Résumé
This research aims at studying the conditions and restrictions which weigh on the teaching of the numeric domain in grade 10 in France. The main aim is to identify, describe and analyze the different approaches teachers have to adopt in order to recycle students' previous knowledge in this area and ensure continuity of teaching between Junior High and Senior High. But these specific approaches are also necessary for recycling knowledge acquired for the first time in grade 10. This research comes within the framework of the observatory observation on numeric practices initiated by Bronner. It implements a tool he has developed: the numeric filter. The methodology is of a clinical type, it relies on data collected in two classes by observing lessons throughout the 2 school years 2006-2007 and 2007-2008. The granularity of the analysis is highly variable and covers different time spans from the whole year to the minute, enabling a comparison between the rationale behind the official curriculum and the real curriculum. The research has revealed that recycling previous knowledge is sometimes avoided, even though it would be possible in the limited framework of the curriculum. Moreover, this "avoided" recycling would be necessary to pursue a study of numeric that would be more appropriate from an epistemological point of view and more efficient in the learning process. The teaching of numeric in grade 10 seems to be a problem for mathematics teachers. This problem does not seem to have been clearly identified and is even underestimated.