Análise das diferentes representações do conceito de função identificadas em livros didáticos dos anos finais do ensino fundamental

Abstract

Learning the concept of function is essential for students, given its importance in solving everyday problems, other areas of knowledge and mathematics itself. Considering the importance of the concept of function and seeking to understand aspects related to its teaching, this research has as its guiding question: How a collection of mathematics textbooks, approved by the National Textbook Program - PNLD / 2017, for the years Elementary school students approach the concept of function? To this end, we seek theoretical grounding in research on the development of algebraic thinking and on the process of teaching and learning function, especially on the different representations of this concept. The methodological option is a qualitative research in the form of document analysis based on the source of data production, ie a collection of textbooks. The data analysis concluded that the collection of textbooks implicitly addresses the concept of function in the 6th, 7th and 8th grades, as the authors only explicitly present this concept in the 9th grade. Moreover, it was observed that the authors of the textbook collection do not address situations that allow students to understand the articulation between the fields of mathematics. Regarding the different representations of the concept of function, it was found that pattern / generalization is the most explored in all years, but most situations do not require students to generalize in algebraic representation, ie most require only identification of a pattern. It was found that it is in the 9th grade, when the different representations of the concept of function are most explored. It was found that the most explored algebra dimension is the equation, which ends up not favoring a teaching that articulates fundamental equations and functions for the development of algebraic thinking.