Os conteúdos de divisibilidade nos livros didáticos de matemática do 6º ano e documentos curriculares do ensino fundamental anos finais

Abstract

Divisibility contents (multiples, divisors, divisibility criteria, prime numbers, prime factor decomposition, maximum common divisor, and least common multiple) in sixth grade math textbooks and documents elementary school math curricula final years. In terms of theoretical contributions, it is emphasized the grounding in authors such as Chevallard, Chervel, Fiorentini, Miorim and Valente, to discuss the scientific knowledge and the teaching knowledge of mathematical knowledge; and, in Resende (2007), Barbosa (2008), Fonseca (2015), to deal with the theory of numbers in mathematics teaching. In a qualitative approach of the research, 27 sixth grade math textbooks, six elementary school math curriculum documents of the final years and three teaching plans of state schools of Boa Vista (RR) were analyzed. Methodologically, this study is assumed as a documentary research, being developed in two stages: in the first stage, we analyze the presence of the divisibility contents in the National Common Curricular Base (NCCB) and in the curricular documents of six Brazilian states (Minas Gerais, Paraná , Pernambuco, Rio de Janeiro, Roraima and São Paulo); In the second stage, we analyzed the presence of divisibility contents in the summaries and within the chapters of 27 math textbooks of the sixth grade. For the analysis of textbooks and curriculum documents, we prepared a script with the divisibility contents, classified as main and secondary. We also elaborate the categories and indicators to compute the presence and absence of the divisibility contents within the 6th grade math book chapters. As a result of the analysis of the six curricular documents researched, we found that, in most of these documents, there was a significant reduction in the divisibility contents as an indication for the study in the sixth year. The result of the research showed a moderately expressive absence of divisibility contents in most of the 27 mathematics textbooks analyzed and, mainly, in the last two PNLDs (2014 and 2017). Only in the math textbooks of the first period (1926 to 1979) did we find the presence of most divisibility contents. The result of the analysis of the National Common Curricular Base (NCCB) Mathematics references pointed out that there is no indication of all the main divisibility contents for the sixth year, which constituted a significant reduction. Considering the BNCC (2017) as the reference adopted for the reformulation of curricular documents of all Brazilian states, it is likely that in the future there will be a significant reduction in the divisibility contents in mathematics textbooks and, consequently, their application in the classroom, since teachers are based on official documents and textbooks to make their annual, semester, and daily plans. However, the choice and application of class divisibility content will depend on each math teacher, which is a topic to be addressed in future research.