A formação do pensamento teórico do conceito de adição de fração: um experimento de ensino baseado na teoria do ensino desenvolvimental de Davydov

Abstract

This coursework aims to identify the contributions of a didactic formative experiment designed for the formation of the theoretical thought of the concept of fraction addition. For this, a formative didactic experiment was planned, according to Davydov's Theory of Developmental Teaching, which aims at the formation of theoretical thinking by the method of ascending from abstract to concrete. This method aims at the fulfillment of five actions, by the students, for the formation of theoretical thinking: (1) Transformation of the task data aiming to identify the general relationship of the object of study; (2) Modeling the general relationship of the object of study; (3) Transformation of the model of the general relation of the object of study in order to study its properties in pure form; (4) Construction of the system of particular tasks that can be solved by a general procedure and (5) Control or monitoring of the actions performed previously. In short, students must: identify the general relationship of the concept of adding fractions with different denominators, which is the equivalence of fractions; based on the history of fractions, establish a graphic, literal model that expresses this relationship and, finally, solve some particular situations using the general procedure previously established. The didactic training experiment, as an intervention method, was developed in a class of 6th grade of elementary school of a Public School in the central region of Goiânia, where it aimed to answer the following investigative question: What contributions did a didactic training experiment on the concept of addition of fraction in the light of the Developmental Teaching Theory can bring to the formation of students' theoretical thinking? To answer this question, the following data collection instruments were used: an observation script, recorded in a field diary; a mixed questionnaire applied to students and, finally, the learning tasks that make up the didactic training experiment. As a form of data organization, the following categories were listed: concept formation (theoretical thinking / empirical thinking), zone of proximal development, shared communication / interaction, mediation and study activity. The analysis of the data took place in a qualitative way, being analyzed according to the particularities of the categories listed in the perspective of the Historical- cultural Theory and the Theory of Developmental Teaching.