Learning Translation in Geometric Transformations Through Digital and Manipulative Artefacts in Synergy

  • Antonella Montone
  • Michele Giuliano FiorentinoEmail author
  • Maria Alessandra Mariotti
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11590)


In this paper we report a study that aims to highlight the potentialities of the combined use of both digital and manipulative artefacts to construct and conceptualize mathematical meanings related to the notion of translation. The research hypothesis of our study is that, the alternating use of a digital and a manipulative artefact foster synergically the construction of mathematical meanings. Both the design and the analysis of data is framed by the Theory of Semiotic Mediation in a Vygotskijan perspective. The study involved a class of 20 students, aged 13–14, of a secondary school in the Apulia Region, Italy. Data collection of the study is based on student interaction transcriptions during experimental task execution, written answers to given questions, and finally the transcripts and video analysis of the collective discussions concluding each experimental cycle.


Semiotic mediation Digital artefact Translation Interaction Synergy 


  1. 1.
    Hoyles, C., Lagrange, J.-B.: Mathematics Education and Technology—Rethinking the Terrain: The 17th ICMI Study. Springer, New York (2010). Scholar
  2. 2.
    Drijvers, P., Kieran, C., Mariotti, M.A.: Integrating technology into mathematics education: theoretical perspectives. In: Hoyles, C., Lagrange, J.-B. (eds.) Mathematics Education and Technology—Rethinking the Terrain: The 17th ICMI Study, pp. 89–132. Springer, New York (2010). Scholar
  3. 3.
    Drijvers, P., Tacoma, S., Besamusca, A., Doorman, M., Boon, P.: Digital resources inviting changes in mid-adopting teachers’ practices and orchestrations. ZDM 45(7), 987–1001 (2013)CrossRefGoogle Scholar
  4. 4.
    Santi, G., Baccaglini-Frank, A.: Forms of generalization in students experiencing mathematical learning difficulties. PNA 9(3), 217–243 (2015)Google Scholar
  5. 5.
    Calder, N., Campbell, P.: Using mathematical apps with reluctant learners. Digit. Exp. Math. Educ. 2(1), 50–69 (2016)CrossRefGoogle Scholar
  6. 6.
    Hegedus, S., Tall, D.: Foundations for the future: the potential of multimodal technologies for learning mathematics. In: English, L.D., Kirshner, D. (eds.) Handbook of International Research in Mathematics Education, 3rd edn, pp. 543–562. Routledge, New York (2016)Google Scholar
  7. 7.
    Sinclair, N., Chorney, S., Rodney, S.: Rhythm in number: exploring the affective, social and mathematical dimensions of using TouchCounts. Math. Educ. Res. J. 28(1), 31–51 (2016)CrossRefGoogle Scholar
  8. 8.
    Faggiano, E., Ferrara, F., Montone, A. (eds.): Innovation and Technology Enhancing Mathematics Education. MEDE, vol. 9. Springer, Cham (2017). ISBN 9783319614878. ISSN 2211-8136CrossRefGoogle Scholar
  9. 9.
    Hollebrands, K.F.: The role of a dynamic software program for geometry in the strategies high school mathematics students employ. J. Res. Math. Educ. 38(2), 164–192 (2007)Google Scholar
  10. 10.
    Faggiano, E., Montone, A., Mariotti, M.A.: Synergy between manipulative and digital artefacts: a teaching experiment on axial symmetry at primary school. Int. J. Math. Educ. Sci. Technol. (2018).
  11. 11.
    Bartolini Bussi, M.G., Mariotti, M.A.: Semiotic mediation in the mathematics classroom: artifacts and signs after a Vygotskian perspective. In: English, L. (ed.) Handbook of International Research in Mathematics Education, 2nd edn, pp. 746–783. Routledge (2008)Google Scholar
  12. 12.
    Faggiano, E., Montone, A., Rossi, P.G.: The synergy between manipulative and digital artefacts in a mathematics teaching activity: a co-disciplinary perspective. Je-LKS: J. e-Learn. Knowl. Soc. 13, 33–45 (2017). ISSN 1971-8829CrossRefGoogle Scholar
  13. 13.
    Rabardel, P.: Les hommes et les technologies; approche cognitive des instruments contemporains. Armand Colin, Paris (1995)Google Scholar
  14. 14.
    Mariotti, M.A., Maracci, M.: Resources for the teacher from a semiotic mediation perspective from text to ‘Lived’ resources: mathematics curriculum materials and teacher development. In: Gueudet, G., Pepin, B., Trouche, L. (eds.) Mathematicsteacher Education, Part 1, vol. 7, pp. 59–75. Springer, Dordrecht (2012). Scholar
  15. 15.
    Mariotti, M.A.: Transforming images in a DGS: the semiotic potential of the dragging tool for introducing the notion of conditional statement. In: Rezat, S., Hattermann, M., Peter-Koop, A. (eds.) Transformation - A Fundamental Idea of Mathematics Education, pp. 155–172. Springer, New York (2014). Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Antonella Montone
    • 1
  • Michele Giuliano Fiorentino
    • 2
    Email author
  • Maria Alessandra Mariotti
    • 2
  1. 1.Department of MathematicsUniversity of Bari Aldo MoroBariItaly
  2. 2.Department of Information Engineering and Mathematics ScienceUniversity of SienaSienaItaly

Personalised recommendations