O ensino de aritmética nos primeiros anos escolares e o movimento da matemática moderna no Brasil (1960-1980)

Abstract

This work brings the results of an investigation in the area of education, in the sub-area of the History of Education, with the theme linked to the History of Subjects, of which the primary objective was the description of professional knowledge of mathematics, in particular, the problems of arithmetic in school books such as, “Modern Course of Mathematics for Elementary Schools” and “Modern Course of Mathematics for Middle Schools”, together with the student‟s school notebooks. The set of problems that motivated this research mainly related to the production of arithmetic knowledge present in our sources, with a view to understanding the existing connection between the ideal function (of the school books) and the pedagogical reality (in the student‟s notebooks) of the contents of arithmetic. The delimited period for this investigation extended from 1960, time when the Movement for Modern Mathematics in Brazil was implanted, until 1980, when considerable changes in the development of Mathematics happened within the Brazilian scenario. For this reason, research methodology described by Lima and Valente (2019) was used, referenced in the studies of Peter Burke (2016), which consisted of work stages given by: recompiling teaching experiences, comparative analysis of notebooks and classifying the knowledge of the teachers. In the way, one can extract from the notebooks elements of the knowledge of the professionals, distinguishing an arithmetic to be taught and an arithmetic to teach. Knowledge of reflections on theory methodology in the field of the History of Subjects, Chervel (1990), in particular, as well as, in the scope of the culture of the school, Julia (2001). In this text, stemming from the idea of insertion, implementation and development of Modern Mathematics in Brazil. In addition, through the means of recompilation of the experiences of the teachers, select and separate the information organized in a collection of school books. However, in the comparative analysis of the knowledge of the teachers, we sought, from the group of notebooks, information and experience of the teachers that showed to be convergent to point of view of the orientation of the work of a teacher. In the end, in the classification and use of knowledge as knowledge, constitutes in with a dialogue with the development of the ideal modernizer in Brazil, with the Program of the Elementary School in São Paulo in 1969, as well as with notebooks of the students. Concluding that both of the collections present elements constitutive of a professional knowledge of arithmetic and that the problems of arithmetic very often present more characteristics of exercises of application of arithmetic in everyday life than the idea of a change in teaching mathematics within the modern math profile. In addition, we found that there has been a failure in the harmony between what is written in the school books, as an ideal goal, with what is effectively taught in schools, as part of the pedagogical reality. Key words: History, Education, School, Mathematics, Arithmetic