Teaching and learning in mathematics first grade students: continuity of the students' experience and systems of the representation, an example

Our study is based on a national research project called Arithmetic and Cooperation at Elementary school (ACE). The main objective of this research is the designing of a curriculum for first grade students. Our paper focuses on the analysis of an extract from a lesson proposed by this curriculum. During this lesson, the students work on specific piece of mathematical knowledge, the notion of difference, which is introduced with the help of several systems of representation. These systems are already known by the students. Our article examines the continuity of the students' experience, especially through the handling of the systems of representation. We assume that continuity is necessary in order to elaborate a real mathematical experience for the students. The analysis of the extract shows that the past and future situations can be related to each other. We point out that the students' continuity of experience can produce knowledge growth. This growth specifically occurs when the teacher's uttering activity directs the students' actions while they use the systems of representation. This uttering activity allows a reshaping / remodeling /modification of former knowledge through the systems of representation.