To promote the geometric properties of the quadrilaterals at primary school: Study of a learning situation in the surrounding space
In this article, we try to determine, in the context of the teaching of plane figures in primary schools, how the confrontation of pupils with learning situations in the surrounding space (meso-space) enhances the mobilization and verbalization of spatial and geometric knowledge. To do this we produce the clinical analysis of a sequence implemented in a class of the end of primary school whose objective for the students is the reproduction of plane figures in the meso-space. In order to identify precisely the knowledge and learning mobilized by the students in action and formulation situations, we carry out a detailed analysis of the various forms of reasoning that underlie their resolution and formulation procedures. To achieve this, we use a model of reasoning analysis, developed by Bloch and Gibel (2011), which results from the articulation of two theoretical frameworks: the Didactic Situations Theory and Peirce’s Semiotics. Beyond the rational use of the tools available to pupils in the reproduction activity of figures, didactic analysis reveals particularly rich elements of the action-formulation dialectic. This study makes it possible to account for the variety, appropriateness and relevance of the geometric properties mobilized and formulated by the students, thus facilitating the transition from instrumented geometry to deductive geometry.