sense-making—looking for coherence between the structure of the mathematical formalism and causal or functional relations in the world—is a core component of physics expertise. Some physics education research studies have explored what mathematical sense-making looks like at the introductory physics level, while some historians and “science studies” have explored how expert physicists engage in it. What is largely missing, with a few exceptions, is theoretical and empirical work at the intermediate level—upper division physics students—especially when they are learning difficult new mathematical formalism. In this paper, we present analysis of a segment of video-recorded discussion between two students grappling with a quantum mechanics question to illustrate what mathematical sense-making can look like in quantum mechanics. We claim that mathematical sense-making is possible and productive for learning and problem solving in quantum mechanics. Mathematical sense-making in quantum mechanics is continuous in many ways with mathematical sense-making in introductory physics. However, in the context of quantum mechanics, the connections between formalism, intuitive conceptual schema, and the physical world become more compound (nested) and indirect. We illustrate these similarities and differences in part by proposing a new symbolic form, eigenvector eigenvalue, which is composed of multiple primitive symbolic forms.

Two motivational factors—self-efficacy and interest—may be especially relevant to deepening students’ understanding of astronomy. We examined the relationship between students’ self-efficacy for, interest in learning about, and changes in their knowledge of stars, as measured by the Star Properties Concept Inventory (SPCI). Approximately 700 undergraduate students taking introductory astronomy responded to surveys at the start and end of their semester-long course. A sequential multiple regression analysis showed that self-efficacy post explains an appreciable percentage of variance in SPCI posttest scores, more than twice the percentage explained by all the pretest variables (SPCI, self-efficacy, and interest) combined. Knowledge and self-efficacy improved significantly over instruction; interest did not. Follow-up analyses revealed that instructors whose classes increased in self-efficacy also had the greatest increases in knowledge scores. Interviews with these instructors suggest they provide their students with more opportunities for mastery experiences with elaborated, performance-related feedback, as well as strong positive verbal persuasion and vicarious experiences through peer instruction. Through increased understanding of the relationship between motivational constructs (e.g., self-efficacy, interest) and knowledge, we can both improve our models and better inform instruction.

In this paper we put forward a proposal for the design and evaluation of teaching and learning sequences in upper secondary school and university. We will connect our proposal with relevant contributions on the design of teaching sequences, ground it on the design-based research methodology, and discuss how teaching and learning sequences designed according to our proposal relate to learning progressions. An iterative methodology for evaluating and redesigning the teaching and learning sequence (TLS) is presented. The proposed assessment strategy focuses on three aspects: (a) evaluation of the activities of the TLS, (b) evaluation of learning achieved by students in relation to the intended objectives, and (c) a document for gathering the difficulties found when implementing the TLS to serve as a guide to teachers. Discussion of this guide with external teachers provides feedback used for the TLS redesign. The context of our implementation and evaluation is an innovative calculus-based physics course for first-year engineering and science degree students at the University of the Basque Country.

The advent of new educational technologies has stimulated interest in using online videos to deliver content in university courses. We examined student engagement with 78 online videos that we created and were incorporated into a one-semester flipped introductory mechanics course at the Georgia Institute of Technology. We found that students were more engaged with videos that supported laboratory activities than with videos that presented lecture content. In particular, the percentage of students accessing laboratory videos was consistently greater than 80% throughout the semester. On the other hand, the percentage of students accessing lecture videos dropped to less than 40% by the end of the term. Moreover, the fraction of students accessing the entirety of a video decreases when videos become longer in length, and this trend is more prominent for the lecture videos than the laboratory videos. The results suggest that students may access videos based on perceived value: students appear to consider the laboratory videos as essential for successfully completing the laboratories while they appear to consider the lecture videos as something more akin to supplemental material. In this study, we also found that there was little correlation between student engagement with the videos and their incoming background. There was also little correlation found between student engagement with the videos and their performance in the course. An examination of the in-video content suggests that students engaged more with concrete information that is explicitly required for assignment completion (e.g., actions required to complete laboratory work, or formulas or mathematical expressions needed to solve particular problems) and less with content that is considered more conceptual in nature. It was also found that students’ in-video accesses usually increased toward the embedded interaction points. However, students did not necessarily access the follow-up discussion of these interaction points. The results of the study suggest ways in which instructors may revise courses to better support student learning. For example, external intervention that helps students see the value of accessing videos may be required in order for this resource to be put to more effective use. In addition, students may benefit more from a clicker question that reiterates important concepts within the question itself, rather than a clicker question that leaves some important concepts to be addressed only in the discussion afterwards.

Pretesting and early intervention measures to identify and remediate at-risk students were implemented in algebra-based introductory physics to help improve student success rates. Pretesting via a math and problem-solving diagnostic exam administered at the beginning of the course was employed to identify at-risk students based on their scores. At-risk students were encouraged to utilize an online math tutorial to increase their chances of passing the course. The tutorial covers the same math topics covered by the diagnostic exam. Results from 643 students enrolled in the course showed that the 61 at-risk students who successfully completed the math tutorial increased their odds of passing the course by roughly 4 times those of the at-risk students who did not. This intervention is easily implemented, short term, and can be administered concurrently with the course. Based on these results, the Department of Physics has implemented the math tutorials in all sections of the introductory algebra as well as the calculus-based physics courses.

