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Mathematical Problem Solving and the Use of Digital Technologies

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Mathematical Problem Solving

Part of the book series: ICME-13 Monographs ((ICME13Mo))

Abstract

The goal in this chapter is to analyze and document ways in which the use of digital technologies provides affordances for teachers/students to develop knowledge and solve mathematical problems. What types of representations and problem explorations appear and characterize a technology enhanced problem-solving approach? What does the systematic and coordinated use of digital technologies bring to the students’ process of delving into problem statements, to the ways of representing and exploring tasks, and to the development of their problem-solving competencies? Four groups of problems are examined to illustrate what strategies and ways of reasoning emerge and are enhanced in a technological problem-solving approach. Focusing on the reconstruction of figures that often appear in problem statements, the transformation of a routine problem into an investigation task, the representation and exploration of a variation phenomenon task, and the construction of a dynamic configuration to pose and pursue questions shed lights on ways to frame a problem-solving approach that fosters and values the use of digital technologies. The discussion of these types of problems might provide students an opportunity to pay attention to and develop ways of reasoning that include the construction of dynamic models, the controlled movement of some model elements, the search and exploration of loci of points or lines to analyze some variation phenomena, the use of sliders to control parameters to delve into concepts, and to examine object attributes to formulate, validate, and support conjectures.

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Acknowledgements

This chapter is part of a project that deals with teachers and students’ use of digital technologies in extending both mathematics and didactic knowledge. I acknowledge the support received from research projects with references Conacyt-168543 and EDU2017-84276-R.

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Authors and Affiliations

  1. Center for Research and Advanced Studies, Cinvestav-IPN, Av. IPN 2508, San Pedro Zacatenco, Mexico City, Mexico

    Manuel Santos-Trigo

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  1. Manuel Santos-Trigo
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Correspondence to Manuel Santos-Trigo .

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Editors and Affiliations

  1. Faculty of Education, Simon Fraser University, Burnaby, BC, Canada

    Peter Liljedahl

  2. Department of Mathematics Education, Cinvestav-Instituto Politecnico Nacional, Mexico City, Distrito Federal, Mexico

    Manuel Santos-Trigo

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Santos-Trigo, M. (2019). Mathematical Problem Solving and the Use of Digital Technologies. In: Liljedahl, P., Santos-Trigo, M. (eds) Mathematical Problem Solving. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-030-10472-6_4

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  • DOI: https://doi.org/10.1007/978-3-030-10472-6_4

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  • Print ISBN: 978-3-030-10471-9

  • Online ISBN: 978-3-030-10472-6

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