Flexibilidade de cálculo aditivo suportada por relações numéricas

Abstract

This article aims to discuss how students in the first cycle of basic education develop the additive calculation flexibility, interconnecting it with the evolution in the construction of number concept. Two tasks are presented, one explored in a first grade and another in the second grade in the same class, with the same teacher. The data were collected through participant observation, supported by video recording and subsequent transcription of the activities developed. In the data analysis we try to understand how the students approach each of the situations in order to solve the problem and how this is intertwined with their conceptual development and the additive calculation flexibility. In both classes, the students began by exploring the tasks autonomously, followed by a moment of collective discussion. The data show an evolution in the students' flexibility of calculation interconnected with their conceptual development. Students establish numerical relationships, namely, in the first grade, the various possibilities of decomposition of 13 and the understanding of the commutative property of addition, and in the second grade, the relationships between different decompositions of the numbers that are used to deduce unknown values.