An Epistemology Approach to mathematical thought in the intersection “Language / Communication / Knowledge” in the Italian Math High School

Abstract

Scientific research on the epistemological foundations of mathematical thought represents, in the panorama of scientific theorizing, one of the
themes of greatest interest, both for the definition of mathematical concepts and for the cognitive-symbolic specification that follows. One of the constants of the discourse in progress is represented by the dialectic that is established
between “thinking” and “knowing” where thinking becomes the generative substrate of “knowledge” and “knowledge” the structural basis of “thought”. This is true both in the stracturing of “basic mathematical concepts”
and in the stucturing of the “mathematical thinking”. From this point of view, a new vision of High School, is emerging: the Math High School.
Here, the learning of mathematics follows the indications of an autopoietic and generative approach, more oriented towards the acquisition of strategic skills and creative problem solving. From a methodological point of view, the Capability approach provides a significant contribution to the evolution of the discourse. In this context, every “didactic action” is transformed into an act of perturbation, capable of generating new “objects” of knowledge through an autopoietic, hermeneutic-ideational process of new worlds. Here two different forms of learning are implemented (intentional learning and deep learning) which interact in a synergistic way influencing each other in a dialectical alternation of linear didactics (objects of knowledge) and nonlinear didactics (ideational processes). Therefore, there is a need to overcome the dichotomy between the humanistic culture and the scientific culture within a critical thought capable of grasping the synthesis between
imagination and rationality by approving a third culture, understood as a capable strategic action to ensure equal dignity to scientific and humanistic knowledge.