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We analyze the identity trajectory of a single case study, Cassidy, within the physics community. We focus our analysis on two settings in the physics community: an undergraduate research experience, and undergraduate coursework. We use video data from three interviews (spanning roughly fifteen months) to longitudinally analyze shifts in participation. We discuss Cassidy's experience through two constructs: "normative identities," Cassidy's sense of the valued roles within physics, as well as "personal identity," who Cassidy is within the physics community and the extent to which she aligns with "normative identities." In attending to shifts in the alignment between personal and normative identities, we identify several "entry points," or salient events that open up new opportunities for participation.

Professional problem-solving practice in physics and engineering relies on mathematical sense making--reasoning that leverages coherence between formal mathematics and conceptual understanding. A key question for physics education is how well current instructional approaches develop students' mathematical sense making. We introduce an assessment paradigm that operationalizes a typically unmeasured dimension of mathematical sense making: use of calculations on qualitative problems and use of conceptual arguments on quantitative problems. Three assessment items embodying this calculation-concept crossover assessment paradigm illustrate how mathematical sense making can positively benefit students' problem solving, leading to more efficient, insightful, and accurate solutions. These three assessment items were used to evaluate the efficacy of an instructional approach focused on developing students' mathematical sense making skills. In a quasi-experimental study, three parallel lecture sections of first-semester, introductory physics were compared: two mathematical sense making sections, one with an experienced instructor and one with a novice instructor, and a traditionally taught section, as a control group. Compared to the control group, mathematical sense making groups used calculation-concept crossover approaches more often and gave more correct answers on the crossover assessment items, but they did not give more correct answers to associated standard problems. In addition, although students' postcourse epistemological views on problem-solving coherence were associated with their crossover use, they did not fully account for the differences in crossover approach use between the mathematical sense making and control groups. These results demonstrate a new assessment paradigm for detecting a typically unmeasured dimension of mathematical sense making and provide evidence that a targeted instructional approach can enhance engagement with mathematical sense making in introductory physics.

[This paper is part of the Focused Collection on Curriculum Development: Theory into Design.] In the "standard" physics education research curriculum-development model, researchers are cast primarily as producers of curricula and instructors are cast primarily consumers, i.e., adopters and adapters. We illustrate a complementary model in which researchers' curricular modules, and also their "pure" research unattached to curriculum development, can serve as instructionally generative fodder that inspires and loosely guides instructors in creating their own curricular materials. Drawing on experiences from our graduate student days, we show how particular curricula and research papers influenced our curriculum development and instruction in particular ways. We then argue that the physics education ecosystem could benefit if researchers were more intentional about creating potential "instructionally generative fodder," and we suggest ways to do so. Although not intended to replace the standard curriculum-development model, which has a history of producing effective tutorials and other curricular modules, our alternative model casts the researcher and instructor as co-equal contributors to the research-based yet creative process of curriculum generation.

[This paper is part of the Focused Collection on Curriculum Development: Theory into Design.] This paper proposes the rethinking of the division of labor between physics education research curriculum developers and classroom instructors. Historically, both curriculum developers and instructors have taken responsibility for fostering students' conceptual development, epistemological development, and other learning goals related to physics content knowledge and practices or process skills. By contrast, responsibility for fostering productive group dynamics has been taken up almost entirely by instructors. Tutorial and lab developers structure their materials to be used in small groups, but have not generally designed, tested, and refined their materials to minimize problematic group dynamics. In this paper, we argue that the written tutorial can and should do more to prevent negative group dynamics from arising. To make this claim plausible, we describe an example from our own experience. While revising a tutorial, we noticed some problematic dynamics emerging; one of the students was unfairly blamed for a simulation-setting mistake and was later left out of a conversation. We came up with hypotheses about factors that might have contributed to those dynamics. A few of those factors, we argue, could be addressed in part through tutorial revision. While acknowledging that instructors will always have more capacity and hence more responsibility than curriculum writers to foster productive group dynamics, we call for tutorial writers, during the testing and revision of their materials, to monitor how the tutorial impacts team dynamics and to be transparent (in publications and presentations) about how they modified the tutorial to address problematic dynamics they observed.

