O uso do Gnômon como recurso didático no ensino e aprendizagem do Teorema de Pitágoras no ensino fundamental

Abstract

This work presents results obtained from a research carried out with 72 students from the 8th and 9th grades of Basic Education, with ages ranging from 12 to 18 years old during Mathematics classes, at Colégio Estadual José Ferreira Pinto located in Feira de Santana, held between March and August 2019. In view of the difficulties presented by students of this age group, in building an abstract reasoning, to understand Mathematics problems, mainly problems involving Geometry, a research hypothesis was proposed, according to which Astronomy will contribute as a didactic resource in the acquisition of geometric knowledge. And Astronomy, being the oldest of the sciences, offers excellent examples of simple and interesting applications of elementary geometric facts, which can contextualize and enchant the student, stimulating even more his scientific curiosity and helping him to understand the role of Mathematics as an instrument of applied science. The research methodology used was Didactic Engineering by Michéle Artigue and the results obtained will be analyzed with the goal of improving teaching and learning in Mathematics. The research shows in a succinct way the relationship between mathematics and Astronomy in Ancient Greece, the history of Pythagoras of Samos and all the results obtained in the application of pedagogical products. The research is based on the theoretical framework of Didactics of Mathematics, Guy Brosseau's Theory of Didactic Situations. The educational products generated in this work were: a Didactic Sequence that used gnomon as a resource in teaching and learning the Pythagorean Theorem, and a game named Astromatematizar, which is a track with questions involving contents related to Astronomy and Arithmetic.