A construção da noção de número: um estudo com crianças do 1o ano do Ensino Fundamental numa abordagem psicogenética

Abstract

This investigation, based on Genetic Psychology, aims to evaluate the level of operativity in first-grade elementary school children, based on the tests of conservation of continuous and discontinuous quantities, classification, and operative seriation. As a complementary objective, it seeks to relate these aspects to the construction of the notion of number. Two studies were conducted: a systematic literature review and an empirical study. For the latter, an intentional sample of 35 children, aged between 6 and 7 years, of both sexes, enrolled in the first grade of elementary school at a public school in the Central-West region of Brazil, was selected. As an instrument, four tests of operative behavior were used, developed by Piaget and Szeminska (1981), with adaptations by Mantovani de Assis (2002). In the experimental situations, Piaget's clinical or critical method was employed. The results indicated that most children had not yet consolidated the basic logical operations: more than 90% did not perform operative seriation; 80% did not carry out classification; 60% did not conserve discontinuous quantities; and 63% did not conserve continuous quantities. A strong correlation was observed between the two types of conservation and a moderate correlation between conservation and classification. Children who showed good performance in the conservation of discontinuous quantities (counters) also tended to perform well in the conservation of continuous quantities (mass), with progression toward classification. Children who demonstrated more elaborated classification skills also obtained better results in rod seriation. In parallel, the systematic literature review, covering publications from 2010 to 2024, revealed that playful and contextualized approaches, such as the use of games and practical activities, promote the connection between mathematical concepts and students' everyday lives, fostering greater engagement and understanding. The most effective methodologies are those that employ innovative practices to promote the construction of the notion of number in a progressive and functional way. The continuous training of educators was also identified as fundamental for adapting pedagogical strategies to students’ needs. It is concluded that the construction of the notion of number depends on innovative pedagogical practices that consider students’ experiences and contexts, promote autonomy and cooperation, and foster a stimulating environment, free from tension and coercion, which enables action upon the object of knowledge. This study offers support for more efficient and meaningful pedagogical practices, contributing to the development and construction of number sense and arithmetic operations in the early years of elementary education.