Evidence from psychology, cognitive science, and neuroscience suggests that cognition and emotions are coupled. Education researchers have also documented correlations between emotions (such as joy, anxiety, fear, curiosity, boredom) and academic performance. Nonetheless, most research on students' reasoning and conceptual change within the learning sciences and physics and science education research has not attended to the role of learners' emotions in describing or modeling the fine timescale dynamics of their conceptual reasoning. The few studies that integrate emotions into models of learners' cognition have mostly done so at a coarse grain size. In this study, toward the long-term goal of incorporating emotions into models of in-the-moment cognitive dynamics, we present a case study of Judy, an undergraduate electrical engineering and physics major. We show that shifts in the intensity of a fine-grained aspect of Judy's emotions, her annoyance at conceptual homework problems, co-occur with shifts in her epistemological stance toward differentiating knowledge about and the practical utility of real circuits and idealized circuit models. We then argue for the plausibility of a cognitive model in which Judy's emotions and epistemological stances mutually affect each other. We end with discussions on how models of learners' cognition that incorporate their emotions are generative for instructional purposes and research on learning.

Mathematical sense-making--looking for coherence between the structure of the mathematical formalism and causal or functional relations in the world--is a core component of physics expertise. Some physics education research studies have explored what mathematical sense-making looks like at the introductory physics level, while some historians and "science studies" have explored how expert physicists engage in it. What is largely missing, with a few exceptions, is theoretical and empirical work at the intermediate level--upper division physics students--especially when they are learning difficult new mathematical formalism. In this paper, we present analysis of a segment of video-recorded discussion between two students grappling with a quantum mechanics question to illustrate what mathematical sense-making can look like in quantum mechanics. We claim that mathematical sense-making is possible and productive for learning and problem solving in quantum mechanics. Mathematical sense-making in quantum mechanics is continuous in many ways with mathematical sense-making in introductory physics. However, in the context of quantum mechanics, the connections between formalism, intuitive conceptual schema, and the physical world become more compound (nested) and indirect. We illustrate these similarities and differences in part by proposing a new symbolic form, "eigenvector eigenvalue," which is composed of multiple primitive symbolic forms.

This study investigates how elite Turkish high school physics students claim to approach learning physics when they are simultaneously (i) engaged in a curriculum that led to significant gains in their epistemological sophistication and (ii) subject to a high-stakes college entrance exam. Students reported taking surface (rote) approaches to learning physics, largely driven by college entrance exam preparation and therefore focused on algorithmic problem solving at the expense of exploring concepts and real-life examples more deeply. By contrast, in recommending study strategies to "Arzu," a hypothetical student who doesn't need to take a college entrance exam and just wants to understand physics deeply, the students focused more on linking concepts and real-life examples and on making sense of the formulas and concepts--deep approaches to learning that reflect somewhat sophisticated epistemologies. These results illustrate how students can epistemically compartmentalize, consciously taking different epistemic stances--different views of what counts as knowing and learning--in different contexts even within the same discipline.

Undergraduate research can support students' more central participation in physics. We analyze markers of two coupled shifts in participation: changes in students' views about the nature of science coupled to shifts in self-efficacy toward physics research. Students in the study worked with faculty and graduate student mentors on research projects while also participating in a seminar where they learned about research and reflected on their experiences. In classroom discussions and in clinical interviews, students described gaining more nuanced views about the nature of science, specifically related to who can participate in research and what participation in research looks like. This shift was coupled to gains in self-efficacy toward their ability to contribute to research; they felt like their contributions as novices mattered. We present two case studies of students who experienced coupled shifts in self-efficacy and views about nature-of-science shifts, and a case study of a student for whom we did not see either shift, to illustrate both the existence of the coupling and the different ways it can play out. After making the case that this coupling occurs, we discuss some potential underlying mechanisms. Finally, we use these results to argue for more nuanced interpretations of self-efficacy measurements.