Although there is widespread agreement on the importance of communication in physics-intensive careers, there is little prior research on how mathematics is integrated into communication. To examine how and what math is communicated in the workplace, we interviewed managers and recently hired employees from optics companies. Using a priori and emergent thematic coding, we found that symbolic math was purposefully hidden in many communication situations to avoid confusion. Alternatively, visual communication through blueprints, diagrams, and visuals of data was widely used across the optics workplace. Spreadsheets were a universal tool for exchanging mathematics through data, formulas, graphs, and calculations; however, different people relied on the spreadsheets for different purposes (e.g., executing calculations or programming formulas). Our data illuminates the value of specific strategies for communicating math and how math is communicated between employees, managers, and clients. These findings suggest the importance of teaching physics majors how to explain mathematical ideas for a variety of audiences and purposes.

It is important to develop models about how mathematics is used in professional physics settings. Existing models of math use focus on mathematical modeling for problem solving. However, workplace problems often include design problems, troubleshooting, and more. To study workplace mathematics, we conducted hour-long, semi-structured interviews with employees at photonics and optics companies in Rochester, NY. We applied an emergent coding process to classify instances of math in the workplace, and present two models of mathematics use within workplace tasks. We describe a four-phase engineer task consisting of defining the problem, designing a product, testing the product, and communicating results. A common technician task replaces the design phase with manufacturing the product. Workplace math is embedded in these phases through various representations such as simulations, schematics, and machining codes. Educators should consider using diverse problem types since they require additional mathematical representations and techniques to be brought to the forefront.

As physics departments increasingly emphasize computational training within the physics curriculum, there is a need for educators to have guiding principles for deciding how and when to use computational approaches over analytical math and vice versa. We investigated the use of analytical and computational mathematics in professional practice by conducting ten semi-structured interviews with PhD students in the physical sciences. The interviews revealed context-rich situations where computational and analytical math were valued and used. Through an emergent and thematic coding process, key contextual features were distilled. Although analytical math was valued as a calculational tool (e.g., manipulating equations), the most prevalent use of analytical math was to develop a preliminary understanding of a problem, which included modeling systems through equations, developing simplified toy models, understanding background concepts, and understanding how varying parameters affected system behavior. Computational tools had a complementary role of data analysis, complex numerical simulations, and visualization.

Student clickstream data can provide valuable insights about student activities in an online learning environment and how these activities inform their learning outcomes. However, given the noisy and complex nature of this data, an ongoing challenge involves devising statistical techniques that capture clear and meaningful aspects of students' click patterns. In this paper, we utilize statistical change detection techniques to investigate students' online behaviors. Using clickstream data from two large university courses, one face-to-face and one online, we illustrate how this methodology can be used to detect when students change their previewing and reviewing behavior, and how these changes can be related to other aspects of students' activity and performance.

Emotions play a critical role during learning and problem solving with advanced learning technologies (ALTs). Despite their importance, relatively few attempts have been made to understand learners' emotional monitoring and regulation by using data visualizations of their own (and others') cognitive, affective, metacognitive, and motivational (CAMM) self-regulated learning (SRL) processes to potentially foster their emotion regulation (ER). We present a theoretically based and empirically driven conceptual framework that addresses ER by proposing the use of visualizations of one's own and others' CAMM SRL multichannel data to facilitate learners' monitoring and regulation of emotions during learning with ALTs. We use an example with eye-tracking data to illustrate the mapping between theoretical assumptions, ER strategies, and the types of data visualizations that can enhance learners' ER, including key processes such as emotion flexibility, emotion adaptivity, and emotion efficacy. We conclude with future directions leading to a systematic interdisciplinary research agenda that addresses outstanding ER-related issues by integrating models, theories, methods, and analytical techniques for the cognitive, learning, and affective sciences; human computer interaction (HCI); data visualization; big data; data mining; and SRL.

