ABSTRACT
This chapter presents two main developments of the praxeological model. In relation to the theory of didactical situations, it introduces the two notions of variable and generator of a type of tasks. The introduction of the notion of variable in the ATD is linked to research studies developed within the Models and Technologies for Human Learning team on the design, development and use of technology-enhanced learning (TEL). T4TEL is in line with the praxeological approach. It represents a formalisation and an extension of the praxeological model to answer a twofold need: from the one side, to have a model that is computable from a computational point of view and, from the other side, to produce different TEL applications. The chapter aims to distinguish a global mathematical organisation of the algebraic domain starting from three regional mathematical organisations (RMO): RMO1 “Algebraic expressions”, RMO2 “Formulas” and RMO3 “Equations”.
