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ORDER OF CONSTRUCTION IN DYNAMIC GEOMETRY ENVIRONMENT

Varda Talmon
vardat@construct.haifa.ac.il
Faculty of Education
University of Haifa
Israel

Abstract

Order and dependency are two fundamental concepts of mathematics. The order of geometric constructions in DGEs, is central from the very beginning.

The sequential organization of actions necessary to produce a figure in any Dynamic Geometry Environment (DGE) introduces an explicit order of construction. In a complex figure this sequential organization produces what is, in effect, a hierarchy of dependencies as each part of the construction depends on something created earlier. This hierarchy of dependencies is one of the main factors that determine DB within DGE (Jackiw & Finzer, 1993; Laborde, 1993).

The longer DGEs are in use and under study the more we learn about their contribution to the learning of geometry but also about the obstacles they are liable to pose to such learning. (Chazan & Yerushalmy, 1998; Goldenberg & Cuoco, 1998; Healy & Hoyles, 2001; Mariotti, 2002)

This abstract focus on user's perceptions of dragging and their accordance to the hierarchy of dependencies, which derive from the order of construction. As a part of a larger study on the complexities involved in understanding DB, Junior high students and graduate students in math education were asked to predict the DB of points that were part of a geometric construction. The study reveals that while hierarchy in geometric constructions in a DGE is mirrored by the DB, user actions and perceptions of DB indicate that users often grasp a reverse hierarchy in which dragging a child affects its parent.

References

Chazan, D., & Yerushalmy, M. (1998). Charting a Course for Secondary Geometry. In R. Lehrer, and D. Chazan (eds.),Designing Learning Environments for Developing Understanding of Geometry and Space, Hillsdale, N J: Lawrence Erlbaum Associates, pp. 67-90.
Goldenberg, E. P., & Cuoco, A. A. (1998). What is Dynamic Geometry? In D. Chazan (ed.),Designing Learning Environments for Developing Understanding of Geometry and Space., Lawrence Erlbaum Associates, NJ, pp. 351-368.
Healy, L., & Hoyles, C. (2001). Software Tools for Geometrical Problem Solving: Potentials and Pitfalls. International Journal of Computers for Mathematical Learning 6, 235-256.
Jackiw, R. N., & Finzer, F. W. (1993). The Geometer's Sketchpad: Programming by Geometry. In A. Cypher (ed.),Watch What I Do: Programming by Demonstration, The MIT Press., Cambridge, London, pp. 293-308.
Laborde, C. (1993). The Computer as Part of the Learning Environment: The Case of Geometry. In C. Keitel, and K. Ruthven (eds.),Learning from Computers: Mathematics Education and Technology., NATO ASI Series, Springer-Verlag, Berlin Heidelberg, Vol. 121, pp. 48-67.
Mariotti, M. A. (2002). The Influence of Technological Advances on Students' Mathematics Learning. In L. D. English (ed.),Handbook of International Research In Mathematics Education, Lawrence Erlbaum Associates, NJ, pp. 695-723.


 
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