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Classical and Digital Technologies for the Pythagorean Theorem

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Uses of Technology in Primary and Secondary Mathematics Education

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

Abstract

This paper aims to discuss the use of material tools, called mathematical machines, and digital tools in approaching the Pythagorean theorem. These mathematical machines are related to different proofs of the theorem. Teaching experiments with 13-year old students were carried out within the laboratory approach developed from the theoretical frameworks of the Theory of Semiotic Mediation and Instrumental approach in mathematics education. Their analysis shows that behind the kinesthetic experience with the machines, there are important cognitive processes such as the identification of invariants, relationships between the components and usage schemes. It also shows the only manipulation of the first machine does not imply the emergence of the mathematical meanings embedded in the materials tools and the crucial role of the teacher with his different instrumental orchestrations in that process.

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Notes

  1. 1.

    http://www.macchinematematiche.org/ and http://archiviomacmat.unimore.it/CR/Copertina.html. Accessed: 2 January 2017.

  2. 2.

    http://www.mathunion.org/fileadmin/ICMI/files/Digital_Library/ICMEs/Bulletin_Maschietto_BartoliniBussi2_01.pdf. Accessed: 2 January 2017.

  3. 3.

    https://www.unige.ch/math/EnsMath/Rome2008/WG4/WG4.html. Accessed: 2 January 2017.

  4. 4.

    http://www.cut-the-knot.org/pythagoras/index.shtml. Accessed: 2 January 2017.

  5. 5.

    http://www.dynamicgeometry.com/JavaSketchpad/Gallery/Geometry/Pythagoras.html. Accessed: 2 January 2017.

  6. 6.

    http://nlvm.usu.edu/en/nav/frames_asid_164_g_3_t_3.html?open=instructions&from=category_g_3_t_3.html. Accessed: 2 January 2017.

  7. 7.

    Pitagora e il suo teorema, https://php.math.unifi.it/archimede/archimede/pitagora/immagini/virtuale.php?id=1. Accessed: 2 January 2017.

  8. 8.

    Referring to the example of a pair of compasses (Bartolini Bussi & Maschietto, 2008), this can be used as technical tools to produce round shapes. It is externally oriented (Vygotskij, 1978). As a psychological tool it has the potentiality to evoke the peculiar feature of circles (i.e., the constancy of the radius) and to create the link with the geometrical static relational definition of Euclid. It is internally oriented (Vygotskij, 1978).

  9. 9.

     http://www.umi-ciim.it/wp-content/uploads/2013/10/Mat2003.zip. Accessed: 2 January 2017. 


  10. 10.

    http://www.macchinematematiche.org/index.php?option=com_content&view=article&id=162&Itemid=243&lang=it. Accessed: 2 January 2017.

  11. 11.

    They regularly follow the methodology of mathematics laboratory with their classes and take part of the research team of mathematics education at the Laboratory of Mathematical Machines at the University of Modena and Reggio Emilia.

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Acknowledgements

I wish to sincerely thank the teachers Stefano Barbieri and Francesca Scorcioni, and the anonymous referees for their precious suggestions.

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Authors and Affiliations

  1. Department of Education and Humanities, University of Modena and Reggio Emilia, Reggio Emilia, Italy

    Michela Maschietto

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  1. Michela Maschietto
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Correspondence to Michela Maschietto .

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Editors and Affiliations

  1. Melbourne Graduate School of Education, The University of Melbourne, Melbourne, Victoria, Australia

    Lynda Ball

  2. Freudenthal Institute, Utrecht University, Utrecht, The Netherlands

    Paul Drijvers

  3. University of Saarland, Saarbrücken, Germany

    Silke Ladel

  4. Institute of Mathematics, University of Würzburg, Würzburg, Germany

    Hans-Stefan Siller

  5. School of Education, Tel Aviv University, Tel Aviv, Israel

    Michal Tabach

  6. Faculty of Education, Monash University, Melbourne, Victoria, Australia

    Colleen Vale

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Maschietto, M. (2018). Classical and Digital Technologies for the Pythagorean Theorem. In: Ball, L., Drijvers, P., Ladel, S., Siller, HS., Tabach, M., Vale, C. (eds) Uses of Technology in Primary and Secondary Mathematics Education. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-76575-4_11

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  • DOI: https://doi.org/10.1007/978-3-319-76575-4_11

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