| Summary: | The aim of this article is to propose a reflexive analysis on researches using observation methodology. This observation concerns the pupils’ cognitive activity, the teacher’s professional activity and the interwoven relations within these activities. The stress is laid on the results of such utilisations on the observations of the teachers’ professional activities. The aim of the professional activities of the teacher is among other things to follow the development of the knowledge of each pupil, mainly based on the information gathered on the learner’s level of reasoning and his/her behaviour throughout his /her period of learning. The examples studied in the first year of primary school, according to the French system (concerning children of average age between 6 and 7) during the first steps of their learning period of the numbers. The results of such researches show us that the analysis on the teacher’s activity while under observation, will become more precise and more acute when performed by the said teacher together with the researcher, as a team work, during their exchanges and autoconfrontations centred around the learners’ knowledge in mathematics. This observation then led by the researcher’s questions is said to be implemented (according to Vygotski). The said implementation is bound to bring on changes in the teacher’s professional practices as well as in her didactic mediation.
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