The extension of the instrumental approach to dynamic geometry
This sixth module is devoted to the extension of the Instrumental Approach to dynamic geometry. I prepared it with Colette Laborde, a well-known researcher in the field of dynamic geometry who has been directly involved in this extension, through her investment in the MAGI project, “Learning better geometry with computers”. Relying on the research carried out in this project and the associated doctoral thesis by Angela Restrepo focusing on the development of dragging schemes by 6 graders, I show how this research made clear the complexity of the instrumental genesis of dragging, and proved the pertinence of the instrumental approach also for technologies designed with educational purposes.
Arzarello, F., Olivero, F., Paola, D., & Robutti, O. (2002). A cognitive analysis of dragging practises in Cabri environments. Zentralblatt fur Didaktik der Mathematik, 34 (3), 66-72.
Duval, R. (2020). Registers of semiotic representation. In S. Lerman (Ed.), Encyclopedia of Mathematics Education (Second Edition). New York: Springer.
Healy, L. (2000) Identifying and explaining geometrical relationship: Interactions with robust and soft Cabri constructions. In Proceedings of the 24th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1 , pp. 103-117). Hiroshima: Tadao Nakahara, Masataka Koyama.
Laborde, C., Assude, T., Grugeon, B., & Soury-Lavergne, S. (2006). Study of a teacher professional problem: how to take into account the instrumental dimension when using Cabri-geometry? In C. Hoyles, J.-B. Lagrange, L.-H. Son, & N. Sinclair (Eds.), Proceedings of the Seventeenth ICMI Study Conference “Technology Revisited” (pp. 317-325). Hanoi Institute of Technology.
Laborde, C., & Laborde, J.-M. (2014). Dynamic and Tangible Representations in Mathematics Education. In S. Rezat, M. Hattermann, & A. Peter-Koop (Eds.), Transformation – A Fundamental Idea of Mathematics Education (pp.187-202). New-York: Springer.
Restrepo, A. (2008). Genèse instrumentale du déplacement en géométrie dynamique chez des élèves de 6ème. Doctoral thesis. Université Joseph Fourier Grenoble 1.