This article is about the place of traces in education and legitimates their use in TEL. The first part presents the Aplusix learning environment which allows students to freely make calculation steps, as they do in the paper environment, and which records all the students’ actions in logs. From these logs, visualisation and statistics are built. The second part is about local diagnostic of the learner and production of enriched trace: a student’s transformation is diagnosed with a sequence of rewriting rules. A library of correct and incorrect rules has been built for that purpose. The third part is about global model of the learner in the field of the movement concept in equations and inequations