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Analogical Mapping by Constraint Satisfaction
 COGNITIVE SCIENCE 13, 295 (1989)
, 1989
"... A theory of analogical mopping between source and target analogs based upon interacting structural, semantic, and pragmatic constraints is proposed here. The structural constraint of fsomorphfsm encourages mappings that maximize the consistency of relational corresondences between the elements of th ..."
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Cited by 389 (28 self)
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A theory of analogical mopping between source and target analogs based upon interacting structural, semantic, and pragmatic constraints is proposed here. The structural constraint of fsomorphfsm encourages mappings that maximize the consistency of relational corresondences between the elements of the two analogs. The constraint of semantic similarity supports mapping hypotheses to the degree that mapped predicates have similar meanings. The constraint of pragmatic centrality fovors mappings involving elements the analogist believes to be important in order to achieve the purpose for which the anology Is being used. The theory is implemented in a computer progrom called ACME (Analogical Constraint Mapping Engine), which represents constraints by means of a network of supporting and competing hypotheses regarding what elements to map. A coop erative algorithm for parallel constraint satisfaction identifies mapping hypotheses that collectively represent the overall mapping that best fits the interactlng constraints. ACME has been applied to a wide range of examples that include problem analogies, analogical arguments, explanatory analogies, story analogies, formal analogies, and metaphors. ACME is sensitive to semantic and prag matic information if it is available,.and yet able to compute mappings between formally isomorphic analogs without any similar or identical elements. The theory Is able to account for empirical findings regarding the impact of consistenty and similarity on human processing of analogies.
A new look at Newton’s inequalities
 2000), Article 17. [ONLINE: http://jipam. vu.edu.au/v1n2/014_99.html
"... Communicated by A. Lupa¸s ABSTRACT. New families of inequalities involving the elementary symmetric functions are built as a consequence that all zeros of certain real polynomials are real numbers. ..."
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Cited by 30 (2 self)
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Communicated by A. Lupa¸s ABSTRACT. New families of inequalities involving the elementary symmetric functions are built as a consequence that all zeros of certain real polynomials are real numbers.
Relative frequency and probability in the Everett interpretation of Heisenbergpicture quantum mechanics
, 2003
"... The existence of probability in the sense of the frequency interpretation, i.e. probability as “long term relative frequency, ” is shown to follow from the dynamics and the interpretational rules of Everett quantum mechanics in the Heisenberg picture. This proof is free of the difficulties encounter ..."
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Cited by 9 (6 self)
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The existence of probability in the sense of the frequency interpretation, i.e. probability as “long term relative frequency, ” is shown to follow from the dynamics and the interpretational rules of Everett quantum mechanics in the Heisenberg picture. This proof is free of the difficulties encountered in applying to the Everett interpretation previous results regarding relative frequency and probability in quantum mechanics. The ontology of the Everett interpretation in the Heisenberg picture is also discussed.
The Nature of Knowledge in Composition and Literary Understanding: The Question of Specificity
 Review of Educational Research, Fall
, 1992
"... Psychologists have long debated the extent to which people transfer knowledge from context to context. This debate has emerged in the study of literacy where researchers of composition and literary understanding have begun to examine the extent to which different tasks require particular knowledge a ..."
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Cited by 8 (0 self)
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Psychologists have long debated the extent to which people transfer knowledge from context to context. This debate has emerged in the study of literacy where researchers of composition and literary understanding have begun to examine the extent to which different tasks require particular knowledge and the extent to which different interpretive communities require specific understandings. This article reviews issues related to transfer and knowledge specificity as articulated in psychology and then examines theory and research in composition and literary understanding which parallel the debate in psychology. The authors identify three positions that have emerged in literacy debates: the case for general knowledge, the case for taskspecific knowledge, and the case for communityspecific knowledge. Each position carries with it certain assumptions about learning and transfer, and each has clear implications for curriculum and instruction. The authors delineate the positions and the assumptions that drive them and detail their instructional consequences, arguing that researchers and teachers need an articulated understanding of their assumptions about knowledge and transfer in order to establish a clear and coherent relationship between theory and practice.
ARISTOTELIAN REALISM
"... Aristotelian, or nonPlatonist, realism holds that mathematics is a science of the real world, just as much as biology or sociology are. Where biology studies living things and sociology studies human social relations, mathematics studies the quantitative or structural aspects of things, such as rat ..."
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Aristotelian, or nonPlatonist, realism holds that mathematics is a science of the real world, just as much as biology or sociology are. Where biology studies living things and sociology studies human social relations, mathematics studies the quantitative or structural aspects of things, such as ratios, or patterns, or complexity,
35th ASEE/IEEE Frontiers in Education Conference T2C21 Can Discovery and Intuition Be Taught?
"... opportunity to investigate how to teach through discovery. One of the results was to organize the method into four steps: the teacher discovers, realizes how he or she discovers, guides the student in a similar experience, and uncovers why the student did so poorly. Following this method, the stud ..."
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opportunity to investigate how to teach through discovery. One of the results was to organize the method into four steps: the teacher discovers, realizes how he or she discovers, guides the student in a similar experience, and uncovers why the student did so poorly. Following this method, the students in the class showed a natural skill in using discovery when dealing with math puzzles, but they lost that sense when dealing with their engineering discipline. We look at the reasons for this and list roadblocks that keep discovery from being generally taught. This paper looks at methods to shorten the time and increase the success of teaching discovery. It seeks a balance in which some material is presented in the traditional lecture mode, but some material the students are allowed to discover for themselves. Index Terms – creativity, design, discovery, insight, intuition.
THE MATHEMATICAL DISCOURSE OF UNDERGRADUATE MATHEMATICS MAJORS: THE RELATION TO LEARNING PROOF AND ESTABLISHING A LEARNING COMMUNITY
, 2009
"... Candidate for the degree of Doctor of Education ..."
MRC Applied Psychology Unit
"... ABSTRACT It seems plausible that the conception of the mind has evolved over the first hundred years ofpsychology in America. In this research, we studied this evolution by tracing changes in the kinds of metaphors used by psychologists to describe mental phenomena. A corpus of metaphors from 1894 t ..."
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ABSTRACT It seems plausible that the conception of the mind has evolved over the first hundred years ofpsychology in America. In this research, we studied this evolution by tracing changes in the kinds of metaphors used by psychologists to describe mental phenomena. A corpus of metaphors from 1894 to the present was collected and examined. The corpus consisted of all metaphors for mental phenomena used in the first issue of Psychological Review in each decade, beginning with the inception of the journal in 1894 and continuing with 1905, 1915, and so on through 1975. These nine issues yielded 265 mental metaphors, which were categorized according to the type of analogical domain from which the comparison was drawn.