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Mathematical Problem Solving with Technology: the Techno-Mathematical Fluency of a Student-with-GeoGebra

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Abstract

This study offers a view on students’ technology-based problem solving activity through the lens of a theoretical model which accounts for the relationship between mathematical and technological knowledge in successful problem solving. This study takes a qualitative approach building on the work of a 13-year-old girl as an exemplary case of the nature of young students’ spontaneous mathematical problem solving with technology. The empirical data comprise digital records of her approaches to two problems from a web-based mathematical competition where she resorted to GeoGebra and an interview where she explains and describes her usual problem solving activity with this tool. Based on a proposed model for describing the processes of mathematical problem solving with technologies (MPST), the main results show that this student’s solving and expressing the solution are held from the early and continuing interplay between mathematical skills and the perception of the affordances of the tool. The analytical model offers a clear picture of the type of actions that lead to the solution of each problem, revealing the student’s ability to deal with mathematics and technology in problem solving. By acknowledging this as a case of a human-with-media in solving mathematical problems, the students’ efficient way of merging technological and mathematical knowledge is portrayed in terms of her techno-mathematical fluency.

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Acknowledgments

This work was supported by the project Problem@Web (PTDC/CPE-CED/101635/2008) and the PhD grant SFRH/BD/73363/2010, both funded by Fundação para a Ciência e Tecnologia.

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Authors and Affiliations

  1. UIDEF, Instituto de Educação, Universidade de Lisboa, Alameda da Universidade, 1649-013, Lisbon, Portugal

    Hélia Jacinto & Susana Carreira

  2. Departamento de Matemática, Faculdade de Ciências e Tecnologia, Universidade do Algarve, Campus de Gambelas, 8005-139, Faro, Portugal

    Susana Carreira

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  1. Hélia Jacinto
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  2. Susana Carreira
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Correspondence to Hélia Jacinto or Susana Carreira.

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Jacinto, H., Carreira, S. Mathematical Problem Solving with Technology: the Techno-Mathematical Fluency of a Student-with-GeoGebra. Int J of Sci and Math Educ 15, 1115–1136 (2017). https://doi.org/10.1007/s10763-016-9728-8

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  • DOI: https://doi.org/10.1007/s10763-016-9728-8

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