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practices within a classroom and what the teacher says on them, between learning and its
social usefulness.
Discipline awareness as it comes up in what students say is not, therefore, the sum of the
different perceived characteristics, but rather the delicate elaboration of links between these
different characteristics. To make it possible to describe knowledge networks is one of the
interesting aspects of S.I.A. since this possibility is directly linked to one of the problematic
in didactics, the study of students and teachers representations and conceptions.
2.3. Rules interpreted as tracks of skills.
One of the last S.I.A. fields of applications in Mathematics didactics that we will present
is that of skills reconstruction stemming from observation of student behaviours. As done
before, rules of the type “if A then B” showed by S.I.A. must be interpreted.
A and B still refer to observable behaviours. The implicative relationship can be interpreted,
according to the different cases, such as : B is a consequence of A or A is an explicative
factor of B. The reconstruction of students’ skills to be able to complete a particular task can
be read in the implicit rules which govern over students behaviours.
The example that we have chosen to explore stems from a study registered in the didactics
of mathematics, even though it is only a part of a much wider research which involves
different didactical disciplines.
The main problematic in which this study makes sense is in the relationships of teaching and
learning, or to be more precise, that of measuring the effects of a particular pedagogical set of
devices on some mathematics learning. Numerous prior studies can be quoted on this theme,
amongst which two equally interesting syntheses have been recently and simultaneously
published (on one hand Mercier and Buty and on the other hand Bru, Altet, Blanchard-
Laville). They prove legitimate the hypothesis according to which the particularities of didactic
management of teaching and learning situation by the teacher can influence the building of
mathematical knowledge and the appropriation of other knowledge of the discipline by the
concerned students. We will extend this hypothesis to attitudes and behaviours when faced
to specific tasks.
The study tries to measure the effects of a pedagogical set of devices, which make it necessary
to compare skills developed by students within the set up and the skills of students who are
not in it. We will get back to our goal later. However, one of stages of this undertaking, is
first to describe the skills brought forth by the group of students while they were doing the
specific subjects tasks.
The example we will bring out here is, as we have mentioned above, is in this perspective of
research . It is backed up by the analysis of skills in geometry and language skills of 9 and
10 years old pupils who had to do a writing geometry task.
The task is the following : “how to draw this figure ?”
These results come from an IUFM Resarch « Effet d’un mode de travail pédagogique Freinet en
Z.E.P. R/RIU/04/007
IUFM Nord-Pas de Calais
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