College students are experiencing a significant mental health crisis, with rising rates of psychological distress. To help understand this trend, this study examines recursive relationships in the classroom between perceived mindset beliefs—that is, whether students perceive others in their classroom to view intelligence as malleable or fixed—and psychological distress. Across three time points, 288 undergraduates taking a physics course completed measures of perceived classroom mindset and psychological distress. Random intercept cross-lagged panel analyses, which controlled for demographic factors and students’ own mindset beliefs, revealed that perceiving the classroom culture as more fixed-minded early in the semester was associated with increased psychological distress later. Likewise, increased psychological distress early in the semester was associated with perceiving the classroom culture to be more fixed-minded later. These findings suggest that perceived mindset and distress are mutually reinforcing, highlighting the importance of addressing both in interventions aimed at alleviating student distress.

We conducted two studies to investigate the extent to which brief, spaced, mastery practice on skills relevant to introductory physics affects student performance. The first study investigated the effect of practice of “specific” physics skills, each one relevant to only one or a few items on the course exam. This study employed a quasiexperimental design with 766 students assigned to “intervention” or “control” conditions by lecture section sharing common exams. Results of the first study indicate significant improvement in the performance for only some of the exam items relevant to the specific skills practiced. We also observed between-section performance differences on other exam items not relevant to training, which may be due to specific prior quiz items from individual instructors. The second study investigated the effect of practice on the “general” skill of algebra relevant to introductory physics, a skill which was relevant to most of the exam items. This study employed a similar quasiexperimental design with 363 students assigned to treatment or control conditions, and we also administered a reliable pre- and post-test assessment of the algebra skills that was iteratively developed for this project. Results from the second study indicate that 75% of students had high accuracy on the algebra pretest. Students in the control condition who scored low on the pretest gained about 0.7 standard deviations on the post-test, presumably from engagement with the course alone, and students in the algebra practice condition had statistically similar gains, indicating no observed effect of algebra practice on algebra pre- to post-test gains. In contrast, we find some potential evidence that the algebra practice improved final exam performance for students with high pretest scores and did not benefit students with low pretest scores, although this result is inconclusive: the point estimate of the effect size was 0.24 for high pretest scoring students, but the 95% confidence interval [−0.01, 0.48] slightly overlapped with zero. Further, we find a statistically significant positive effect of algebra practice on exam items that have higher algebraic complexity and no effect for items with low complexity. One possible explanation for the added benefit of algebra practice for high-scoring students is fluency in algebra skills may have improved. Overall, our observations provide some evidence that spaced, mastery practice is beneficial for exam performance for specific and general skills, and that students who are better prepared in algebra may be especially benefitting from mastery practice in relevant algebra skills in terms of improved final exam performance.

Accuracy on assessments is commonly studied in education research but response time (RT) is relatively less investigated even though decades of research in cognitive sciences indicate that time can be an important dimension for understanding student learning. To better understand RT and the potentially important relations between accuracy and RT in physics education, we conducted an exploratory investigation by collecting and analyzing both accuracy and RT data on physics-relevant math skills on low-stakes pre and posttests as well as course exam scores in algebra-based and calculus-based introductory physics courses over two semesters for a total of N=1936 participants. Overall, we found a high level of variation in response times revealing weak but consistent patterns of associations between RT and accuracy on skills and exam scores. First, we found a nonlinear relationship between RT and accuracy on the pretest and on the post-test, which may indicate a variety of strategies and engagement among students on these participation-credit-only tests. Second, the results indicate that while RT alone does not predict course grade, when controlling for accuracy on pre or posttest math skills, students with lower RT on these skills are more likely to get better grades. Therefore, both pre or posttest accuracy and speed predicted course grades, though accuracy explained a substantial amount of variance (∼35%) while pretest RT explained a much smaller amount of variance (∼1%). Third, controlling for both pretest accuracy and pretest RT, we found that students who sped up from pre to posttest were likely to get higher exam scores; however, students who slowed down were on average likely to have a higher post-test score. Fourth, since systemic inequities in STEM education have been documented via measured mean differences between some demographic groups for exam scores and accuracy on math skills, we compared RTs by sex, race, first-generation status, and citizenship to potentially gain more insight into these inequities. We found no consistent or conclusive evidence of demographic differences, though in multiple comparisons, Black, Hispanic, Native American, and Pacific Islander students had larger RTs on average, and in one comparison they were slightly faster. We found that RT was not a mediator of demographic differences in physics grades, though, as expected, accuracy on math skills was a mediator. We briefly discuss how our results relate to various cognitive models such as cognitive ability, speed-accuracy trade-offs, fluency and cognitive load, dual-process theories, and student psychological factors like self-efficacy, anxiety, and motivation. We argue that, based on which (if any) of the above mechanisms are at play, valuing speed in physics may have benefits, such as improving fluency to reduce cognitive load and drawbacks, such as unintentionally using speed as a proxy for achievement or inducing excessive stress that may interfere with performance and student well-being.

