3,682 research outputs found
Theoretical frameworks for the learning of geometrical reasoning
No full textWith the growth in interest in geometrical ideas it is important to be clear about the nature of geometrical reasoning and how it develops. This paper provides an overview of three theoretical frameworks for the learning of geometrical reasoning: the van Hiele model of thinking in geometry, Fischbein’s theory of figural concepts, and Duval’s cognitive model of geometrical reasoning. Each of these frameworks provides theoretical resources to support research into the development of geometrical reasoning in students and related aspects of visualisation and construction. This overview concludes that much research about the deep process of the development and the learning of visualisation and reasoning is still needed
Human reasoning and cognitive science
No full textIn Human Reasoning and Cognitive Science, Keith Stenning and Michiel van Lambalgen—a cognitive scientist and a logician—argue for the indispensability of modern mathematical logic to the study of human reasoning. Logic and cognition were once closely connected, they write, but were "divorced" in the past century; the psychology of deduction went from being central to the cognitive revolution to being the subject of widespread skepticism about whether human reasoning really happens outside the academy. Stenning and van Lambalgen argue that logic and reasoning have been separated because of a series of unwarranted assumptions about logic. Stenning and van Lambalgen contend that psychology cannot ignore processes of interpretation in which people, wittingly or unwittingly, frame problems for subsequent reasoning. The authors employ a neurally implementable defeasible logic for modeling part of this framing process, and show how it can be used to guide the design of experiments and interpret results. They draw examples from deductive reasoning, from the child's development of understandings of mind, from analysis of a psychiatric disorder (autism), and from the search for the evolutionary origins of human higher mental processes. The picture proposed is one of fast, cheap, automatic but logical processes bringing to bear general knowledge on the interpretation of task, language, and context, thus enabling human reasoners to go beyond the information given. This proposal puts reasoning back at center stage
Learning to Solve Syllogisms By Watching Others' Learning
No full textIntroduction This experiment arose from the confluence of two interests, one in "vicarious" learning (learning by observing others learning) (see e.g. McKendree, Stenning, Mayes, Lee, & Cox, 1998), and the other in the learning of elementary logic (see e.g. Stenning, Cox, & Oberlander, 1995; Stenning & Yule, 1997; Monaghan & Stenning, 1998). The experiment involves teaching students a method of solving syllogisms using Euler's Circles. The teaching session includes "vicarious" learning through video clips of students solving syllogisms with this method. The study addresses several questions: how do students respond to graphical methods of problem solving? what are the individual differences in students' abilities to acquire and utilise a graphical method for problem solving? does "vicarious learning" aid acquisition and use of the graphical method? what are the effects of watching a fellow student st
Jersey Homesteads -- A Triple Co-operative
No full textChapter 11, pages 256-276, of
Title: "Tomorrow a new world: the New Deal communuity program."
Publisher: Ithaca, NY, Published for the American Historical Association (by) Cornell University Press, 1959.
Author; Conkin, Paul Keith
The shaping of student knowledge: learning with dynamic geometry software
No full textThe focus of this paper is a software genre usually referred to as ‘dynamic geometry’ because of the ability of the user to dynamically manipulate geometrical figures created with the software tool. Using data from a longitudinal study of 12-13 students’ use of dynamic geometry software, the focus of the analysis is on the interpretations the students make of geometrical objects and relationships when using this form of software. The analysis suggests that the students’ mathematical reasoning is shaped by their interactions with the software in that their ability to explain geometrical facts and relationships evolves from imprecise, ‘everyday’ expressions, through reasoning that is overtly mediated by the software environment, to mathematical explanations of the geometric situation that transcend the particular tool being used. Such findings suggest that curriculum initiatives that encourage the use of dynamic geometry software are appropriate but that the incorporation of such software into classroom practices is unlikely to be straightforward
Art, Biography, Sexuality: Patrick Procktor and Keith Vaughan
No full textThis critical review forms a reflection on the research published within the following publications:
Patrick Procktor: Art and Life (Unicorn Press, 2010)
Keith Vaughan: The Mature Oils 1946-1977, (Sansom & Co., 2012)
The research is on two artists, Patrick Procktor (1936-2003), and Keith Vaughan (1912-1977). The monograph on Procktor – previously one of the least documented of the generation of artists who came to prominence in London in the Sixties – positions him in a history of art from which he had been notably absent. The research on Vaughan asserts a new reading of his work, one that is both deeper and more nuanced in its analysis of the ways in which personal experience and sexuality are encoded autobiographically within his work. Crucially, in both artists biography and work are symbiotically linked; the research therefore examines the links between life and art.
