Mathematical Creativity, Analogical Reasoning and Visualization

Publications pertinent to mathematical creativity include: Mathematical Creation by Henri Poincaré, An Essay on the Psychology of Invention in the Mathematical Field by Jacques Hadamard, The State of Art in Mathematical Creativity by Erkki Pehkonen, The Characteristics of Mathematical Creativity by Bharath Sriraman, Creativity, Cognitive Mechanisms, and Logic by Ahmed Abdel-Fattah, Tarek Besold and Kai-Uwe Kühnberger, What is Mathematical Thinking by Robert J. Sternberg, Mathematical Thinking and Learning by Herbert P. Ginsburg, Joanna Cannon, Janet Eisenband and Sandra Pappas, Creativity in Mathematics Education by Hartwig Meissner, Metaphor in Educational Discourse by Lynne Cameron and Analogy, Explanation, and Education by Paul Thagard.

Publications pertinent to mathematical metaphor, analogy and blending include: The Cognitive Foundations of Mathematics: The Role of Conceptual Metaphor by Rafael Núñez and George Lakoff, A Formal Cognitive Model of Mathematical Metaphors by Markus Guhe, Alan Smaill and Alison Pease, Using Information Flow for Modelling Mathematical Metaphors by Markus Guhe, Alan Smaill and Alison Pease, Metaphoric and Metonymic Signification in Mathematics by Norma C. Presmeg, Mathematics and Plausible Reasoning: Induction and Analogy in Mathematics by George Pólya, Analogical Reasoning and the Development of Algebraic Abstraction by Lyn D. English and Patrick V. Sharry, Using Analogies to Find and Evaluate Mathematical Conjectures by Alison Pease, Markus Guhe and Alan Smaill, Blending and Other Conceptual Operations in the Interpretation of Mathematical Proofs by Adrian Robert, Mathematical Blending by James C. Alexander, Material Anchors for Conceptual Blends by Edwin Hutchins, Mathematical Symbols as Epistemic Actions by Helen De Cruz and Johan De Smedt and A Theoretical Taxonomy of External Systems of Representation in the Learning and Understanding of Mathematics by Andri Marcou and Athanasios Gagatsis.

Publications pertinent to mathematical visualization include: Creativity, Visualization Abilities, and Visual Cognitive Style by Maria Kozhevnikov, Michael Kozhevnikov, Chen Jiao Yu and Olesya Blazhenkova, Representation, Vision and Visualization: Cognitive Functions in Mathematical Thinking. Basic Issues for Learning by Raymond Duval, Image – Metaphor – Diagram: Visualization in Learning Mathematics by Gert Kadunz and Rudolf Sträßer, The Role of Visual Representations in the Learning of Mathematics by Abraham Arcavi, Research on Visualization in Learning and Teaching Mathematics by Norma C. Presmeg, Geometry and the Imagination by David Hilbert and Stephan Cohn-Vossen, Geometry and Spatial Reasoning by Douglas H. Clements and Michael T. Battista, The Nature of Spatial Ability and its Relationship to Mathematical Problem Solving by Barbara Elaine Moses and Spatial Ability, Visual Imagery, and Mathematical Performance by Glen Lean and M. A. (Ken) Clements.

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