This study investigated factors influencing Force and Motion Conceptual Evaluation (FMCE) pretest and post-test scores for a sample (N 1/4 1116 students) collected in the introductory calculus-based mechanics class at a large eastern land-grant university. Several academic and noncognitive factors were examined using correlation analysis and linear regression analysis to understand their relation to students??? physics conceptual understanding. High school physics preparation was the most important factor in predicting FMCE pretest score. The kind of high school physics class (normal or Advanced Placement) and the student???s academic performance in that class also greatly affected pretest scores. The optimal linear regression model explained 28% of the variance of pretest scores. Controlling for pretest score, ACT or SAT verbal and mathematics scores, students??? grade expectation, and self-efficacy significantly predicted post-test score. The optimal linear regression model explained 54% of the variance of post-test scores. Pretest scores completely captured the effect of high school preparation on post-test scores; if pretest scores were included in a model predicting post-test scores, then high school physics preparation variables were not significant. Gender differences were observed on both the pretest and the post-test. These differences were not substantially mediated by either academic or noncognitive factors.

This study examined physics major retention to degree at two institutions with substantially different admissions selectivity. Two modes of leaving the physics major were examined: leaving college and changing to another major while staying in college. The risk of leaving college while still enrolled as a physics major was highest in the spring freshman semester. The changing major risk was substantially different between the two institutions. For the less selective institution, the students changed major at the highest rate in the fall sophomore semester. For the more selective institution, the risk of changing major was high through the first two years of college with highest risk in the fall freshman semester and the fall junior semester. Different features were important in predicting the two modes of leaving; these also differed between institutions. For the less selective institution, math readiness (being academically prepared to enroll in Calculus 1 in the fall freshman semester) was the most predictive feature for leaving the physics major while staying in college; high school GPA was the most important feature for predicting both leaving college and graduating with a physics degree. For the more selective institution, ACT composite scores were the only significant predictor of retention. The role of math readiness was dramatic at the less selective institution with 41% of students not math ready upon enrolling in college as physics majors; 59% of these students failed to enroll in the first required physics class.

The Force Concept Inventory (FCI) is a popular multiple-choice instrument used to measure a student's conceptual understanding of Newtonian mechanics. Recently, a network analytic technique called module analysis has been used to identify responses to the FCI and other conceptual instruments that are preferentially selected together by students; these groups of responses are called communities. This study uses module analysis to explore the misconception structure of the FCI at five U.S. institutions with varying undergraduate populations (sample sizes of N 1/4 9606, 4360, 1496, 466, and 213). Students from these universities had a broad range of prior knowledge in physics and of general high school academic preparation, resulting in large differences in FCI normalized gain, pretest, and post-test scores. In the current work, modified module analysis partial was applied and communities of consistently selected responses within the FCI were identified at the five institutions studied. There was substantial similarity between the communities identified postinstruction; somewhat less similarity preinstruction. This suggests that consistently applied Newtonian misconceptions exist both before and after instruction at a wide range of institutions. The most frequently applied misconceptions were largest force determines motion, Newton's third law misconceptions, and motion implies active forces.These misconceptions were still consistently applied even after instruction by a substantial number of students at all but the highest performing of the five institutions.

Understanding how physicists solve problems can guide the development of methods that help students learn and improve at solving complex problems. Leveraging the framework of cognitive task analysis, we conducted semistructured interviews with theoretical physicists (N 1/4 11) to gain insight into the cognitive processes and skills that they use in their professional research. Among numerous activities that theorists described, here we elucidate two activities that theorists commonly characterized as being integral to their work: making assumptions and using analogies. Theorists described making assumptions throughout their research process, especially while setting their project's direction and goals, establishing their model's interaction with mathematics, and revising their model while troubleshooting. They described how assumptions about their model informed their mathematical decision making, as well as instances where mathematical steps fed back into their model's applicability. We found that theorists used analogies to generate new project ideas as well as overcome conceptual challenges. Theorists deliberately sought out or constructed analogies, indicating this is a skill students can practice. When mapping knowledge from one system to another, theorists used systems that shared a high degree of mathematical similarity; however, these systems did not always share similar surface features. We conclude by discussing connections between the ways theorists use assumption and analogy and offering potential new avenues of research regarding applications to instruction.

The COVID-19 pandemic has necessitated disease surveillance using group testing. Novel Bayesian methods using lattice models were proposed, which offer substantial improvements in group testing efficiency by precisely quantifying uncertainty in diagnoses, acknowledging varying individual risk and dilution effects, and guiding optimally convergent sequential pooled test selections. Computationally, however, Bayesian group testing poses considerable challenges as computational complexity grows exponentially with sample size. HPC and big data stacks are needed for assessing computational and statistical performance across fluctuating prevalence levels at large scales. Here, we study how to design and optimize critical computational components of Bayesian group testing, including lattice model representation, test selection algorithms, and statistical analysis schemes, under the context of parallel computing. To realize this, we propose a high-performance Bayesian group testing framework named HiBGT, based on Apache Spark, which systematically explores the design space of Bayesian group testing and provides comprehensive heuristics on how to achieve highperformance, highly scalable Bayesian group testing. We show that HiBGT can perform large-scale test selections (> 250 state iterations) and accelerate statistical analyzes up to 15.9x (up to 363x with little trade-offs) through a varied selection of sophisticated parallel computing techniques while achieving near linear scalability using up to 924 CPU cores.