This study investigates the evolution and associations between exam grades and social comparison concern (SCC) among students in an introductory calculus-based physics course. We begin with a descriptive characterization of midterm and final exam scores as well as pre-post SCC scores, including the concurrent evolution of these scores during the course. We hypothesize a feedback loop in which changes in SCC scores are mediated by exam grades, and changes in exam scores are mediated by SCC scores. We employ a structural equation model to determine whether the data are consistent with these hypotheses. Results indicate that there were significant within-student changes in the relative grade standing from exam to exam and that changes in SCC scores depended on both the pre-SCC scores and scores on the first midterm exam. Further, we find evidence that exam scores partially mediate the association between preand post-SCC scores, and in turn, post-SCC scores partially mediate associations between midterm and final exam scores, though the mediation effects are somewhat small, comprising 5%-10% of the total effects between exam scores and SCC. We also find that while SCC scores are somewhat correlated with exam scores, they are only very weakly correlated with nonexam grade components, consistent with the idea that exam scores (rather than nonexam scores) are driving changes in SCC and vice versa. Overall, the results provide empirical, correlational evidence to motivate further experimental investigation into a hypothesized dynamic and iterative feedback loop in which student concern about ability or performance compared to others (SCC) can either negatively or positively interfere with student performance on exams.

We have investigated the temporal patterns of algebra (N = 606) and calculus (N = 507) introductory physics students practicing multiple basic physics topics several times throughout the semester using an online mastery homework application called science, technology, engineering, and mathematics (STEM) fluency aimed at improving basic physics skills. For all skill practice categories, we observed an increase in measures of student accuracy, such as a decrease in the number of questions attempted to reach mastery, and a decrease in response time per question, resulting in an overall decrease in the total time spent on the assignments. The findings in this study show that there are several factors that impact a student's performance and evolution on the mastery assignments throughout the semester. For example, using linear mixed modeling, we report that students with lower math preparation for the physics class start with lower accuracy and slower response times on the mastery assignments than students with higher math preparation. However, by the end of the semester, the less prepared students reach similar performance levels to their more prepared classmates on the mastery assignments. This suggests that STEM fluency is a useful tool for instructors to implement to refresh student's basic math skills. Additionally, gender and procrastination habits impact the effectiveness and progression of the student's response time and accuracy on the STEM fluency assignments throughout the semester. We find that women initially answer more questions in the same amount of time as men before reaching mastery. As the semester progresses and students practice the categories more, this performance gap diminishes between males and females. In addition, we find that students who procrastinate (those who wait until the final few hours to complete the assignments) are spending more time on the assignments despite answering a similar number of questions as compared to students who do not procrastinate. We also find that student mindset (growth vs fixed mindset) was not related to a student's progress on the online mastery assignments. Finally, we find that STEM fluency practice improves performance beyond the effects of other components of instruction, such as lectures, group-work recitations, and homework assignments.

