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 modalities, 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.
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