Contribution
Description: This research is part of sciences of education and is in the theoretical field of didactic of mathematics.
I propose to analyze in what mathematical plannings of ordinary teaching diverge from those of the specialized institutions and of the possible impact that that could generate on the acquisition of knowledge at the pupils.
A pupil placed in specialized institutions has opportunities of training more restricted than its pars frequenting ordinary classes (Maréchal, 2004). In fact teachers in institutions must take in consideration this reality in order to program their teaching.
Taking into account the fact that real time of teaching is restricted in the specialized institutions, two strategies of planning by the professionals are identifiable: all subjects are approached quickly or else certain objects of mathematical knowing are selected and treat more deeply.
In Geneva, there are several proposals of plannings for the primary school teachers (COROM, plan of study, "propositions pour une planification de l'enseignement" by the sector of mathematics, objectives of training). However, it seems that none of them is complete and employable in the state, without making any modifications or complements. Thus, teachers have obligatory a part of freedom in their school programming. This is why it is interesting to observe how they act and how they "prepare" the knowledge on the temporal axis. I propose to base my research on the theory of the didactical transposition which is presented by Yves Chevallard who introduces the reflexion over didactical time with aspects on the "chronogénèse" and the "topogénèse" (Chevallard 1978, 1980, 1985).
The second aspect questioned in this research, concern how function specialized teachers compared to ordinary teachers. Indeed, specialized institutions function with dual mandate; teaching and therapeutic, which produces a decreasing of working time for academics disciplines. Consequently, having less time, teachers must make a choice concerning their annual planning. The aim is to understand if these two places are governed according to same principles or if, from their different functions, they have divergent strategies of planning.
Methodology: It is a comparative study between one ordinary class of 1P and a specialized class in institution in Geneva gathering pupils with personality disorders and training. This research is consequently qualitative.
Initially, I will compare two annual plannings of mathematics in order to locate which objects of teaching are approached in specialized institution and ordinary class as well as time that they occupy. In second hand, I will collect various planning's in ordinary classes concerning specifically the addition. I would put in relation these informations. I will observe the articulation between mathematical contents and the didactic organization observing planning of activities around the addition which is the subject of this study. This will permit to question on relevance of the order of activities suggested in class in order to avoid "évanouissement du sens" for pupils (Johsua & Dupin, 1993). Finally, I will discuss with teachers in order to apprehend their choices. I will complete these informations with observations made in the specialized institution.
Conclusions: Concerning the awaited results, I make the assumption that the specialized teacher will select some contents of teaching to the detriment of others. Thus, specialized pupils would not profit as much as ordinary pupils of a transmission of knowledge. Moreover, first selected objects by the teacher will concern modules treating the number and the operations and will leave aside modules 5-6-7 (about space and measurements). Teachers will tend to accentuate the technical side (to be able to add, to withdraw, multiply and divide) rather than the conceptual aspect (to know in which situations to use these techniques of calculations).
I also imagine that there will not be a fundamental difference between teachers's acting concerning articulation between the mathematical organization and didactic organization. Indeed, my opinion is that teachers will organize their activities in an "intuitive" way and without "a priori" analysis.
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