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Search Results: 1 - 10 of 9031 matches for " Ben Radford "
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Malaysian Family Physician , 2009,
On the development of early algebraic thinking (Sobre el desarrollo de pensamiento algebraico temprano)
Luis Radford
PNA , 2012,
Abstract: This article deals with the question of the development of algebraic thinking in young students. In contrast to mental approaches to cognition, we argue that thinking is made up of material and ideational components such as (inner and outer) speech, forms of sensuous imagination, gestures, tactility, and actual actions with signs and cultural artifacts. Drawing on data from a longitudinal classroom-based research program where 8-year old students were followed as they moved from Grade 2 to Grade 3 to Grade 4, our developmental research question is investigated in terms of the manner in which new relationships between embodiment, perception, and symbol use emerge and evolve as students engage in patterning activities. Este artículo aborda la cuestión del desarrollo del pensamiento algebraico en estudiantes jóvenes. En contraste con los enfoques mentales de la cognición, sostenemos que el pensamiento está compuesto por componentes materiales y del mundo de las ideas tales como el discurso (interior y exterior), formas de imaginación sensitiva, gestos, tacto y acciones reales con signos y artefactos culturales. Con base en datos obtenidos de un programa de investigación longitudinal basado en el aula en el que se siguió el paso de estudiantes de 8 a os de segundo grado a tercero y a cuarto, nuestra pregunta de investigación acerca del desarrollo es investigada en términos de la forma en que surgen y evolucionan nuevas relaciones entre el cuerpo, la percepción y el inicio del uso de símbolos a medida que los estudiantes participan en actividades sobre patrones.
Diagrammatic Thinking: Notes on Peirce’s Semiotics and Epistemology (Pensamiento Diagramático: Notas sobre la Semiótica y la Epistemología de Peirce)
Luis Radford
PNA , 2008,
Abstract: In this paper, I discuss the role of diagrammatic thinking within the larger context of cognitive activity as framed by Peirce’s semiotic theory of and its underpinning realistic ontology. After a short overview of Kant’s scepticism in its historical context, I examine Peirce’s attempt to rescue perception as a way to reconceptualize the Kantian “manifold of senses”. I argue that Peirce’s redemption of perception led him to a series of problems that are as fundamental as those that Kant encountered. I contend that the understanding of the difficulties of Peirce’s epistemology allows us to better grasp the limits and possibilities of diagrammatic thinking. En este artículo se discute el papel que desempe a el concepto de pensamiento diagramático en el contexto de la actividad cognitiva, tal y como es concebida dentro del marco de la teoría semiótica de Peirce y su subyacente ontología realista. Luego de presentar una visión general del escepticismo kantiano en su contexto histórico, se examina el esfuerzo de Peirce por rescatar la percepción, esfuerzo que lo lleva a indagar de manera innovadora el “multiespacio de los sentidos” del que hablaba Kant. Se mantiene que este esfuerzo lleva a Peirce a una serie de problemas que son tan fundamentales como los que Kant encontró en su propio itinerario epistemológico. Se sostiene que la comprensión de las dificultades intrínsecas a la epistemología de Peirce nos permite cernir mejor los límites y posibilidades de su pensamiento diagramático.
Layers of Generality and Types of Generalization in Pattern Activities (Niveles de Generalidad y Tipos de Generalizaciones en Actividades de Patrones)
Luis Radford
PNA , 2010,
Abstract: Pattern generalization is considered one of the prominent routes for introducing students to algebra. However, not all generalizations are algebraic. In the use of pattern generalization as a route to algebra, we —teachers and educators— thus have to remain vigilant in order not to confound algebraic generalizations with other forms of dealing with the general. But how to distinguish between algebraic and non-algebraic generalizations? On epistemological and semiotic grounds, in this article I suggest a characterization of algebraic generalizations. This characterization helps to bring about a typology of algebraic and arithmetic generalizations. The typology is illustrated with classroom examples. La generalización de patrones es considerada como una de las formas más importantes de introducir el algebra en la escuela. Sin embargo, no todas las generalizaciones de patrones son algebraicas. Como consecuencia, en el uso de patrones como recurso didáctico, se debe tener mucho cuidado en no confundir generalizaciones algebraicas con otras formas de generalización. Ahora bien, cómo distinguir entre las unas y las otras? En este articulo, basado en ideas epistemológicas y semióticas, sugiero una caracterización de generalizaciones algebraicas. Dicha caracterización permite establecer una tipología, la cual es ilustrada a través de ejemplos concretos.
