ORDER OF CONSTRUCTION IN DYNAMIC GEOMETRY ENVIRONMENT

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

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