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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.] Common models of curricular development in physics education research (PER) have typically involved a hierarchical relationship between researchers and students, where researchers lead the design and testing of curriculum for students. We draw from work in students as partners and related fields in order to codesign curriculum in partnership with students. Such work has the potential to disrupt typical hierarchical relationships and interactions between students and faculty by involving students in the process of making curricular decisions. We invited undergraduate students to participate in a partnership to codesign a set of curricular materials for topics in quantum mechanics that students often struggle with. Four undergraduate students, one PER graduate student, and one PER faculty member met for a series of codesign meetings. We collected videotapes of the meetings, written artifacts, and meeting reflections. This paper presents a fine-grained analysis of one interaction in which researchers attempted to create space for students to contribute to decision making about how the collaboration should proceed. Through analyzing the complex dynamics of how participants negotiated decision-making space, including characterizing the types of decisions that were made, we describe how access to those decisions were opened up or cut off, and how those decisions contested or reaffirmed participants' roles. Working towards partnership is a complex and messy process: attempts to open up space for some forms of decision making closed off access to other forms of decision making. In some ways, the interactions between the participants also reified the traditional student and faculty roles that the partnership had intended to disrupt. Through closely analyzing these dynamics, we aim to self-critically reflect on the challenges and tensions that emerge in codesign partnerships. We discuss our own areas for growth and speak to implications for more responsible partnerships.

Problem solving in groups can be rich with tension for students. This tension may arise from conflicting approaches (conceptual and/or epistemological) and/or from conflict emerging in the social relations among group members. Drawing on video records of undergraduate students working collaboratively, we use three cases to illustrate the multifaceted ways in which conflict arises--combining conceptual, epistemological, and socioemotional dynamics--and a specific way of managing the tension that can emerge from the multifaceted conflict, "taking an escape hatch." An escape hatch is a set of discourse moves through which participants close the conversational topic, thereby relieving tension, but before a conceptual resolution is achieved. We describe how epistemological twists and turns can be recruited as a means of managing the strong emotions experienced by the students, showing the coupling of emotion and epistemology in students' conceptual sense making during group work. We help to provide the groundwork necessary for instructors to notice, understand, and respond to one way in which conceptual--epistemological--social--emotional aspects of interaction are coupled in the emergence of tension, rather than narrowly targeting instructional moves based on only conceptual or epistemological considerations. Instead, instructors should often respond to--and help students become aware of--the emotional component of peer interactions and its entanglement with the "cold cognitive" conceptual and epistemological components.

Background: Quantitative researchers have noted the impact of mentoring and support programming for students from underrepresented groups in engineering. Qualitative researchers have also noted the importance of student agency in persistence through marginalization. Nevertheless, challenges and questions remain in identifying practices which are effective in supporting underrepresented students. Purpose: The study applies scholarship from critical theory and narrative as a new resource for approaching and understanding the process of supporting marginalized student agency. Method: A longitudinal interview study with a female undergraduate engineering student, Emilia, developed into a way for her to process marginalizing educational experiences and to develop new narratives that expanded her agency. After an in-depth member check, Emilia became a co-author contributing a post hoc account of the impact of these discussions. Results: Our analysis indicates that naming one's own oppression and creating narratives that repurpose and resituate stereotypical stories of oppression was a liberatory act for Emilia. We trace three marginalizing themes of the participant's experience that are subverted and resisted through the student co-constructed narrative. Conclusions: The paper builds theory for diversity support, suggesting critical theorizing may present a new form of agency not yet represented in the literature. It also points to possible value for student participants from qualitative methodologies exploring student experiences. Finally, it suggests supporting critical theorizing as a potential new orientation for diversity practitioners.

