Télécharger le tome 2 - IUFM

Figure 1 : « how to draw this figure ? »
(See figure 1). It has been asked in seven different classes, by the teachers themselves,
without any outside observer. It seemed then as a more or less ordinary task within the
class. 165 texts have been collected of which 163 can be taken into account.
It is therefore about a writing task taken from “an instruction program to reproduce a complex
figure”. To be carried out, the writer is required first to identify and to name some of the
constructible elements, then to point out the constructible relationships that exist among
the different elements. We analyze these texts as pupils productions, that is to say we try
to take into account the context in which it was done and the different pupils’ status. It is not
the same for instance, for a 9 years old or a ten years old pupil to produce, as a construction
program the following: “draw two perpendicular lines of which centre is the meeting point
of lines and link the intersection of the two lines and of the circle” or “trace a square, its
diagonals and its centre, trace the circle of which centre is the square’s which goes by the
square’s summits” or “draw a circle and a square inside the circle.” As a matter of fact, the
first text points out to objects and geometrical relationships between the objects that are
constructible by pupils at this school level. On the other hand, the second one needs the
drawing of a square, which isn’t as easy for them. Lastly, the last one avoids the necessary
drawings to be able to fit a square in a circle. Taking into account the pupils’ school level and
considering the outcomes as productions, we have chosen not to grade them according to
how right they are, but according to the choices pupils made.
We have kept as first indicators of the way pupils write, the chosen elements and their
designations, the geometrical relationships mentioned and their designation. The
corresponding indicators are the numbers of geometrical terms used, the chosen elements
– circles, lines, summits etc. – relationships such as perpendicular, topological positions
etc. Therefore, the point is to figure out the figure analysis pupils have chosen to make
throughout what they say. The way of analyzing can be quite different from one pupil to the
other. Some of them only dealt with the lines that shape the diagram : the two lines, the circle
and the square, O or the four summits of square A, B, C, D. From a theoretical point of view,
these two ways of looking at it are linked to different analytical skills. As a matter of fact,
looking at a geometrical figure as a punctual structure requires going beyond immediate
perception, which only shows lines entangled. The use of S.I.A. makes it possible to test the
theoretical hypothesis of the different analytical stages in a geometrical diagram.
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