This paper is grounded on a design-based research, in which a curriculum for the First and Second Grades in Arithmetics has been built. This curriculum, termed Arithmetic and Comprehension at Elementary School (ACE), has been elaborated within a team composed of teachers and researchers, and implemented in classrooms. We present a concrete example of the way teachers and researchers work together to improve some aspects of the ACE curriculum, by designing “Inquiry and Training Threads”. This improvement work relies on the use a Picture-Text-Audio Hybrid System (PTAHS) that we briefly sketch.