External Representation

In this article I bring artistic production into the learning sciences conversation by using the production of representations as a bridging concept between art making and the new literacies. Through case studies with 4 youth media arts organizations across the United States I ask how organizations structure the process of producing autobiographical digital art through a focus on representational tasks and how learning can be traced by examining youth artists' representations over time. Using a distributed cognition framework I analyze data on the process of making digital art in terms of the macro and micro tasks performed in order to identify occasions for external representation construction and use across organizations. I then examine how individual youth engage in these macro and micro tasks by producing representations that demonstrate their understanding. These analyses show that youth media arts organization production processes engage young artists in a representational trajectory that begins with developing a story about the self, moves toward a focus on how the tools of the medium afford representation of that story, and culminates in digital representations that reflect an understanding of the relationship between story and tools.

An exploratory study of77 high ability Grade 5 and 6 children investigated links between their understanding of the numeration system and their representations of the counting sequence 1–100. Analysis of children’s explanations, and pictorial and notational recordings of the numbers 1–100 revealed three dimensions of external representation—pictorial, ikonic, or notational characteristics—thus providing evidence of creative structural development of the number system, and evidence for the static or dynamic nature of the internal representation. Our observations indicated that children used a wide variety of internal images of which about 30% were dynamic internal representations. Children with a high level of understanding of the numeration system showed evidence of both structure and dynamic imagery in their representations.

Learning science research has examined how external representations can be used to foster student reasoning and understanding. This paper describes additional roles that students' representations play in a reform mathematics classroom. The paper describes three ways in which students' representations were used in a classroom: (a) to provide information on how an individual student thinks about a mathematical issue, (b)

Many current neurophysiological, psychophysical, and psychological approaches to vision rest on the idea that when we see, the brain produces an internal representation of the world. The activation of this internal representation is assumed to give rise to the experience of seeing. The problem with this kind of approach is that it leaves unexplained how the existence of such a detailed internal representation might produce visual consciousness. An alternative proposal is made here. We propose that seeing is a way of acting. It is a particular way of exploring the environment. Activity in internal representations does not generate the experience of seeing. The outside world serves as its own, external, representation. The experience of seeing occurs when the organism masters what we call the governing laws of sensorimotor contingency. The advantage of this approach is that it provides a natural and principled way of accounting for visual consciousness, and for the differences in the ...

Living humans are unique among the animal kingdom with respect to their ability to externalize mental representations outside the brain through a variety of media and in a recursive or creative manner (i.e., generating a potentially infinite array of combinations). Earlier humans evolved two specialized organs—the hand and the vocal tract—as primary instruments for externalizing artificial or semantic representations. These organs and the externalized representations may have co-evolved with the Homo brain. The archaeological record yields examples of simple representations by 1.6 mya. More complex, hierarchical, and recursive forms are evident by roughly 0.25 mya. Complex and highly recursive representations in a wide range of media (including representations of representations in the form of visual art) emerge after 0.1 mya among anatomically modern humans.

The nodes of a Blue Gene supercomputer are connected by five networks, four of unusual design. Only the I/O nodes have a conventional IP-based Ethernet. Plan 9�s internal and external representations of networks is simple and clean yet powerful enough to encompass those networks directly, without having to emulate existing network types. In supercom­ puter environments, applications often use the

Multimedia learning environments usually combine multiple forms of representations like texts, pictures, animations, tables or formulas. However, knowledge acquisition from multiple representations requires the integration of these sources in order to construct a coherent mental representation. The present paper therefore outlines a first theoretical framework for the process of coherence formation within cognitive load theory. Despite the benefits of dealing

Computer-supported collaborative learning (CSCL) environments, particularly environments where students share external representations, are discussed as an interesting area for the application of cognitive load theory (CLT). CSCL environments share a number of characteristics that will induce considerable cognitive load. This article reflects on the characteristics of CSCL environments and external representations and the research opportunities they offer to CLT. We argue that CLT can contribute to our understanding of CSCL by pinpointing situations in which high levels of cognitive load are generated. CLT also raises a number of particular issues: from a CLT point of view studying of worked out external representations may lead to better learning outcomes than (co)-construction which is the standard mode of operation in CSCL. The ontology and specificity of the representational scheme used are crucial factors, as they define what can be expressed and how much room for interpretation is left in the representation. CLT may help identify mismatches between representational schemes and execution of (sub)tasks. CLT has lead to a number of recommendations on the integration of diagrammatic and textual information. We relate this to discussion and chat facilities in CSCL and describe how these can be more firmly anchored in the external representation.

Computer Supported Collaborative Learning (CSCL) systems are assumed to have the potential to enhance the effectiveness of peer learning interactions (Andriessen et al., 1996; Dillenbourg, 1999). Groupware programmes are used for CSCL as they generally support and integrate three functions: task support, communicative support, and group support. Computer tools in groupware programmes are either task-oriented (information sharing, cooperation and coordination), communication-oriented (interpersonal exchange) or ...

Sketching in a design context serves not only as a visual aid to store and retrieve conceptualizations but also as a medium to facilitate more ideas, and to revise and refine them. We examine whether designing is possible without sketching by conducting a protocol analysis study with six expert architects. Each architect is required to think aloud and design in two different conditions: one where s/he has access to sketching and one where s/he is blindfolded (and not allowed to sketch). At the end of the blindfold condition the architects ...

Fakultät für Mathematik, Universität Wien Nordbergstr. 15, A-1090 Wien, Austria email: Arnold.Neumaier@univie.ac.at WWW: http://www.mat.univie.ac.at/~neum ... Bo Einarsson, Maarten van Emden, Michel Hack, Nate Hayes, Ulrich Kulisch, Jens Maurer, Ian McIntosh, Sylvain Pion, John Pryce, Hermann Schichl, Wolff von Gudenberg, Paul Zimmermann, and Dan Zuras ... Abstract. This document contains a detailed proposal for a future IEEE 1788 standard on interval arithmetic. It is written in a form that should be not too difficult to transform into a formal, ...

The nodes of a Blue Gene supercomputer are connected by five networks, four of unusual design. Only the I/O nodes have a conventional IP-based Ethernet. Plan 9s internal and external representations of networks is simple and clean yet powerful enough to encompass those networks directly, without having to emulate existing network types. In supercom puter environments, applications often use the network hardware directly, but that makes it hard or impossible to share. We wish system services to make good use of the specialized networks too, in order to build fault-tolerant distributed services. Our kernel must therefore medi ate access to those networks, just as it does for IP traffic.

WS02: EMBODIMENT, METAPHOR & GESTURE IN MATHEMATICS ... Laurie Edwards St. Mary's College of California, USA Ornella Robutti Università di Torino, Italia Janete Bolite Frant Pontificea Universidade Catolica do Rio de Janeiro, Brasil The purpose of the Working Session is to ...