Organização do processo de ensino do conceito de número nos anos iniciais do ensino fundamental: uma análise histórico-cultural

Abstract

The organization of the number concept teaching process in the initial years of elementary school is the theme of this research based on Davydov theories about the Historical-Cultural Theory and the Developmental Teaching Theory. The school and the teaching in these fundamentals are considered essential for the integral development of the personality (cognitive, affective, moral) and means of the psychological neoformations enlargement that lead to the child’s mental development. The school emphasizes the teacher’s professional performance as a fundamental condition in the organization of the teaching and learning process in order to assure students the appropriation of the fundamentals theoretical knowledge for the students development and its confrontation with awareness of individual and collective needs. This allows us to retake Vygotsky (2007)’s thesis to which properly organized learning leads to the students' mental development. The problem that was tried to clarify was how the teacher who teaches mathematics in the initial years of Elementary School organizes the process of teaching the concept of number.Using the theoretical framework of Historical-Cultural Theory and Developmental Theory the research aimed to understand the peculiarities teaching organization of the number’s concept in the initial years in order to contribute with the teachers in their teaching performance; to apprehend the teachers' understanding of the number’s concept; to analyze the organization of the teaching process of the number’s concept in the initial years; to detail knowledge about the formulations of Vygotsky’s Cultural Historical Theory and Davydov Developmental Teaching Theory in order to guide the methodological proposals for the teaching number’s concept. To investigate the problem were realized the bibliographic research and field research. The bibliographical research was done during 2010 to 2016 focused on the organization of the teaching process of the number’ concept in the initial years. The field research involved two municipal schools in Goianira (Go) with effective teachers who worked mathematics teaching in the initial years. The data collection included interviews with teachers and observations of its math classes. For the collected data analysis categories were delineated: the number’s concept expressed by the teachers; the organization of teaching number’s concept by the teachers of the initial years; the tasks proposed by the teachers and the tasks proposed by Davydov. The results achieved revealed an understanding on the part of the teachers that the number’s concept is everything related directly to the quantity given by discrete objects (like sticks, strawberries, illustrations in sets), that is, focuses on the natural number, whose actions and teaching methodologies remain focused on the sensorial concrete. It is consistent with the traditional fundamentals of the formal logic without ascension to the concrete thought that is the foundations of dialectical logic. Finally, it is understood that in the Davydov theories the actions and tasks carried out in the study activity of the number’s concept make it possible to overcome the organization way of the teaching process in the researched reality.