The theory of didactic situations in Math Olympics teaching: An application of the Pitot Theorem

Abstract

In this article, we intend to present a partial cut of a master’s research, in which we describe specifically, an Olympic Educational Situation (SDO) that is structured with the support of Geogebra software. An intervention carried out adequately by the exploitation of software, allows students to overcome obstacles that may arise in the construction and application of geometric concepts. In a particular way, the described SDO proposes to the student the possibility of experiencing the process of learning from the methodological point of view of Theory of Educational Situations (TSD). The theory of situations analyzes and decomposes this process into four distinct and interconnected phases - action, formulation, validation and institutionalization - in which the knowledge has different functions with no relation to the learner. In addition, the analysis of the mathematical elements and the identification of their properties, through the modeling of the didactic situation, allows the students to solve the proposed problem and to validate the Pitot theorem. Thus, SDO represents an alternative to classes directed to the Math Olympics, their indication and structuring, describes elements related to didactic mediation during the teaching and learning process, which emphasize details that hold the possibility to control/predict the actions of students, as well as provide a more meaningful motivation for the study of geometry in the Olympic context.