Light interference is an essential topic for understanding the wavelike nature of light, however, there are limited studies on modeling and assessing students’ misconceptions and learning difficulties in this area. Based on the knowledge integration modeling approach, a conceptual framework for light interference is developed and used to model student understanding and guide the development of an assessment tool on light interference. The conceptual framework provides a representation of students’ reasoning pathways to clearly show their connections through different conceptual components and contextual features of problem-solving settings. This type of representation focuses on showing students’ knowledge structures regarding the features of integration and fragmentation. Experts’ reasoning pathways always flow through a central idea of a concept with well-established connections to a wide range of contextual features and conditions. These connections form an integrated knowledge structure, which demonstrates deep understanding. In contrast, novices often focus on surface details without linking the central idea, forming fragmented local connections that link directly between contextual features and task outcomes. As a result, novice students’ problem solving often relies on memorization of formula and solutions without any deep understanding. Through testing and interviews at a large Chinese university, a light interference test (LIT) has been developed and validated. Assessment results also demonstrate that students with a strong conceptual understanding of the central idea are able to apply expertlike reasoning to familiar and novel questions regardless of the contextual details. Meanwhile, students with weaker or nonexistent understanding of the central idea often struggle when novel situations are presented. LIT provides a useful tool to measure students’ conceptual understanding on light interference and probe thought pathways of students’ reasoning that can further indicate students’ knowledge structure and levels of deep understanding.

While numerous studies have analyzed the conceptions probed by the Force Concept Inventory (FCI), assessments dedicated to electricity and magnetism lack similar analyses. This paper investigated the conceptions explored by the Brief Electricity and Magnetism Assessment (BEMA) and the Conceptual Survey of Electricity and Magnetism (CSEM) using exploratory factor analysis techniques. Exploratory factor analysis (EFA) was performed on both assessments using 5368 and 4941 postinstruction student responses for the BEMA and CSEM, respectively. A 6-factor EFA generated model was found for the CSEM, and was fit against another sample of 4964 student responses using confirmatory factor analysis to supply evidence for the possible generalizability of the model. The 5-factor EFA generated model for the BEMA could not be fit against another sample when trying to check for generalizability. The EFA generated factor models for the BEMA and CSEM were then compared and found to be similar in conceptual content, with the exception of one or two factors. Thus, from a factor analysis perspective, the BEMA and CSEM were found to be similar in conceptual content as revealed by student responses. With a better understanding of these electricity and magnetism assessments, future research into this domain of physics will then be able to make stronger conclusions based on students’ results within these assessments.

Understanding perceptions of graduate admissions from multiple stakeholders can cultivate an improved understanding about the process of graduate induction, the role that admissions plays in restricting diversity in physics, and contribute to more informed practices for all involved. Prior studies in graduate admissions have reported on how certain admission criteria weigh in the consideration of applicants primarily from faculty perspectives. Motivated by the concept of multivocal knowledge, in this article, we report on prospective students’ perspectives of the importance of the same admission criteria—a stakeholder group that is critical but underempowered in the admissions process. We identify a substantial agreement between students and faculty regarding the importance of recommendation letters, undergraduate math or physics GPA, and standardized exam scores (GRE). On the other hand, students rated several criteria, including personal statements, prior research experiences, publications, and familiarity with department as significantly more important than did faculty. A perceived “overimportance” of criteria may be detrimental to students’ admissions-related decision making and reduce their chances of success, so these results emphasize the importance of taking students’ perspectives into account in the admissions process.

We investigated the influence of context on students’ understanding of cross products of vectors using three isomorphic multiple-choice tests asking for the direction of a cross product in different geometrical settings. One version of the test involved the Lorentz force, the second version involved the torque on an electric dipole, and the third version was without physics context. We administered the tests to 216 first-year pre-med students at a Belgian (Flemish) university. We found that students perform significantly better in the context of the Lorentz force. Students more often chose the incorrect alternative corresponding to the vector sum in the test versions involving an electric dipole or without physics context when the vectors are not orthogonal. For orthogonal vectors, a sign error—i.e., inverting the direction of the resulting vector—was the most common mistake in both tests with physics context, while without physics context selecting the alternative corresponding to the sum remained the most common mistake. Prior familiarity with a right-hand rule in a specific context seems to be able to explain improved scores in the test version concerning the Lorentz force. Instructors and curriculum developers can benefit from adopting an integrated approach in which the mathematical aspects of the cross product are treated together with multiple examples in physics, allowing students to transition from using specific rules to determine a cross product, to a more integrated understanding of it.

