Reflections on the Socio-Constructive Nature of Mathematics: Pedagogical-didactic implications

Abstract

Mathematical education involves a wide range of objects, actions, tools, and
disciplines, but built in a socio-pedagogical context. In these pages we intend
to sketch the hypothesis that any productive dialogue between theory and
practice that one wants to support in the specific field of mathematical education
must be in the dialectic between the concrete context and contextual
abstraction. We believe that the context must play a key role, since it has to
link different perspectives, based on various professional activities, and offers
the creation of referential connections with significant meanings and aspects,
albeit comparable. This sense the requirement that the teacher must
have is to be always ready to explore the conceivable relationships between
the complexity of an exemplary concrete situation and its destination. New
knowledge cannot simply be “donated” to students, which makes it severely
inactive. The teacher must be aware of the way students are trying to reconstruct the meaning of the signs and the actions he has presented, to encourage generative and activation processes. This is not just about a plan of psychological process, but as activation agitated in a socio-cultural horizon.