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Task Mathematical Modelling Design in a Dynamic Geometry Environment: Archimedean Spiral’s Algorithm

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Numerical Computations: Theory and Algorithms (NUMTA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11973))

Abstract

Over the last twenty years, several research studies have recognized that integrating, not simply adding, technology (Computer Algebra System - CAS, Dynamic Geometry Software - DGS, spreadsheets, programming environments, etc.) in the teaching of mathematics helps students develop essential understandings about the nature, use, and limits of the tool and promotes deeper understanding of the mathematical concepts involved. Moreover, the use of technology in the Mathematics curricula can be important in providing the essential support to make mathematical modelling a more accessible mathematical activity for students. This paper presents an example of how technology can play a pivotal role in providing support to explore, represent and resolve tasks of mathematical modelling in the classroom. Specifically, a mathematical modelling task design on the tracing of Archimedean spiral with use of a Dynamic Geometry Environment is shown. The aim is to emphasize the meaning and the semantic value of this rich field of study that combines tangible objects and practical mechanisms with abstract mathematics.

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Notes

  1. 1.

    Dragging in DGE is a powerful dynamic tool to acquire mathematical knowledge. It serves as a kind of interactive amplification tool for leaner to see global behavior via variation.

  2. 2.

    https://www.mathunion.org/activities/international-commission-mathematical-instruction-icmi.

  3. 3.

    GeoGebra was created by Markus Hohenwater and now has been translated into 40 languages. Users all over the world can freely download this software from the official GeoGebra website at http://www.geogebra.org.

  4. 4.

    A concrete image of the Archimedean spiral is the grooves of a vinyl disc, equidistant from each other and separated by a very small constant distant.

  5. 5.

    The mechanical generation of the spiral is described in a plane by a point that moves with a uniform motion along a straight line, while the line rotates in a uniform circular motion around a point.

  6. 6.

    Archimedes, (born c. 287 BCE, Syracuse, Sicily [Italy]-died 212/211 BCE, Syracuse), the most-famous mathematician and inventor in ancient Greece.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Calabria, Rende, CS, Italy

    Annarosa Serpe

  2. IIS IPSIA-ITI “E. Aletti”, Trebisacce, CS, Italy

    Maria Giovanna Frassia

Authors
  1. Annarosa Serpe
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  2. Maria Giovanna Frassia
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Correspondence to Annarosa Serpe .

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Editors and Affiliations

  1. University of Calabria, Rende, Italy

    Yaroslav D. Sergeyev

  2. University of Calabria, Rende, Italy

    Dmitri E. Kvasov

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Serpe, A., Frassia, M.G. (2020). Task Mathematical Modelling Design in a Dynamic Geometry Environment: Archimedean Spiral’s Algorithm. In: Sergeyev, Y., Kvasov, D. (eds) Numerical Computations: Theory and Algorithms. NUMTA 2019. Lecture Notes in Computer Science(), vol 11973. Springer, Cham. https://doi.org/10.1007/978-3-030-39081-5_41

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  • DOI: https://doi.org/10.1007/978-3-030-39081-5_41

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