The relationship between ideology and learning remains insufficiently theorized and sparsely investigated in the learning sciences. Drawing on Stuart Hall's theorization of ideology, Judith Butler's notion of the (un)grievability of lives, and Sara Ahmed's construct of stickiness, we illustrate how insights from critical social theory are indispensable to understanding processes of learning and how perspectives from the learning sciences can enrich critical social theory. Through the analysis of a classroom discussion on the use of militarized drones in an undergraduate engineering ethics course, we show how ideological convergence among participants constructed locally significant categories of "civilian," "terrorist," and (un)grievability, which narrowed the possible trajectories for students' disciplinary learning in engineering and engineering ethics. Our analysis also shows that fleeting moments of ideological expansion offered opportunities for new learning; however, most of these instances of possibility were not sustained through the classroom discussion. We explicate how ideological convergences and expansions, as interactional achievements, profoundly matter for disciplinary learning and students' identities. In conclusion, we explore the implications of our findings for broader contexts of learning and for the field of the learning sciences.

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.

Background: To explain educational problems such as student attrition, engineering education literature often focuses on the characteristics of individuals. In 2006, Ray McDermott and Hervé Varenne called for examining the "cultural construction" of educational problems, uncovering how multiple actors create and inscribe meaning to the educational problem. Purpose: We apply the cultural construction framework to examine how the educational problem of a student being "not cut out for engineering" is constructed within the context of a specific electrical engineering course. We focus on culturally taken-for-granted course structures, practices, and interactions, all of which produce the local enactment of this common educational problem. Method: We used ethnographic methods, including field-noted participant observations, one-on-one participant interviews, and video-recorded student work on lab assignments. Coordinating multiple data streams enabled us to question explanations couched in terms of individual ability and background, and to illustrate how ability hierarchies were constructed in the educational context. Results: Our findings illustrate how several mundane and seemingly innocuous aspects of engineering classrooms add up to construct the educational problem of our focal student as "not cut out" for engineering. Contributions to this construction included lecture seating positions, interactional norms in lecture and lab, and labels made meaningful through institutional and interactional processes. Conclusions: The forces at play in constructing educational problems for students are deeply embedded in institutions, disciplines, and society, making it difficult to generate a simple list of instructional interventions. We highlight cultural construction analysis as a potentially fruitful orientation for researchers and practitioners to find the particular sites and tools for local intervention.

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.

Energy is an abstract science concept, so the ways that we think and talk about energy rely heavily on ontological metaphors: metaphors for what kind of thing energy is. Two commonly used ontological metaphors for energy are "energy as a substance" and "energy as a vertical location." Our previous work has demonstrated that students and experts can productively use both the substance and location ontologies for energy. In this paper, we use Fauconnier and Turner's conceptual blending framework to demonstrate that experts and novices can successfully blend the substance and location ontologies into a coherent mental model in order to reason about energy. Our data come from classroom recordings of a physics professor teaching a physics course for the life sciences, and from an interview with an undergraduate student in that course. We analyze these data using predicate analysis and gesture analysis, looking at verbal utterances, gestures, and the interaction between them. This analysis yields evidence that the speakers are blending the substance and location ontologies into a single blended mental space.

Background: Students' identities and sense of belonging in a program affect whether they stay in engineering. Research suggests that students' ways of knowing and beliefs about what counts as knowing and learning -- their personal epistemologies -- can be aspects of their identities, or sense of self as knowers and learners. Purpose/Hypothesis: Combining personal epistemology and identity theories suggests epistemological aspects of students' identities can influence whether they feel they belong in their engineering program. We have two research questions: Can a high-achieving engineering student be in danger of leaving a program because of a mismatch between epistemological aspects of his identity and his perceptions of the intellectual climate of their program? How does such a mismatch affect the student's day-to-day academic experiences? Design/Method: For three years, we followed Michael, an electrical engineering student, through interviews and in-class observations. From more than 12 hours of semistructured clinical interviews, more than 10 hours of videotaped discussion sections, and two in-class observations in lectures, we produced a case study to characterize epistemological aspects of Michael's identity and how they influenced his perception of his program. Results: Michael expressed and enacted a sense-making epistemology that is a fundamental aspect of his identity as a learner. Due to this sense-making aspect of Michael's identity, he often felt alienated from the intellectual climate of his program, and he considered leaving engineering. Conclusion: Researchers focused on student retention should attend to epistemological aspects of student identities. Instructors and administrators focused on retention should attend to the epistemological messages students hear from their programs.

