Percurso de aprendizagem de expressões e equações no 8º ano do ensino fundamental à luz da Teoria dos Campos Conceituais

Abstract

This work is linked to the Graduate Program in Education, Culture, and Communication in Peripheries (PPGECC) of the Faculty of Education of Baixada Fluminense - State University of Rio de Janeiro (UERJ-FEBF). It is part of the research line "Education, School, and its Social Subjects" coordinated by the supervising professor Dr. Gabriela dos Santos Barbosa. Its objective is to describe the learning process of simple algebraic expressions and first-degree equations of 8th-grade students in Elementary School. For this purpose, a field research will be conducted with 35 students from a public school located in the municipality of Duque de Caxias/RJ. The choice of 8th-grade students is because they have been exposed to algebra since the previous year. To underpin this work, the Theory of Conceptual Fields developed by Gérard Vergnaud was chosen, along with the notions of algebraic conceptions and algebraic thinking. The methodology chosen for the work is qualitative, classified as a case study. The field research was divided into three stages, with the first one consisting of a questionnaire with personal response questions and a diagnostic test with algebraic expressions and first-degree equation questions. The second stage involves a teaching intervention aimed at students' understanding of algebraic concepts and structures, building schemas. The third stage consists of a new diagnostic test to assess the impacts of the teaching intervention. The Theory of Conceptual Fields will be used in all stages of the field research, and it is expected that through the use of situations and representations, students mobilize operational invariants that aid in the development of algebraic thinking. The results of the research showed the importance of identifying false schemas mobilized by students and the role of representations in learning, as students showed a greater understanding of algebraic concepts after the activities.