DEFENDING, ACCORDING TO COMPLEXITY THEORY, DIALOGUES BETWEEN ARGUING AND DEMONSTRATING

OPENING SPACES FOR THE REPERCUSSIONS OF SUCH DIALOGUES IN THE IDENTIFICATION OF MATHEMATICIANS AND MATHEMATICS TEACHERS

Abstract

The investigation described in the following pages is theoretical in nature. It turns to the possibility of transformations in the identities of the mathematicians and the mathematics teachers. Mathematicians and mathematics teachers (of the school and of the university) differentiate between arguing and demonstrating, linking argumentation more to elementary or school mathematics, and demonstration more to scientific or academic mathematics. However, arguing and demonstrating are not restricted, in terms of their characteristics, to distinct processes. Argumentation and demonstration are contrasting, yes, and even opposites; however, making use of a non-Aristotelian logic, it can be said that, in addition to opposing each other, argumentation and demonstration complement each other: this is the dialogical complex principle. Two other complex principles that are also used in this dissertation, to deal with argumentation and demonstration, are the recursive and the hologrammatic. It is believed that epistemic discussions, in the sense recommended here, involving teachers and students, in the school and university contexts, contribute to changing the conception about the roles that the argumentation and the demonstration play in the mathematical dynamics, stimulating changes in the identities of the mathematicians and the teachers mathematics (elementary and academic).