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95
Reuniting perception and conception
, 1998
"... Work in philosophy and psychology has argued for a dissociation between perceptuallybased similarity and higherlevel rules in conceptual thought. Although such a dissociation may be justified at times, our goal is to illustrate ways in which conceptual processing is grounded in perception, both for ..."
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Cited by 76 (15 self)
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Work in philosophy and psychology has argued for a dissociation between perceptuallybased similarity and higherlevel rules in conceptual thought. Although such a dissociation may be justified at times, our goal is to illustrate ways in which conceptual processing is grounded in perception, both for perceptual similarity and abstract rules. We discuss the advantages, power and influences of perceptuallybased representations. First, many of the properties associated with amodal symbol systems can be achieved with perceptuallybased systems as well (e.g. productivity). Second, relatively raw perceptual representations are powerful because they can implicitly represent properties in an analog fashion. Third, perception naturally provides impressions of overall similarity, exactly the type of similarity useful for establishing many common categories. Fourth, perceptual similarity is not static but becomes tuned over time to conceptual demands. Fifth, the original motivation or basis for sophisticated cognition is often less sophisticated perceptual similarity. Sixth, perceptual simulation occurs even in conceptual tasks that have no explicit perceptual demands. Parallels between perceptual and conceptual processes suggest that many mechanisms typically associated
Aesthetic Computing
, 2006
"... The Eprints service at the University of Westminster aims to make the research output of the University available to a wider audience. Copyright and Moral Rights remain with the authors and/or copyright owners. Users are permitted to download and/or print one copy for noncommercial private study or ..."
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Cited by 28 (5 self)
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The Eprints service at the University of Westminster aims to make the research output of the University available to a wider audience. Copyright and Moral Rights remain with the authors and/or copyright owners. Users are permitted to download and/or print one copy for noncommercial private study or research. Further distribution and any use of material from within this archive for profitmaking enterprises or for commercial gain is strictly forbidden.
The Garden of Knowledge as a Knowledge Manifold  A Conceptual Framework for Computer Supported Subjective Education
 CID17, TRITANAD9708, DEPARTMENT OF NUMERICAL ANALYSIS AND COMPUTING SCIENCE
, 1997
"... This work presents a unied patternbased epistemological framework, called a Knowledge Manifold, for the description and extraction of knowledge from information. Within this framework it also presents the metaphor of the Garden Of Knowledge as a constructive example. Any type of KM is defined in te ..."
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Cited by 27 (18 self)
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This work presents a unied patternbased epistemological framework, called a Knowledge Manifold, for the description and extraction of knowledge from information. Within this framework it also presents the metaphor of the Garden Of Knowledge as a constructive example. Any type of KM is defined in terms of its objective calibration protocols  procedures that are implemented on top of the participating subjective knowledgepatches. They are the procedures of agreement and obedience that characterize the coherence of any type of interaction, and which are used here in order to formalize the concept of participator consciousness in terms of the inversedirect limit duality of Category Theory.
THE ROLE OF VISUAL REPRESENTATIONS IN THE LEARNING of Mathematics
, 2003
"... Visualization, as both the product and the process of creation, interpretation and reflection upon pictures and images, is gaining increased visibility in mathematics and mathematics education. This paper is an attempt to define visualization and to analyze, exemplify and reflect upon the many diff ..."
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Cited by 21 (0 self)
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Visualization, as both the product and the process of creation, interpretation and reflection upon pictures and images, is gaining increased visibility in mathematics and mathematics education. This paper is an attempt to define visualization and to analyze, exemplify and reflect upon the many different and rich roles it can and should play in the learning and the doing of mathematics. At the same time, the limitations and possible sources of difficulties visualization may pose for students and teachers are considered.
Cognitive growth in elementary and advanced mathematical thinking
 In D. Carraher and L. Miera (Eds.), Proceedings of PME X1X
, 1995
"... This paper addresses the development of mathematical thinking from elementary beginnings in young children to university undergraduate mathematics and on to mathematical research. It hypothesises that mathematical growth starts from perceptions of, and actions on, objects in the environment. Success ..."
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Cited by 18 (10 self)
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This paper addresses the development of mathematical thinking from elementary beginnings in young children to university undergraduate mathematics and on to mathematical research. It hypothesises that mathematical growth starts from perceptions of, and actions on, objects in the environment. Successful “perceptions of ” objects lead through a Van Hiele development in visuospatial representations with increasing verbal support to visually inspired verbal proof in geometry. Successful “actions on” objects use symbolic representations flexibly as “procepts ” — processes to do and concepts to think about — in arithmetic and algebra. The resulting cognitive structure in elementary mathematical thinking becomes advanced mathematical thinking when the concept images in the cognitive structure are reformulated as concept definitions and used to construct formal concepts that are part of a systematic body of shared mathematical knowledge. The analysis will be used to highlight the changing status of mathematical concepts and mathematical proof, the difficulties occurring in
Creating Polyhedral Models by Computer
 Journal of Computers in Mathematics and Science Teaching
, 1997
"... This paper describes a computer application named HyperGami that permits users to design, explore, decorate, and study a rich variety of paper polyhedral models. In structure, HyperGami is a "programmable design environment", including both a direct manipulation interface as well as a doma ..."
