The Possibility of Direct Relationships between the Human Being and the Thought, in Mathematics (and in Classes of Subjects of Courses for Undergraduate of the Mathematics Teachers), in Accordance with Complexity Theory

Abstract

The research described in these pages is/was theoretical in nature and focused on the subjects “Man, Language (Mediation) and Thinking”. Specifically, “Man, Mathematical Language (ML or Mediating Element / ME) and Mathematical Thinking” were investigated. For this, we used the Philosophy of the Complexity (by Edgar Morin). Emphasis was placed on the “Dialogical, Recursive and Hologrammatic” Complex Principles. We sought to study the possibility of links between Man (A) and Mathematical Thinking (B) without the existence of the intermediation provided by Mathematical Language (ML). In this sense, the pairs that make up the set “A ó ME ó B” were examined, that is, the following subsets were researched: “A ó ME”; “ME ó B”; “A ó B”. The pairs, primarily “A ó B”, were analyzed from the angle of the three Morinian “complex principles”. It was concluded that, in theory, there can be immediate links (that is, without the action of ML – Mathematical Language), in such a way that the viability of the pair “A ó B” (Man ó Mathematical Thinking) was evidenced, as much as it is and was always viable the structure “A ó ME (ML) ó B” (Man ó Mathematical Language ó Mathematical Thinking). The main objective of the investigation was the elaboration of arguments that could integrate conversations, between trainers and students of Degrees in Mathematics, (conversations) with an impact on the constitutions of the identities of members of both (trainers and students of Degrees) groups.