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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.

Background: While there has been increasing recognition of the importance of attending to students' views about what counts as knowing and learning a STEM field, surveys that measure these "epistemological" beliefs are often used in ways that implicitly assume the fields, e.g., "physics," to be a single domain about which students might have sophisticated or naïve beliefs. We demonstrate this is not necessarily the case and argue for attending to possible differences in students' epistemological beliefs across different sub-domains of physics. In modern physics and quantum mechanics courses for engineering and physics students, we administered a set of modified Colorado Learning Attitudes about Science Survey (CLASS) items. Each selected item was turned into two items, with the word "physics" changed to "classical physics" in one and "quantum physics" in the other. Results: We found significant splits between students' survey responses about classical vs. quantum physics on some items, both pre- and post-instruction. In classical physics, as compared to quantum physics, students were more likely to report the salience of real-world connections and the possibility of combining mathematical and conceptual reasoning during problem solving. Conclusions: These findings suggest that attending to sub-domain specificity of students' beliefs about physics can be fruitful and ought to influence our instructional choices.

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.

Many science education researchers have argued that learners' commitment to a substance (matter-based) ontology impedes the learning of scientific concepts that scientists typically conceptualize as processes or interactions, such as force, electric current, and heat. By this account, students' tendency to classify these entities as substances or properties of substances leads to robust misconceptions, and instruction should steer novices away from substance-based reasoning. We argue that substance-based reasoning can contribute to the learning and understanding of these very same physics concepts. Our case study focuses on a group of elementary school science teachers in our professional development program. Starting from substance-based metaphors for gravity, the teachers build a sophisticated explanation for why objects of different masses fall with the same acceleration. We argue that, for conceptual, epistemological, and affective reasons, instructional interventions should focus on tapping these productive substance-based resources when they arise rather than attempting to suppress them.

Students' epistemological views about biology--their ideas about what "counts" as learning and understanding biology--play a role in how they approach their courses and respond to reforms. As introductory biology courses incorporate more physics and quantitative reasoning, student attitudes about the role of equations in biology become especially relevant. However, as documented in research in physics education, students' epistemologies are not always stable and fixed entities; they can be dynamic and context-dependent. In this paper, we examine an interview with an introductory student in which she discusses the use of equations in her reformed biology course. In one part of the interview, she expresses what sounds like an entrenched negative stance toward the role equations can play in understanding biology. However, later in the interview, when discussing a different biology topic, she takes a more positive stance toward the value of equations. These results highlight how a given student can have diverse ways of thinking about the value of bringing physics and math into biology. By highlighting how attitudes can shift in response to different tasks, instructional environments, and contextual cues, we emphasize the need to attend to these factors, rather than treating students' beliefs as fixed and stable. (Contains 2 figures and 2 footnotes.)

Much research in engineering and physics education has focused on improving students' problem-solving skills. This research has led to the development of step-by-step problem-solving strategies and grading rubrics to assess a student's expertise in solving problems using these strategies. These rubrics value "communication" between the student's qualitative description of the physical situation and the student's formal mathematical descriptions (usually equations) at two points: when initially setting up the equations, and when evaluating the final mathematical answer for meaning and plausibility. We argue that (i) neither the rubrics nor the associated problem-solving strategies explicitly value this kind of communication "during" mathematical manipulations of the chosen equations, and (ii) such communication is an aspect of problem-solving expertise. To make this argument, we present a case study of two students, Alex and Pat, solving the same kinematics problem in clinical interviews. We argue that Pat's solution, which connects manipulation of equations to their physical interpretation, is more expert-like than Alex's solution, which uses equations more algorithmically. We then show that the types of problem-solving rubrics currently available do not discriminate between these two types of solutions. We conclude that problem-solving rubrics should be revised or repurposed to more accurately assess problem-solving expertise. (Contains 2 tables, 1 figure and 4 footnotes.)

This study explored how researchers' views about the form of students' epistemologies influence how the researchers develop and refine surveys and how they interpret survey results. After running standard statistical analyses on 505 physics students' responses to the Turkish version of the Maryland Physics Expectations-II survey, probing students' epistemologies and expectations, we interpreted the results through two different theoretical lenses, the beliefs perspective and the resources perspective. We showed that the beliefs and resources frameworks provided different interpretations of the psychometric analyses, leading to different conclusions about how the survey results should be interpreted and how the survey should be improved. (Contains 6 tables.)

