Abstract
This paper in two parts aims to reflect the work conducted by the group “Didactique” of the IREM of Montpellier for five years. Learning and teaching difficulties about linear equations in high school led the group to reflect on the Cartesian plane and coordinates systems. This first part intends to first examine the mathematical usual construction of graduated lines, coordinate systems and cartesian plane in order to highlight the underlying axiomatic choices. Then, on the basis of historical and epistemological elements, are presented didactical issues. This reflection should provide deeper inside into choices made by the institution, textbooks’authors, or teachers in their classrooms, as well as their potential impact on students’learning. It leads to highlight that didactical issues related to these objects cannot be reduced to issues of visually representing objects, even if these last ones are crucial. The second part of the article extends the reflection by providing an analysis of official instructions in the light of the above-mentioned didactical issues, as well as a presentation of some learning situations for middle school and high school students which may allow to handle (partly) these issues in classrooms in a profitable manner.