From usage analysis to automatic diagnosis: The case of the learning of algebra

User modelling is a significant part of usage analysis. We present a case study in the field of the learning of algebra that aims at producing automatic diagnosis rules, based on the analysis of tracks of students solving algebra exercises within the Aplusix learning environment. We present two experiments that were conducted among 8th and 9th grade students. Manual analyses performed on the data made it possible to contribute to the construction of a library of rules aiming at modelling students by hand or automatically. The automatic diagnosis, based on the use of a library of correct and incorrect rules, and on a heuristic search algorithm, reveals a high performance on some of the algebra fields and will be extended to other fields through iterative comparisons with the results of the manual diagnosis