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Problem-Solving and Mathematical Research Projects: Creative Processes, Actions, and Mediations

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Broadening the Scope of Research on Mathematical Problem Solving

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

Abstract

Based on the idea that the creative process is one that involves skills that can be learned and developed with practice, this chapter presents the design and development of a Mathematical Research Project (MRP) for teaching. It examines the output and development of the modalities of mediations during processes of instrumental genesis working from problem-solving tasks (PST) to arrive at Mathematical Research Projects (MRPs). We will respond to the question: What teacher mediations articulate student creativity in Mathematical Research Projects? It will specify (1) identification of the student’s activity by the teacher – the operational mathematical invariants of the students’ schemes, the cognitive processes the student puts into action, and the domains of mathematical knowledge – and (2) mediated activity between the teacher and students regarding the instrument, the object, and the subject.

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Notes

  1. 1.

    The arithmetic progression will be denoted by a.p.

  2. 2.

    The final report of MRP will be denoted by TN-PI. The pages of the presented extracts are included.

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Acknowledgements

This study was funded by the Spanish Ministry of the Economy and Competitive Affairs under project EDU2013-44047-P entitled “Characterization of specialized knowledge in Mathematics Teachers” and by special action grant from Cátedra UCM Miguel de Guzmán (Spain) under project “Mathematical Working Space” (UCM-CmdeGuzman-2015-01).

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Authors and Affiliations

  1. Instituto de Matemática Interdisciplinar, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Madrid, Spain

    Inés M. Gómez-Chacón

  2. Universidad Complutense de Madrid, Madrid, Spain

    Constantino de la Fuente

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  1. Inés M. Gómez-Chacón
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  2. Constantino de la Fuente
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Correspondence to Inés M. Gómez-Chacón .

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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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Gómez-Chacón, I.M., de la Fuente, C. (2018). Problem-Solving and Mathematical Research Projects: Creative Processes, Actions, and Mediations. 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_15

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  • DOI: https://doi.org/10.1007/978-3-319-99861-9_15

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