A co-construção da generalização nas discussões coletivas: Um estudo com uma turma do 4.º ano

Abstract

This paper focuses on the development of the generalisation as a process of mathematical reasoning, in a context of a teaching experiment to promote algebraic thinking in one grade 4 class. It analyses the moments of collective discussions of three mathematical tasks explored in the classroom, in different stages of the teaching experiment, to understand how generalisation emerges and develops over time in the context of classroom social practices, according to a dialogic inquiry of mathematical knowledge construction. The lessons were taught by the researcher (the first author) and the data were collected by video recordings. This study shows the importance of the collective discussion moments to the emergence and evolution of the generalisation and to the appearance and maturation of symbolic mathematical language as a tool to the generalisation expression. Generalisations start to emerge as students begin to find ways of expressing the numerical relationships according to the computation strategies they explored in the first task. In the second and third tasks discussed in the paper, they already are able to express easily the gene- ralisation in natural language and start to give evidence of being in a process of meaning making of symbolic mathematical language, as a form of expression of generalisation. The process of development of the generalisation expression described in this study reflects its collective construction, as the final product results from the work of the class as a community of inquiry.