Uma análise sobre a elaboração e resolução de problemas de divisão por alunos do 5º e 9º ano do ensino fundamental

Abstract

During Elementary School I, students are introduced to the division operation and the algorithms related to it. However, elementary school II students, or even high school, present difficulties in performing calculations that involve division, either in the interpretation of the statements of the problems or in the recording of their resolutions, through algorithms or not. Therefore, this paper aims to investigate what is revealed regarding the elaboration of utterances, and about the resolution, of problems involving the division operation, by students of 5th and 9th years of elementary school. The research-guide questions were summarized as follows: i) What are the characteristics of division problems elaborated by 5th and 9th grade students? ii) What forms are mobilized, algorithms and how are these employed by 5th and 9th graders, to solve division problems? Materials consisting of statements of problems, involving the operation of division, elaborated and solved by students of the 5th and 9th grade of elementary school, constitute the source of data of this work. The interpretative analysis of the written production of the students made it possible to establish groupings. For this, we sought to identify in the statements elaborated the types of problems produced, if they contained the information necessary to be solved, as well as the maternal, symbolic and numerical languages mobilized. And in the resolutions, it was identified the use, or not, of algorithms, what they are and, the way students used the algorithms, identifying the difficulties, errors and potentialities in their use. As results, it was identified that there was no significant variation in relation to the characteristics of the problems elaborated by the students of the 5th and 9th grade, and most of the students elaborated problems classified as partition and made use of natural numbers. However, there was the use of fractional and decimal numbers and in the statements elaborated by the 9th grade students there was the incorporation of concepts learned in Elementary School II, such as calculation of the triangle area and factoring. Regarding the resolutions, the 5th grade students needed auxiliary calculations, presented the rest as an answer, forced the procedures to find zero rest and in some cases demonstrated not knowing how to use the division algorithm. It was also identified that students from both school years exhibited, for the most part, a final response to the proposed utterance, in addition to making use of a single algorithm, the algorithm of division by the long process.