Histórias do sistema de numeração decimal produzidas na pós-graduação brasileira (1990-2018): potencialidades para o ensino de aritmética nos anos iniciais

Abstract

This dissertation is a result of an investigation linked to two research projects funded by the National Council for Scientific and Technological Development (CNPq). It comprises a bibliographical documentary study in the modality of a research on thesis and dissertations about the History of Mathematics produced in Brazilian stricto sensu Postgraduate programs. The corpus has analyzed short course books of the Brazilian Society of Mathematical History (SBHMat), proceedings of national academic events discussing the History of Mathematics (SNHM), Mathematical Education (ENEM), among others. Worth mentioning too articles published in journals qualified by the evaluation system of the Higher Education Personnel Improvement Coordination (CAPES). Our objective was to characterize the histories that make it possible to teach the Decimal Numbering System in Primary school, based on researches that deal with history for the teaching of Mathematics in that country. In this sense, we established the following research question: how was the history for the teaching of the Decimal Numbering System in Primary school treated in Brazil, in a pedagogical sense, in the History of Mathematics productions ranging from 1990 to 2018? To answer this question, we ground our reflections on four concepts established by Mendes (2006; 2008; 2013; 2015; 2017): 1) history as an agent of cognition in Mathematical Education; 2) history as a cognitive reorganizer in mathematical learning; 3) history of mathematics as a didactic and conceptual mediator and 4) history for the teaching of mathematics as a didactic reinvention for the classroom. To accomplish this study, we initially conducted a survey of these productions, dividing them into three trends in the History of Mathematics: 1) Mathematics History and Epistemology; 2) History for the Teaching of Mathematics and 3) History of Mathematical Education. Then, we took into consideration the productions listed in the second trend, selected and grouped those which explored histories in order to teach the Decimal Numbering System in Primary school, so as to characterize these productions based on an analytical tool elaborated from the four concepts previously mentioned. Subsequently, we proposed some pedagogical suggestions and didactic activities to support the teacher's work in the classroom. Finally, we combine the activities that deal with this content, potentially elaborated in the researches, with the content addressed in 4th and 5th grades textbooks. Based on the results, we understand that these activities can be implemented by the teacher in the classroom. Likewise, we point out that there are researches that suggest activities, but some of them need adaptations so they can be effectively used in a didactic way by the teacher. Therefore, we consider that the researches potentially related to histories for the teaching of the Decimal Numbering System in Primary school, when they do exist, can be inserted in classrooms in association with textbook contents, and thus enrich the teacher's didactic approach in the teaching of arithmetic within the importance of the students learning.