Aspectos históricos das diferentes representações dos números racionais

Abstract

This work presents an investigation defined as qualitative and exploratory research whose study object is the Set of Rational Numbers and its different personalities. Sometimes, the teaching and learning process are more complex for the students because this set of numbers have different interpretations. For this reason, the research chose the analysis of the textbooks from different school ages that approach those concepts/contents. Therefore, the goal is to answer the question: How happens the construction of Set of Rational Numbers and how it is worked in its different personalities into the math didactic books? In Math History it is searched elements to demystify and clarify the Rational Numbers teaching in the Basic Education (Elementary and High school), focusing on your different representations. Based on the historical development of the content, your construction is investigated till the presentation way known currently in the textbooks. In order to know the trajectory of this set of numbers and your presentation in the Basic Education textbooks provided for National Plan of Textbook and Didactic Material – PNLD, it presents an analysis of the textbooks from the collection A Conquista da Matemática that approach the content, during the period of 1980-2020. In that direction, it was verified how this content is explored and showed to the students, considering the different meanings that the Rational Numbers can presented according to the context. For this analysis, it was considered what the official documents indicated in relation to the theme, namely the Official Curricular Proposals, National Curricular Parameters (PCN) and National Common Curricular Bases (BNCC). From this analysis it was possible realize the collection passed for meaningful changes in each official orientation alteration, however, collections from different decades but the same curricular orientation maintained the same characteristics. In relation to the personalities, it was possible to identify, in different decades, your application in exercises, examples or problems, and also, in content explanation. The Math History, the background of this research, provided an acknowledgment of the construction process of the Set of Rational Numbers and your insertion in the textbooks indicated for the PNLD throughout the period studied.