Um estudo da transposição didática no conceito de cilindro mediada pelo GeoGebra

Abstract

This paper aims to discuss the process of didactic transposition based on the general definition of cylinders, mediated by the GeoGebra software. In this sense, the methodology was based on a bibliographic study regarding the definitions of cylinders found in the books considered and descriptive in relation to the representations of GeoGebra. Thus, three books were consulted at two different times. In Chapter One - the first moment - only “Fundamentals of Elementary Mathematics, 10: Geometry Space, Position and Metrics”, by Osvaldo Dolce and José Nicolau Pompeo. was used, whose definitions of cylinders supported the discussion of this theme in the research. In addition, the study is of the qualitative type, which favored the discussion of the second moment. In Chapter three - the second moment - we use the definition of cylinder in “Mathematical prism: Geometry: mathematics and its technologies 1”, by José Roberto Bonjorno, José Ruy Giovanni Júnior and Paulo Roberto Câmara de Sousa. And also, the definition addressed in “Analytical Geometry: a vector treatment”, by Ivan de Camargo and Paulo Boulos. Among the books mentioned in the second moment, it is worth mentioning that, while the first is used in high school, the second is used in higher education and, when examined simultaneously with the contribution of GeoGebra, it is possible to notice some specificities in the knowledge contained in the first book, which makes it suitable for implementation in basic education, while the knowledge coming from the second book needs to undergo some modifications to adapt to the same level of education. The set of these changes made is called Didactic Creations, which arise from the need to adapt this knowledge in order to meet the demands of basic education. Therefore, this study contributes both to the discussion on the changes that occurred in the definition of cylinders, the didactic creations arising from the transposition processes, and to opening a debate about the use of technologies that make it possible to establish a relationship between the mathematical contents studied.