25,037 research outputs found
Designing Effective Questions for Classroom Response System Teaching
Classroom response systems (CRSs) can be potent tools for teaching physics.
Their efficacy, however, depends strongly on the quality of the questions used.
Creating effective questions is difficult, and differs from creating exam and
homework problems. Every CRS question should have an explicit pedagogic purpose
consisting of a content goal, a process goal, and a metacognitive goal.
Questions can be engineered to fulfil their purpose through four complementary
mechanisms: directing students' attention, stimulating specific cognitive
processes, communicating information to instructor and students via
CRS-tabulated answer counts, and facilitating the articulation and
confrontation of ideas. We identify several tactics that help in the design of
potent questions, and present four "makeovers" showing how these tactics can be
used to convert traditional physics questions into more powerful CRS questions.Comment: 11 pages, including 6 figures and 2 tables. Submitted (and mostly
approved) to the American Journal of Physics. Based on invited talk BL05 at
the 2005 Winter Meeting of the American Association of Physics Teachers
(Albuquerque, NM
The State-of-the-Art of Set Visualization
Sets comprise a generic data model that has been used in a variety of data analysis problems. Such problems involve analysing and visualizing set relations between multiple sets defined over the same collection of elements. However, visualizing sets is a non-trivial problem due to the large number of possible relations between them. We provide a systematic overview of state-of-the-art techniques for visualizing different kinds of set relations. We classify these techniques into six main categories according to the visual representations they use and the tasks they support. We compare the categories to provide guidance for choosing an appropriate technique for a given problem. Finally, we identify challenges in this area that need further research and propose possible directions to address these challenges. Further resources on set visualization are available at http://www.setviz.net
Internal representations, external representations and ergonomics: towards a theoretical integration
Spatial Aggregation: Theory and Applications
Visual thinking plays an important role in scientific reasoning. Based on the
research in automating diverse reasoning tasks about dynamical systems,
nonlinear controllers, kinematic mechanisms, and fluid motion, we have
identified a style of visual thinking, imagistic reasoning. Imagistic reasoning
organizes computations around image-like, analogue representations so that
perceptual and symbolic operations can be brought to bear to infer structure
and behavior. Programs incorporating imagistic reasoning have been shown to
perform at an expert level in domains that defy current analytic or numerical
methods. We have developed a computational paradigm, spatial aggregation, to
unify the description of a class of imagistic problem solvers. A program
written in this paradigm has the following properties. It takes a continuous
field and optional objective functions as input, and produces high-level
descriptions of structure, behavior, or control actions. It computes a
multi-layer of intermediate representations, called spatial aggregates, by
forming equivalence classes and adjacency relations. It employs a small set of
generic operators such as aggregation, classification, and localization to
perform bidirectional mapping between the information-rich field and
successively more abstract spatial aggregates. It uses a data structure, the
neighborhood graph, as a common interface to modularize computations. To
illustrate our theory, we describe the computational structure of three
implemented problem solvers -- KAM, MAPS, and HIPAIR --- in terms of the
spatial aggregation generic operators by mixing and matching a library of
commonly used routines.Comment: See http://www.jair.org/ for any accompanying file
The Effectiveness of Representations in Mathematics
This article focuses on particular ways in which visual representations contribute to the development of mathematical knowledge. I give examples of diagrammatic representations that enable one to observe new properties and cases where representations contribute to classification. I propose that fruitful representations in mathematics are iconic representations that involve conventional or symbolic elements, that is, iconic metaphors. In the last part of the article, I explain what these are and how they apply in the considered examples
The Effectiveness of Representations in Mathematics
This article focuses on particular ways in which visual representations contribute to the development of mathematical knowledge. I give examples of diagrammatic representations that enable one to observe new properties and cases where representations contribute to classification. I propose that fruitful representations in mathematics are iconic representations that involve conventional or symbolic elements, that is, iconic metaphors. In the last part of the article, I explain what these are and how they apply in the considered examples
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