In didactics, we usually consider that learning geometry is linked to problem solving, as this makes the knowledge useful. Nevertheless, learning geometry also involves discovering ways of acting, of talking, of interpreting the problems, based on a social construction that is specific to geometry. Then, the question is to understand how these two dimensions of the geometrical activity are intertwined, and how they interact in the knowledge construction process. The role of language during the learning process seems to be crucial for this, so we try in this article to use a methodological tool, so called frequentation modes, to describe a pupil’s activity and its evolution. This aims at combining language analysis to the more usual ones about problem solving, and at studying the interactions between the many faces of the pupils’geometrical activity. At the end, it helps better understanding the mechanism of its evolution, due both to adaptation mechanism and social construct of knowledge.

Rôle des interactions langagières dans l'élaboration du travail individuel et collectif Reproduire un cercle et en parler en classe de mathématique : est-ce si simple ? Quelques éléments d'analyse d'une étude didactique comparant trois mises en oeuvre d'une même situation Reproducing a circle and talking about it in math class: is it that simple? Some elements of analysis of a didactic study comparing three implementations of the same situation

Didactic, Semantic and Metaphors: Analysis of Languages in Class of Geometry. This work focuses on the role taken by different forms of language during the first academic experience of symmetry by young children, in the context of primary school in France. We pay special attention to. A situation of introduction of symmetry in a class of CE1 (grade 7 or 8 years) was observed to this purpose. This paper aims to provide our analysis of this situation, which are grounded into a didactical theoretical framework enriched with semantic, discursive and metaphorico-conceptual analysis tools. This original approach allows us to understand the symmetry in all its complexity and to analyze finely the inter-influence of three dimensions (acting-talking-thinking) that characterize both the mathematical activity of the students and of the teacher.Résumé. Ce travail s'intéresse au(x) rôle(s) que tiennent différentes formes de langage lors de la première rencontre explicite des élèves avec le concept scolaire de la symétrie, dans le contexte de l'école primaire en France. Nous nous appuyons pour cela sur l'observation d'une situation d'introduction de la symétrie dans une classe de CE1 (élèves de 7 ou 8 ans) en France. L'objectif de l'article est de rendre compte de nos analyses qui s'appuient sur un cadre théorique didactique enrichi d'outils d'analyse sémantiques, discursifs et métaphoricoconceptuels. Cette approche originale nous permet d'appréhender la symétrie dans toute sa complexité et d'analyser de façon fine l'inter-influence de trois dimensions (agir-parlerpenser) qui caractérisent selon nous l'activité mathématique des élèves mais aussi celle de l'enseignant.Mots-clés. Langages, apprentissage, géométrie, symétrie, métaphores, modes de fréquentation, agir-parler-penser. ______________________________________________________________________ 1 D'après le dictionnaire de Reuter (2013 p.33), les concepts scolaires sont les concepts « construits et travaillés dans l'espace scolaire » et se distinguent des concepts « scientifiques » qui sont « élaborés dans les disciplines de recherche » ou les concepts « quotidiens de la vie de tous les jours ». 2 Dans cet article, nous parlons de symétrie pour symétrie axiale.

Which professional teaching actions in the service of a school geometric discursive community? Our work seeks to describe professional teaching actions in geometry classes. We rely on the analysis of a collection of observations of sessions in a 6th grade class (pupil ages 11-12 years) conducted by the same teacher during the same school year, based on a progression designed collectively and collaboratively within an IREM group. In our work, the study of the links between teaching and learning in the geometry class is examined through the relations between professional action and the School Mathematical Discursive Community.