Télécharger le tome 2 - IUFM

Didactic of mathematics and implicative
statistical analysis
Contribution à l’ouvrage collectif : Statistical Implicative Analysis :
theory and applications, à paraître.
Dominique Lahanier-Reuter
Université Charles-de-Gaulle, Lille III
Équipe THEODILE E.A. 1764
dominique.reuter@univ-lille3.fr
Abstract: Didactic of mathematics has constantly regarded statistical implicative analysis
as a profitable and heuristic way of data analysis. We first intend to make clear reasons of
this interest : implicative links S.I.A. pointed out may be interpreted as rules and regulations
connecting actions, discourses etc. or as groups characteristics. We develop some examples
showing how S.I.A. can be used and what special research results it can provide. We insist
upon some points it may be interesting methodologically to focus on : asymmetrics links,
nods and separate implicative ways.
To theorize the relations between these two fields of research in terms of producers of models
and techniques on one hand and on the other in the field of application is without doubt too
reductive, from a historical point of view. In fact the still very brief history of the emergence of
these two scientific domains shows us some more complex connections : the coincidence of
the time of emergence and recognition, that of their geographical and institutional situations
– some universities and associations of researchers in France – finally and above all the
presence of common actors – Regis Gras particularly – imply dynamic which is specific to
these relations. Thus the implicative analysis of data has been able to be identified as a
preferred method of analysis in mathematical didactics and reciprocally in some way, some
problems of didactics have been able to raise questions in implicative analysis.
Firstly we seek to clarify the reasons that we see for this fruitful cooperation, in seeking to
understand how the clarification of rules (or quasi-rules) that implicative analysis allows
proves to be a valuable and pertinent tool for mathematical didacticians. Then we will explain
two of the principle problems in which these rules have meaning in mathematical didactics :
that of the regulation of observable behaviours of students in a situation and that of controls
in this instance understood as effects of teaching devices.
1. Rules and regulations
The implicative analysis of data allows us to show rules, (or quasi rules) that structure a
set of data from calculations of the co-occurrences of some modalities of variables. These
rules can be generically represented by an expression of the type “if A then B”. They are
consequentially hierarchical, that means that they operate a dissymmetry between the
regulated modalities. In this the implicative analysis of data (henceforth S.I.A) is distinguished
from other modes of statistical analysis that, if they are equally based on calculations of cooccurrences
of modalities of variables, only exhibit symmetrical rules that therefore do not
IUFM Nord-Pas de Calais
105