Invariantes operatórios na transição entre dois campos conceituais: o caso do tempo relativo

Abstract

This thesis had as main research question: how do students organize their knowledge in action in order to build the notion of time and how do they use this notion to recognize situations where it is necessary to solve the problems? We investigate the construction of the notion of relative time from the transition between the Classical Mechanics and Special Theory of Relativity. For this, we applied a didactic sequence whose emphasis was on the study of relativity of motion and how the Theory of Relativity demanded a change in the epistemological status of time. The research was carried out in 16 class hours in a classroom of third grade of high school from a public school. The didactic activities were diversified (theoretical exposition by the teacher, reading texts, use of audiovisual resources, debate and discussion among students in small groups). The theoretical framework was the Theory of Conceptual Fields by Gérard Vergnaud. In addition, we promote a link between Vergnaud's ideas and the Piaget's formulation of schème , as well we used its researches on the construction of the notion of time. We analyze the cognitive trajectories of five students in the process or construction of the relative time . Thus, we investigated the evolution of operational invariants used by students. Thus, we conclude that understanding the relative time is linked to a broader framework that encompasses the notions of movement and speed. In this regard, we highlight three main points: (1) Considering time as a schème allows us to analyze the necessary changes in operational invariants required for an individual realizes the novelties brought by the Theory of Relativity. (2) To be able to operate with concepts of relativity, the subject must carry out mutual assimilation between the schèmes of time and motion. (3) The study the Theory of Relativity provided a new context for the schèmes of motion and it allowed the occurrence of reformulations in operational invariants for some students.