The Transfer of Scientific Principles Using Concrete and Idealized Simulations
Concepts and Categories
From the Pragmatics of Classification Systems to the Metaphysics of Concepts
How DOORKNOB Gets Its Meaning
Reconstructing the Learning Sciences
Cognitive Work and Material Practice
In this paper, I explore the relation between the socio-cultural and individual cognitive structuring as elementary school students, high school students, and adults play the strategic game of dominoes. I present data from a study in which players at each level were observed and video-recorded during domino tournament play. Findings reveal the cognitive and mathematical skills players developed, as well as how those skills were fundamentally integrated with shifts in the activity structures of the game as players got older. Implications for understanding cognition and context, and for teaching and learning are discussed.
Project-based curricula have the potential to engage students’ interests. But, how do students become interested in the goals of a project? This article documents how a group of 8th-grade students participated in an architectural design project called the Antarctica Project. The project is based on the imaginary premise that students need to design a research station in Antarctica. This premise is meant to provide a meaningful context for learning mathematics. Using ethnography and discourse analysis, the article investigates students’ engagement with the imaginary premise and curricular tasks during the 7-week project. A case study consisting of scenes from main phases of the project shows how the students took on concerns and responsibilities associated with the figured world proposed by the Antarctica Project and how this shaped their approaches to mathematical tasks (Holland, Lachicotte, Skinner, & Cain, 1998). Participating in the figured world of Antarctica and evaluating situations within this world was important for how students used mathematics meaningfully to solve problems. Curricular tasks and classroom activities that facilitated students in assuming and shifting between roles relevant to multiple figured worlds (i.e., of the classroom, Antarctica, and mathematics) helped them engage in the diverse intentions of curricular activities.
Participants in two experiments interacted with computer simulations designed to foster understanding of scientific principles governing complex adaptive systems. The quality of participants’ transportable understanding was measured by the amount of transfer between two simulations governed by the same principle. The perceptual concreteness of the elements within the first simulation was manipulated. The elements either remained concrete throughout the simulation, remained idealized, or switched midway into the simulation from concrete to idealized or vice versa. Transfer was better when the appearance of the elements switched, consistent with theories predicting more general schemas when the schemas are multiply instantiated. The best transfer was observed when originally concrete elements became idealized. These results are interpreted in terms of tradeoffs between grounded, concrete construals of simulations and more abstract, transportable construals. Progressive idealization (“Concreteness fading”) allows originally grounded and interpretable principles to become less tied to specific contexts and hence more transferable.