Da régua e do compasso: as construções geométricas como um saber escolar no Brasil

Abstract

This study aims at the discussion of the development of the teaching of geometrical constructions in the Euclidean geometry, starting from the middle of the 19th. From the end of the 19th century, in Brazil, the geometrical constructions became an autonomous discipline, valid and legitimate school knowledge. Some textbooks were published where the theory of the Euclidean geometry was absent. Through to the official legislation it was possible to demarcate the periods where the main alterations in the school curricula happened. The analysis of Geometrical Drawing textbooks allows us to verify the modifications of programs and how this discipline was developed in the schools. The law LDB 5692 was sanctioned in 1971. According to this law the schools are free to build their own curricula, as part of their option to select themselves certain subjects, and the Geometrical Drawing is no longer obligatory. These facts, among other, contributed to exclude the Geometrical Drawing from many school institutions. In spite of the Geometrical Drawing is not included in the curriculum of most of the Brazilian schools, this discipline, in the 1980's, won a new impulse, since new collections were published. Other proposals of working with the geometrical constructions reappeared in the 1990's. Mathematical textbooks started to include activities or chapters dedicated to the geometrical constructions with ruler and compasses. In 1998, the Parâmetros Curriculares Nacionais de Matemática, for the 3o and 4o cycles of the fundamental teaching, suggested that the geometrical constructions should be treated inside the Mathematical discipline. This research indicates that, in some schools, the teaching of the geometrical constructions was always present in the classes of Geometrical Drawing or classes of Artistical Education. If we look at the New Sociology of the Education, we can see a possible reason for the directions that the teaching of the geometrical constructions were taking, not only in Brazil but also in other countries. We inferred that the compartimentation of this knowledge corresponds to socioeconomic motivations that will be decisive in the didactical transposition. In Brazil, the permanence of teaching geometrical constructions in some schools demonstrates the superiority of this knowledge over others, revealing the stratification of the contents and school knowledges