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Mathematical Problem Solving Beyond School: A Tool for Highlighting Creativity in Children’s Solutions

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Broadening the Scope of Research on Mathematical Problem Solving

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

Abstract

The study that is partially reported in this chapter has been developed, in theoretical and empirical terms, within the Problem@Web Project. The overall goal of the project was to study mathematical problem solving in a context outside the classroom, namely, web-based mathematical problem-solving competitions. One of the research foci of this project is the creativity manifested in the solutions of mathematical problems produced by the participating children. Thus, the project sought to analyse and examine the close and also complex relationship between creativity and problem solving. The perspectives that emphasize the development of creativity also look for tools that allow their assessment. We have considered, in a first approach, the components of creativity that are most often found in the research on divergent thinking, i.e. originality, fluency and flexibility. The next step was to find mathematical problem-solving dimensions, supported by the research in the field, which would lead to mathematical creativity as a combination of divergent thinking, convergent thinking and other abilities. An analytical tool that integrates the dimensions of originality, activation of mathematical knowledge and activation of forms of representation was then achieved. This tool is here applied to a sample of ten solutions to a problem of the mathematical competition SUB12. In combining a qualitative description and a numerical-graphical interpretation, the results highlight the three dimensions contributing to the overall score of mathematical creativity. They also illustrate the relevance of the ability to represent and express mathematical ideas involved in solving problems.

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Author information

Authors and Affiliations

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

    Susana Carreira

  2. Agrupamento de Escolas Cardoso Lopes, Amadora, and UIDEF, Instituto de Educação, Universidade de Lisboa, Lisbon, Portugal

    Nuno Amaral

Authors
  1. Susana Carreira
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  2. Nuno Amaral
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Correspondence to Susana Carreira .

Editor information

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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Carreira, S., Amaral, N. (2018). Mathematical Problem Solving Beyond School: A Tool for Highlighting Creativity in Children’s Solutions. 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_9

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  • DOI: https://doi.org/10.1007/978-3-319-99861-9_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-99860-2

  • Online ISBN: 978-3-319-99861-9

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