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criteria). 3.2. Characteristic abilities S.I.A. makes it possible to perceive the cases where characteristics are those of a part of the group of pupils studied, compared to a group where all the pupils of the group were studied. They “almost” all share the same characteristics, contrary to the modes of analysis which produce symmetrical links. We will start by presenting a case where a characteristic comes up as specific to one of the groups. The example is that of the characteristic “writing a text using “I” which is the characteristic of one of the classes coded CM1WB. – (1) “Writing a text using “I”” implies “belonging to class CM1 WB” (99%) Only the pupils of this class chose a particular writing behaviour, which indicates that pupils read into a suggested situation an evaluation situation : the expected reader is the teacher and pupils show what they can do. But what seems even more important is the fact that the implicative link of maximal intensity means that no pupil “or rather almost none” in other classes have reacted in that way. To explain this specificity, we venture the hypothesis that the way the task was done has been singularized in class : maybe only this CM1 teacher has presented the exercise as an evaluation, or at least like an exercise that he would check on. 3.3. Groups characterized by capacities On the other hand, other implicative links show that almost all pupils of a same class share some skills and also make the same mistakes etc. Let’s keep in mind some of them : (95%) – – (1) “Belonging to CM2H03” implies “using “tu””(90%) (2) “Belonging to CM2WB” implies “Mentioning point 0 and changing its status” This time, these characteristics are met in almost all the pupils of a same class. We think that they are the results – sometimes indirect – of the didactical or pedagogical ways used in class. What is left is to interpret these different rules. If almost all the pupils of the first particularized class address a reader who acts like “a peer” in their writings, it is no doubt because help and cooperation are legitimized and encouraged in these classes or because these forms of communication are used. If almost all the pupils of the second class show good geometrics skills, it is no doubt thanks to the teaching techniques used. But this geometrics skill cannot be understood without linguistic skills which make it possible to communicate it. Using “tu” (informal “you”) is not always the required school form required. Now, these two classes have pupils from different social backgrounds : in the second class the pupils come from more privileged families than the other studied classes. Relationships between social classes and linguistic ways are certainly complex and not mechanical. However, the results we are getting are coherent with those of other studies on these relations. As a consequence, we cannot neglect the explicative factor of cohesion between observed behaviours. We are bumping here into a recurrent problem : the principles of subjects’ categorisation are obviously never unique or uniform. The gatherings of pupils in this particular case cover both institutional groups (school classes) and “social” 116 IUFM Nord-Pas de Calais
groups (coming from more or less privileged families). This remark makes it very clear that evaluating the effects of teaching methods cannot take the shape of simple cause to affect relationships. This being said, it is in any case obvious that using S.I.A., even if it doesn’t help to find cause to effect relationships, makes it possible to accumulate, little by little, shared behaviours, common capacities, specific mistakes etc… to groups of subjects. What is left to find then, is global coherence to the groups characteristics. 4. Conclusion Using central problematic in mathematical didactics, we have been able to show the efficiency of dealing with S.I.A. techniques. The input of this method to analyze data cannot be disregarded for several reasons. The almost-rules established by S.I.A. from observables can easily lend themselves to interpretation in terms of actions regulations. The implicative paths can be read in terms of networks. Lastly, the asymmetry of links seems essential to expose any explicative hypothesis of certain phenomenon pertinent to teaching and learning. We have also been able to adumbrate, through the detailed relationships of research examples, particular methodological behaviours : the attention to give the interpretation of the internal cohesion of implicative graphs, but also to the separation of these graphs, as well as the graphs’ nodes and of the univocal links. These are only thinking tracks to be pursued. References 1. Brousseau G. : Le contrat didactique : le milieu. Recherches en didactique des mathématiques vol 3/3. La Pensée Sauvage, Grenoble (1990) (990) 309-336. 09-6. 2. Brousseau G.: Théorie des situations didactiques. La Pensée Sauvage, Grenoble (1998) 3. Bru M., Altet M., Blanchard-Laville C.: À la recherche des processus caractéristiques des pratiques enseignantes dans leurs rapports aux apprentissages. Revue Française de pédagogie, n°148. INRP. Paris (2005) 4. Gras R. : L’analyse des données : une méthodologie de traitement de questions de didactique. Recherches en didactique des mathématiques vol 12/1. La Pensée Sauvage, Grenoble (1992) 59-72. 5. Gras R., Totohasina A, Almouloud S., Ratsimba-Rajohn H., Bailleul M. : La méthode d’analyse implicative en didactique. Applications. In : Artigue M., Gras R., Laborde C., Tavignot P. (eds.) : Vingt ans de didactique des mathématiques en France. La Pensée Sauvage, Grenoble (1994) 349-363. 6. Gras R. : L’implication statistique, Nouvelle méthode exploratoire de données. La Pensée Sauvage, Grenoble (1996) 7. Lahanier-Reuter D.: Conceptions du hasard et enseignement des probabilités et statistiques. P.UF., Paris (1999) 8. Lahanier-Reuter D.: Exemple d’une nouvelle méthode d’analyse de données : l’analyse implicative. Carrefours de l’éducation, n°9. CRDP Amiens (2000) 96-109. IUFM Nord-Pas de Calais 117
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Rapport de Recherche Institut Unive
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dans les séances de « Recherches
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2. Présentation de la recherche et
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Analyser un mode de travail pédago
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par la Régionale Nord-Pas de Calai
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Les discours tenus par les enseigna
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donc pu effectuer tous les recueils
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Il nous paraissait important de sui
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avons notamment mis en œuvre : - d
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d’existence et les principes qui
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touchées chez les élèves en tena
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concernés au premier chef, posséd
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voit l’intérêt de cette logique
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Enseignement et apprentissages math
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menées en sciences. Ensuite, ces c
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dire autrement, nous avons tenté,
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L’analyse comparative des product
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constater la trace d’une absence
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gestes etc. Cette unité, comme nou
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7. Conclusion Nous n’avons rappor
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Le « je » de l’élève est-il c
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se sent dépendant des autres « je
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s’il ne sait pas ou si on ne lui
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Une « didactique appropriée aux d
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les 4 morceaux ? ») ou de lui sugg
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d’abord un seul triangle, prend l
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compte que le défaut. Psychologues
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qu’au point de départ cet élèv
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sont aussi très révélateurs de c
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situé dans le REP de Mons en Baroe
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(problème 3). Cependant, le fait q
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les élèves dans cette tâche et l
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