O “problema da mistura” envolvendo porcentagens : um estudo da mobilização das estratégias de resolução de estudantes do 9º ano do ensino fundamental

Abstract

The main objective of this study was to analyze the strategies that 9th grade students use when solving a problem situation involving percentage calculations. The theoretical basis of this work addressed the resolution of problems in mathematics and the difficulties of students, the types of problems in mathematics, the strategies in the process of problem solving and the rule of three as a strategy for problems involving percentage. In methodological terms, the research conducted is classified, as to the approach to the object, as qualitative. As to the objectives, it is classified as exploratory, and as to the technical procedures, as a case study. The research objectives were achieved through five stages: survey and study of a mathematical problem involving percentage calculations (stages 1 and 2); elaboration and proposition of the selected problem to a class of 36 students in the 9th grade of a municipal school in Capim/PB (stage 3); categorization (stage 4) and verification of the resolution strategies adopted by the students participating in this research (stage 5). The problem was worked in the classroom in two phases. In the first phase, students were to represent the problem with a drawing and solve it with their own strategies. In the second phase, the strategies of rule of three, inverse resolution with trial and error, and building a table were indicated as strategies that would help students solve the proposed problem. The students participating in the research mobilized, with more effort, the strategy of the rule of three, but the strategy of building a table also appears in the resolutions, but in a smaller quantity. While 23 students chose to use the rule of three, 10 preferred to adopt the strategy of building a table. The analyses allow us to infer that students do not know different problem solving strategies and that the study involving percentages is a challenging mathematical knowledge object for 9th grade students.