O ensino de funções no 9º ano: construindo significados para função a partir de generalizações

Abstract

The interest for this research came from the experiences that I had as a teacher in the early years and later as a mathematics teacher in the final years of elementary school, when I could observe how the positive feeling of the students, in relation to mathematics, decreased over the years of Basic Education. According to João Pedro da Ponte, Numbers and Algebra are important themes and present in the educational guidelines of many countries, but, traditionally, numbers are worked at the beginning of schooling, while algebra appears in the final years, causing a rupture between one content and another. Moreover, authors such as James J. Kaput and Caroline Kieran claim that traditionally algebraic contents have been worked as a set of rules of procedures that often have no connection with the other mathematical content nor the situations of the real world. This may contribute to students' lack of interest in understanding mathematical content, especially algebraic content. Contradicting this reductive vision of algebra, several researchers (João Pedro da Ponte, Luis Radford and David Carraher) defend the idea that the main objective for the work with this content should be the development of the algebraic thought, which can be realized through the study of sequences and patterns with a view to the construction of generalizations, since the initial years of schooling. From this perspective, we developed a survey which the research question was "Is it possible to build the concept of function in 9th grade classes of elementary school from the study of sequences focusing on the generalization of patterns?" The survey was conducted in my 9th grade classes of the Escola Municipal Ana Amélia de Queiroz, which is located in the city of Itabirito/MG. The objective of the research was to investigate the possibility of constructing the concept of function in 9th grade classes of elementary school, from tasks involving sequences and contextualized problems with a focus on the generalization of patterns. For this, two activities were prepared, the first consisting of two tasks and worked in three classes and the second with three tasks and applied in only one class. The results obtained point to the difficulty that many students have in constructing mathematical generalizations. Many still use natural language, others can find the rules through trial and error, and only a few perceive the existing regularities, expressing them in mathematical language. These results suggest that working with sequences and patterns should be carried out since the early years, as they are important steps for the development of algebraic thinking and also of functional thinking. The research generated as a product, a booklet for teachers with some notes for the development of a work from sequences and patterns focusing on generalizations as well as problem situations for the construction of the concept of function.