Even graduate physics students have many misconceptions about basic wave optics phenomena. This suggests that there is much room for improvement of the traditional wave optics curriculum. An effective way for initiating a curriculum change is to reconsider and revise the expected learning outcomes and corresponding assessment instruments. By systematically enriching our wave optics instruction and assessment with conceptual tasks, we may increase the probability of students actively engaging in learning the conceptual aspects of wave optics. In this paper, we present the process of developing an item bank for measuring understanding of wave optics in typical introductory physics courses at universities. Thereby, the Rasch modeling approach has been used. The development of the item bank has been guided by results from multiple expert and student surveys, as well as from group interviews and think aloud interviews. Altogether 65 multiple-choice items with a single correct answer and three distractors have been prepared for field testing. Until now, 35 out of 65 items have been field tested by means of a paper and pencil survey which included 188 participants from five universities in Bosnia and Herzegovina, Croatia, and Slovenia. The field test showed that 32 out of 35 items have good psychometric characteristics and that they may be very useful for uncovering students’ misconceptions in wave optics.

Computation is a central aspect of 21st century physics practice; it is used to model complicated systems, to simulate impossible experiments, and to analyze mountains of data. Physics departments and their faculty are increasingly recognizing the importance of teaching computation to their students. We recently completed a national survey of faculty in physics departments to understand the state of computational instruction and the factors that underlie that instruction. The data collected from the faculty responding to the survey included a variety of scales, binary questions, and numerical responses. We then used random forest, a supervised learning technique, to explore the factors that are most predictive of whether a faculty member decides to include computation in their physics courses. We find that experience using computation with students in their research, or lack thereof and various personal beliefs to be most predictive of a faculty member having experience teaching computation. Interestingly, we find demographic and departmental factors to be less useful factors in our model. The results of this study inform future efforts to promote greater integration of computation into the physics curriculum as well as comment on the current state of computational instruction across the United States.

We discuss an investigation of student difficulties with the corrections to the energy spectrum of the hydrogen atom for the intermediate field Zeeman effect using degenerate perturbation theory (DPT). The investigation was carried out in advanced quantum mechanics courses by administering free-response and multiple-choice questions and conducting individual interviews with students. We find that students share many common difficulties related to relevant physics concepts. They had difficulty with mathematical sense making in this context of quantum mechanics, which requires the ability to interpret the implications of the degeneracy in the unperturbed energy spectrum and how the Zeeman perturbation will impact the splitting of the energy levels. Many of the common student difficulties arise from challenges in mathematical sense making and applying linear algebra concepts incorrectly in this novel context of quantum mechanics. We describe how the research on student difficulties was used as a guide to develop and evaluate a Quantum Interactive Learning Tutorial (QuILT), which strives to help students develop a functional understanding of the concepts necessary for finding the corrections to the energy spectrum of the hydrogen atom for the intermediate field Zeeman effect using the DPT. We also discuss the development and validation of the DPT QuILT focusing on these issues and its in-class evaluation in the undergraduate and graduate courses.

In upper-division physics courses, students’ use of differential line, area, and volume elements and their facility with the various multivariable coordinate systems consistently go hand in hand. As part of an effort to investigate student understanding of the structure of non-Cartesian coordinate systems and the associated differential elements, we interviewed students (mostly in pairs) in junior-level electricity and magnetism courses at two universities. In a sequence of tasks, students were asked to construct a differential length vector and a differential volume element in an unconventional spherical coordinate system. None of the students were able to arrive at a correct differential length element initially. This work addresses the construction and checking of the volume element. Volume element construction occurred by either combining associated lengths, an attempt to determine sides of a differential cube, or mapping from the existing spherical coordinate system. Students who constructed volume elements from differential length components corrected their length element terms as a result of checking the volume element expression by integration. Other students who relied heavily on spherical coordinates displayed further difficulty connecting dimensionality and projection ideas to differential construction.

