MATHEMATICAL MODELING IN THE TEACHING OF EXPONENTIAL FUNCTIONS: A DIDACTIC SEQUENCE WITH THE TOWER OF HANOI AND THE LEGEND OF CHESS

Abstract

This article analyzes the contributions of mathematical modeling to the teaching of the exponential function through a didactic sequence developed with 3rd grade high school students from a public school in Palmeirais, Piauí, Brazil. The qualitative research was conducted using an experimental approach and based on active methodologies, aiming to investigate how the use of concrete tools can enhance the understanding of exponential growth. The pedagogical intervention was structured in workshops involving two investigative scenarios: the Tower of Hanoi and the Legend of Chess. In the first, students explored the relationship between the number of discs and the minimum number of moves, identifying the exponential model 2ⁿ – 1. In the second, they analyzed the doubling of grains on the chessboard, constructing a model of the sum of a geometric progression. During the activities, they formulated hypotheses, organized data in tables, constructed graphs, and interpreted the results. The findings show that the approach fostered the development of logical reasoning, the understanding of exponential behavior, and the active participation of the students. It is concluded that mathematical modeling, combined with the use of manipulable materials, constituted an effective and meaningful strategy for teaching exponential functions.