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Cited by 16 (7 self)
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This paper describes a computer application named HyperGami that permits users to design, explore, decorate, and study a rich variety of paper polyhedral models. In structure, HyperGami is a "programmable design environment", including both a direct manipulation interface as well as a domainenriched programming environment based on the Scheme language; the application is thus designed to be accessible to students of geometry while providing challenging projects for longterm or expert users (such as professional mathematicians and designers). In the course of this paper, we describe the HyperGami interface and language; illustrate the construction of "customized polyhedra" of various sorts; discuss the results of our initial experiences using the system in working with middleschool students; and argue for the utility of embedding programming languages in educational design environments such as this one. 1. Introduction Over the centuries, human beings have been fascinated by polyhe...
Managing the Requirements Engineering Process
, 2001
"... Process management is a crucial issue in developing information or computer systems. Theories of software development process management suggest that the process should be supported and managed based on what the process really is. However, our learning from an action research study reveals that the ..."
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Cited by 15 (7 self)
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Process management is a crucial issue in developing information or computer systems. Theories of software development process management suggest that the process should be supported and managed based on what the process really is. However, our learning from an action research study reveals that the requirements engineering (RE) process differs significantly from what the current literature tends to describe. The process is not a systematic, smooth and incremental evolution of the requirements model, but involves occasional simplification and restructuring of the requirements model. This revised understanding of the RE process suggests a new challenge to both the academic and industrial communities, demanding new process management approaches. In this paper, we present our understanding of the RE process and its implications for process management.
How can Nature help us compute
 SOFSEM 2006: Theory and Practice of Computer Science – 32nd Conference on Current Trends in Theory and Practice of Computer Science, Merin, Czech Republic, January 21–27
, 2006
"... Abstract. Ever since Alan Turing gave us a machine model of algorithmic computation, there have been questions about how widely it is applicable (some asked by Turing himself). Although the computer on our desk can be viewed in isolation as a Universal Turing Machine, there are many examples in natu ..."
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Cited by 11 (3 self)
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Abstract. Ever since Alan Turing gave us a machine model of algorithmic computation, there have been questions about how widely it is applicable (some asked by Turing himself). Although the computer on our desk can be viewed in isolation as a Universal Turing Machine, there are many examples in nature of what looks like computation, but for which there is no wellunderstood model. In many areas, we have to come to terms with emergence not being clearly algorithmic. The positive side of this is the growth of new computational paradigms based on metaphors for natural phenomena, and the devising of very informative computer simulations got from copying nature. This talk is concerned with general questions such as: • Can natural computation, in its various forms, provide us with genuinely new ways of computing? • To what extent can natural processes be captured computationally? • Is there a universal model underlying these new paradigms?
How Mathematicians Prove Theorems
 IN PROC. OF THE ANNUAL CONFERENCE OF THE COGNITIVE SCIENCE SOCIETY
, 1994
"... This paper analyzes how mathematicians prove theorems. The analysis is based upon several empirical sources such as reports of mathematicians and mathematical proofs by analogy. In order to combine the strength of traditional automated theorem provers with humanlike capabilities, the questions aris ..."
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Cited by 11 (7 self)
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This paper analyzes how mathematicians prove theorems. The analysis is based upon several empirical sources such as reports of mathematicians and mathematical proofs by analogy. In order to combine the strength of traditional automated theorem provers with humanlike capabilities, the questions arise: Which problem solving strategies are appropriate? Which representations have to be employed? As a result of our analysis, the following reasoning strategies are recognized: proof planning with partially instantiated methods, structuring of proofs, the transfer of subproofs and of reformulated subproofs. We discuss the representation of a component of these reasoning strategies, as well as its properties. We find some mechanisms needed for theorem proving by analogy, that are not provided by previous approaches to analogy. This leads us to a computational representation of new components and procedures for automated theorem proving systems.
Interactive Evolution for Systematic Exploration of a Parameter Space
 Proceedings of ANNIE 2003
, 2003
"... Interactive evaluation of a fitness function for a genetic algorithm through direct manipulation is known as interactive evolution. Because it removes the need to specify a fitness function prior to exploration, the user can change evaluation criteria over time. This is especially important when ..."
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Cited by 9 (6 self)
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Interactive evaluation of a fitness function for a genetic algorithm through direct manipulation is known as interactive evolution. Because it removes the need to specify a fitness function prior to exploration, the user can change evaluation criteria over time. This is especially important when the fitness function is unknown or not easily specified beforehand. This paper describes a system that allows the user to evaluate and evolve small collections of candidate solutions that represent the range of available solutions in order to explore parameter ranges of interest. Although users may be expert with respect to their particular tasks, some may be novices in relation to their software. For them, interactive evolution removes syntactic barriers to the specification of alternative candidate solutions and navigation amongst them.