Acquiring and presenting Aboriginal art in art museums: my first 30 years
Ronald Radford
Journal of Art Historiography , 2011,
Abstract: Today, Aboriginal art is celebrated as one of the most popular areas in any Australian art museum. The author charts his role in presenting and acquiring Aboriginal art as art, in art museums, against the backdrop of related developments in the Australian art world. He traces developments from the late 1970s when he was director of the Ballarat Fine Art Gallery, though his 23 years at the Art Gallery of South Australia, as a curator then director, to his current position as director of the National Gallery of Australia in Canberra, which now has the largest collection and display of Australian Indigenous art. He also describes the steady progress long before his time, some of which has not been documented before, made by art museums around Australia as they gradually accepted, collected and prominently displayed Aboriginal art. He was invited to present this paper.
The spherical symmetry of static stellar systems in general relativity
Chris Radford
Physics , 2006,
Abstract: Paper withdrawn. Error lemma 7.
The Stationary Maxwell-Dirac Equations
Chris Radford
Mathematics , 2001,
Abstract: The Maxwell-Dirac equations are the equations for electronic matter, the "classical" theory underlying QED. In this article we examine the stationary Maxwell-Dirac equations under weak regularity and decay assumptions. We prove that: There are no embedded eigenvalues in the essential spectrum, $-m\leq E\leq m$. If $|E|< m$ then the Dirac field components (and their derivatives) decay exponentially at spatial infinity. If $E|=m$ then the system is "asymptotically" static and decays exponentially if the total charge is non-zero.
Localised Solutions of the Maxwell-Dirac Equations
Chris Radford
Mathematics , 1995, DOI: 10.1063/1.531663
Abstract: The full ``classical" Dirac-Maxwell equations are considered under various simplifying assumptions. A reduction of the equations is performed in the case when the Dirac field is {\em static} and a further reduction is performed in the case of {\em spherical symmetry}. These static spherically symmetric equations are examined in some detail and a numerical solution presented. Some surprising results emerge: * Spherical symmetry necessitates the existence of a magnetic monopole. * There exists a uniquely defined solution, determined only by the demand that the solution be analytic at infinity. * The equations describe highly compact objects with an inner onion-like shell structure.
Architectures of Virtual Decision-Making: The Emergence of Gender Discrimination on a Crowdfunding Website
Jason Radford
Computer Science , 2014,
Abstract: The increasing relevance of Internet-based markets requires a sustained investigation into the relationship between design and user behavior. This research begins within the sociology of quantification and markets to investigate the impacts of basic design decisions on user behavior and individual success on a widely used crowdfunding website. This study looks at one common design feature, publishing recipients' sex, on the probability of receiving funding. Following research in the sociology of gender, these effects are defined along individual, behavioral, and structural dimensions. The results reveal that before teachers' sex was published, gender discrimination was weak and inconsistent. However, afterward gender discrimination increases by an order of magnitude and becomes systematized. Contrary to expectation, donors did not discriminate by sex category, but by teachers' structural position and the kinds of language they used. Implications for research on gender discrimination, priming, and online behavior are discussed.
Symbiodinium Genotypic and Environmental Controls on Lipids in Reef Building Corals
Timothy F. Cooper, Michael Lai, Karin E. Ulstrup, Sandra M. Saunders, Gavin R. Flematti, Ben Radford, Madeleine J. H. van Oppen
PLOS ONE , 2011, DOI: 10.1371/journal.pone.0020434
Abstract: Background Lipids in reef building corals can be divided into two classes; non-polar storage lipids, e.g. wax esters and triglycerides, and polar structural lipids, e.g. phospholipids and cholesterol. Differences among algal endosymbiont types are known to have important influences on processes including growth and the photobiology of scleractinian corals yet very little is known about the role of symbiont types on lipid energy reserves. Methodology/Principal Findings The ratio of storage lipid and structural lipid fractions of Scott Reef corals were determined by thin layer chromatography. The lipid fraction ratio varied with depth and depended on symbiont type harboured by two corals (Seriatopora hystrix and Pachyseris speciosa). S. hystrix colonies associated with Symbiodinium C1 or C1/C# at deep depths (>23 m) had lower lipid fraction ratios (i.e. approximately equal parts of storage and structural lipids) than those with Symbiodinium D1 in shallow depths (<23 m), which had higher lipid fraction ratios (i.e. approximately double amounts of storage relative to structural lipid). Further, there was a non-linear relationship between the lipid fraction ratio and depth for S. hystrix with a modal peak at ~23 m coinciding with the same depth as the shift from clade D to C types. In contrast, the proportional relationship between the lipid fraction ratio and depth for P. speciosa, which exhibited high specificity for Symbiodinium C3 like across the depth gradient, was indicative of greater amounts of storage lipids contained in the deep colonies. Conclusions/Significance This study has demonstrated that Symbiodinium exert significant controls over the quality of coral energy reserves over a large-scale depth gradient. We conclude that the competitive advantages and metabolic costs that arise from flexible associations with divergent symbiont types are offset by energetic trade-offs for the coral host.
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