Os livros didáticos de matemática, a variedade de problemas propostos e o Binômio de Newton

Abstract

In this research we analyzed and classified – according to the problem categorization elaborated by Dante (2000) – the activities proposed in the second volumes of the textbook collections approved for the 2015 and 2018 National Program of Textbook and Teaching Material (Programa Nacional do Livro Didático e do Material Didático – PNLD), when referring to the approach of Newton's Binomial as mathematical content, relating them to the legal prerogatives that rule the Brazilian school curriculum at federal and state level. Through a qualitative research with exploratory purposes, in the theoretical framework we presented remarks about the PNLD and guides of textbooks, which were made available to the teachers in public schools for choosing the textbook. We also present theoretical reflections on the legal aspects that guide the organization of the school curriculum in relation to Newton's Binomial and mathematical theory related to the subject, perspectives for Problem Solving and the problem classification formulated by Dante (2000). This theoretical structure supported the qualitative analysis of the activities suggested by six samples of second volumes of the collections approved for the 2015 PNLD and eight samples of second volumes of the collections approved for the 2018 PNLD. Throughout the analysis of the textbooks we concluded that there was a decrease on the number of collections that explore the subject of Newton's Binomial in the 2018 PNLD in relation to the 2015 PNLD. We also verified that the proposed activities are not enough to meet the requirements imposed by the curricular guidelines, nor do they meet the specificities mentioned in the textbook guides. We observed that most of the activities are solvable with mechanical procedures – algorithm exercises. Such problems are in disagreement with what the educational guidelines aim for the teaching of mathematical contents: presentation of problems that lead to reflections, questions, causing students to create and seek resolution strategies and thus develop skills, produce knowledge in a pleasurable and motivating way. Therefore, we suggest that textbook edition incorporate the information contained in the official documents and textbook guides so that they may be actual instruments that provide greater effectiveness to the learning process, along with other educational policies and practices.