Um estudo sobre o ensino do conceito de número e suas relações a partir da análise de um conjunto de manuscritos de Charles Sanders Peirce (1839-1914) - Oliveira, Alexandre Souza de (2020)
In this work we present a study on the teaching of the concept of number and its relations from the analysis of a set of manuscripts dedicated to arithmetic, which is organized in a collection entitled The New Elements of Mathematics by Charles Sanders Peirce, organized and published in 1976 by Carolyn Eisele. For that, we selected some manuscripts in which Peirce not only criticizes the textbooks dedicated to the teaching of arithmetic in his time, but also others that propose new ways to introduce the notion of number in elementary education. This study shows that Peirce's criticism, as well as his teaching proposal, were related to the expansion of elementary education programs in the United States of America in the 19th century, motivated by the need to propose a curriculum revision of the teaching of school mathematics. This review involved debates with the objective of proposing new teaching methods, as well as training teachers who were qualified to meet new demands related to commerce, industry and scientific research. In this context, Peirce stated that the teaching of elementary arithmetic did not sufficiently meet the practical and scientific demands of that time. Thus, through the analysis of Peirce's proposal to introduce the notion of number in the teaching of elementary arithmetic, we aim here to point to aspects that sometimes approximate and sometimes separate Peirce's proposal from other textbooks published at that time. In this respect, our research indicated that the concept of number in textbooks published in the last quarter of the 19th century was approached in its most practical sense, using resources that would allow to apprehend it through its application, always emphasizing the relationship of the number to the quantity it expresses. In this way, the proposal sought, through counting and, therefore, the concrete quantity of objects counted, to generalize the concept of number and, in an inverse movement, apply it to practical and concrete everyday situations. Faced with this, Peirce proposes an alternative way, to make children understand that the number is not a mere quantity, nor an intrinsic property of the objects counted, but an idea related to them in some way. It deals with the number in its most essential aspect and proposes a more “scientific” teaching, without, however, departing from the reality of children. This research was based on original documents on which we focus an analytical look based on the three spheres of analysis, namely, historiographic, epistemological and contextual