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.
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