Étude exploratoire de la description et de la reproduction de figures géométriques chez des élèves du 2e cycle du primaire
This exploratory research focuses on how description of geometrics figures is involved in the success of reproduction tasks (Pierrard, 2001). In fact, to analyze figures properly and to perceive their properties, pupils must deepen their knowledge of the use of geometric instruments (Offre, 2006) and change the way they look at figures (Duval, 2005). To understand how the elements of the geometric figure are articulated, we refer to the semiotic-instrumental [SEM-INS] plane of mathematical work spaces (ETM) linking the geometric object (representamen), the instruments (artefact), the pupil's visualization of this geometric object and the construction it makes (Kuzniak, 2014). For this purpose, pupils in 4th grade had to reproduce six complex figures (composed of two basics figures) according to three "scenarios" in which the description of the figure was requested before or after its reproduction: 1) Figure, reproduction, description, 2) Figure, description, reproduction, 3) construction program, construction. The results indicate that scenario 2 led pupils to describe the figure more accurately and allowed them to better reproduce it. In scenario 3, where pupils had only a construction program, the difficulties were more numerous. In addition, the framework of the ETMGs, and in particular the [SEM-INS] plane and its genesis, made it possible to highlight different profiles of pupils when executing the task of description and reproduction of geometric figure.
ETM geometry elementary school Grade 4 reproduction of figures description of figures construction program dimensional deconstruction change of view geometry instruments