Equações diferenciais ordinárias e modelagem matemática: aplicações a fenômenos reais e propostas para o ensino na educação básica

Abstract

This study investigates the role of first-order Ordinary Differential Equations (ODEs) as mathematical modeling tools. The theoretical framework addresses linear and separable ODEs, as well as the Existence and Uniqueness Theorem for Initial Value Problems (IVPs). Subsequently, two real-world applications of significant social and historical relevance are developed: an analysis of the evolution of dengue cases in the city of Sorocaba, São Paulo, in 2024, using the Verhulst logistic model; and the radiocarbon dating of “Ötzi, the Iceman”, based on the radioactive decay model. To bring mathematical concepts closer to students in Basic Education, an educational product consisting of two lesson plans is proposed. The first, designed for first-year upper secondary school students, uses a coin-toss experiment to introduce the concept of radioactive decay and its representation through exponential functions. The second, implemented in a ninth-grade lower secondary school class, replaces coins with dice in a probabilistic experiment representing radioactive decay. The results of the practical activities indicated that experimentation and the historical approach contributed to student engagement, facilitated the understanding of abstract concepts, and highlighted the potential of contextualized situations as a teaching resource in Mathematics education.