Ayush Gupta

How students blend conceptual and formal mathematical reasoning in solving physics problems

Current conceptions of quantitative problem-solving expertise in physics incorporate conceptual reasoning in two ways: for selecting relevant equations (before manipulating them) and for checking whether a given quantitative solution is reasonable (after manipulating the equations). We make the case that problem-solving expertise should include opportunistically blending of conceptual and formal mathematical reasoning even while manipulating equations. We present analysis of interviews with two students, Alex and Pat. Interviewed students were asked to explain a particular equation and solve a problem using that equation. Alex used and described the equation as a computational tool. By contrast, Pat found a shortcut to solve the problem. His shortcut blended mathematical operations with conceptual reasoning about physical processes, reflecting a view—expressed earlier in his explanation of the equation—that equations can express an overarching conceptual meaning. Using case studies of Alex and Pat, we argue that this opportunistic blending of conceptual and formal mathematical reasoning (i) is a part of problem-solving expertise, (ii) can be described in terms of cognitive elements called symbolic forms (Sherin, 2001), and (iii) is a feasible instructional target.

Beyond Epistemological Deficits: Dynamic explanations of engineering students’ difficulties with mathematical sense-making

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.

Resonant heating of a cluster plasma by intense laser light

Cluster heating by a strong laser field is studied using a particle-in-cell code (PIC) for a range of intensities and cluster sizes. Above a threshold intensity, heating is dominated by a nonlinear resonant absorption process.

Gases of exploding laser-heated cluster nanoplasmas as a nonlinear optical medium

The manner in which strongly heated nanoclusters explode in the presence of intense laser fields influences all applications of this interaction. By measuring, with femtosecond time resolution, the ensemble average polarizability in a gas of intense laser-heated clusters, we have inferred the cluster explosion dynamics. The time evolution of the polarizability is characteristic of competition in the optical response between supercritical and subcritical density regions of the exploding cluster. These results are consistent with complementary time-resolved Rayleigh scattering measurements and with the predictions of a near-field plasma hydrodynamic model of the laser–cluster interaction. A significant implication of this cluster evolution appears in its macroscopic effect on a laser beam: a gas of exploding cluster plasmas causes nonlinear beam propagation owing to the space and time dependence of the ensemble polarizability. A strong self-focusing effect is observed experimentally that strongly contrasts ...

On Static and Dynamic Intuitive Ontologies

We appreciate Professor Slotta’s responding to our critique (Slotta, this issue) and the editors’ providing him and us space in the Journal of the Learning Sciences for this exchange. It is often difficult to understand subtle new ideas without seeing them defended against misinterpretations. If we have misunderstood Chi’s ideas, then we believe others have as well, and we would be glad to contribute to their further explication. For our part, we believe that Professor Slotta has misinterpreted aspects of our position. There is not space, and it would not be appropriate, for us to reiterate our arguments from the article in question (Gupta, Hammer, & Redish, 2010), but there are two particular points we feel we should clarify. First, we explain here our use of “static ontologies,” which we maintain applies. Second, we respond to the question of how our dynamic view could account for evidence of stabilities. In addition, we take the opportunity to note differences in methodology that, we believe, underlie much of this debate.

Applying Conceptual Blending to Model Coordinated Use of Multiple Ontological Metaphors

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 Turners 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.

Teaching cross-platform design and testing methods for embedded systems using DICE

DICE (the DSPCAD Integrative Command Line Environment) is a package of utilities that facilitates efficient management of software projects. Key areas of emphasis in DICE are cross-platform operation, support for projects that integrate heterogeneous programming languages, and support for applying and integrating different kinds of design and testing methodologies. The package is being developed at the University of Maryland to facilitate the research and teaching of methods for implementation, testing, evolution, and revision of engineering software. The platform- and language-independent focus of DICE makes it an effective vehicle for teaching high-productivity, high-reliability methods for design and implementation of embedded systems for a variety of courses. In this paper, we provide an overview of features of DICE --- particularly as they relate to testing driven design practices --- that are useful in embedded systems education, and discuss examples and experiences of applying the tool in courses at the University of Maryland aimed at diverse groups of students --- undergraduate programming concepts for engineers, graduate VLSI architectures (aimed at research-oriented students), and graduate FPGA system design (aimed at professional Masters students).

Why Ideology Matters for Learning: A Case of Ideological Convergence in an Engineering Ethics Classroom Discussion on Drone Warfare

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.

Piecemeal Versus Integrated Design: Framing meets Design Thinking

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.

Coupling epistemology and identity in explaining student interest in science

In this paper, we present the case of Estevan, an eighth-grader from Honduras whose interest in science lies primarily at the intersection of personal epistemology and identity. Drawing on video data from classroom interactions as well as interviews with Estevan and his teacher, Ms. K, we show how Estevan’s passionate engagement in sensemaking about the seasons arose from an alignment between his epistemological stance that science involves figuring things out for yourself and his enacted identity as someone who faces challenges head-on. We use Estevan’s case to highlight the importance of remaining open to the multiplicity of connections that might exist between interest in science and students’ identities and to motivate looking deeper into such issues before prescribing how to engage students in science.