Hometetia e semelhança de triângulos: uma proposta de ensino utilizando materiais concretos e manipuláveis

Abstract

This work was motivated by our concern as a teacher-educator, for the dif fi culties faced by students from the ninth grade of elementary school in understanding the concept of similar triangles, as well as their application in problem situations encountered in daily life. As theoretical background, we turn to the history of geometry, the theorists who have studied the difficulties in the process of teaching and learning of mathematics, the pedagogical guidelines of the National Curriculum Parameters and a study of Geometric Transformations that preserve distances (isometries) and those without preserve the distances, but preserve angles (homotheties). The methodology used was action research, which is born of the need for rapprochement between theory and practice and is characterized by intervention in the process. This research was conducted in two groups of a state school, which has revealed some factors that affect the construction of the concept of similarity of triangles. To validate our hypotheses, we have developed two different models deliver the same content: One of them introducing the concept of Dilation and the other only the similarity of triangles, along with team and individual activities. One hypothesis is associated with teaching practice, which depends on the scienti fi c knowledge, knowledge of teachers and teaching resources used. As didactic intervention, we suggest some activities with concrete, manipulative materials that contribute to the construction of the concept of similarity of triangles.