In order to support physics students in their future careers, there is a need to understand the relationship between undergraduate education and professional practice in physics-related fields. This study investigated high-level goal driven mathematical problem-solving activities that are found within two disciplinary cultures: physical science research labs in academia and photonics workplaces in industry. We conducted semistructured interviews with 10 Ph.D. students and 22 engineers and technicians. Math use in professional workplaces was characterized through an adaptation of epistemic games framework, which revealed six common epistemic games in these workplaces: conceptual math modeling, analytical-numerical math modeling, design-oriented math modeling, fabrication, improving processes, and making meaning out of data games. The workplace-specific epistemic games capture the goals, starting and ending conditions, constraints and contextual features, moves, tools, and representations. The games involve a broad spectrum of math that ranges from arithmetic to computational modeling. The games reveal how goals and particular contextual features impact approaches to mathematical problem solving. The findings extend prior work on mathematical problem solving in physics to a new population of professional researchers, engineers, and technicians in their workplaces. The research may guide new approaches for developing problems and explicitly teaching problem solving in diverse physics contexts, which may additionally benefit undergraduate students’ preparation for their future careers.

This paper aims to provide a contribution to the research in physics education regarding the interplay between mathematics and physics in teaching and learning physics at the university level. The argument is developed through a study focused on the historical case study of the blackbody that led Planck to make one of the most significant scientific breakthroughs in physics: the introduction of discreteness and quantization into physical processes. The study is methodologically guided by the model that Udhen, Karam, Pietrocola, and Pospiech elaborated to highlight the interplay between physics and mathematics within teaching and learning practices [O. Uhden, R. Karam, M. Pietrocola, and G. Pospiech, Modelling mathematical reasoning in physics education, Sci. Educ. Netherlands 21, 485 (2012).]. The model emphasizes the distinction between the technical and structural roles of mathematics in physics, with the latter role being argued to correspond to processes of mathematization and interpretation. We used this model to analyze Planck’s original papers and to reconstruct the reasoning that, thanks to the structural role played by mathematics, paved the way for the quantistic scientific breakthrough. The results of the analysis led us to design a teaching tutorial that we implemented with mathematics and physics university students. Students’ reactions are reported to discuss the educational potential of the approach beyond the specific case and to argue for its potential general application to other similar physics topics.

Over the course of instruction, not only does most introductory physics students’ content knowledge evolve but their attitudes and approaches to problem solving are also likely to evolve. This change may depend on many factors including the curricula and pedagogies used, the degree to which instruction actively engages students in the learning process, as well as the gender of the students. While changes in epistemology and beliefs about physics have been examined in the literature, how students’ attitudes and approaches to problem solving change from the beginning to the end of instruction in introductory physics and how method of instruction or gender of the student impact them remain largely unexplored. To examine the potential changes in attitudes and approaches to problem solving over a semester, we administered a previously validated attitudes and approaches to problem solving (AAPS) survey both at the beginning (pre) and at the end of instruction (post) in eight large enrollment calculus-based introductory physics classes at a large research university in the United States. At both points in time (beginning and end of a semester of instruction), each class was also given surveys measuring students’ conceptual understanding: the Force Concept Inventory (FCI) or the Conceptual Survey of Electricity and Magnetism (CSEM), depending upon whether it was the first or second semester course. In addition, final exam scores, gender of students, and descriptions of the instructional methods used for each class were collected. The AAPS survey was used to measure students’ attitudes and approaches to problem solving, and the conceptual surveys and exam scores were used to measure the degree to which each course helped students learn physics concepts. We examined students’ performance on the AAPS survey, FCI or CSEM, and final exams, and compared the results for different instructional methods, and gender of students. Moreover, we examined whether or not there were correlations between the expertlike response on the AAPS survey and the performance on FCI or CSEM or final exams. We found that all classes exhibited a decline in score on the AAPS survey suggesting worse attitudes related to problem solving after instruction. Furthermore, controlling for the initial scores, classes which involved significant use of evidence-based active engagement methods exhibited statistically significantly better scores on the AAPS survey at the end of the course compared to classes which were taught primarily using a traditional lecture-based approach. Equally importantly, unlike broader epistemological surveys, female students were found to exhibit less of a decline in AAPS scores than did their male counterparts in all classes and the AAPS scores were always higher for female students at the end of the course. Future research should contemplate how this novel finding may be effectively exploited to develop and implement curricula and pedagogies to reduce the gender gap in performance often observed in introductory physics.

