Advertisement

Mathematics Education Research Journal

, Volume 28, Issue 1, pp 9–30 | Cite as

Learning with touchscreen devices: game strategies to improve geometric thinking

  • Carlotta Soldano
  • Ferdinando Arzarello
Original Article
First Online:

Abstract

The aim of this paper is to reflect on the importance of the students’ game-strategic thinking during the development of mathematical activities. In particular, we hypothesise that this type of thinking helps students in the construction of logical links between concepts during the “argumentation phase” of the proving process. The theoretical background of our study lies in the works of J. Hintikka, a Finnish logician, who developed a new type of logic, based on game theory, called the logic of inquiry. In order to experiment with this new approach to the teaching and learning of mathematics, we have prepared five game-activities based on geometric theorems in which two players play against each other in a multi-touch dynamic geometric environment (DGE). In this paper, we present the design of the first game-activity and the relationship between it and the logic of inquiry. Then, adopting the theoretical framework of the instrumental genesis by Vérillon and Rabardel (EJPE 10: 77–101, 1995), we will present and analyse significant actions and dialogues developed by students while they are solving the game. We focus on the presence of a particular way of playing the game introduced by the students, the “reflected game”, and highlight its functions for the development of the task.

Keywords

Logic of inquiry Game-activity Strategic rules DGE Reflected game 
This is a preview of subscription content, log in to check access.

References

  1. Arbib, M. A. (1990). A Piagetian perspective on mathematical construction. Synthese, 84, 43–58.CrossRefGoogle Scholar
  2. Arzarello, F., & Sabena, C. C. (2011). Semiotic and theoretic control in argumentation and proof activities. Educational Studies in Mathematics, 77, 189–206.CrossRefGoogle Scholar
  3. Balacheff, N. (1988). Aspects of proof in pupils’ practice of school mathematics. (In D.Pimm (Ed.), Mathematics, teachers and children. London: Hodder and Stoughton). 216–235.Google Scholar
  4. Borwein, J. M., & Bailey, D. H. (2008). Mathematics by experiment: plausible reasoning in the 21st century, extended second edition. Natick, MA: A K Peters.Google Scholar
  5. Devlin, K. (2011). Mathematics education for a new era: video games as a medium for learning. CRC PressGoogle Scholar
  6. Dewey, J. (1925). Logic: The theory of inquiry (1938). The later works, 1953, 1--549.Google Scholar
  7. Dvora, T. (2012). Unjustified assumptions in geometry made by high school students in Israel, PhD Dissertation, Tel Aviv University-The Jaime and Joan Constantiner School of EducationGoogle Scholar
  8. Fischbein, E. (1982). Intuition and proof. For the Learning of mathematics, 3((2), 8–24.Google Scholar
  9. Fischbein, E. (1987). Intuition in science and mathematics. Dordrecht: Kluwer.Google Scholar
  10. Hanna, G., & de Villiers, M. (2012). Proof and proving in mathematics education. The 19th ICMI Study. Series: New ICMI Study Series, Vol. 15. Berlin/New York: Springer.Google Scholar
  11. Healy, L., & Hoyles, C. (2000). A study of proof conceptions in algebra. Journal for Research in Mathematics Education, 31(4), 396–428.CrossRefGoogle Scholar
  12. Hintikka, J. (1998). The principles of mathematics revisited. Cambridge: Cambridge University Press.Google Scholar
  13. Hintikka, J. (1999). Inquiry as inquiry: a logic of scientific discovery. Springer Science + Business Media DordrechtGoogle Scholar
  14. Hodges, W. (2014). “Tarski’s truth definitions”, The Stanford Encyclopedia of Philosophy (Fall Edition), Edward N. Zalta (ed.).Google Scholar
  15. Kosko, K. W., Rougee, A., & Herbst, P. (2014). What actions do teachers envision when asked to facilitate mathematical argumentation in the classroom? Mathematics Education Research Journal, 26(3), 459–476.CrossRefGoogle Scholar
  16. Mason, J. (2005). Frameworks for learning, teaching and research: theory and practice. Proceedings of the 27th Annual Meeting of PME-NA, Roanoke.Google Scholar
  17. Rabardel, P. (1995). Les hommes et les technologies, approche cognitive des instruments contemporains. Armand ColinGoogle Scholar
  18. Rav, Y. (1999). Why Do We Prove Theorems? Philosophia Mathematica (3) Vol. 7, 5–41.Google Scholar
  19. Reiss, K., Klieme, E., & Heinze, A. (2001). Prerequisites for the understanding of proofs in the geometry classroom. In M. van den Heuvel-Panhuizen (Ed.), Proceedings of the 25th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 97–104). Utrecht: PME.Google Scholar
  20. Sinclair, N., Watson, A., Zazkis, R., & Mason, J. (2011). The structuring of personal example spaces. The Journal of Mathematical Behavior, 30(4), 291–303.CrossRefGoogle Scholar
  21. Soldano, C., Arzarello, F., & Robutti, O. (2015). Game approach with the use of technology: a possible way to enhance mathematical thinking. Krainer K. & Vondrová N. (Ed.) To appear in Proceedings of CERME 9. Prague: Czech Republic.Google Scholar
  22. Stewart, I. (1992). The problems of mathematics (Newth ed.). Oxford University Press: New York.Google Scholar
  23. Tarski, A. (1933). “The concept of truth in the languages of the deductive sciences” (Polish), Prace Towarzystwa Naukowego Warszawskiego, Wydzial III Nauk Matematyczno-Fizycznych 34, Warsaw; expanded in English Translation in Tarski 1983, pp. 152–278Google Scholar
  24. Tarski, A. (1983). In J. Corcoran (Ed.), Logic, semantics, metamathematics, papers from 1923 to 1938. Indianapolis: Hackett Publishing Company.Google Scholar
  25. Trouche, L. (2004). Managing the complexity of human/machine interactions in computerized learning environments: guiding students’ command process through instrumental orchestrations. International Journal of Computers for Mathematical Learning, 9(3), 281–307.CrossRefGoogle Scholar
  26. Vergnaud, G. (1982). Cognitive and developmental psychology and research in mathematics education: some theoretical and methodological issues. For the learning of Mathematics, 31–41.Google Scholar
  27. Vergnaud, G. (1996). Au fond de l’apprentissage, la conceptualisation (pp. 174–185). IREM, Clermont-Ferrand: Actes de l’école d’étéde didactique des mathématiques.Google Scholar
  28. Vérillon, P., & Rabardel, P. (1995). Cognition and artifacts: a contribution to the study of though in relation to instrumented activity. European Journal of Psychology of Education, 10(1), 77–101.CrossRefGoogle Scholar

Copyright information

© Mathematics Education Research Group of Australasia, Inc. 2016

Authors and Affiliations

  1. 1.University of TurinTurinItaly

Personalised recommendations

Cite article

Buy options