ZDM

, Volume 43, Issue 3, pp 325–336 | Cite as

An epistemic model of task design in dynamic geometry environment

Original Article

Abstract

Dynamic geometry environment (DGE) has been a catalytic agent driving a paradigm shift in the teaching and learning of school geometry in the past two decades. It opens up a pedagogical space for teachers and students to engage in mathematical explorations that niche across the experimental and the theoretical. In particular, the drag-mode in DGE has been a unique pedagogical tool that can facilitate and empower students to experiment with dynamic geometrical objects which can lead to generation of mathematical conjectures. Furthermore, the drag-mode seems to open up a new methodology and even a new discourse to acquire geometrical knowledge alternative to the traditional Euclidean deductive reasoning paradigm. This discussion paper proposes an epistemic model of techno-pedagogic mathematic task design which serves as a theoretical combined-lens to view mathematics knowledge acquisition. Three epistemic modes for techno-pedagogic mathematical task design are proposed. They are used to conceptualize design of dynamic geometry tasks capitalizing the unique drag-mode nature in DGE that opens up an explorative space for learners to acquire mathematical knowledge.

Keywords

Task design Dynamic geometry environment Drag-mode 

References

  1. Ainley, J., Pratt, D., & Hansen, A. (2006). Connecting engagement and focus in pedagogic task design. British Educational Research Journal, 32(1), 21–36.CrossRefGoogle Scholar
  2. Arzarello, F., Olivero, F., Paola, D., & Robutti, O. (2002). A cognitive analysis of dragging practices in Cabri environments. Zentralblatt für Didaktik der Mathematik, 34(3), 66–72.CrossRefGoogle Scholar
  3. Baccaglini-Frank, A., & Mariotti, M. A. (2010). Generating conjectures in dynamic geometry: The maintaining dragging model. International Journal of Computers for Mathematical Learning, 15, 225–253.CrossRefGoogle Scholar
  4. Baccaglini-Frank, A., Mariotti, M. A., & Antinini, S. (2009). Different perceptions of invariants and generality of proof in dynamic geometry. In M. Tzekaki, M. Kaldrimidou, & H. Sakonidis (Eds.), Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 89–96). Thessaloniki, Greece: PME.Google Scholar
  5. Brown, J. (2005). Affordances of a technology-rich teaching and learning environment. In P. Clarkson, A. Downton, D. Gronn, M. Horne, A. McDonough, R. Pierce, M. Horne, & A. Roche (Eds.), Building connections: Theory, research, and practice, Proceedings of the 28th annual conference of the Mathematics Education Research Group of Australasia, Melbourne (Vol. 1, pp. 177–184). Sydney: MERGA.Google Scholar
  6. Duval, R. (1995). Geometrical pictures: Kinds of representation and specific processing. In R. Sutherland & J. Mason (Eds.), Exploiting mental imagery with computers in mathematics education (pp. 142–157). New York: Springer.Google Scholar
  7. Freudenthal, H. (1968). Why to teach mathematics so as to be useful. Educational Studies in Mathematics, 1, 3–8.CrossRefGoogle Scholar
  8. Freudenthal, H. (1991). Revisiting mathematics education. Dordrecht: Kluwer Academic Publishers.Google Scholar
  9. Gibson, J. J. (1979). The ecological approach to visual perception. Boston: Houghton Mifflin.Google Scholar
  10. Laborde, C. (2005). Robust and soft constructions: Two sides of the use of dynamics geometry environments. In Proceedings of the Tenth Asian Technology Conference in Mathematics (pp. 22–35). Korea National University of Education, Cheong-Ju, South Korea.Google Scholar
  11. Leung, A. (2003) Dynamic geometry and the theory of variation. In N. A. Pateman, B. J. Dougherty, & J. Zilliox (Eds.), Proceedings of PME 27: Psychology of Mathematics Education 27th International Conference (Vol. 3, pp. 197–204). Honolulu, USA.Google Scholar
  12. Leung, A. (2008). Dragging in a dynamic geometry environment through the lens of variation. International Journal of Computers for Mathematical Learning, 13, 135–157.CrossRefGoogle Scholar
  13. Leung, A. (2009). Written proof in dynamic geometry environment: Inspiration from a student’s work. In Proceedings of the ICMI 19 Study Conference: Proof and Proving in Mathematics Education (Vol. 2, pp. 15–20). Taipei, Taiwan.Google Scholar
  14. Leung, A., Chan, Y. C., & Lopez-Real, F. (2006). Instrumental genesis in dynamic geometry environments. In Proceedings of the ICMI 17 Study Conference: Technology Revisited, Part 2 (pp. 346–353). Hanoi, Vietnam.Google Scholar
  15. Leung, A., & Lopez-Real, F. (2002). Theorem justification and acquisition in dynamic geometry: A case of proof by contradiction. International Journal of Computers for Mathematical Learning, 7, 145–165.CrossRefGoogle Scholar
  16. Leung, A., & Or, A. (2009). Cognitive apprehension in Cabri 3D environment. In M. Tzekaki, M. Kaldrimidou, & H. Sakonidis (Eds.), Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, p. 417). Thessaloniki, Greece: PME.Google Scholar
  17. Lopez-Real, F., & Leung, A. (2006). Dragging as a conceptual tool in dynamic geometry environments. International Journal of Mathematical Education in Science and Technology, 37(6), 665–679.CrossRefGoogle Scholar
  18. Mariotti, M. A. (2002). Influence of technologies advances on students’ maths learning. In L. English, M. Bartolini Bussi, G. Jones, R. Lesh, & D. Tirosh (Eds.), Handbook of international research in mathematics education (pp. 695–721). New Jersey: Lawrence Erlbaum Associates.Google Scholar
  19. Mason, J., & Johnston-Wilder, S. (2006). Designing and using mathematical tasks. St. Albans: Tarquin Publications.Google Scholar
  20. Noss, R., & Hoyles, C. (1996). Windows on mathematical meanings. Dordrecht: Kluwer Academic Publishers.Google Scholar
  21. Pratt, D., & Noss, R. (2010). Designing for mathematical abstraction. International Journal of Computers for Mathematical Learning, 15, 81–97.CrossRefGoogle Scholar
  22. Restrepo, A. M. (2008). Genese instrumentale du deplacement en geometrie dynamique chez des eleves de 6eme. Unpublished Ph.D. Thesis. Universite Joseph Fourier.Google Scholar
  23. Talmon, V., & Yerushalmy, M. (2004). Understanding dynamic behaviour: Parent–child relations in dynamic geometry environments. Educational Studies in Mathematics, 57, 91–119.CrossRefGoogle Scholar
  24. Vérillon, P., & Rabardel, P. (1995). Cognition and artifacts: A contribution to the study of thought in relation to instrumented activity. European Journal of Psychology of Education, 10(1), 77–101.CrossRefGoogle Scholar

Copyright information

© FIZ Karlsruhe 2011

Authors and Affiliations

  1. 1.Department of Education StudiesHong Kong Baptist UniversityKowloon TongChina

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