A framework of cyclic observation and triangulation was applied over a period of 4 years to graduate student difficulties related to quantum spin, in which numerous in-class observations and interviews were used to identify common, persistent difficulties. Written items were iteratively developed over two years to add a quantitative component. Items were administered to graduate students at two collaborating institutions, over three years. We find that students generally obtained scores or correct proportions ranging from 30%-70% on the written items, and answering patterns were similar across all institutions. All items were identified by the course instructors as being relevant to instructional goals of the course. We report on a number of graduate student difficulties with spin, including orthogonality of spin-1/2 states, projections of spin states, spin addition, and exchange symmetry. We briefly discuss possible theoretical frameworks through which to interpret these results.

Students' cost perceptions have been associated with lower retention and academic performance in science, technology, engineering, and mathematics (STEM). Guided by expectancy-value theory, we examined whether relations between perceived costs and physics outcomes (i.e., engagement and achievement) varied as a function of self-efficacy or task values among undergraduate physics students (N = 1,124). We also examined whether the interactive relations were further moderated by course level in the curricular sequence. Overall, findings from moderated moderation analyses indicated that perceived costs were negatively related to different components of engagement (i.e., effort, persistence, procrastination, and choice) and achievement (i.e., physics course grades). However, the magnitude of relations often depended on levels of self-efficacy or task value. Some of the interactive relations between these variables also differed between introductory- and upper-level physics courses. Taken together, results indicated that higher self-efficacy or task values do not compensate for the negative effects of perceiving high cost on engagement. Moreover, cost perceptions were in some cases more negatively related to engagement when students reported higher self-efficacy or task values. Finally, mitigating cost perceptions may be particularly important in introductory undergraduate physics courses. Implications and directions for future research are discussed.

Research into dual-process theories of reasoning from cognitive psychology suggests ways to improve classroom instruction in physics.

In this study we characterize student procrastination habits and investigate associations between these habits and student performance on graded course components, student beliefs about their own procrastination behavior, and gender. The procrastination habits of calculus-based introductory physics students are measured via the amount of time before the assignment deadline or "completion time" that students submit their work on relatively short (>30 min) weekly online assignments. With the aid of latent profile analysis, we find that one can meaningfully categorize students into 4 completion time classes that clearly distinguish students between their mean completion time, their week-to-week completion time patterns, assignment completion rates, mean course grades, and proportion of women. Consistent with many studies in a variety of contexts, we find that procrastinating students tend to have lower course grades. Closer examination of exam and nonexam grade components reveals that completion time is directly associated with the nonexam component, but its association with the exam component is weaker and completely mediated by the nonexam component grade. This is in contrast to student ACT score, which is strongly associated with exam component but only weakly associated with the nonexam component, and the direct association of ACT with the exam scores is only weakly mediated by nonexam scores. Further, we find that ACT score is at best very weakly correlated with completion time. Taken together this supports the idea that exam and nonexam components are separately predicted by the two somewhat "orthogonal" measures of ACT score and completion time, and we propose that these are measuring so-called cognitive and noncognitive factors, respectively. Regarding gender differences, we found that on average women tended to procrastinate less than men, submitting the assignments on average 8 h earlier than men. Considering previous studies documenting that women tend to score higher than men on nonexam components, we found that completion time completely mediates the gender differences in nonexam components, providing support for the hypothesis that procrastination mediates the gender differences in performance on nonexam components. Finally, we found that the overwhelming majority (90%) of students did not strategically ("actively") intend to delay completion of the assignment, and that students who did indicate actively delaying were 2-3 times more likely to receive a D or E in the course.