Self-regulated learning (SRL) is a process that highly fluctuates as students actively deploy their metacognitive and cognitive processes during learning. In this paper, we apply an extension of latent profiling, latent transition analysis (LTA), which investigates the longitudinal development of students' SRL latent class memberships over time. We will briefly review the theoretical foundations of SRL and discuss the value of using LTA to investigate this multidimensional concept. This study is based on college students (n = 75) learning about the human circulatory system while using MetaTutor, an intelligent tutoring system that adaptively supports SRL and targets specific metacognitive SRL processes including judgment of learning (JOL) and content evaluation (CE). Preliminary results identify transitional probabilities of SRL profiles from four distinct events associated with the use of SRL.

The incorporation of computer-based platforms in the classroom has introduced the ability to conduct numerous randomized control trials at scale with student-level randomization. Such systems are able to collect vast amounts of data on each student while completing work in the classroom and at home. It is often the case, however, that the effects of these trials are reported across all students, ignoring the potential for personalized learning. Personalized learning, or the observation of heterogeneous treatment effects, considers that the effects of a studied learning intervention may differ for individual students; while an intervention may work well for low-performing students, for example, it may have no effect for higher performing students. Personalized learning can lead to better instructional practices that maximizes the learning benefits for each individual student, and with the use of computer-based platforms, such individualized instruction is made feasible at large scales. In this work we use a causal decision tree to observe treatment effects in 9 experiments run in the ASSISTments online learning platform.

I investigate how the educational demands of local labor markets shape high school course offerings and student course taking. Using the Education Longitudinal Study of 2002 linked to the U.S. Census 2000, I focus on local economic variation in the share of jobs that do not demand a bachelor's degree. I find that schools in local labor markets with higher concentrations of subbaccalaureate jobs devote a larger share of their course offerings to career and technical education (CTE) courses and a smaller share to advanced college-preparatory courses compared to schools in labor markets with lower concentrations of subbaccalaureate jobs, even net of school resources. Students in labor markets with higher concentrations of subbaccalaureate jobs take greater numbers of CTE courses, and higher-achieving students in these labor markets are less likely to take advanced math and Advanced Placement/International Baccalaureate courses. These course-taking disparities are largely due to school course offerings. This study shows how local economic inequalities shape high school curricular stratification, and suggests that school curricula linked to the educational demands of local jobs delimits the college preparation opportunities of high-achieving students.

The general view in psychological science is that natural categories obey a coherent, family-resemblance principle. In this investigation, we documented an example of an important exception to this principle: Results of a multidimensional-scaling study of igneous, metamorphic, and sedimentary rocks (Experiment 1) suggested that the structure of these categories is disorganized and dispersed. This finding motivated us to explore what might be the optimal procedures for teaching dispersed categories, a goal that is likely critical to science education in general. Subjects in Experiment 2 learned to classify pictures of rocks into compact or dispersed high-level categories. One group learned the categories through focused high-level training, whereas a second group was required to simultaneously learn classifications at a subtype level. Although high-level training led to enhanced performance when the categories were compact, subtype training was better when the categories were dispersed. We provide an interpretation of the results in terms of an exemplar-memory model of category learning.

Equitable gender representation is an important aspect of scientific workforce development to secure a sufficient number of individuals and a diversity of perspectives. Biology is the most gender equitable of all scientific fields by the marker of degree attainment, with 52.5% of PhDs awarded to women. However, equitable rates of degree completion do not translate into equitable attainment of faculty or postdoctoral positions, suggesting continued existence of gender inequalities. In a national cohort of 336 first-year PhD students in the biological sciences (i.e., microbiology, cellular biology, molecular biology, developmental biology, and genetics) from 53 research institutions, female participants logged significantly more research hours than males and were significantly more likely than males to attribute their work hours to the demands of their assigned projects over the course of the academic year. Despite this, males were 15% more likely to be listed as authors on published journal articles, indicating inequality in the ratio of time to credit. Given the cumulative advantage that accrues for students who publish early in their graduate careers and the central role that scholarly productivity plays in academic hiring decisions, these findings collectively point to a major potential source of persisting underrepresentation of women on university faculties in these fields.