TEORIA DOS CAMPOS CONCEITUAIS: INTEGRANDO ARITMÉTICA, GEOMETRIA E ÁLGEBRA NO ENSINO DAS FRAÇÕES / CONCEPTUAL FIELDS THEORY: INTEGRATING ARITHMETIC, GEOMETRY AND ALGEBRA IN THE FRACTIONS TEACHING

One of the most well-known theories in the field of mathematics teaching, elaborated by Gérard Vergnaud in the twentieth century, starts from the premise that knowledge is constituted by conceptual fields and the assimilation about this knowledge area is built through experience, maturity and contact with the different representations of a study object. Based on this, the present research aims at analyzing the potentialities of a learning based on said theory and developed through a didactic sequence, involving the content of Fractions, to a group of 6th Grade Elementary of Regular Education. It is a qualitative research anchored in the own practice, through the development of a case study, and in the bibliography of renowned mathematical educators and researchers of the area. In this context, the researcher worked as math teacher in the class in question, focusing on the constant analysis about the construction of the student knowledge from a previously planned teaching with a view to the different representations and structures of fractions. The results evidenced a significant learning process, in which the relation of the concepts constructed led to the assimilation of new knowledges, allowing the development of different skills.