We developed and validated a conceptual survey that focuses on the formalism and postulates of quantum mechanics covered in upper-level undergraduate quantum mechanics courses. The concepts included in the quantum mechanics formalism and postulate survey (QMFPS) focus on Dirac notation, the Hilbert space, state vectors, physical observables and their corresponding Hermitian operators, compatible and incompatible observables, quantum measurement, time dependence of quantum states and expectation values, and spin angular momenta. Here we describe the validation and administration of the survey, which has been administered to over 400 upper-level undergraduate and graduate students from six institutions. The QMFPS is valid and reliable for use as a low-stakes test to measure the effectiveness of instruction in an undergraduate quantum mechanics course that covers relevant content. The survey can also be used by instructors to identify students’ understanding of the formalism and postulates of quantum mechanics at the beginning and end of a graduate quantum mechanics course since graduate students are expected to have taken an undergraduate quantum mechanics course that covers the content included in the survey. We found that undergraduate students who engaged with research-validated learning tools performed better than students who did not on the QMFPS after the first semester of a junior or senior level quantum mechanics course. In addition, the performance of graduate students on QMFPS after instruction in the first semester of a core graduate-level quantum mechanics course was significantly better than the performance of undergraduate students at the end of the first semester of an undergraduate quantum mechanics course. However, both undergraduate and graduate students struggled with many questions on the QMFPS. A comparison with the base line data on the validated QMFPS presented here can aid instructors in assessing the effectiveness of their instructional approaches and help them identify the difficulties their students have with quantum formalism and postulates in order to help students develop a solid grasp of the formalism and postulates of quantum mechanics.

Much of the literature contributing to physics instructors’ knowledge of student ideas (KSI) reports common patterns of reasoning that are framed as discontinuous with canonical concepts. Our work contributes new KSI about mechanical wave propagation from a resources perspective, framing student thinking in terms of context-sensitive pieces of knowledge that are continuous with canonical physics concepts. The intent of this work is to inform instruction on mechanical waves by identifying and illustrating some of the conceptual resources that instructors might expect their students to use. To support instructor predictions about student thinking, we identify resources that are common across multiple samples and questions. Our data include written responses to three versions of a conceptual question about mechanical pulse propagation. We use an emergent coding scheme to characterize a total of 851 written responses from 6 universities in the United States. Our analysis reveals three common conceptual resources: (i) properties of the medium either impede or facilitate the motion of the pulse, (ii) the speed or duration of transverse motion affects pulse speed, and (iii) the speed of the pulse is affected by its kinetic energy. We show how each of these resources can be viewed as continuous with formal understandings of pulse propagation.

Here we demonstrate the benefits of a new curriculum for introductory calculus-based physics that motivates classical mechanics using a modified version of Hamiltonian mechanics. This curriculum shifts the initial focus of instruction away from forces and the associated vector mathematics, which are known to be problematic for students, to the scalar quantity energy, which is more closely aligned with their previously established intuition, and associated differential and integral calculus. We show that implementation of this calculus-enhanced “energy-first” curriculum resulted in higher normalized gains on the Force Concept Inventory exam for all students and improved performance in downstream engineering courses for students with lower ACT math scores. In other words, the downstream benefits were largest for students with lower math abilities who also pose a larger retention risk. This new curriculum thus has the potential to improve student retention by specifically helping the students who need help the most, including traditionally underserved populations who often have weaker mathematics preparation. We propose future work to investigate whether this new curriculum has lowered the math transference barrier to learning in introductory physics, resulting concomitantly in improvements in student learning of classical mechanics and in student fluency with applied mathematics.

An essential skill for success in upper-division physics curricula is the ability to work with and apply mathematical and physical concepts through Cartesian and non-Cartesian coordinate systems. These skills are most notably necessary in electricity and magnetism, wherein students must build and solve integrals and perform vector derivatives in Cartesian, spherical, and cylindrical coordinate systems. While limited in scope, early investigations into students understanding of coordinate systems has shown that students have considerable difficulty. Through the analysis of four one-on-one semistructured interviews, students were observed to activate numerous productive resources, despite frequently incorrect answers. This paper will revisit our previously identified student resource clusters for unit vectors. We also identify additional resources that cast additional light on students’ thinking about position vectors, and velocity vectors in non-Cartesian coordinate systems. Through detailed analysis of a single student, we identify several groupings of resources that will serve as a baseline for future analysis of additional students and provide initial insight into potential curriculum development.

