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

In this paper we analyse, with a perspective of mathematics education, a videotape showing two 9 th grade students cooperating to write instructions in order that other students could construct a circle tangent to the sides of a given angle. Our aim is to understand how they articulate with their geometric knowledge different semiotics means (mainly words and figures, freehand or drawn with usual instruments) in an evolving semiotic bundle so that the solution as well as the geometric knowledge progress. We also try to identify the way each student contributes to develop the semiotic bundle and how each contribution evolves in the course of their solving.

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RésuméCette recherche vise à enquêter sur le rôle des croyances dans les pratiques en classe de mathématiques d’un professeur des écoles novice. Ici, nous illustrons le cas d’une enseignante qui travaille sur le calcul mental : dans l’analyse de sa praxéologie personnelle, ses croyances sont incluses dans le bloc « technologico-théorique ».Mots-clés : Théorie anthropologique du didactique, Croyance, Praxéologie personnelle, Calcul mental.AbstractThis research aims to investigate the role of beliefs in the mathematical practices of a novice teacher. In particular, we will show the case of a teacher who works on the mental computation: in the analysis of her personal praxeologie, we consider beliefs within the “technological-theoretical” bloc.Keywords: Anthropological theory of didactics, Belief, Personal Praxeology, Mental calculation.

While research in mathematics education has invested many questions related to teacher training, the role of the teacher trainer remains little developed. It is a matter of questioning the trainer's practices, the possible effects on the professional development of the trainees, the knowledge or conceptions that he/she mobilizes, the constraints he/she is confronted with, his/her interactions with other actors, etc. This thematic issue brings together original studies using a variety of approaches that reflect emerging issues and mobilize various theoretical and methodological tools, with the aim of contributing to the development of this field of research.