O conceito de isometria em livros didáticos dos anos finais do ensino fundamenta : um estudo sob a ótica das teorias dos campos conceituais e da transposição didática

Abstract

Isometries are important components of the study of geometric transformations, being present in the Common National Curriculum Base and consequently in textbooks. Therefore, this dissertation aimed to analyze the approach of this content in mathematics collections in the final years of elementary school, with based on the theories of Didactic Transposition, according to Yves Chevallard, and of the Conceptual Fields, developed by Gerard Vergnaud. Books from the 7th and 8th grades were analyzed (series where the content is covered) in 5 collections. We observe the didactic transposition of the concepts of axial symmetry, translation and rotation to textbooks, investigating the changes made by the noosphere, with an emphasis on the epistemological surveillance of the concepts. From this study, we realized that, in general, the transposition of the BNCC programmability to books was followed by the authors, but there were differences in the way each collection interpreted such recommendations. We also found some divergences in the conceptualization of some symmetries in relation to our theoretical framework, where one of the books excludes points belonging to the symmetry axis of transformation by reflection. Regarding the investigation according to the Theory of Conceptual Fields, we created analysis criteria based on the concepts of operational invariant and signifiers. When observing the activities proposed by the books, we noticed that there is a preference for situations with axes of symmetry and vectors parallel to the margins of the sheet, the use of gridded mesh and straight figures, indicating a gap in the variety of situations in relation to the significant ones.