O tangram e o ensino de frações: construindo o ensino e aprendizagem de frações para o 6º ano do ensino fundamental

Abstract

This study aims to pave the way for teaching and learning fractions, focusing on 6th-grade elementary school students. The work presents methods for teaching fractions using the tangram as a concrete pedagogical tool, an essential and high-quality didactic resource for mathematics education. Initially, the study explores the history of fractional numbers, highlighting their roots in Ancient Egypt and the importance of fractional numbers for the advancement of Egyptian civilization. It also addresses the origin of fractions, their relevance in the divisions made at that time, in engineering works, in agriculture—especially in wheat harvesting—and in the technologies developed during that period. After detailing the origin of fractions, we move forward to discuss the difficulties students face when learning fractions. For example, operations performed with natural numbers are not as intuitive in the set of rational numbers, as it is necessary to equalize denominators. Furthermore, many students carry accumulated difficulties from previous years. To overcome these obstacles, pedagogical materials prove to be effective tools, facilitating success in the teaching and learning process. They allow for the practical and everyday representation of fractions. Using the tangram, we explore a bit of its history and construction. The Brazilian National Common Curricular Base (BNCC) provides guidance on how to structure the teaching of fractions, emphasizing the development of skills and concepts in the classroom so that students acquire solid knowledge. The main focus is on students' cognitive skills, and the pedagogical resources employed reinforce all discussed concepts, stimulating students' creativity and autonomy.