ROLE VARIABLES VS. CONTEXTUAL VARIABLES IN THE THEORY OF DIDACTIC SYSTEMS

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.