We present one episode in an engineering process at primary school level in mathematics. We observe the co-elaboration between teachers and researchers of learning sequences in first grade. This programme is for the building of basic numerical capacities of six-year-old pupils. It is part of a design-based research: Arithmetic and Comprehension at Elementary School (ACE), which has the particularity of being a cooperative engineering. Sensevy, Forest, Quilio and Morales (2013) describe it as an iterative structure which is founded on a principle of symmetry between teachers and researchers. There are not those ‘who act’ and those ‘who think’; all the participants are necessarely involved in the conceptual work. Both teachers and researchers have to work together on the knowledge at stake, and share common ends and means as regards the learning of pupils. The authors present some fundamental issues: (i) teachers and researchers have to share their raisons d’être, making explicit their relationship to the knowledge system at stake, both for themselves and the group, and they do this in order to build a common design rationale. (ii) A common vocabulary and a common background must be constructed. (iii) By transforming practice, i.e. by implementing learning sequences, understanding is acquired which results in transforming pratice anew, and so one. As in the lesson studies (Miyakawa & Winsløw, 2009), the relevance of the used strategies and each point of the cooperative engineering are assessed by the group.

This research is being implemented for the third school year (2013-2014) with 120 French experimental classes, but the process of this engineering began earlier in 2011-2012. During this first year, one initial group (termed sphère 1), composed of researchers in mathematics education, PhD students, teacher trainers and four study-class’ teachers, had to design a curriculum in order to enable the pupils to build a first-hand relationship to the system of knowledge at stake. In this way, the initial elaborated situations were implemented in the four study-classes. A second group (termed sphère 2), composed of 60 teachers, experimented the engineering the following year (2012-2013). Both of the two groups met regulary in a training session to work out together and redesign the implementation process of the curriculum during the course of the engineering project. The third year, 60 new teachers joined the group and in turn experimented the engineering. During these three years a thought collective (Fleck, 1981) was constructed in this way.

Our study concerns 14 teachers and a researcher from Marseille, who composed one sub-group. We will try to show one moment of this sub-group’s work and we will consider how teachers who experimented this project for the first time reflect with the researcher on a didactic object. We will attempt to clarify the nature of the cooperative work.

Fleck, L. (1981). Genesis and development of a scientific fact. Chicago : University of Chicago Press. Glock, H.-J. (1996). A Wittgenstein dictionary. Oxford : Blackwell publishers. Miyakawa, T. & Winsløw, C. (2009). Un dispositif japonais pour le travail en équipe d’enseignants : étude collective d’une leçon. Education & didactique, 3(1), 77-90. Sensevy, G. (2012). About the Joint Action Theory in Didactics. Zeitschrift für Erziehungswissenschaft, 15, 503-516. Sensevy, G., Forest, D., Quilio, S. & Morales, G. (2013). Cooperative engineering as a specific design-based research. ZDM, 45(7), 1031-1043.