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.)

Researchers have argued against deficit-based explanations of students' difficulties with mathematical sense-making, pointing instead to factors such as epistemology. Students' beliefs about knowledge and learning can hinder the activation and integration of productive knowledge they have. Such explanations, however, risk falling into a "deficit trap"--substituting a concepts/skills deficit with an epistemological one. Our interview-based case study of a freshman engineering major, "Jim," explains his difficulty solving a physics problem (on hydrostatic pressure) in terms of his epistemology, but avoids a deficit trap by modeling the dynamics of his epistemological stabilities and shifts in terms of fine-grained cognitive elements that include the seeds of epistemological expertise. Specifically, during a problem-solving episode in the interview, Jim reaches and sticks with an incorrect answer that violates common sense. We show that Jim has all the mathematical skills and physics knowledge he would need to resolve the contradiction. We argue that his difficulty doing so stems in part from his epistemological views that (i) physics equations are much more trustworthy than everyday reasoning, and (ii) physics equations do not express meaning that tractably connects to common sense. For these reasons, he does not view reconciling between common sense and formalism as either necessary or plausible to accomplish. But Jim's in-the-moment shift to a more sophisticated epistemological stance highlights the seeds of epistemological expertise that were present all along: he does see common sense as connected to formalism (though not always tractably so), and in some circumstances, this connection is both salient and valued. (Contains 1 figure, 1 table, and 3 notes.)

The authors appreciate Professor Slotta's responding to their critique (Slotta, this issue). For their part, they believe that Professor Slotta has misinterpreted aspects of their position. In this commentary, the authors clarify two particular points. First, they explain their use of "static ontologies," which they maintain applies. Second, they respond to the question of how their dynamic view could account for evidence of stabilities. In addition, they take the opportunity to note differences in methodology that underlie much of this debate. (Contains 3 footnotes.)

In a series of well-known papers, Chi and Slotta (M. T. H. Chi, 1992, 2005; M. T. H. Chi & J. D. Slotta, 1993; M. T. H. Chi, J. D. Slotta, & N. de Leeuw, 1994; J. Slotta & M. T. H. Chi, 2006; J. D. Slotta, M. T. H. Chi, & E. Joram, 1995) have contended that a reason for students' difficulties in learning physics is that students think about concepts as "things" rather than as "processes" and that there is a significant barrier between these 2 ontological categories. We contest this view, arguing that expert and novice reasoning often and productively traverses ontological categories. We cite examples from everyday, classroom, and professional contexts to illustrate this. We agree with Chi and Slotta that instruction should attend to learners' ontologies, but we find that these ontologies are better understood as dynamic and context dependent rather than as static constraints. To promote 1 ontological description in physics instruction, as suggested by Slotta and Chi, could undermine novices' access to productive cognitive resources that they bring to their studies and inhibit their transition to the dynamic ontological flexibility required of experts. (Contains 15 footnotes.)

Energy is an abstract science concept, so the ways that we think and talk about energy rely heavily on ontological metaphors: metaphors for what kind of thing energy is. Two commonly used ontological metaphors for energy are energy as a substance and energy as a vertical location. Our previous work has demonstrated that students and experts can productively use both the substance and location ontologies for energy. In this paper, we use Fauconnier and Turner's conceptual blending framework to demonstrate that experts and novices can successfully blend the substance and location ontologies into a coherent mental model in order to reason about energy. Our data come from classroom recordings of a physics professor teaching a physics course for the life sciences, and from an interview with an undergraduate student in that course. We analyze these data using predicate analysis and gesture analysis, looking at verbal utterances, gestures, and the interaction between them. This analysis yields evidence that the speakers are blending the substance and location ontologies into a single blended mental space. [ABSTRACT FROM PUBLISHER]