MATHEMATICS AS THE ART OF SEEING THE INVISIBLE

Jun 21st, 2015
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Black Hills State University
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The role of metaphors and the switch in cognitive modes in relation to visualization in learning and teaching mathematics is discussed, based on examples and case studies with students and teachers. We present some preliminary evidence supporting our claims that visualization requires the activation of various metaphors, that it is rather hampered than facilitated by traditional teaching in mathematics, but it is however a trainable capacity in teachers and students.

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MATHEMATICS AS THE ART OF SEEING THE INVISIBLE Jorge Soto-Andrade 1Department of Mathematics, Faculty of Science Centre for Advanced Research in Education (CARE)University of ChileThe role of metaphors and the switch in cognitive modes in relation to visualization in learning and teaching mathematics is discussed, based on examples and case studies with students and teachers. We present some preliminary evidence supporting our claims that visualization requires the activation of various metaphors, that it is rather hampered than facilitated by traditional teaching in mathematics, but it is however a trainable capacity in teachers and students. Introduction When teaching mathematics to first year undergraduates who intend to major in Humanities or Social Sciences at the University of Chile, we usually ask them to concoct aphorisms to describe their ongoing experience of mathematics, as the course unfolds. An often emerging aphorism is: Mathematics is the art of seeing the invisible, a close kin to Visualization offers a method of seeing the unseen (McCormick, DeFanti, & Brown, 1987, p. 3), taken up as leitmotiv in Arcavi (2003) when discussing the role of visual representations in the learning of mathematics. At the other end of the spectrum, in a recent paper (Faux & Gates, 2004) on supersymmetric representation theory, in theoretical physics, we read: The use of symbols to connote ideas which defy simple verbalization is perhaps o

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