Revisionary in intent, the work examines trajectories of experience of gay British (or rather, English) artists in the twentieth century, artists who sought to express themselves and forge careers within the constraints of a heteronormative society, albeit one in which attitudes to sexuality were undergoing change. As gay men, both were constrained by the social mores of their times, and each used painting as a means to affirm personal and sexual identities. A key research interest is in the ways in which sexuality and persona are reflected in critical responses to the artist’s work: in Vaughan, Procktor and other gay male artists of the period. The writing on both Procktor and Vaughan examines the relationship between their personal and professional/artistic lives, framed within a broader socio-political and art historical context. It asserts the place of biography as a means to understand and form new readings of the work. The work adds substantially to the literature and wider discourse on post-war British painting and social history
The spontaneity drain: the social pressures that shaped and then exiled Keith Johnstone's improvisation
No full textKeith Johnstone’s Improvisation had an oppositional relationship to the social and historical conditions of 1950s Britain under which it developed. Its structure and performative dynamic were protests against the normalising forces exerted by the social elite upon the broader population and by civilised society upon the individual. Within this context, the Royal Court Theatre acted as an incubator that allowed Johnstone to develop his subversive theories of performance, drawing on elements of professional wrestling to break down the regimented conventions of the theatre space and enliven the spectator-performer relationship. Eventually Johnstone entered a self-imposed exile from the society that shaped this form of performance and established The Loose Moose Theatre in Calgary, Canada.
This paper will analyse three relationships vital to this narrative: The oppositional reaction of Johnstone's improvisation to the social pressures of 1950's Britain, the creative glasshouse that The Royal Court Theatre provided for Johnstone within this broader cultural context, and the effects that the new social situation of Calgary, Canada had on Johnstone's practice.
At the conclusion of the paper I will draw out the consequences of these analyses for contemporary British society and attempt to identify the normalising forces at work within this context, how our arts institutions and creative incubators might foster novel reactions to these pressures, and how public policy might be shaped in order to encourage artists to remain in Britain so that we might benefit from their continued contribution to our cultural discourses
Michael Rodriguez interviews historian and author Keith Widder
No full textHistorian and author Keith Widder talks about his move to Michigan from Wisconsin, his career as Curator of History for the Mackinac Island State Park Commission, his research interests, his book "Michigan Agricultural College", and his current projects. Widder is interviewed by Michigan State University Librarian Michael Rodriguez for the MSU Libraries' Michigan Writers Series. Held in the MSU Main Library
Spatial Inclusion and Analogy for Set Membership: A Case Study of Analogy at Work
No full textThe analogy between spatial inclusion and set membership offers the opportunity to go beyond the study of how we establish analogical mappings to the investigation of the impact of those mappings on mental process. This analogy is the basis of longstanding didactic techniques for teaching elementary logic (Eulers Circles and Venn Diagrams) and therefore bears on psychological theories of human deductive reasoning (e.g. Erickson 1974).An adequate cognitive theory of analogy must explain how mental processing is aided by analogical mappings. In the case of spatial inclusion as an analogy for set membership this comes down to requiring a theory of how graphical representations aid processing. Here we sketch a general theory in terms of the specicity of graphics which we have developed further elsewhere (see Stenning Oberlander 1991a, 1991b). This general approach to graphical representations rests on the observation that graphical representation systems limit abstraction and thereby purchase computational tractability. In applying this general theory to the case of graphical methods of syllogism solution we sketch a method of using Eulers Circles and show how interpretative conventions for graphical objects allow the necessary abstractions. In particular we show that even choosing the least expressive system of diagrams limited to circles, still gives the requisite expressive power.The Euler's Circle method sketched is then used as a guide to connectionist implementation of corresponding internal representations Graphical representations share some general computational properties with connectionist systems. In the domain of the syllogism the central issue is the implementation of the binding of attributes into type descriptions. Various proposals for connectionist variable binding in the literature are assessed as partial implementations. Some proposals are made for implementation of novel graphical features of the Eulers Circle algorithm. This case study of an analogy suggests the hypothesis that one important role that analogy may play is providing a representation which is more limited in expressive power and therefore more computationally tractable than the literal representations analogies supplant
Selection procedures for module discovery : exploring evolutionary algorithms for cognitive science
No full textEvolutionary algorithms are playing an increasingly important role as search methods in cognitive science domains. In this study, methodological issues in the use of evolutionary algorithms were investigated via simulations in which procedures were systematically varied to modify the selection pressures on populations of evolving agents. Traditional roulette wheel, tournament, and variations of these selection algorithms were compared on the “needle-in-a-haystack” problem developed by Hinton and Nowlan in their 1987 study of the Baldwin effect. The task is an important one for cognitive science, as it demonstrates the power of learning as a local search technique in smoothing a fitness landscape that lacks gradient information. One aspect that has continued to foster interest in the problem is the observation of residual learning ability in simulated populations even after long periods of time.\ud
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Effective evolutionary algorithms balance their search effort between broad exploration of the search space and in-depth exploitation of promising solutions already found. Issues discussed include the differential effects of rank and proportional selection, the tradeoff between migration of populations towards good solutions and maintenance of diversity, and the development of measures that illustrate how each selection algorithm affects the search process over generations. We show that both roulette wheel and tournament algorithms can be modified to appropriately balance search between exploration and exploitation, and effectively eliminate residual learning in this problem
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