Abstract
Dragging in Dynamical Geometry Software (DGS) is described by introducing a hierarchy of its functions. This is suitable for classifying different attitudes and aims of students who investigate a geometric problem, such as exploring, conjecturing, validating and justifying. Moreover the hierarchy has cognitive features and can be used to describe the twofold modulities namely ascending and descending in which students interact with external representations (e.g. Cabri drawings). Switching from one modality to the other through dragging often allows them to produce fruitful conjectures and to pass from the empirical to the theoretical side of the question. The genesis of such different functions in students does not happen automatically but is the consequence of specific didactical interventions of the teacher in the pupils' apprenticeship of Cabri practises. A worked-out example illustrates the theoretical concepts introduced in the paper.
Kurzreferat
Der Text führt eine Funktionshierarchie für den Gebrauch des Zugmodus in Dynamischer Geometrie Software (DGS) ein Diese ist zur Klassifikation von Verhaltensweisen und Zielen der Lernenden geeignet, wenn diese geometrische Problem explorieren, Vermutungen aufstellen, bestätigen und rechtfertigen und dabei theoretische und empirische Aussagen in Cabri-Zeichnungen in Beziehung setzen (wechselweise “auf”-und “absteigen”) Der Wechsel zwischen diesen Sichtweisen unter Nutzung des Zugmodus erlaubt es ihnen oft, gehaltvolle Vermutungen zu formulieren und von einer empirischen zu einer theoretischen Sicht auf das Problem zu wechseln. Der Sichtwechsel stellt sich allerdings nicht automatisch ein, sondern ist die Folge besonderer didaktischer Maßnahmen des Lehrenden. Ein ausgearbeitetes Beispiel illustriert die neu eingeführten theoretischen Begriffe.
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Arzarello, F., Olivero, F., Paola, D. et al. A cognitive analysis of dragging practises in Cabri environments. Zentralblatt für Didaktik der Mathematik 34, 66–72 (2002). https://doi.org/10.1007/BF02655708
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DOI: https://doi.org/10.1007/BF02655708