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Partisans of the constructivist approach to mathematics education, such as Brousseau or Chevallard, developed an accurate theoretical framework in which didactical systems are viewed in a systemic perspective. What they somewhat fail to draw, however, is a sharp distinction between role variables – concerning the roles played in the didactical interaction by the individual elements of the system (Student-Teacher-Knowledge) – and contextual variables – concerning the action on the learning process of the system as a whole.

Our research in progress on 2nd graders' word problem solving strategies applies the previous dichotomy to class management strategies adopted by teachers. Partial evidence collected so far points to the tentative conclusion according to which, contextual variables being equal, differences in teaching styles and methods may deeply reshape the role component of didactical systems. If we take into careful account this distinction, we can shed additional light into some hitherto unexplained phenomena observed in the literature.

The Theory of Didactic Situations in Mathematics (TDSM) has been proposed as a systemic theoretical model, designed to describe teaching and learning phenomena. This theory aims to become an experimental and application-oriented paradigm grounding the research activity within this domain. This contribution deals with an investigation about the occurrence, within TDSM, of the minimal conditions needed to qualify such a theory as "systemic". In this regard it contains a discussion about the features of the elements of the didactic system, their usefulness to account for the typical characteristics of interacting agents, as well as the interactions between the features themselves. In particular, we will deal with the conditions which, within TDSM, allow considering learning processes as emergent from situations, that is specific didactic applications of mathematical objects or concepts, viewed under the form of a concrete implementation by an agent operating in an environment, and characterized by the effects produced on the environment itself by this agent.