The design and engineering of E-learning systems must be considered as a transdisciplinary problem requiring the integration of different scientific approaches. The design process of E-learning systems needs to consider several theories, models and artifacts – the e-learning system. We claim it is essential to ensure the traceability and the interpretation of phenomena related to the use of artifacts in studying precisely the relationships between theories, models and artifacts. Consequently, we develop a co-design methodology to deal with these goals. The main contribution of this paper is to describe a methodological approach enabling the co-design of problem-based learning scenarios in sciences which are based on teacher real practices acquired by means of the theory in didactic anthropology of knowledge and to show why we can formalize them in a hierarchical task model to design an adaptive E-learning system.