Uma caracterização de enunciados e orientações para usos dos problemas matemáticos a partir de exemplares de revistas pedagógicas publicados em São Paulo (1893-1961)

Abstract

This study presents the outcome of a research which aimed at characterizing the command words and instructions for the usage of mathematical problems in pedagogical journals’ issues from Brazil between 1893 and 1961. As the main references for the understanding of mathematical problems, the studies of Virgens (2014), Fernandes (2017) and Souza (2021) were used; for the historic research on mathematical problems, Nascimento (2018); Souza (2021) for arithmetic problems and knowledge; and Santos (2017) e Santos (2022) for geometric problems and knowledge. The script and aim of the study were formulated from the following problematic issue: how is it possible to characterize the command questions and instructions for mathematical problems application in pedagogical journal issues from Brazil published between 1893 and 1961? In order to answer that question, sources were examined by two approaches: a first one by mapping the pedagogical issues from the Repositório Institucional da Universidade de Santa Catariana (RI-UFSC) – Institutional Repository of the Santa Catarina University. At a second approach, a charactetization of the command questions and instructions mapped was carried out. There were eight hundred sixty-six journal issues from different states identified, from which two hundred ninety presented wording or instructions for mathematical problem applications. As most journals were located in the state of São Paulo, analyzing the issues from that state with the largest number of copies and with wording/instructions for the application of mathematical problems within the chronological period from 1893 and 1961. Thus, it analyzed fifty-two journal issues such as A Eschola Publica (1893-1897); Revista de Ensino (1902-1918); Revista Educação (1927-1946); and Revista de Educação (1930-1961). For the collected data systematization, a chronology was stablished with a first period between 1893 and 1930, and a second one between 1931 and 1961. It was possible to identify arithmetic and geometric problems for topic as numbers (Roman numbers and fractions, mathematical operations) and angles, there being a larger presence of practical and narrative question commands in the first years, however it was possible to associate that, due to the need of new teaching practices, the command questions of arithmetic and geometric problems became of a real-situation type, without a sequence, arithmetic tales, incomplete and proposed for the children. As regards the instruction characterization, the authors pointed out that, between 1893 and 1930, teachers should gradually introduce the problems, in oral and written form, making use of objects when they would approach aspects related to geometric shapes (cube, sphere, cylinder, square, and rectangle), ratios and units of measurement, whereas between 1931 and 1961 they should gradually introduce the problems by written form through everyday situations.