To Be Presented in the 11th Asian Technology Conference in Mathematics
December 12-16, 2006, Hong Kong SAR, China

Instrumentation of the Drag Mode in the Introduction to Deductive Reasoning with Cabri-geometry

Sophie Soury-Lavergne
IUFM of Grenoble & University Joseph Fourier


The question addressed in this paper is how 11 years old pupils can use dynamic geometry to change the way they identify the geometrical properties of a figure. When they enter in the secondary level school, they are supposed to gradually surrender perceptive identification and begin to use new means to establish the validity of a geometrical property. The final aim is that they state it as a hypothesis or deductible from the hypothesis. Actually, the drag mode in Cabri-geometry allows the user to distinguish the properties of geometrical figure (hypothesis and their consequences) from the ones of a specific diagram. The first ones are preserved while dragging and not the second ones. Thus, Cabri-geometry is a relevant tool for pupils at the very beginning of the learning of deductive reasoning. Nevertheless, the potential of Cabri-geometry aks for a right use of the drag mode, which is far to be obvious. All along the 20 years of use of Cabri-geometry, it has been observed that beginners are reluctant to move their constructions. Even when they finally start to drag elements, they face many difficulties:

  • they only drag partially the diagram (just one point or very little movements around the initial position),
  • they interpret the retroactions on a spacio-graphic level (i.e. the diagram moves up or down or becomes flat etcíK),
  • they are not able to perceptively recognize geometrical properties in some particular positions,
  • they want to fix the moving points instead of analysing the diagram on a geometrical point of view.
Within the instrumental approach, we focus our analysis on the instrumental genesis that turns the dragging into a pupilíŽs instrument which makes them able to state about the validity of a geometrical property. We have identified instrumental schemes involved in the use of the artefact "dragging functionality":
  • to choose the points to drag (different category of points)
  • to identify, by the mean of perception, the geometrical property to be controlled
  • to decide if a geometrical property is conserved or not, always by the mean of perception,
  • to conclude about the property and the figure (is it a counter-example?...).
We have elaborated activities in the context of a French project MAGI (better learning geometry with computers), in order to sustain this process of instrumental genesis of the drag instrument. We have tested those activities during 2 years, with a teacher in 3 different classes. Besides the activities, we also brought out elements, which help the process:
  • to make explicit the different category of points and their consequences on drag.
  • to produce instructions for individual use of Cabri which ask to specify the points to be dragged and those to observe,
  • to produce instructions for the use of Cabri during debates with the whole class; only one pupil manipulates the software and the others have to propose which points to drag and what to look for during dragging.

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