We investigate the effects of guided group work sessions on graduate student performance on a quantum mechanics assessment. Data from a single large Midwestern university were taken over a five-year period, during which guided group work sessions were offered to accompany the graduate-level quantum mechanics course. Students were pre- and post-tested using a set of mostly conceptual items that we call the graduate quantum mechanics assessment. The reliability and validity of this assessment are addressed. A mixed linear model is used to analyze the dependence of post-test scores on factors such as group work attendance, pretest scores, GRE Physics scores, and others. We find a statistically significant effect of group work attendance on post-pre gains, specifically that attendance of one 60-min group work session improves performance on a related post-test item by 6.4%, administered 2-10 weeks after the session. We discuss the lack of a randomized control group and address possible confounding effects such as student self-selection, and attitudinal and motivational factors. Overall, the results of this study indicate that guided group work sessions at the graduate level can be feasible and effective. We note preliminary observations of differences in group interactions and classroom logistics compared to group work at the undergraduate level.

Two set of studies were conducted to better understand grades and grading practices in physics courses, and how these might influence demographic representational disparities in physics. The first study investigates the relationships between grades and the student-level factors of standardized test scores, (binary) gender, underrepresented minority (URM) status, first generation (FG) status, citizenship status, and age of over 20 000 students enrolled in algebra-based and calculus-based introductory physics courses. Consistent with other studies, we find differences in mean grades for all of these factors, except for gender, and when standardized test scores are included in a regression model predicting grades, the demographic differences in grades decreases, though typically remain nonzero. We also find gender by test score and URM by test score interactions when predicting grades. The second study examines grade component scores, and replicates the finding that compared to men, women achieve higher scores on nonexam components and lower scores on exam components. We also find that the gap in score between URM and FG students and their counterparts is less for non-exam components than for exam components. Because of these differentials in components, we compared different models of grade components weighting and find that women and URM students differentially benefit from stronger weighting of nonexam components. While the benefit to grades is relatively small, the relative shift in percentages of grade rates of A, D, and F can have dramatic differential shifts. We also find that while exam components are moderately strongly correlated with standardized tests scores, nonexam components are not. These results suggest that grade component weighting is inevitably tied to issues of demographic equity, in the sense that altering the weights may change demographic disparities in grades and change the dependency of grades on standardized test scores. We conclude with a call for more attention to grading practices and what is rewarded in introductory physics courses.

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.

Prelecture questions have long been used in a variety of courses within STEM to motivate prelecture reading and to help class time be used more efficiently. It is difficult to incorporate prelecture questions into many advanced topics courses and to determine their effectiveness, due to the necessary content knowledge within specialized areas, and due to the small number of students enrolled in these courses. Here, we report on the implementation of a set of approximately 110 prelecture questions over two years of instruction in a special topics course in condensed matter physics. We report quantitatively on student difficulties with different prelecture questions and on their improvement on a survey of condensed matter concepts given at the beginning and end of the course. We report qualitatively on interviews with students in a graduate condensed matter course.

A critical component of scientific reasoning is the consideration of alternative explanations. Recognizing that decades of cognitive psychology research have demonstrated that relative cognitive accessibility, or "what comes to mind," strongly affects how people reason in a given context, we articulate a simple "cognitive accessibility rule", namely that alternative explanations are considered less frequently when an explanation with relatively high accessibility is offered first. In a series of four experiments, we test the cognitive accessibility rule in the context of consideration of alternative explanations for six physical scenarios commonly found in introductory physics curricula. First, we administer free recall and recognition tasks to operationally establish and distinguish between the relative accessibility and availability of common explanations for the physical scenarios. Then, we offer either high or low accessibility explanations for the physical scenarios and determine the extent to which students consider alternatives to the given explanations. We find two main results consistent across algebra- and calculus-based university level introductory physics students for multiple answer formats. First, we find evidence that, at least for some contexts, most explanatory factors are cognitively available to students but not cognitively accessible. Second, we empirically verify the cognitive accessibility rule and demonstrate that the rule is strongly predictive, accounting for up to 70% of the variance of the average student consideration of alternative explanations across scenarios. Overall, we find that cognitive accessibility can help to explain biases in the consideration of alternatives in reasoning about simple physical scenarios, and these findings lend support to the growing number of science education studies demonstrating that tasks relevant to science education curricula often involve rapid, automatic, and potentially predictable processes and outcomes.