Vector calculus and multivariable coordinate systems play a large role in the understanding and calculation of much of the physics in upper-division electricity and magnetism. Differential vector elements represent one key mathematical piece of students’ use of vector calculus. In an effort to examine students’ understanding of non-Cartesian differential length elements, students in junior-level electricity and magnetism were interviewed in pairs and asked to construct a differential length vector for an unconventional spherical coordinate system. One aspect of this study identified symbolic forms invoked by students when building these vector expressions, some previously identified and some novel, given the vector calculus context. Analysis also highlighted several common ideas in students’ concept images of a non-Cartesian differential length vector as they determined their expressions. As no interview initially resulted in the construction of an appropriate differential, analysis addresses the role of the evoked concept images and symbolic forms on students’ performance.

Time dependence is of fundamental importance for the description of quantum systems, but is particularly difficult for students to master. We describe the development and evaluation of a combined simulation-tutorial to support the development of visual understanding of time dependence in quantum mechanics. The associated interactive simulation shows the time dependence of an energy eigenstate and a superposition state, and how the time dependence of the probability density arises from that of the wave function. In order to assess transitions in student thinking, we developed a framework to characterize student responses in terms of real and complex mathematical reasoning and classical and quantum visual reasoning. The results of pre-, mid-, and post-tests indicate that the simulation-tutorial supports the development of visual understanding of time dependence, and that visual reasoning is correlated with improved student performance on a question relating to the time evolution of the wave function and the probability density. The results also indicate that the analogy of a classical standing wave for the infinite well energy eigenfunctions may be problematic in cueing incorrect ideas of time dependence.

Analogies are suitable for teaching scientific concepts by comparing an unknown with a known. For this reason, they are widely used by textbook authors or science teachers for different aims such as introduction, clarification, or discrimination of new concepts. This study examines the analogies used in elementary science textbooks from 3rd to 8th grades and criticizes the use of analogies. By considering Glynn’s teaching-with-analogies approach, this study identifies the missing parts of the analogies that should be revised and presents examples of how textbook analogies could be improved by teachers in teaching physics concepts.

University professors’ views of nature of science play an important role when guiding undergraduate students into the culture of practicing physicists. While these topics have a long-standing tradition in U.S. curricula they are not part of German educational standards or curricula. Additionally professors’ views—in contrast to those of their students—are relatively under-researched. In this contribution, we establish the possibility of testing German physics professors’ views in an economically administrable survey. We first ask for their views of the nature of science, and then about how important they see these aspects for students and how intensive they address them in their own physics classes at the university. We demonstrate that an established test instrument can be reliably used with this demographic. The results indicate that the professors tend to views of naive empiricism but besides that hold mostly adequate beliefs. Learning about the nature of science in university courses, in general, is considered of much importance, which is also reflected in the professors’ reported teaching habits. However, there are aspects in this area which are considered more or less important by the professors.

Epistemologically oriented reforms of physics courses aim to change the way students think about knowledge and approach learning in physics. A broader goal of these reforms is to impact how students think about knowledge and learning in other courses. We investigate the effects of epistemological reforms in a physics course on knowing and learning in biology courses through a case study of a biology major, Phillip, who was enrolled in a year-long reformed introductory physics for the life sciences (IPLS) course. First, we show that Phillip’s epistemological framing of the physics course became more sophisticated, aligning with reforms designed to emphasize reasoning with foundational principles, seeking meaning and coherence. He also developed an approach to learning physics that involved coordinating understanding between course readings and class discussions and reconciling discrepancies with peers and the teaching assistant. Second, we present evidence of the impact of this new epistemological framing on Phillip’s interpretation of his biology courses. Before the year in physics, Phillip framed his biology courses as about understanding. By the end of the year, Phillip reversed his stance on biology learning, reporting that he had actually been memorizing all this time. We discuss these results to highlight the success of epistemological reforms in physics beyond the confines of the physics classroom, to motivate attention epistemological reform beyond physics, and to offer suggestions for how IPLS courses can work towards creating epistemological connections to other disciplines.

