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A paper summarizing the discussions that happened during the Physics Education Research (POC in PERC) parallel sessions at the 2017 and 2018 Physics Education Research Conference (PERC).

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

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)

Physics makes powerful use of mathematics, yet the way this use is made is often poorly understood. Professionals closely integrate their mathematical symbology with physical meaning, resulting in a powerful and productive structure. But because of the way the cognitive system builds expertise through binding, experts may have difficulty in unpacking their well established knowledge in order to understand the difficulties novice students have in learning their subject. This is particularly evident in subjects in which the students are learning to use mathematics to which they have previously been exposed in math classes in complex new ways. In this paper, we propose that some of this unpacking can be facilitated by adopting ideas and methods developed in the field of cognitive semantics, a sub-branch of linguistics devoted to understanding how meaning is associated with language., GIREP Conference, Leicester, UK, 2009, 15 pages

Researchers have argued against deficit-based explanations of students' troubles with mathematical sense-making, pointing instead to factors such as epistemology: students' beliefs about knowledge and learning can hinder them from activating and integrating productive knowledge they have. In this case study of an engineering major solving problems (about content from his introductory physics course) during a clinical interview, we show that "Jim" has all the mathematical and conceptual knowledge he would need to solve a hydrostatic pressure problem that we posed to him. But he reaches and sticks with an incorrect answer that violates common sense. We argue that his lack of mathematical sense-making-specifically, translating and reconciling between mathematical and everyday/common-sense reasoning-stems in part from his epistemological views, i.e., his views about the nature of knowledge and learning. He regards mathematical equations as much more trustworthy than everyday reasoning, and he does not view mathematical equations as expressing meaning that tractably connects to common sense. For these reasons, he does not view reconciling between common sense and mathematical formalism as either necessary or plausible to accomplish. We, however, avoid a potential "deficit trap"-substituting an epistemological deficit for a concepts/skills deficit-by incorporating multiple, context-dependent epistemological stances into Jim's cognitive dynamics. We argue that Jim's epistemological stance contains productive seeds that instructors could build upon to support Jim's mathematical sense-making: 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., Comment: Submitted to the Journal of Engineering Education

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)