Ensino da divisão no primeiro ciclo do ensino fundamental : análise das práticas pedagógicas de professores

Abstract

The purpose of this project was to analyze the implications of the pedagogical practices of the teacher in conducting the comprehension of mathematical division operation for the student in the first cycle of the primary School. Keeping that in mind, the intention of this research was to produce data on which allowed to comprehend how the practices of the mathematic teaching, developed in the first years of scholarship, can contribute for the creation of cognitive structures by the student on which allows to elaborate notion about the mathematical division concept. Appeared as the specific objectives: analyze the pedagogical practices developed by the teachers regarding the four operations (subtraction, addition, multiplication and division); and, as a second specific objective, inquire the contribution of the pedagogical practices in the comprehension of the division operation process by the student. The question that drove this project was: how the pedagogical practices instructed by the teachers that teach mathematics in the first cycle can conduct the children to comprehend the division operation? This project has pursuit to emphasize on how the comprehension of the division operation is understood, after theoretical acknowledgment in the Piaget constructiveness, and in the Vergnoud conceptual fields.The methodology used has qualitative character, where it was sought to comprehend the main practices developed in school class, by three teachers of the primary schools third grade in three different schools in the city of Cuiabá. Semistructured interviews, mathematic class observation and documentation analyses (example: the teachers planing book and the students notebooks) were the instruments used for data collection. These tools were essential for the unveil of how the mathematic teaching are thought end carry on in the Schools, and what aspects it allows to the comprehension of the mathematical contents. The data analyses was arranged in two main topics: the teachers epistemological concepts; and teaching practices. The first topic sought (with the semistructured interviews) to comprehend the relation of the teachers with the mathematic; on what they think about this area of knowledge, and how their conception with it were elaborated. The second topic was realized making cross reference of observing the school class and the students notebook. The objective was to analyze what are the possibilities of elaboration knowledge that the lessons drive the children to realize. Considering the data gathered was concluded that the mathematic teaching, in the investigated schools, still vacillates between fragmented practices that little contribute to the relations of mathematic contents, and more constructive practices that seek out to value the actions of children in the process of notion construction that later will serve as pillars in the elaboration of concepts, including the mathematic division operations.