Níveis do pensamento aritmético de estudantes do ensino fundamental II identificados em situações do campo multiplicativo

Abstract

This work investigated how the theory of conceptual fields of multiplicative structure can contribute to students' arithmetic thinking. The study is based on Vergnaud's theory of conceptual fields and on studies on arithmetic thinking by authors such as A.N. Leontiev, Lins and Gimenez, and Raisa Guberman, among others, who discuss the mode of arithmetic thinking. This qualitative research, conducted through action research, was carried out with 29 ninth-grade students, seeking to identify difficulties in the use of multiplicative structures, analyze the schemas employed, and understand the levels of arithmetic thinking evidenced in their problem-solving. Data collection involved questionnaires and diagnostic activities, observation of interactions, and problem-solving situations focused on quaternary relationships. The results reveal a strong influence of traditional teaching, marked by a focus on algorithms and a limited conceptual understanding of situations. Many students operate at level 1 (performance) of arithmetic thinking, while others demonstrate more consistent mastery, compatible with level 3 (informal arithmetic). In conclusion, the analysis of situations in the multiplicative field allowed us to understand how students mobilize mathematical concepts, procedures, and representations, favoring the identification of different levels of arithmetic thinking.