Análise e simulação da conta de água: uma proposta de ensino de funções poligonais através da resolução de problemas

Abstract

This dissertation aims to present an educational product as a proposal for teaching polygonal functions via teaching-learning-assessment through Problem Solving methodology as pedagogical approach. The mentioned product, which can be applied in High School groups, consists of developing a water bill simulator in a spreadsheet software. This work is composed of an Introduction, two chapters and Final Considerations. In the Introduction, I present my academic trajectory, my motivations for choosing the theme and how they were articulated until they culminated in this dissertation, as well as a summary of its structure. In the first chapter, a literature review about problem conceptions and Problem Solving was done, followed by a brief discussion about new technologies – in particular simulations and the use of electronic spreadsheets – and their importance in the educational context. At the end of this chapter, polygonal functions, examples, propositions and theorems are presented, which can be used to help simulate water bills. The educational product is characterized in the second chapter, in which technical and legal information about the billing system and the tariff structure of water bills in the State of Bahia are displayed, so that we are able to present the proposed activity. The educational product is structured in three stages. The first step of the activity is to understand and discuss general aspects and characteristics of the water bills brought by students. The second part of the activity intends, based on the teaching-learning-assessment through Problem Solving methodology, to prompt students to think about functional relationships associated with the context of the water bills, by seeking to relate the volume of water consumed and the amount paid for each range of consumption to piecewise functions. The third, and last, stage of the activity consists of building a water bill simulator in an electronic spreadsheet program, thus resuming the analyzes carried out in previous activities. In the last chapter of this dissertation, final remarks were made, followed by an appendix containing a brief tutorial on how to use some features of a spreadsheet program.