This paper is based on the study of an instructional sequence designed for Kindergarten by Brousseau and his team at the beginning of the 1980s. This sequence, that is called “Treasures Game”, is a months-long didactical sequence. Brousseau (2004) considered it as a fundamental situation for the notion of a representation.

This sequence leads pupils from 5 to 6 years old to construct signs to represent objects, in a 4 steps situation :

1. building a collection of objects, and give us au name, as a reference
2. memorizing i) 3 items and ii) a list of 10 item of the collection. This informational jump from 3 to 10 lead pupils to re-invent the system of graphic coding to obtain a list on a paper.
3. drawing some objects on a list to communicate with a group of other pupils in the class
4. building a common graphical code for each object, for the whole classroom.

So, the Treasures Game consists of producing a list of objects to be remembered and communicated, and the situation is thus devoted to the joint production of signs necessary to represent the objects. We implemented a new version of this instructional sequence in a cooperative teaching design with teachers and researchers, in a process close to lesson studies described by Miyakawa & Winslöw (2009).

The communication will focus on the third step of the situation, the "list communication" game. In this phase pupils experiment a double process : a communication process and a signification process. (Eco, 1979, 1988). In order to represent objects by relying on a shared code, pupils have to make connections between observed features on objects and a type of iconic signs. They have to gradually select effective signs for the representation of these objects that will provide reliability and stability in successive coding conventions.

We assume that in these situations, pupils experiment fundamental principles of coding. They approach the idea that a code is a model agreement that allows to communicate messages. Trough this experience pupils can prepare using other codes, like mathematical ones.

To describe teacher and pupils action in this meaning-making process, we use the theoretical framework of the Joint Action Theory in Didactics (Sensevy & Mercier, 2007, Sensevy, in press).

Brousseau, G. (2004). Les représentations : étude en théorie des situations didactiques. Revue des sciences de l'éducation (30) 2, 241-277. Eco, U. (1979). A Theory of Semiotics. Bloomington: Indiana University Press. Eco, U. (1988). Le signe. Brussels: Labor. Forest, D. (2009). Agencements didactiques, pour une analyse fonctionnelle du comportement non-verbal du professeur. Revue française de pédagogie, 165, 77-89 Hall, E. T. (1963). A system for a notation of proxemic Behavior. American Anthropologist, 65, 1003-1026 Miyakawa T., Winslöw C. (2009). Didactical designs for students' proportional reasoning: an "open approach" lesson and a "fundamental situation". Educational studies in mathematics, 72 (2), 199-218. Sensevy, G., & Mercier, A. (2007). Agir ensemble. Presses Universitaires de Rennes. Sensevy, G. (In press). Overcoming fragmentation: towards a joint action theory in didactics. In Hudson, B. & Meyer, M. A. (Eds.) Beyond Fragmentation: Didactics, Learning, and Teaching. Leverkusen, Germany, Barbara Budrich Publishers.