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Generalized Integration Networks
"... The expression "blends " is often used to refer to a type of data where, very visibly, two or more inputs are partially mapped onto each other and selectively projected to a new mental space in which novel structure can emerge (Fauconnier and Turner 1994, 1998, 2002). Famous examples of su ..."
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The expression "blends " is often used to refer to a type of data where, very visibly, two or more inputs are partially mapped onto each other and selectively projected to a new mental space in which novel structure can emerge (Fauconnier and Turner 1994, 1998, 2002). Famous examples of such blends are The Buddhist Monk, Regatta, Nixon in France, Complex Numbers, The Image Club. As it turns out, far from being exceptional, marginal, or genrespecific, such blends are all over the place, and especially visible in fields as different as scientific discovery, humor, advertising, or religious rituals. What warranted a new category for this kind of data when we first studied it was that it didn't fit into any of the known mapping schemes, in particular the source– target scheme of metaphor theory as understood at the time, or analogy, or metonymy, or simple framing. Methodologically, the abundance of previously unnoticed (and hence never analyzed) "blending " data suddenly offered a wealth of empirical resources to study with precision the cognitive operations 1 of mapping and integration that made such
How Blending Illuminates Understanding of Calculus 1 How Blending Illuminates Understandings of Calculus
"... Conceptual blending is gaining momentum amongst mathematics educators interested in better conceptualizing mathematical meanings students are building. We used conceptual blending as a lens to illuminate students ’ understandings of calculus concepts as they emerged during sustained mathematical inq ..."
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Conceptual blending is gaining momentum amongst mathematics educators interested in better conceptualizing mathematical meanings students are building. We used conceptual blending as a lens to illuminate students ’ understandings of calculus concepts as they emerged during sustained mathematical inquiry. We share some of the insights we have gained by using this lens in our analysis. Viewing the mathematical connections along with the emergent structure that follows allowed us to more fully characterize students ’ constructions of meaning for mathematics. Additionally we have found that conceptual blending is flexible in the unit of analysis, aids comparisons between conceptions held by a student or different students, brings to the forefront elements of the input and blended spaces and the connections between them, emphasizes the meaning that students are building for important mathematics. Conceptual blending (Fauconnier & Turner, 2002) is gaining momentum amongst mathematics educators interested in better conceptualizing mathematical meanings students are building (Núñez, 2004; Megowen & Zandieh, 2005). We use conceptual blending as a lens to illuminate individual and collective understandings of calculus concepts as they emerge from sustained mathematical inquiry. In this paper, we share some of the insights we have gained through using conceptual blending in our analysis. Theoretical perspective Agency and Purposeful Choice We defined personal Agency as “the requirement, responsibility and freedom to choose based on prior experiences and imagination, with concern not only for one’s own understandings of mathematics, but with mindful awareness of the impact one’s actions and choices may haveHow Blending Illuminates Understanding of Calculus 2 on others ” (Walter & Gerson, 2007 p. 209). We further suggest that agency is a requirement for leaning to occur. Because we hold this view we carefully examine students choices and the connected understanding they build through this lens.
A Loop is a Compression
"... Abstract. An outcome from a larger research project is described. This places work seeking to understand how novices learn elementary programming notions in a wider framework derived from cognitive science, and in particular the group of ideas centered on conceptual blends. The framework is outlined ..."
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Abstract. An outcome from a larger research project is described. This places work seeking to understand how novices learn elementary programming notions in a wider framework derived from cognitive science, and in particular the group of ideas centered on conceptual blends. The framework is outlined and the research methodology is described, followed by some of the data gathered. It is suggested that students ' consideration of code fragments can be analysed in terms of mental spaces, and that loop statements represent compressions. The implications for teaching are discussed, and future work is outlined. 1
Ontological Blending in DOL
"... Abstract. We introduce ontological blending as a method for combining ontologies. Compared with existing combination techniques that aim at integrating or assimilating categories and relations of thematically related ontologies, blending aims at creatively generating (new) categories and ontological ..."
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Abstract. We introduce ontological blending as a method for combining ontologies. Compared with existing combination techniques that aim at integrating or assimilating categories and relations of thematically related ontologies, blending aims at creatively generating (new) categories and ontological definitions; this is done on the basis of input ontologies whose domains are thematically distinct but whose specifications share structural or logical properties. As a result, ontological blending can generate new ontologies and concepts and it allows a more flexible technique for ontology combination compared to existing methods. Our approach to computational creativity in conceptual blending is inspired by methods rooted in cognitive science (e.g., analogical reasoning), ontological engineering, and algebraic specification. Specifically, we introduce the basic formal definitions for ontological blending, and show how the distributed ontology language DOL (currently being standardised within the OntoIOp—Ontology Integration and Interoperability—activity of ISO/TC 37/SC 3) can be used to declaratively specify blending diagrams. 1
COMPRESSION AND EMERGENT STRUCTURE 1
"... Thinkers have always been fascinated by mental patterns that are commonly classified under labels such as analogy, category extension, metaphor, framing, counterfactuals, and grammatical constructions. Typically, they are considered part of distinct disciplines: counterfactuals in philosophy and log ..."
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Thinkers have always been fascinated by mental patterns that are commonly classified under labels such as analogy, category extension, metaphor, framing, counterfactuals, and grammatical constructions. Typically, they are considered part of distinct disciplines: counterfactuals in philosophy and logic, metaphor in literature, analogy in psychology, framing in sociology and artificial intelligence, grammatical constructions in linguistics. We have recently discovered, however, that the mental principles behind all of these patterns are uniform. The patterns are all products of conceptual integration networks. A central feature of integration networks is their ability to compress diffuse conceptual structure into intelligible and manipulable humanscale situations in a blended space. These compressed blends are memorable and can be expanded flexibly to manage their integration networks. Compressions have been studied in great detail. They operate on a set of twenty or so vital conceptual relations, such as CauseEffect, Analogy and Disanalogy, Time, Space, Change, Identity, PartWhole, and Representation. Relations can be compressed into a humanscale version of themselves, or into different vital relations. As an example of compression, consider a statement like "Dinosaurs changed into birds, " used to suggest the new theory according to which birds are descendants of dinosaurs. At one level, this evolutionary story spans millions of 1 What follows assumes some familiarity with conceptual integration (also called "blending"). A useful website for learning about this area of research is