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The Power of Seeing in Problem Solving and Creativity: An Issue Under Discussion

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Broadening the Scope of Research on Mathematical Problem Solving

Part of the book series: Research in Mathematics Education ((RME))

Abstract

This paper discusses some assumptions in the teaching and learning of problem solving, including the particular importance of a problem-solving strategy towards a visual solution, named seeing, which can be a complementary contribution to the approach and development of problem-solving abilities in students and its relation with mathematical creativity. In this path of stressing visual strategies and representations, we present and discuss different potentialities of visualization, as students use it to solve problems, pointing out some appropriate tasks to illustrate them, and we also underline some constraints of the use of visualization. Within problem solving, we make the connection between the use of visual solutions and mathematical creativity, which allows producing new and elegant solutions to a problem, clarifying and deepening the understanding of it, as well as suggesting productive paths for reasoning. Finally, we illustrate the ideas discussed based on examples emerging from some studies that we carried out with elementary pre-service teachers.

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Authors and Affiliations

  1. School of Education of the Polytechnic Institute of Viana do Castelo, Viana do Castelo, Portugal

    Isabel Vale & Ana Barbosa

  2. Escola Secundária de Santa Maria Maior de Viana do Castelo, Viana do Castelo, Portugal

    Teresa Pimentel

Authors
  1. Isabel Vale
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  2. Teresa Pimentel
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  3. Ana Barbosa
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Correspondence to Isabel Vale .

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Editors and Affiliations

  1. Universidade do Algarve and UIDEF Instituto de Educação, Universidade de Lisboa, Lisbon, Portugal

    Nélia Amado

  2. Universidade do Algarve and UIDEF Instituto de Educação, Universidade de Lisboa, Lisbon, Portugal

    Susana Carreira

  3. School of Education, University of Southampton, Southampton, UK

    Keith Jones

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Vale, I., Pimentel, T., Barbosa, A. (2018). The Power of Seeing in Problem Solving and Creativity: An Issue Under Discussion. In: Amado, N., Carreira, S., Jones, K. (eds) Broadening the Scope of Research on Mathematical Problem Solving. Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-99861-9_11

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  • DOI: https://doi.org/10.1007/978-3-319-99861-9_11

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  • Online ISBN: 978-3-319-99861-9

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