Crianças, algoritmos e sistema de numeração decimal

Abstract

Although many studies in Mathematics Education (in the national as well as in the international sphere) approach possible problems about an "incorrect" introduction of formal educational procedures in the arithmetic's teaching during the beginning stages of learning, it is important to recognize that these discussions haven't emerged completely in the scholars limits to provoke an important rupture on the present scholar practices, which remains taking priority to repetition instead of the mathematical knowledge construction. In this sense, the present research proposed to investigate if the arithmetical teaching, with emphasis in algorithm, contributes to the mathematical knowledge construction. It was decided to analyze only the additives structures - addition operation and/or subtraction - as these structures make possible to investigate: a) if the conventional operations techniques (the algorithms) utilization, in addition and subtraction operations solving, allow the flexibility of the child's thinking and; b) if the child, while using the formal addition and subtraction algorithms, perceives the principles and properties of the Decimal Numeration System which are implicit in this procedure. Aiming to achieve the proposed objectives, it was interviewed, through Piaget's Clinical Method, twenty children of a public school of Maringá, being that, ten children belonged to the third grade of the basic cycle and the other ten to the fifth grade of the Fundamental Education. Each one of these two groups were subdivided into other two smaller groups, composed by five children who, according to their teachers, had a good performance and five children who had an insufficient performance in mathematical learning. The results analysis indicates that children from both educational stages reproduce mechanically the conventional operations techniques, without a real comprehension of the actions executed by them. While using the conventional algorithms of addition and subtraction, they make it automatically, repeating rules that they were taught to without realizing the existing relation between this mechanism and the principles and properties of the Decimal Numeration System. Regarding the learning performance in the subject (good or insufficient), it is not possible to affirm if it is related to the Decimal Numeration System comprehension, it seems that these classifications point toward to other variables of the educative process.