Explorando as equações do primeiro grau sob caracterização de estrutura Algébrica

Abstract

Mathematics is considered by many students to be a challenging subject, especially regarding algebraic content. Therefore, this work aims to understand how the concepts of Groups and Rings contribute to the teaching and learning of students in Basic Education. To this end, we opted for a bibliographic and qualitative exploratory study. Thus, this paper will discuss algebra in Basic Education, how official documents address the topic, and will highlight algebraic thinking and the importance of teaching algebra in teacher education programs. This discussion aims to emphasize the key points to underline the significance of studying Groups and Rings in Mathematics teacher education courses. Finally, we proposed a didactic sequence as a way to enhance students’ algebraic thinking in Basic Education. In summary, when studying first-degree equations, the solution set is formed by a structure we call a group when ax+b = 0 for a = −1 or a = 1, and a ring when a ̸= −1 or a ̸= 1. Based on this sequence, we observed that content involving Groups and Rings is fundamentally relevant for teacher training, as it allows future teachers to develop a deeper understanding of the structures related to algebraic content.