O jogo da trilha na construção do raciocínio aditivo no ensino fundamental

Abstract

The main objective of this study is to analyze how board games (track games) contribute to the transition from basic counting strategies to initial forms of additive reasoning in first-grade elementary school children. The specific objectives were: to identify the counting strategies used by children during board game matches; to analyze the transformations in these strategies by observing signs of transition from counting to initial forms of additive reasoning; and to examine how the characteristics of the board game (rules, movement, and peer interaction) facilitate this transition. The theoretical framework used concepts of reflective abstraction (Piaget), the educational function of play (Kishimoto), modes of knowledge representation (Bruner), and additive reasoning (Nunes et al.; Vergnaud). The methodology was characterized as participatory research, conducted in a private school with 8 first-grade students, through a didactic sequence of four meetings, outside of regular school hours. As instruments for data production, a board game and a written task were used, serving as a pedagogical "scaffolding" for the consolidation of concepts, such as the reversibility of thought, articulating the playful moment with the activity of written recording, respecting the transition between active, iconic, and symbolic representations. The data analysis also considered the action schemes of joining, separating, and completing quantities, typical of additive structures. The results revealed a gradual evolution in the participants' reasoning, who transitioned from simple counting to overcounting. Regarding the task performed after the game, the systematization of the written record allowed the identification of different strategies, consolidating the passage from concrete thought to symbolic representation. It was observed that the researcher's intensive mediation was fundamental, offering security for the children to demonstrate their thinking. It is concluded that the board game combined with problem-solving enhances cognitive autonomy and sociability, as it requires the student to negotiate rules and use different mathematical strategies in a context of real interaction.