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In this paper we provide a characterization of VSE that takes into account the relation between the properties of the formative domain (the system of knowledge the student should learn) and those of the formative object (the speciﬁ c VSE).The result is a model of knowledge based on the concept of action as a connection between formative states.
Studying topological properties of the representations and dynamics of VSEs, we identify three basic structures: convergent, multi-convergent, and by propagation. Each of these structures has speciﬁ c properties which should be considered during the design and assessment of learning processes by VSE.
Firstly, we provide the theoretical analysis by the means of which we build the single model: we show how to formalize system actions and conﬁ guration and we describe how to apply this analysis to the learning dynamics which takes place as the VSE is being used. Secondly, we introduce a case study for each model in order to clarify empirically how they work.
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