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What kind of problem-solving instruction can help students apply what they have learned to solve the new and unfamiliar problems they will encounter in the future? We propose that mathematical sensemaking, the practice of seeking coherence between formal mathematics and conceptual understanding, is a key target of successful physics problem-solving instruction. However, typical assessments tend to measure understanding in more disjoint ways. To capture coherence-seeking practices in student problem solving, we introduce an assessment framework that highlights opportunities to use these problem-solving approaches more flexibly. Three assessment items embodying this calculation-concept crossover framework illustrate how coherence can drive flexible problem-solving approaches that may be more efficient, insightful, and accurate. These three assessment items were used to evaluate the efficacy of an instructional approach focused on developing mathematical-sensemaking skills. In a quasi-experimental study, three parallel lecture sections of first-semester, introductory physics were compared: two mathematical sensemaking sections, with one having an experienced instructor (MS) and one a novice instructor (MS-nov), and a traditionally-taught section acted as a control group (CTRL). On the three crossover assessment items, mathematical sensemaking students used calculation-concept crossover approaches more and generated more correct solutions than CTRL students. Student surveyed epistemological views toward problem-solving coherence at the end of the course predicted their crossover approach use but did not fully account for the differences in crossover approach use between the MS and CTRL groups. These results illustrate new instructional and assessment frameworks for research on mathematical sensemaking and adaptive problem-solving expertise.

Responsive teaching, in which teachers adapt instruction based on close attention to the substance of students' ideas, is typically characterized along two dimensions: the level of detail at which teachers attend and respond to students' ideas, and the stance teachers take toward what they hear - evaluating for correctness vs. interpreting meaning. We propose that characterizations of progress in responsive teaching should also consider the disciplinary centrality of the practices teachers notice and respond to within student thinking. To illustrate what this kind of progress can look like, we present a case study of a middle school science teacher who implemented the "same" lesson on the motion of freely falling objects in two subsequent years. We argue that his primary shift in responsiveness stemmed from a shift in which disciplinary practices he preferentially noticed and foregrounded. He moved from a focus on causal factors or variables to a more scientifically productive focus on causal stories or explanations. We explore how participation in a professional development community, institutional constraints, and a shift in personal epistemology may have contributed to the nature and stability of this shift in responsiveness., Comment: This manuscript is under review at the Journal of the Learning Sciences

In collaborative small-group work, physics students need to both manage social conflict and grapple with conceptual and epistemological differences. In this paper, we document several outlets that students use as tools for managing social conflict when addressing quantum mechanics tutorials in clinical focus groups. These resources include epistemic distancing, humor, playing on tutorial wording and looking ahead to subsequent questions. We present preliminary analysis of episodes where students work through a Particle in a Box tutorial. Each episode highlights a different manner of navigating social tension: through shared epistemic humor in one case, and reinterpretation of the question in the other., Comment: 4-page PERC preceedings

Research has documented a sharp decline in students' interest and persistence in science, starting in middle school, particularly among students from underrepresented populations. In working to address this problem, we can learn a great deal from positive examples of students getting excited about science, especially students who were previously disengaged. In this paper, we present a case study of Estevan, an 8th grade student who came into Ms. K's science class with a reputation as a potential "problem student," but left as a leader of the class, even making plans to pursue a career in science. Through analysis of interviews and classroom interactions, we show how Estevan's love of science can be partially explained by an alignment between his identity as a lover of challenges and his epistemology of science as involving the challenge of figuring things out for yourself. This alignment was possible in part because it was supported by his caring teacher, who attended to his ideas and constantly challenged him and the rest of her students to figure things out for themselves instead of just "giving them the answers.", Comment: This manuscript is currently under review at the Journal of the Learning Sciences

Systems thinking is an important component of engineering design thinking but one that is often difficult for beginning designers. In this paper, we present an empirically grounded case that sometimes the novice-like design behaviors emerge, not due to a lack of skills/knowledge on part of the student designers, but by the nature of the way the activity is structured and the implicit and explicit messages communicated to the students on the nature of the design task. Our analysis draws on video-records of brainstorming and design review and briefing meetings between students, instructors, and stakeholders in the context of a service-learning course. The project involved designing a treehouse for campers with disabilities. Our analysis flags a central tension participants faced: whether students were expected to create a piecemeal set of disparate design elements, or an integrated overall design concept for the treehouse. We find that an ambiguous framing by stakeholders coupled with a reification of the design as piecemeal through individual moments of activity and conversation, largely produced a framing and a resulting product of piecemeal design.

Many prominent lines of research on student's reasoning and conceptual change within learning sciences and physics education research have not attended to the role of learners' affect or emotions in the dynamics of their conceptual reasoning. This is despite evidence from psychology and cognitive- and neuro- sciences that emotions are deeply integrated with cognition and documented associations in education research between emotions and academic performance. The few studies that have aimed to integrate emotions within models of learners' cognition, have mostly done so at a coarse grain size. In this manuscript, toward the long-term goal of incorporating emotions into fine-grained models of in-themoment cognitive dynamics, we present a case study of Judy, an undergraduate electrical engineering and physics major. We argue that a fine-grained aspect of Judy's affect, her annoyance at a particular kind of homework problem, stabilizes a context-dependent epistemological stance she displays, about an unbridgeable gulf she perceives to exist between real and ideal circuits., Comment: Submitted to Physical Review Special Topics - Physics Education Research on June 30, 2013 (15 pages; 4 figures)

Research has linked a student's affect to her epistemology (Boaler & Greeno, 2000), but those constructs often apply broadly to a discipline and/or classroom culture. Independently, an emerging line of research shows that a student in a given classroom and discipline can shift between multiple locally coherent epistemological stances (Hammer, Elby, Scherr, & Redish, 2005). Our case study of Judy, an undergraduate engineering major, begins our long-term effort at uniting these two bodies of literature., 2-page paper: ICLS 2010 Conference Proceedings

Researchers have argued against deficit-based explanations of students' troubles with mathematical sense-making, pointing instead to factors such as epistemology: students' beliefs about the nature of knowledge and learning can hinder them from activating and integrating productive knowledge they have. But such explanations run the risk of substituting an epistemological deficit for a concepts/skills deficit. Our analysis of an undergraduate engineering major avoids this "deficit trap" by incorporating multiple, context-dependent epistemological stances into his cognitive dynamics., Comment: Proceedings of the International Conference of the Learning Sciences, 2010, (In Press)

Funding for Open Access provided by the UMD Libraries Open Access Publishing Fund., 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.