Instrumentation
of the Drag Mode in the Introduction to Deductive Reasoning with
Cabrigeometry
Sophie SouryLavergne
IUFM of Grenoble & University Joseph Fourier
France
Abstract
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 Cabrigeometry 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, Cabrigeometry is a relevant tool
for pupils at the very beginning of the learning of deductive reasoning.
Nevertheless, the potential of Cabrigeometry aks for a right use of the
drag mode, which is far to be obvious. All along the 20 years of use of
Cabrigeometry, 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 spaciographic level (i.e. the diagram
moves up or down or becomes flat etc¡K),
 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 pupil¡¦s 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 counterexample?...).
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.
