This communication presents a study in progress based on a “cooperative engineering” paradigm (Morales, Sensevy & Forest, 2017). In an iterating process (Elliott, 2012), a collective of teachers and researchers are working on the stakes of teaching geometry, designing and realizing teaching and learning situations (Cobb & al., 2003), for students with lasting learning difficulties. In the communication, we begin to present the six main principles of cooperative engineering (Sensevy & Bloor, 2019). The second part of the communication aims to describe a case study. The cooperative engineering is organized over three years. During the first year, the collective chose to design one situation with strong links between dynamic geometry (a Dynamic Geometry Software) and standard tools (Assude, 2005 ; Ruthven, 2017). In the initial implementation of this situation, students and teachers had to deal with a problem: some students didn’t understand what appeared on the screen, and teachers had to improvise to help them. Examining this initial implementation, the teachers’ and students’ actions were discussed in the collective. During the second and the third year, this situation was redesigned, taking into account the previous implementation and the discussions. The third part of this communication presents the theoretical framework. The teachers’ and students’ actions and the discussions in the collective have been analyzed by the researchers using elements of the Joint Action Theory in Didactics (Sensevy, 2019). As we can see, the theoretical elements will therefore be used in two different contexts, for the analysis of action taken by the students and the teacher in the class situation, and for the analysis of joint action between teachers and researchers during the engineering process. This theoretical framework allows us to deal with our research questions: how does the development of the “engineering dialogue”, within the collective, can reveal practical problems? How can these practical problems can be shared? How this sharing of the problems can lead to possible answers, based on shared knowledge? To try to answer our questions, we collect a lot of video: the vast majority of class sessions and collective meetings are filmed. The fourth part of this communication exposes some results. We aim to show how the teacher, thanks to the cooperative engineering collective, can provide students with opportunities to develop new geometrical strategies based on conceptual properties (Laborde, 2005), grounded on a new way of seeing the geometric objects.

Assude, T. (2005). Time management in the work economy of a class, a case study: integration of cabri in primary school mathematics teaching. Educational Studies in Mathematics, 59, 183-203. Cobb, P., Confrey, J., diSessa, A, Lehrer, P et Schaube, L (2003). Design Experiments in Educational Research. Educational Researcher, 32(1), 9-13. Elliott J (2012). Developing a science of teaching through lesson study. International Journal For Lesson and Learning Studies, 1(2), 108–125. Laborde, C. (2005). The hidden role of Diagrams in Students’ Construction of Meaning in Geometry. In J. Kilpatrick, C. Hoyles, O. Skovsmose & P. Valero (Eds). Meaning in Mathematics Education, 159-179. Morales, G., Sensevy, G. & Forest, D. (2017). About cooperative engineering: theory and emblematic examples. Educational Action Research, 25(1), 128-139. Ruthven, K. (2017). Constructing dynamic Geometry : insights from a study of teaching practices in English schools. In G. Kaiser et al. (Eds), Invited Lectures from the 13th International Congress on Mathematical Education, ICME-13 Monographs, 521-539. Sensevy, G. & Bloor, T. (2019). Cooperative Didactic Engineering. In: Lerman S. (Eds) Encyclopedia of Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-77487-9_100037-1 Sensevy, G. (2019). Joint Action Theory in Didactics (JATD). In: Lerman S. (Eds) Encyclopedia of Mathematics Education. Springer, Cham. http://doi.org/10.1007/978-3-319-77487-9_100035-1