Students’ epistemological beliefs have been confirmed to influence students’ physics learning in an essential way. The Colorado Learning Attitudes about Science Survey (CLASS) is an assessment instrument for evaluating students’ beliefs towards physics learning. In the present study, 817 students participate in our investigation with the mandarin CLASS version through three years of the undergraduate program among ten universities in China. We compare student performances on the CLASS across different majors, genders, and university tiers via the three-way analysis of variance. From the results, the main effect of major is found to be statistically significant. Students majoring in education consistently have a better performance of attitudes toward physics learning than those majoring in noneducation, regardless of gender and university tier. There are no main effects of gender and university tier, while the interaction between gender and university tier is detected significantly. No three-way interaction is detected among major, gender, and university tier. Therefore, this paper identifies how students’ epistemological beliefs towards physics learning are related to various disciplines in universities, different genders, and qualitatively dissimilar content learning. For future work, it is worth investigating how students’ epistemological beliefs towards physics learning are affected by the variable of year level and how the variable of year level interacts with major, gender, and university tier. According to the significant effect of major, it will make sense to investigate the correlation between epistemological beliefs and career interests or career expectations in future research.

Even though it has been shown that retrieval practice could foster deeper learning and better long-term retention in other domains such as psychology, it is rarely studied in the context of physics learning where students need to solve more complicated problems. To an even lesser degree is comparing retrieval-based learning with other active learning style methods adopted in the physics classroom. In this study, we compared the effects of retrieval-based learning and peer instruction based restudying on physics problem solving and transfer. In both conditions (retrieval and peer instruction), participants were first presented video lectures explaining the definition of speed and energy conservation. In the training session that immediately followed the video lectures, the retrieval condition was asked to recognize, recall, and apply the relevant physics concepts to solving problems; while the peer instruction condition was asked to discuss the two video lectures with each other in a group of three or four members. After this training, an immediate and a delayed (one-week) final test were administered. Both tests contained an initial task, isomorphic to the training materials, near transfer tasks, and far transfer tasks for each topic. Subjective judgment of learning (JOL) was collected immediately after watching the video lectures, after the training, and right before the delayed final test. We found a retention advantage of the retrieval practice for the initial tasks, but not for the near and far transfer tasks. We also found an advantage of the retrieval practice on far transfer on the immediate final test. Peer instruction training inflated the participants’ JOL compared to the retrieval practice. Both JOL scores were significantly lower than after the video lecture but did not differ from before the delayed final test.

There has been little work done in exploring the variations in admissions practices between different types of physics graduate programs. In this paper, we compared admissions practices in master’s programs to a parallel data set collected from doctoral departments to understand the relative importance of particular admission criteria and looked especially at similar sized and “pressured” programs (as measured by the ratio of applications received-to-intended cohort size). We found that master’s programs experience notably lower application pressure compared to doctoral programs overall. In the prioritization of admission criteria, undergraduate course-taking and undergraduate math and physics GPA received the shared highest priority, while recommendation letters and Graduate Record Examination (GRE) quantitative scores are the next important criteria but are statistically less important for master’s programs in comparison with doctoral programs. In the targeted comparison of similarly sized and pressured master’s and doctoral programs, the higher importance of GRE quantitative scores and the lower importance of prior research considerations in master’s programs persist. We argue that the relatively lower importance placed on the quantitative GRE and physics subject GRE scores enhances the likelihood of success for undergraduates applying to master’s programs, particularly for those who did not take or score well on the quantitative GRE and physics subject GRE test, which have been found to incorporate significant biases against many students but are nonetheless normative in many admissions decisions. The research and graduate level course experiences gained through a master’s program may improve postgraduate job opportunities or even continuation on to doctoral research. However, the shared importance of certain factors in admissions between master’s and doctoral programs risks propagating a systematic inequity.

In this study with 153 middle school students, we investigate the influence of the number of decimal places from the reading of a measurement device on students’ decisions to change or keep an initial hypothesis about falling objects. Participants were divided into three groups, introduced to two experiments—the time it takes a free falling object with a zero, and a nonzero initial horizontal velocity to fall a certain distance—and asked to state a hypothesis that compares the falling times of the two experiments. We asked the participants whether they wanted to change or keep their initial hypothesis after they were provided with data sets. Members of each group were given the same number of measurements but with a different number of decimal places. Results show that for an increase in the number of decimal places, the number of participants switching from a false to a correct hypothesis decreases, and at the same time the number of students switching from a correct to a false hypothesis increases. These results indicate that showing more exact data to students—given through different resolutions of the measurement device—may hinder students’ ability to compare data sets and may lead them to incorrect conclusions. We argue that this is due to students’ lack of knowledge about measurement uncertainties and the concept of variance.