Effective physics instruction benefits from respecting the physics ideas that introductory students bring into the classroom. We argue that it is similarly beneficial to respect the teaching ideas that novice physics instructors bring to their classrooms. We present a case study of a tutorial teaching assistant (TA), Alan. When we first examined Alan's teaching, we focused our attention on the mismatch between his actions and those advocated by the TA instructors. Further study showed us that Alan cared about helping his students and that his teaching was well integrated with his beliefs about how students learn physics and how teachers can best assist students. Learning about Alan's beliefs and motivations changed our thinking about what might constitute effective professional development for Alan and other TAs. We advocate a new perspective on TA professional development: one in which TAs are seen as partners in the endeavor of educating students and one that seeks to find and build upon productive elements in their beliefs. (Contains 2 figures.)

As part of a long-term program to develop effective, research-based professional development programs for physics graduate student teaching assistants (TAs), we first identify their current classroom practices and why they engage in these practices. In this paper, we identify a set of teaching practices we call "focusing on indicators," which occurs when TAs use signs such as key words or diagrams as evidence that students understand the target idea; these indicators are more superficial than a detailed explanation. Our primary finding is that although the three TAs discussed here share a common behavior, the beliefs and motivations that underlie this behavior vary. We argue that TA professional development focused on changing these TAs' focus-on-indicator behavior is unlikely to be effective. Instead, responsive TA professional development will need to address the TAs' beliefs that guide the observed classroom behavior. (Contains 5 figures, 1 video, and 1 footnote.) [A 50-item list of references and notes is provided.]

Some researchers, including B. K. Hofer and P. R. Pintrich (1997) and W. A. Sandoval (2005), argue for defining "personal epistemology" as views about the nature of knowledge and knowing but not views about the nature of learning. Others continue using a more expansive definition of "personal epistemology" that includes views about learning. I argue that the scope of personal epistemology should not be decided entirely a priori. If people's views about the nature of knowing and knowledge turn out to be separable from (despite being intertwined with) their views about the nature of learning, then it makes sense to define 2 separate areas of study corresponding to those 2 separable sets of psychological constructs. From some theoretical perspectives, however, empirical results may support the interpretation that views about knowledge are inseparably entangled with views about learning. In that case, excluding views about learning from personal epistemology obscures rather than elucidates the content and cognitive structure of students' views. To be clear, I do not think the community should decide, now, to etch "views about the nature of learning" into the definition of "personal epistemology". I argue instead that it is more productive "not" to converge on a definition until further empirical and theoretical progress points us toward the best way to "cut up [nature]...along its natural joints" (Plato, 1995, p. 64). (Contains 2 footnotes.)

Explores connections between naive epistemology and everyday instructional practice. Reviews examples of naive epistemologies as made up of fine-grained, context-sensitive resources. Presents strategies designed to help students tap those resources for learning introductory physics. Reflects on this work as an example of interplay between two modes of inquiry into student thinking, that of instruction and formal research on learning. (Author/KHR)

Explains the effect of students' epistemological beliefs on their approach to physics courses. Discusses instructional practices and curricular elements suitable for both college and high school that help students develop substantially more sophisticated beliefs about knowledge and learning as measured by the Maryland Physics Expectations Survey and by the Epistemological Beliefs Assessment for Physical Science. (Contains 20 references.) (Author/YDS)

We discuss a case study of the influence of epistemology on learning for a student in an introductory college physics course. An analysis of videotaped class work, written work, and interviews indicates that many of the student's difficulties were epistemological in nature. Our primary goals are to show instructors and curriculum developers that a student's personal epistemological stance--her ideas about knowledge and learning--can have a direct, causal influence on her learning of physics, and to describe a mechanism for this interaction. This influence exists even when research-based curriculum materials provide implicit epistemological support. For this reason, curriculum materials and teaching techniques could become more effective by explicitly attending to students' epistemologies.

Using written questionnaires, I surveyed introductory physics students about how they study and about how they would advise a hypothetical student to study if she were trying to learn physics deeply with no grade pressure. The survey teases apart students' 'epistemological' beliefs about learning and understanding physics from their more course-specific beliefs about how to earn high grades. The results indicate that students perceive 'trying to understand physics well' to be a significantly different activity from 'trying to do well in the course.'