Validações do teorema de pitágoras em livros didáticos do 9º do ensino fundamental

Abstract

The present work consists of a qualitative and bibliographic research whose objective is to analyze the validations of the Pythagorean Theorem in textbooks for the 9th grade of middle school, articulating the types of mathematical reasoning according to Balacheff and the semiotic representations of Duval. For this, Bardin's Content Analysis is used as a technique of data analysis. Three collections of Mathematics textbooks for the 9th grade of Elementary School are selected, in the teacher's version, distributed in the last National Program of the Textbook, which occurred in 2020. The condition for choosing the collections is that they contain at least some validations of the Pythagorean Theorem. The following collections were selected: Essential Mathematics, Teláris Mathematics and Mathematics Trails. The validations of the theorem are studied based on two major categories of analysis, the types of mathematical reasoning described by Balacheff and the different registers and semiotic operations described by Duval. Subcategories are also established for the analysis, aiming to enable the articulation between the two authors. The results of the research show that the textbooks of the three collections present different ways to validate the Pythagorean theorem, being the intellectual proofs of the demonstration type, which mobilize simultaneously the figurative register and the geometric register, the most used, followed by the pragmatic proofs that resort only to the figures or the action on them.