Equação do 2º grau: resoluções algébricas alternativas

Abstract

The resolution of second-degree equations is a central theme in the Mathematics curriculum of elementary and high school, frequently addressed through the direct application of the quadratic formula. However, this traditional approach can limit students’ conceptual understanding, leading them to mere memorization of procedures, without a significant connection to the underlying mathematical principles. This dissertation, developed within the framework of the Professional Master’s Degree in Mathematics in National Network (PROFMAT), investigates methodological alternatives for solving second-degree equations, exploring their contributions to teaching and learning. Initially, an analysis of the current educational legislation is conducted, including the Law of Guidelines and Bases of National Education (LDB) and the National Common Curricular Base (BNCC), in order to situate the relevance of the topic in the context of Brazilian schools. Next, historical aspects of Mathematics are explored, highlighting the evolution of quadratic equations and their development over the centuries. In addition to traditional methods, alternative procedures that expand didactic possibilities are presented. The dissertation includes a report of experience regarding the application in the classroom of three specific methods: Al-Khwarizmi’s geometric method, the Single Quotation Method, and the approach developed by Po-Shen Loh. The analysis of the results shows that methodological diversification not only favors a deeper understanding of mathematical content but also sparks greater interest among students and expands the didactic repertoire of teachers. Thus, it is argued that a plural and investigative approach can contribute to a more meaningful and accessible education for different learning profiles.