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6_EDWARDS - The Role of Gestures in Mathematical Discourse...

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The Role of Gestures in Mathematical Discourse: Remembering & Problem Solving Laurie D. Edwards St. Mary’s College of California [email protected]
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Theoretical context Cognition is embodied , at multiple levels: In the moment ( microgenetically ), through gaze, gesture, speech, imagery Developmentally ( ontogenetically ), through individual experiences, for example, with our own bodies, physical objects, electronic artifacts, inscriptions Biologically ( phylogenetically ) through constraints and capabilities developed through evolutionary time. The only mathematics we have access to is the mathematics we are physiologically capable of understanding (Lakoff & Núñez)
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Gesture and multimodality Pervasive Multimodality (Nathaniel Smith): Gesture is integrated with speech, writing and drawing in the construction and communication of mathematical ideas . General research goal: To investigate the form and functions of gestures in the context of talking about and doing mathematics .
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McNeill’s Typology/Dimensions Iconic gestures: “close formal relationship to the semantic content of speech” Metaphoric gestures: “the pictorial content presents an abstract idea” Beat : “indexes the word or phrase ... as being significant” Deictic : “pointing movement [that] selects a part of the gesture space”
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McNeill’s typology was produced using data gathered in a specific context: subjects producing a narrative describing a cartoon they have just seen. Additional research goal: To determine whether McNeill’s categories/dimensions are adequate for describing gesture produced in mathematical situations . Adequacy of McNeill’s Framework
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Methodology 14 women, college sophomores, enrolled in math content course for prospective elementary school teachers Interviewed in pairs about fractions (note: not a learning situation, not involving motion or graphing) Solved five problems involving operations with fractions, with questions fractions before and after the problem-solving portion Interviews videotaped, transcribed, gestures coded
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Interview Questions How were you first introduced to the idea of fractions?
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