Background Math anxiety (MA) and math achievement are generally negatively associated. Aims This study investigated whether and how classroom engagement behaviors mediate the negative association between MA and math achievement. Sample Data were drawn from an ongoing longitudinal study that examines the roles of affective factors in math learning. Participants consisted of 207 students from 4th through 6th grade (50% female). Methods Math anxiety was measured by self-report using the Mathematics Anxiety Scale for Children (Chiu & Henry, 1990, Measurement and valuation in Counseling and Development, 23, 121). Students self-reported their engagement in math classrooms using a modified version of the Math and Science Engagement Scale (Wang et al., 2016, Learning and Instruction, 43, 16). Math achievement was assessed using the Applied Problem, Calculations, and Number Matrices subtests from the Woodcock-Johnson IV Tests of Achievement (Schrank et al., 2014, Woodcock-Johnson IV Tests of Achievement. Riverside). Mediation analyses were conducted to examine the mediating role of classroom engagement in the association between MA and math achievement. Results Students with higher MA demonstrated less cognitive-behavioral and emotional engagement compared to students with lower MA. Achievement differences among students with various levels of MA were partly accounted for by their cognitive-behavioral engagement in the math classroom. Conclusions Overall, students with high MA exhibit avoidance patterns in everyday learning, which may act as a potential mechanism for explaining why high MA students underperform their low MA peers.

This exploratory paper highlights how problem-based learning (PBL) provided the pedagogical framework used to design and interpret learning analytics from Crystal Island: EcoJourneys, a collaborative game-based learning environment centred on supporting science inquiry. In Crystal Island: EcoJourneys, students work in teams of four, investigate the problem individually and then utilize a brainstorming board, an in-game PBL whiteboard that structured the collaborative inquiry process. The paper addresses a central question: how can PBL support the interpretation of the observed patterns in individual actions and collaborative interactions in the collaborative game-based learning environment? Drawing on a mixed method approach, we first analyzed students' pre- and post-test results to determine if there were learning gains. We then used principal component analysis (PCA) to describe the patterns in game interaction data and clustered students based on the PCA. Based on the pre- and post-test results and PCA clusters, we used interaction analysis to understand how collaborative interactions unfolded across selected groups. Results showed that students learned the targeted content after engaging with the game-based learning environment. Clusters based on the PCA revealed four main ways of engaging in the game-based learning environment: students engaged in low to moderate self-directed actions with (1) high and (2) moderate collaborative sense-making actions, (3) low self-directed with low collaborative sense-making actions and (4) high self-directed actions with low collaborative sense-making actions. Qualitative interaction analysis revealed that a key difference among four groups in each cluster was the nature of verbal student discourse: students in the low to moderate self-directed and high collaborative sense-making cluster actively initiated discussions and integrated information they learned to the problem, whereas students in the other clusters required more support. These findings have implications for designing adaptive support that responds to students' interactions with in-game activities.

Much research has found disrupted executive functioning (EF) in deaf and hard-of-hearing (DHH) children; while some theories emphasize the role of auditory deprivation, others posit delayed language experience as the primary cause. This study investigated the role of language and auditory experience in parent-reported EF for 123 preschool-aged children (M-age = 60.1 months, 53.7% female, 84.6% White). Comparisons between DHH and typically hearing children exposed to language from birth (spoken or signed) showed no significant differences in EF despite drastic differences in auditory input. Linear models demonstrated that earlier language exposure predicted better EF (beta = .061-.341), while earlier auditory exposure did not. Few participants exhibited clinically significant executive dysfunction. Results support theories positing that language, not auditory experience, scaffolds EF development.

Relational language is thought to influence mathematical skills. This study examines the association between relational language and number relation skills-knowledge of cardinal, ordinal, and spatial principles-among 104 U.S. kindergartners (5.9 years; 44% boys; 37% White, 25% Black, 14% Asian, 24% other) in the 2017-2018 academic year. Controlling for general verbal knowledge, executive function, and counting and number identification skills, relational language predicted later number relation skills, specifically number line estimation, beta = .30. Relational language did not differentially predict number line estimation performance in children with low or high number relation skills, likely due to the restricted ranges of data within subgroups. Number relation skills, specifically number line estimation and number ordering, may be a pathway between relational language and mathematical skills.