Modelagem matemática e sequência didática: caminhos para um ensino contextualizado de funções exponenciais no ensino médio

Abstract

This research investigated the use of mathematical modeling and a didactic sequence as strategies to promote contextualized teaching of exponential functions in basic education. The study sought to identify which analyses emerge from the implementation of a differentiated pedagogical proposal in the face of historical learning difficulties and the predominantly technical character that marks the teaching of this content in high school. The general objective was to analyze a didactic sequence based on mathematical modeling for teaching exponential functions in a 3rd grade high school class at a public school in Piauí. Methodologically, a qualitative-quantitative approach was adopted, of an exploratory and interventionist nature, framing it as action research. Data collection instruments included questionnaires, observations, and records of activities developed in four main stages: application of a diagnostic pre-test; classes on fundamental concepts and exponentiation; practical workshops involving GeoGebra software, games such as the Tower of Hanoi and the Legend of Chess, and experiments on Newton's Law of Cooling and pharmacokinetics; Finally, a post-test was conducted. Initial results revealed significant conceptual weaknesses, with 88% of participants showing difficulties in reading graphs and translating real-world phenomena into mathematical language. However, after the interventions, a significant improvement in student performance and engagement was observed, with the majority of the class achieving high levels of proficiency and improvement in external assessment scores, such as SAEPI (Educational Assessment System of the State of Piauí). It is concluded that the articulation between modeling and didactic sequence favors the understanding of the exponential function as a tool for investigating reality, overcoming the mechanical memorization of formulas. The study contributed to mathematics education by offering a pedagogical roadmap that stimulates student protagonism and the development of critical and scientific reasoning.