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Uses of Technology in Primary and Secondary Mathematics Education pp 351–361Cite as

Recursive Exploration Space for Concepts in Linear Algebra

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

Abstract

The complexity of the role of digital media in facilitation of learning mathematics can be approached by utilizing multiple theoretical frameworks. In this chapter, three theoretical frameworks have been applied with an aim to analyze the contribution of a created Dynamic Geometry Environment in developing deep understanding of concepts in linear algebra . The first one, which is in the main focus, refers to the integration of different description and thinking modes in linear algebra , such as synthetic-geometric, arithmetic and analytic-structural (Hillel in On the teaching of linear algebra. Springer, Netherlands, pp. 191–207, 2000; Sierpinska in On the teaching of linear algebra. Springer, Netherlands, pp. 209–246, 2000). The second one is related to the attributes of Dynamic Technological Environments, such as Recursive Exploration Space (Hegedus et al. in Proceedings of CERME5, WG 9. Tools and technologies in mathematical didactics 1331, pp. 1419–1428, 2007); and the third one is semiotic mediation (Bussi and Mariotti in Semiotic mediation in the mathematics classroom: artifacts and signs after a Vygotskian perspective handbook of international research in mathematics education. New York, pp. 746–783, 2008) of the dragging tool. A landscape of networking strategies for connecting theories (Prediger et al. in ZDM Math Educ 40(2):165–178, 2008) has been exploited as an attempt to ensure quality of the analysis.

Keywords

  • Linear algebra
  • Dynamic geometry environment
  • Recursive exploration space
  • Thinking modes
  • Semiotic mediation
  • Networking strategies
  • Axiomatic properties

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Author information

Authors and Affiliations

  1. Humboldt-Universität zu Berlin, Berlin, Germany

    Ana Donevska-Todorova

Authors
  1. Ana Donevska-Todorova
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Correspondence to Ana Donevska-Todorova .

Editor information

Editors and Affiliations

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

    Dr. Lynda Ball

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

    Prof. Paul Drijvers

  3. University of Saarland, Saarbrücken, Germany

    Prof. Silke Ladel

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

    Prof. Hans-Stefan Siller

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

    Prof. Michal Tabach

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

    Dr. Colleen Vale

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Donevska-Todorova, A. (2018). Recursive Exploration Space for Concepts in Linear Algebra. 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_20

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  • DOI: https://doi.org/10.1007/978-3-319-76575-4_20

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