For proper assessment selection understanding the statistical similarities amongst assessments that measure the same, or very similar, topics is imperative. This study seeks to extend the comparative analysis between the brief electricity and magnetism assessment (BEMA) and the conceptual survey of electricity and magnetism (CSEM) presented by Pollock. This is accomplished by using large samples ($N_{\mathrm{BEMA}}=5368$ and $N_{\mathrm{CSEM}}=9905$) within classical test theory (CTT) and item response theory (IRT) frameworks. For the IRT comparison, after consideration of the conceptual content addressed in each assessment, it was assumed that each of these assessments are measuring the same student latent ability ($\theta$), specifically a student’s ability to do introductory electricity and magnetism. Via a CTT and IRT analysis it was found that both assessments are essentially equal in overall difficulty. Classical item analysis applied to 7 questions used by both assessments revealed that each assessment functions slightly differently internally. The test information curves found from IRT show that the CSEM has superior information compared to the BEMA in estimating student latent abilities for the entire range of typical latent abilities achieved by students on each assessment, $\theta \approx -2$ to $\theta \approx 3$. Information in this case is interpreted as how well a student’s latent ability was estimated by an assessment as a function of latent ability. When the circuits questions are removed from the BEMA the majority of the information is lost in the $\theta \approx 0$ to $\theta \approx 2$ range. This means the circuits questions on the BEMA are information heavy for higher ability scores. So, special considerations should be made as to which assessment a study uses depending on the specific questions a researcher is attempting to answer.

Typical physics textbook problems often include supportive diagrams that visualize the physical situation although the potential benefits of providing such diagrams is not yet fully established. We used eye tracking to explore the role of supportive diagrams in problem solving. Including a supportive diagram with the text of the problem improved students’ percentage of correct answer in one of the six problems used in the study. Eye-tracking data showed that students typically spent less time on the text of the problem if they were presented with a diagram, but the total viewing time did not change. When a diagram was presented students split their attention between the diagram and the text without speeding up problem solving. Cognitive load theory and dual coding theory suggest that giving information in two formats (verbal and visual) might reduce extraneous cognitive load and leave more cognitive resources available for further steps in problem solving. However, this does not necessarily lead to a higher percentage of correct answers to the problem, because supportive diagrams influence only one step of the complex process of problem solving. In addition to the role of diagrams, we evaluated different eye-tracking measures as measures of visual attention during physics problem solving. It seems that the fixation duration is rather constant, and not always sensitive to the manipulation in the task. On the other hand, dwell time and the number of fixations show more variability across problems and participants, so they seem to be appropriate measures of the visual attention. Since dwell time and fixation number are dependent measures, and they show a similar pattern of responses, in most cases it seems sufficient to report only one of them.

We design, validate, and administer a 24-item test to study student understanding of linear functions in 1D kinematics [$x(t)$] and mathematics [$y(x)$] in the 9th grade. The items assess identification and comparison of initial position and velocity in 1D kinematics and of the $y$ intercept and slope in mathematics using a graph or an algebraic formula. Results show that students’ performance on most mathematics items is significantly better than on their isomorphic kinematic counterparts, but also that most of the easiest as well as the most difficult items are kinematics items. Students achieve the highest accuracies on graphical questions in which they must compare two positive slopes, and they achieve the lowest accuracies on questions in which they must determine or compare a negative slope. We find that students have more difficulties with the $y$ intercept in mathematics and with the slope in kinematics. Furthermore, questions in symbolic representation result in far lower accuracies compared to questions in graphical representation, particularly when the $y$ intercept or the slope has to be determined instead of compared. We also analyze the results qualitatively by categorizing the students’ strategies and errors. We find frequent confusion between the $x$ intercept and the $y$ intercept in mathematics, but far less in kinematics. Negative velocities in kinematics are by far the largest pitfall, whereas negative slope in mathematics is rarely an issue. The results also show a significant frequency of interval or point confusions in kinematics but very little in mathematics. We reaffirm the occurrence of the interval or point confusion in questions with graphs and discuss three different cases of interval or point confusions in questions with algebraic expressions: numerical, algebraic, and unit based. Our results indicate a weak link between kinematics and mathematics and we suggest that closer integration between these two contexts during education could benefit student understanding of linear functions and linear phenomena in kinematics.

