This paper describes some elements of a specific kind of design-based research, cooperative engineering. In the first part of the paper, we argue that cooperative engineering can be analyzed through a joint action framework. We first present some conceptual tools that the Joint Action Theory in Didactics proposes in order to understand didactic and cooperative action. The second part of the paper is devoted to cooperative engineering, a research process that gathers teachers and researchers through a common project. We first give some root principles of this kind of research endeavor. Then we focus on a specific cooperative engineering, Arithmetic and Comprehension at Elementary School, which aims towards building a mathematics curriculum at first and second grades. After a general description of the research project, we analyze one of its core components, the engineering dialogue. We show how this joint action between teachers, researchers, and teachers and researchers, enables the cooperative engineering team to build and rebuild the curriculum in an iterative way.