We present an empirical analysis of students’ use of partial derivatives in the context of problem solving in upper-division thermodynamics. Task-based individual interviews were conducted with eight middle-division physics students. The interviews involved finding a partial derivative from information presented in a table and a contour plot. Using thematic analysis, we classified student problem-solving strategies into two principal categories: the analytical derivation strategy and the graphical analysis strategy. We developed a new flowchartlike analysis method: representational transformation. Our analysis of students’ strategies using this method revealed three types of transformation phenomena: translation, consolidation, and dissociation. Students in this study did not seem to have much difficulty with the concepts underlying the partial derivative; instead, they seemed to have difficulty with the transformation phenomena, particularly the consolidation of multiple representations into a single representation.

Special relativity theory (SRT) has recently gained popularity as a first introduction to “modern” physics thinking in upper level secondary physics education. A central idea in SRT is the absolute speed of light, with light propagating with uniform speed relative to the reference frame of the observer. Previous research suggests that students, building on their prior understandings of light propagation and relative motion, develop misunderstandings of this idea. The available research provides little detail on the reasoning processes underlying these misunderstandings. We therefore studied secondary education students’ preinstructional reasoning about the speed of light in a qualitative study, probing students’ reasoning through both verbal reasoning and drawing. Event diagrams (EDs) were used as a representational tool to support student reasoning. Results show that students productively use EDs to reason with light propagation. In line with previous research, we found two alternative reference frames students could use for uniform light propagation. Most students show a flexibility in their use of reference frame: They not only evaluate light propagation in their preferred frame of reference, but also relative to other frames. Some students experienced conflict between an alternative reference frame and the speed of light and changed their reasoning because of that. This finding suggests promising directions for designing education.

Module analysis for multiple-choice responses (MAMCR) was applied to a large sample of Force Concept Inventory (FCI) pretest and post-test responses ($N_{\mathrm{pre}}=4509$ and $N_{\mathrm{post}}=4716$) to replicate the results of the original MAMCR study and to understand the origins of the gender differences reported in a previous study of this dataset. When the results of MAMCR could not be replicated, a modification of the method was introduced, modified module analysis (MMA). MMA was productive in understanding the structure of the incorrect answers in the FCI, identifying 9 groups of incorrect answers on the pretest and 11 groups on the post-test. These groups, in most cases, could be mapped on to common misconceptions used by the authors of the FCI to create distractors for the instrument. Of these incorrect answer groups, 6 of the pretest groups and 8 of the post-test groups were the same for men and women. Two of the male-only pretest groups disappeared with instruction while the third male-only pretest group was identified for both men and women postinstruction. Three of the groups identified for both men and women on the post-test were not present for either on the pretest. The rest of the identified incorrect answer groups did not represent misconceptions, but were rather related to the blocked structure of some FCI items where multiple items are related to a common stem. The groups identified had little relation to the gender unfair items previously identified for this dataset, and therefore, differences in the structure of student misconceptions between men and women cannot explain the gender differences reported for the FCI.

A common hope of many physics educators and researchers is that students leave the course with a stronger sense that physics is relevant to them than when they entered the course. Multiple survey measures have attempted to measure shifts in students’ beliefs on the relevance of physics but frequently the results show a negative shift in students’ beliefs and are often reported as a failure of students to “see the relevance.” We challenge this view by highlighting the limitations of attitudinal and epistemological surveys’ ability to probe relevance. We then articulate a more expansive view of relevance using ecological systems theory that serves as a lens we apply to analyze students’ experiences. Instead of deficit-framing students’ abilities or challenging their beliefs about the relevance of physics, we show how incorporating their rich disciplinary experiences can make physics classrooms truly more relevant.

The use of machine learning and data mining techniques across many disciplines has exploded in recent years with the field of educational data mining growing significantly in the past 15 years. In this study, random forest and logistic regression models were used to construct early warning models of student success in introductory calculus-based mechanics (Physics 1) and electricity and magnetism (Physics 2) courses at a large eastern land-grant university. By combining in-class variables such as homework grades with institutional variables such as cumulative GPA, we can predict if a student will receive less than a “B” in the course with 73% accuracy in Physics 1 and 81% accuracy in Physics 2 with only data available in the first week of class using logistic regression models. The institutional variables were critical for high accuracy in the first four weeks of the semester. In-class variables became more important only after the first in-semester examination was administered. The student’s cumulative college GPA was consistently the most important institutional variable. Homework grade became the most important in-class variable after the first week and consistently increased in importance as the semester progressed; homework grade became more important than cumulative GPA after the first in-semester examination. Demographic variables including gender, race or ethnicity, and first generation status were not important variables for predicting course grade.

