Visualização, resolução e formulação de problemas: abordando os números racionais a partir de uma linguagem para as frações unitárias

Abstract

Humanity has used concepts of fractions for at least five thousand years and despite the time of use, this knowledge is not easily passed on. We emphasize that the mastery of this concept is important from a practical point of view, in a cognitive perspective, and also for mathematical reasoning. To contribute to the minimization of this problem, we carried out a bibliographic research, and we found evidence that the origin of this knowledge is found in human activities, but, in mathematical education, the utilitarian aspects are not properly considered. Currently, we still see a predominance of a unilateral approach, favoring operational procedures with allusion to structures, notions of numerical sets, without construction of meaning. In view of these findings, this research will seek to propose an approach to fractions, valuing activities with significant representations, previous knowledge, seeking to build a significant reference for the understanding of fractions and other related concepts. We propose to start with visualization and construction leading to the problematization and transformation of the visualized material and we highlight the importance of building a vocabulary for fractions with the idea of the Cuisenaire Ruler for the study of fractions including naming quantities from unit fraction, and using fractions unitary to elaborate problems.