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  1. Trade‐Offs Between Grounded and Abstract Representations: Evidence From Algebra Problem Solving.Kenneth R. Koedinger, Martha W. Alibali & Mitchell J. Nathan - 2008 - Cognitive Science 32 (2):366-397.
    This article explores the complementary strengths and weaknesses of grounded and abstract representations in the domain of early algebra. Abstract representations, such as algebraic symbols, are concise and easy to manipulate but are distanced from any physical referents. Grounded representations, such as verbal descriptions of situations, are more concrete and familiar, and they are more similar to physical objects and everyday experience. The complementary computational characteristics of grounded and abstract representations lead to trade‐offs in problem‐solving performance. In prior research with (...)
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  • Relational Priming Based on a Multiplicative Schema for Whole Numbers and Fractions.Melissa DeWolf, Ji Y. Son, Miriam Bassok & Keith J. Holyoak - 2017 - Cognitive Science 41 (8):2053-2088.
    Why might it be beneficial for adults to process fractions componentially? Recent research has shown that college-educated adults can capitalize on the bipartite structure of the fraction notation, performing more successfully with fractions than with decimals in relational tasks, notably analogical reasoning. This study examined patterns of relational priming for problems with fractions in a task that required arithmetic computations. College students were asked to judge whether or not multiplication equations involving fractions were correct. Some equations served as structurally inverse (...)
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  • Hand Gesture and Mathematics Learning: Lessons From an Avatar.Susan Wagner Cook, Howard S. Friedman, Katherine A. Duggan, Jian Cui & Voicu Popescu - 2017 - Cognitive Science 41 (2):518-535.
    A beneficial effect of gesture on learning has been demonstrated in multiple domains, including mathematics, science, and foreign language vocabulary. However, because gesture is known to co‐vary with other non‐verbal behaviors, including eye gaze and prosody along with face, lip, and body movements, it is possible the beneficial effect of gesture is instead attributable to these other behaviors. We used a computer‐generated animated pedagogical agent to control both verbal and non‐verbal behavior. Children viewed lessons on mathematical equivalence in which an (...)
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  • Moving to Learn: How Guiding the Hands Can Set the Stage for Learning.Neon Brooks & Susan Goldin-Meadow - 2016 - Cognitive Science 40 (7):1831-1849.
    Previous work has found that guiding problem-solvers' movements can have an immediate effect on their ability to solve a problem. Here we explore these processes in a learning paradigm. We ask whether guiding a learner's movements can have a delayed effect on learning, setting the stage for change that comes about only after instruction. Children were taught movements that were either relevant or irrelevant to solving mathematical equivalence problems and were told to produce the movements on a series of problems (...)
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  • Non-formal mechanisms in mathematical cognitive development: The case of arithmetic.David W. Braithwaite, Robert L. Goldstone, Han L. J. van der Maas & David H. Landy - 2016 - Cognition 149 (C):40-55.
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  • Private codes and public structures.Colin Allen - 2012 - In David McFarland, Keith Stenning & Maggie McGonigle (eds.), The Complex Mind. Palgrave-Macmillan. pp. 223.
     
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