Students’ intentions to persevere and their career choices in science, technology, engineering, and math fields can be impacted by their physics identities. Women are severely underrepresented at all levels in physics and engineering. Physics in particular has stereotypes about being a discipline for brilliant men. Therefore, it is particularly difficult for women who do not fit the description of a stereotypical physicist to develop a physics identity. Thus, understanding the factors underlying physics identity in introductory physics classrooms is important for creating an equitable and inclusive physics learning environment and has the potential to at least partly explain the current underrepresentation of women in physics-related majors and careers. In this study, we examined physics identity and several other motivational constructs of male and female students by administering a survey in introductory calculus-based physics courses at a large research university. We found gender differences in how students identify as a physics person and how their perceived recognition from others, such as their teaching assistants or instructors, peers, or family members relates to their physics identities. We tested separate models by gender that examined how different motivational constructs relate to students’ physics identities. We found that the perception of being recognized by influential others such as the course instructor or teaching assistants was differentially related to female and male students’ physics self-efficacy and sense of belonging in the physics classroom. These findings call for improving the physics learning environments to make them equitable so that all students have a high sense of belonging and self-efficacy and opportunity to develop a strong physics identity.

Conceptual inventory surveys are routinely used in education research to identify student learning needs and assess instructional practices. Students might not fully engage with these instruments because of the low stakes attached to them. This paper explores tests that can be used to estimate the percentage of students in a population who might not have taken such surveys seriously. These three seriousness tests are the pattern recognition test, the easy questions test, and the uncommon answers test. These three tests are applied to sets of students who were assessed either by the Force Concept Inventory, the Conceptual Survey of Electricity and Magnetism, or the Brief Electricity and Magnetism Assessment. The results of our investigation are compared to computer simulated populations of random answers.

We examined the variation in Force and Motion Conceptual Evaluation (FMCE) preclass scores according to the type of physics class a student had in high school. This was done for students who had taken Physics 1 at a highly selective university. The majority of students had taken an Advanced Placement (AP) physics course, allowing us to examine in detail the correlation between FMCE score and both taking an AP course and the score on the AP exam. We also carried out regression analyses to determine how FMCE prescores and course final exam scores depend on taking an AP course and AP exam scores, when math SAT scores are included as a proxy of students’ general level of college preparation. Students who take any type of physics course in high school outscore those with no prior physics experience by 26%, but students who have taken AP physics do not significantly outperform those who have taken a normal high school physics course—many students who took AP physics scored very low on the FMCE. Furthermore, while taking AP physics predicts a statistically significant increase in FMCE scores, the effect size (0.30) is smaller than that seen for math SAT scores (0.47). We found that AP exam scores were not correlated with final exam scores after controlling for math SAT score. In all, the data indicate that, though taking an AP physics course is correlated with greater conceptual understanding of physics, scoring well on the AP physics exam may be a rather weak measure of conceptual understanding of physics or the mastery of physics one would expect students to achieve from an introductory university physics course. This work was done with an unusual population. Further studies are needed to determine how general the weak relationship is between AP exam performance and FMCE performance that we observed.

The understanding of graphs and extraction of relevant information from graphs plays a major role in physics education and is also important in several related fields. Recently, Susac et al. [Phys. Rev. Phys. Educ. Res. 14, 020109 (2018)] compared physics and psychology students’ understanding of graphs in the contexts of physics and finance. They showed that physicists scored significantly higher in both domains and that all students solved the slope problems better than the area problems. Moreover, eye-tracking data revealed that physics students spent more time on problems associated with the area under the graph and focused longer on the axis labels of finance graphs, indicating higher cognitive demands. In this eye-tracking study, we aim for a generalization of the results obtained by Susac et al. by comparing physics students to another nonphysics sample, viz., economics students. The findings broadly confirm the results of Susac et al.; that is, physics students perform better than nonphysics students. While economics students likely have better prior knowledge on finance context than psychology students, the physics students still outperform them on the finance questions. In contrast to the work by Susac et al., both groups of students had the same visit duration on the graphs, consequently proving total dwell time to be an inadequate predictor of performance. Instead, we identify that attention on concept-specific areas of interest within the graphs discriminates the correct from the incorrect performers. Furthermore, we analyzed the confidence level of the two student groups and found that physics students have a higher ability to correctly judge their own performance compared to economics students. Overall, our results highlight the importance of an instructional adjustment towards a more mathematical- and graphical-based education.