Conteúdos e metodologias no ensino de matemática nos anos iniciais do processo de escolarização no Brasil e na Rússia

Abstract

The theme addressed in this research is the teaching of mathematics, in the early years of Elementary School, in Brazil and Russia. Based on the historical-Cultural theories and Developmental Teaching, the problem investigated was formulated in the following terms: What are the differences and similarities in relation to the organization and development of mathematics teaching in the early years of schooling in the Brazil and the Elkonin-Davydov system of Russia, based on curriculum guidelines and teaching materials? The objectives were: a) to identify and analyze the criteria for selection and organization of math contents; b) identify which theoretical references give support for the methodologies and didactic procedures proposed in teacher's manuals; c) identify and analyze in the textbooks and manuals of the teacher, the adequacy of the contents and methodologies, at the level of child's psychic; d) critically examine possible contributions from the teaching of mathematics of the Elkonin-Davydov system for the Brazilian education system. Besides literature review on the topic, the bibliographical research (books, chapters and articles) in Portuguese, English and Russian were made. Documentary research included official documents of the ministries of education, also considering the maths books for the level of education investigated. In treatment and analysis bibliographic and documentary material, aspects of these composed of the following categories: purposes and objectives of the teaching of Mathematics expressed in documents; principles of organization and orientation curriculum for the subject of Mathematics; criteria of organization and selection of contents; theoretical guidelines for didactics and teaching methodologies; recommendations regarding learning assessment processes and forms. The results allowed to conclude that: a) in relation to the criteria of selection and organization of the mathematical contents, significant differences are observed in the criteria of selection of the contents as well as in the forms of organization and presentation of the mathematical concepts; b) Regarding the theoretical references that underlie the methodologies and didactical procedures proposed in the teacher's manuals, it can be seen that, in the Brazilian case, although the manuals do not clearly present the theoretical bases that underlie the teaching of mathematics, they converge towards the Piagetian constructivism. In the ElkoninDavydov system, the theoretical frameworks contained in manuals and teacher support materials are based on historical-cultural theories and developmental teaching (DAVYDOV, 1982; 1988; 1996); c) in teaching materials it was found that the contents and methodologies are adequate to the child's psychic development level only in the Elkonin-Davydov system. Finally, it was concluded that the possible contributions of Elkonin-Davydov mathematics teaching to the teaching of this discipline in the early years of schooling are: structuring elementary mathematics from the distinction between “external chronologism” and the internal logic of development of mathematical concepts, making the algebraic structure accessible to children in the early years of primary school; definition of an objective for the teaching of mathematics in basic education which is the assimilation of the concept of real number from the domain of the concept of greatness, with the study of its general properties; organization and presentation of mathematical concepts from the logical and psychological elements that constitute the historical-cultural theories and developmental teaching; modification of the forms of monitoring and evaluation of mathematical knowledge; among others