A national survey of physics faculty was conducted to investigate the prevalence and nature of computational instruction in physics courses across the United States. 1246 faculty from 357 unique institutions responded to the survey. The results suggest that more faculty have some form of computational teaching experience than a decade ago, but it appears that this experience does not necessarily translate to computational instruction in undergraduate students’ formal course work. Further, we find that formal programs in computational physics are absent from most departments. A majority of faculty do report using computation on homework and in projects, but few report using computation with interactive engagement methods in the classroom or on exams. Specific factors that underlie these results are the subject of future work, but we do find that there is a variation on the reported experience with computation and the highest degree that students can earn at the surveyed institutions.

Tutorials in Physics: Quantum Mechanics is a set of curricular materials for supplementing upper-division quantum mechanics instruction, developed by the physics education group at the University of Washington. We describe the development of a sequence of three tutorials that focused on quantum measurements and time dependence. This sequence of tutorials is based on prominent findings in the research literature related to student understanding, as well as classroom techniques and strategies that have proved effective in other instructional contexts in physics. We also present data from a set of four exam questions used to evaluate how effectively these tutorials improve student ability to use correct mathematical and conceptual reasoning to predict the time evolution of quantum probabilities. We find that student performance on each question is significantly better than on corresponding questions given after only traditional instruction, with effect sizes that range from small to moderate. This improvement, along with a decrease in the prevalence of common incorrect lines of reasoning, supports our claim that this set of three tutorials from Tutorials in Physics: Quantum Mechanics assists advanced undergraduate students’ in developing a conceptual understanding of some of the fundamental quantum concepts about time evolution and measurements when given after traditional lecture instruction. However, our results also show that there are some topics with which many students still struggle and, thus, that there remains room for further research and development of materials for these topics.

The present study describes the development and field testing of a simple apparatus-based diagnostic instrument (SABDI) that examines undergraduate students’ understanding of the underlying physics principles that explain how simple acoustic apparatuses work. SABDI comprises 13 items. Based on previous research studies and the history of science, the 38 distractors of SABDI were designed to reflect the following four categories of possible misconceptions: (a) direct and (b) incorrect emergent views of sound; (c) explanations based on a device’s salient feature; and (d) wrong applications of physics knowledge. Field testing carried out on 159 participants showed the salient features category to be the most popular. SABDI is a valid and reliable tool that could be used to determine students’ thinking regarding acoustic devices.

Identifying and understanding student difficulties with physics content in a wide variety of topical areas is an active research area within the physics education research community. Of particular value are investigations of physics topics that appear multiple times in different contexts across the undergraduate physics curriculum. As these common topics reappear, students’ difficulties can perpetuate from one context to the next, or new difficulties can emerge as students encounter new physical contexts. One example of such a topic is boundary conditions, which is broadly considered to be an important topic that advanced physics undergraduates are expected to understand and apply in multiple topical areas including classical mechanics, quantum mechanics, and throughout electricity and magnetism. We report findings from an investigation of student difficulties using boundary conditions while focusing on the context of electromagnetic waves. Our data sources include student responses to traditional exam questions, conceptual survey questions, and think-aloud interviews. The analysis was guided by an analytical framework that characterizes how students activate, construct, execute, and reflect on boundary conditions during physics problem solving. Commonly observed student difficulties include activating boundary conditions in appropriate contexts, constructing a complex expression for the electromagnetic waves, mathematically simplifying and manipulating complex exponentials, and checking if the reflection and transmission coefficients are physical. We also present potential pedagogical implications based on our observations.