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(Des)orientación y sentido espacial: pensamiento topológico en los grados intermedios

  • Autores: Zulma Elizabete de Freitas Madruga, Sean M. McCarthy
  • Localización: PNA: Revista de investigación en didáctica de la matemática, ISSN-e 1887-3987, Vol. 9, Nº. 1, 2014, págs. 41-51
  • Idioma: español
  • DOI: 10.30827/pna.v9i1.6108
  • Títulos paralelos:
    • (Dis)orientation and spatial sense: topological thinking in the middle grades
  • Enlaces
  • Resumen
    • español

      En este trabajo, nos centramos en enfoques topológicos del espacio y sostenemos que las experiencias con topología permiten a los estudiantes de secundaria desarrollar una comprensión más sólida de la orientación y de la dimensión. Enmarcamos nuestro argumento en términos de la literatura fenomenológica de la percepción y el espacio corpóreo. Discutimos los hallazgos de un estudio cuasi-experimental con 9 estudiantes de quinto a octavo curso (10 a 13 años) que participaron en talleres sobre la teoría de nudos durante 6 semanas. Discutimos los datos de vídeo que muestran cómo los estudiantes se involucran con la desorientación intrínseca de los nudos matemáticos mediante el uso del gesto y movimiento.

    • English

      In this paper, we focus on topological approaches to space and we argue that experiences with topology allow middle school students to develop a more robust understanding of orientation and dimension. We frame our argument in terms of the phenomenological literature on perception and corporeal space. We discuss findings from a quasi-experimental study engaging 9 grades 5-8 students (10-13 years old) in a 6-week series of school-based workshops focused on knot theory. We discuss video data that shows how students engage with the intrinsic disorientation of mathematical knots through the use of gesture and movement.

  • Referencias bibliográficas
    • Adams, C. (2004). Why knot? An introduction to the mathematical theory of knots. Englewood, CO: Key College Publishing.
    • Ahmed, S. (2010). Orientations matter. In D. Coole & S. Frost (Eds.), New materialisms: Ontology, agency, and politics (pp. 234-257)....
    • Berthoz, A. (2000). The brain's sense of movement. Cambridge, MA: Harvard University Press.
    • Châtelet, G. (2006). Interlacing the singularity, the diagram and the metaphor. In S. Duffy (Ed.), Virtual mathematics: The logic of difference...
    • Debnath, L. (2010). A brief historical introduction to Euler's formula for polyhedra, topology, graph theory and networks. International...
    • Fielker, D. (2011). Some thoughts about geometries. Mathematics in School, 40(2), 23-26.
    • Gibson, J. J. (1979). The ecological approach to visual perception. Boston, MA: Houghton Mifflin.
    • Gray, J. (1979). Ideas of space: Euclidean, non-Euclidean and relativistic. Oxford, United Kingdom: Clarendon Press.
    • Handa, Y. & Mattman, T. (2008). Knot theory with young children. Mathematics Teaching, 211, 32-35.
    • Hilbert, D. & Cohn-Vossen, S. (1952/1983/1990). Geometry and the imagination (P. Nemenyi, Trans., 2nd Edition). New York, NY: Chelsea...
    • Hostetter, A. B., & Alibali, M. W. (2008). Visible embodiment: Gestures as simulated action. Psychonomic Bulletin & Review, 15(3),...
    • Kuechler, S. (2001). Why knot? Towards a theory of art and mathematics. In C. Pinney & N. Thomas (Eds.), Beyond aesthetics: Art and the...
    • Nemirovsky, R. & Ferrara, F. (2009). Mathematical imagination and embodied cognition. Educational Studies of Mathematics, 70(2), 159-174.
    • Netz, R. & Noel, W. (2007). The Archimedes codex: Revealing the secrets of the worlds greatest palimpsest. Philadelphia, PA: Da Capo Press.
    • Núñez, R., Edwards, L., & Matos, J. F. (1999). Embodied cognition as grounding for situatedness and context in mathematics education....
    • O'Shea, D. (2007). The Poincaré conjecture: In search of the shape of the universe. New York, NY: Walter and Company.
    • Papert, S. (1980). Mindstorms: Children, computers, and powerful ideas. New York, NY: Basic Books.
    • Richeson, D. S. (2008). Euler's gem: The polyhedron formula and the birth of topology. Princeton, NJ: Princeton University Press.
    • Rush, F. (2009). On Architecture. New York, NY: Routledge.
    • Smith, D.W. (2006). Axiomatics and problematics as two modes of formalisation: Deleuze's epistemology of mathematics. In S. Duffy (Ed.),...
    • Stahl, S. (2005). Introduction to topology and geometry. Hoboken, NJ: Wiley-Interscience.
    • Strohecker, C. (1991). Elucidating styles of thinking about topology through thinking about knots. In I. Harel & S. Papert (Eds.), Constructionism...
    • Teissier, B. (2011). Mathematics and narrative: Why are stories and proofs interesting? In A. Doxiadis & B. Mazur (Eds.), Circles disturbed:...

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