We investigate students’ sense of ownership of multiweek final projects in an upper-division optics lab course. Using a multiple case study approach, we describe three student projects in detail. Within-case analyses focused on identifying key issues in each project, and constructing chronological descriptions of those events. Cross-case analysis focused on identifying emergent themes with respect to five dimensions of project ownership: student agency, instructor mentorship, peer collaboration, interest and value, and affective responses. Our within- and cross-case analyses yielded three major findings. First, coupling division of labor with collective brainstorming can help balance student agency, instructor mentorship, and peer collaboration. Second, students’ interest in the project and perceptions of its value can increase over time; initial student interest in the project topic is not a necessary condition for student ownership of the project. Third, student ownership is characterized by a wide range of emotions that fluctuate as students alternate between extended periods of struggle and moments of success while working on their projects. These findings not only extend the literature on student ownership into a new educational domain—namely, upper-division physics labs—they also have concrete implications for the design of experimental physics projects in courses for which student ownership is a desired learning outcome. We describe the course and projects in sufficient detail that others can adapt our results to their particular contexts.

Student views of force and motion reflect the personal experiences and physics education of the student. With a different language, culture, and educational system, we expect that Japanese students’ views on force and motion might be different from those of American students. The Force and Motion Conceptual Evaluation (FMCE) is an instrument used to probe student views on force and motion. It was designed using research on American students, and, as such, the items might function differently for Japanese students. Preliminary results from a translated version indicated that Japanese students had similar misconceptions as those of American students. In this study, we used item response curves (IRCs) to make more detailed item-by-item comparisons. IRCs show the functioning of individual items across all levels of performance by plotting the proportion of each response as a function of the total score. Most of the IRCs showed very similar patterns on both correct and incorrect responses; however, a few of the plots indicate differences between the populations. The similar patterns indicate that students tend to interact with FMCE items similarly, despite differences in culture, language, and education. We speculate about the possible causes for the differences in some of the IRCs. This report is intended to show how IRCs can be used as a part of the validation process when making comparisons across languages and nationalities. Differences in IRCs can help to pinpoint artifacts of translation, contextual effects because of differences in culture, and perhaps intrinsic differences in student understanding of Newtonian motion.

This study examines students’ reasoning surrounding seemingly contradictory Likert-scale responses within five items in the Colorado Learning Attitudes About Science Survey for Experimental Physics (E-CLASS). We administered the E-CLASS with embedded open-ended prompts, which asked students to provide explanations after making a Likert-scale selection. The quantitative scores on those items showed that our sample of the 216 students enrolled in first year and beyond first year physics courses demonstrated the same trends as previous national data. A qualitative analysis of students’ open-ended responses was used to examine common reasoning patterns related to particular Likert-scale responses. When explaining responses to items regarding the role of experiments in confirming known results and also contributing to the growth of scientific knowledge, a common reasoning pattern suggested that confirming known results in a classroom experiment can help with understanding concepts. Thus, physics experiments contribute to students’ personal scientific knowledge growth, while also confirming widely known results. Many students agreed that having correct formatting and making well-reasoned conclusions are the main goal for communicating experimental results. Students who focused on sections and formatting emphasized how it enables clear and efficient communication. However, very few students discussed the link between well-reasoned conclusions and effective scientific communication. Lastly, many students argued it was possible to complete experiments without understanding equations and physics concepts. The most common justification was that they could simply follow instructions to finish the lab without understanding. The findings suggest several implications for teaching physics laboratory courses, for example, incorporating some lab activities with outcomes that are unknown to the students might have a significant impact on students’ understanding of experiments as an important approach for developing scientific knowledge.

Considering the evidence that standard physics graduate admissions practices tend to exclude women and traditionally marginalized racial and ethnic groups from the discipline, we investigate (a) the characteristics of students that physics graduate admissions committee members seek to admit to their programs and (b) the practices associated with these admissions goals. The data for this investigation are interviews with 18 faculty who chair graduate admissions committees in programs that prioritize diversity in their graduate admissions practices. We find that some express elements of an implicit theory of intelligence known as a “fixed mindset,” in which intelligence is understood as an inherent capacity or ability primarily measured by standardized test scores and grades. Some also express elements of a “growth mindset,” in which intelligence is understood in terms of acquired knowledge and effort. Overall, most faculty interviewed expressed elements of both mindsets. A fixed mindset in physics graduate admissions is consistent with research identifying physics as a “brilliance-required” field, whose members tend to believe that raw, innate talent is a primary requirement for success in the discipline. Such a mindset directly affects the participation of women and some racial or ethnic groups, who are stereotyped as lacking such high-level intellectual ability.

We describe a study on the conceptual difficulties faced by college students in understanding hydrodynamics of ideal fluids. This study was based on responses obtained in hundreds of written exams complemented with several oral interviews, which were held with first-year engineering and science university students. Their responses allowed us to identify a series of misconceptions unreported in the literature so far. The study findings demonstrate that the most critical difficulties arise from the students’ inability to establish a link between the kinematics and dynamics of moving fluids, and from a lack of understanding regarding how different regions of a system interact.

Analyzing, constructing, and translating between graphical, pictorial, and mathematical representations of physics ideas and reasoning flexibly through them (“representational competence”) is a key characteristic of expertise in physics but is a challenge for learners to develop. Interactive computer simulations and University of Washington style tutorials both have affordances to support representational learning. This article describes work to characterize students’ spontaneous use of representations before and after working with a combined simulation and tutorial on first-order energy corrections in the context of quantum-mechanical time-independent perturbation theory. Data were collected from two institutions using pre-, mid-, and post-tests to assess short- and long-term gains. A representational competence level framework was adapted to devise level descriptors for the assessment items. The results indicate an increase in the number of representations used by students and the consistency between them following the combined simulation tutorial. The distributions of representational competence levels suggest a shift from perceptual to semantic use of representations based on their underlying meaning. In terms of activity design, this study illustrates the need to support students in making sense of the representations shown in a simulation and in learning to choose the most appropriate representation for a given task. In terms of characterizing representational abilities, this study illustrates the usefulness of a framework focusing on perceptual, syntactic, and semantic use of representations.