Didactical Processes in Early Algebra: an example about the approach to brackets in third-grade classes

This paper contributes to the research strand concerning early algebra and focuses on a classroom episode realized within our ArAl project. The episode concerns the observation of a third grade class dealing with the problem of translating into arithmetical/algebraic code a process of calculation written in natural language. The problem is framed in the ‘matematóca game’, a game specifically conceived in order to bring the pupils to face the first experiences about the use of letters to represent natural numbers variable in a small set of cases and about the writing of easy algebraic sentences. Beside the good mathematical results, the episode highlights a significant role of the teacher and also the question of relational dynamics among the pupils.