O Conceito de Sequências Numéricas: Análise de Materiais Didáticos do Ensino Médio e Ensino Superior

Abstract

This research aims to discuss issues related to the process of developing algebraic thinking, in particular, the concept of numerical sequence. Therefore, it analyzes how this concept is presented in two collections of textbooks of high school three schools in the city of Itaqui, approved by PNLD (2015) and a specific section of a work of calculation, and the relationship the concept of sequence with the concept of limit. The theoretical and methodological choice was based on a qualitative research through a documentary analysis. More specifically, we used content analysis to work with documents. Data analysis enabled us to verify that the Number Sequences, in high school collections, are covered mostly in chapters related to progressions (arithmetic and algebraic), or addressed practically only in the 1st year. As for the stages of a pattern, the C1 collection explored the three phases in more activities than C2 collection. Regarding semiotic representations, the C1 collection opted for figural representation in a larger number of activities that C2. There are changes in cognitive emphasis on numerical treatment C2 instead of C1. However, in the C2 collection teacher's manual, there are suggestions to work with the 3 phases of a standard and the figural representation as a starting record. It was found that the collection C1 approaches the limit concept and convergence intuitive, allowing mobilization advanced mathematical aspects of thinking. Regarding the calculation section of the book (C3), it was noticed that the sequences have been proposed in the same series chapter, and more are proposed activities for the latter. In the sequence of activities emphasized that the 3 phases of a standard, since most of the activities required generalizing the process, a process important in abstraction. Regarding cognitive changes, there was an excessive algebraic treatment, justified in Higher Education. The C3 collection addressed harder the features of Advanced Mathematical Thinking, as expected due to the education level. Given these results, we emphasize the importance of working with high school students and higher education, in the standard it is understood as a structural axis of numerous concepts and fundamental in the development of algebraic thinking and advanced mathematical thinking.