Abstracts Mathematics

Análise de erros em problemas de combinatória com invariantes implícitos e explícitos resolvidos por crianças

by Renata Palhares FERREIRA

Combinatorial reasoning plays an important role in the cognitive development of children and adolescents. The present study, based on the theory of conceptual fields, investigated the effect of making the invariants explicit on the errors employed by children in solving problems of arrangement, permutation and combination in two conditions: with statements that made the invariants explicit or with statements that left the invariants implied. The study was built from the Silva et al. were divided into three groups with twenty children. Each group responded to four problems of a type of combinatorial situation, two with implicit invariants and two with explicit invariants. Qualitative analysis identified five types of reasoning involved in inappropriate and common responses to the three combinatorial situations. In general, the results indicate that the condition of explicitation of the invariants qualitatively denoted more elaborate responses, due to the cognitive sophistication. Statistical analysis confirmed the differences in the distribution of error types as a function of the implicit and explicit condition. These results bring contributions to the field of cognitive psychology, related to the understanding of the intellectual organization of children in the early years regarding the mechanisms of acquisition of combinatorial knowledge, as well as to the field of mathematics education.