Os números racionais nos níveis curriculares da rede estadual de ensino de São Paulo

Abstract

The purpose of the research in the present dissertation is to analyze what relations show between the prescribed, presented and assessed curricular levels, considering rational numbers teaching in the context of São Paulo state educational system. It is intended to contribute to the debate about teaching and learning process of School Mathematics, especially regarding the selected mathematical topic – Rational Numbers. The theoretical support is related to Curriculum, Rational Numbers and External Assessments. The Spanish researcher Gimeno Sacristán’s perspective on curricular levels is the main theoretical reference for this research. The research has a qualitative methodology, with techniques of document and bibliographical analysis. Official curricular documents (state and federal) were analyzed, ‘Matriz de Avaliação de Matemática do Saresp’, ‘Matriz Curricular da Secretaria de Estado da Educação – SEE/SP’ and ‘Base Nacional Comum Curricular – BNCC’, representing the prescribed curricular level. The textbook and the Student and the Teacher Notebooks, provided by SEE/SP, represented the presented curriculum. To represent the assessed curriculum, the issues of ‘Avaliação da Aprendizagem em Processo – AAP’, applied in 2018, were analyzed. From such analyses, convergences and divergences were found in the analyzed material from 6th to 9th school grade. A great amount of conceptual and procedural aspects of rational numbers are developed in didactic material, many of them explicitly prescribed. By analyzing the convergences between the documents, regarding prescribed contents for the 7th grade, an aspect to be considered is the teaching of fractional and decimal representations of a rational number, their uses, sorting and association with numerical straight line points and operations involving those representations. The recognition of rational numbers in different contexts, the part/whole relation, the quotient, the ratio and the operator, the recognition that rational numbers can be expressed in fractional and decimal form, establishing relations between the representations, and the different meanings of the operations are referred in the prescribed curricular levels PCN and BNCC and in the assessed Saresp and AAP as skills to be developed. It was observed that prescriptions show differences in classifications in the documents for the same object or particular aspect of content, such as: fraction, fractional numbers and fractional representation; decimal numbers, decimal notation and decimal representation, among others. Although PCNs recommend the location of rational numbers on the straight line, this is little explored in the presented curriculum. The skills in the Student and the Teacher Notebooks (material provided by São Paulo state educational system for final grades of elementary school and for high school) are evaluated, and not in the textbook, since there are no specific prescriptions for them in the official documents. Some issues of AAP evaluate skills developed in grades prior to their application. The teacher must be attentive to that material and to the differences of approach and classifications used, in order to improve teaching process and better understand the setbacks that often affect the teaching and learning process involving rational numbers.