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This article proposes a model for the education of project design based on a strategy of collaborative work in e-learning environment. The model is described through three related sub-models: the specialist, the apprentice and the collaborative environment. The article concentrates in the specification of the apprentice model describing the activities during the collaborative effort of project development in e-learning environments. The proposed model represents an important contribution to the research of Computer Supported Cooperative Learning (CSCL)system. The model suggests ways to innovate in the pedagogical process and it uses a finite automaton to formalize the coordination of interactions between the members of the design group.