Dinâmica etária da população de Minas Gerais utilizando matriz de Leslie com aplicações didáticas no ensino médio

Abstract

The Leslie model is a mathematical model used to predict the growth and distribution of a female population over time. The model calculates the number of female individuals distributed into age groups in the next period of time, by multiplying the called Leslie matrix by a column matrix that contains the initial female age distribution of the population. We initially address Linear Algebra concepts that are important for understanding Leslie's model, such as eigenvalue, eigenvector and diagonalization of matrices. We made a detailed study of the Leslie matrix. We demonstrate the main results and as an example we apply the model to the female population of the state of Minas Gerais using IBGE information from the year 2010. The objective of this work is to analyze how Leslie's model can contribute to learning multiplication of matrices, providing the student with a visualization of the applicability of matrices. To meet this objective, a didactic sequence was developed and applied, which works constructively on Leslie's model, in a second-year high school class at a public school in the south of Minas Gerais. The didactic sequence is made up of three contextualized activities that introduce the Leslie matrix and a questionnaire to find out students opinions about the activities. To perform matrix multiplications, the Matrix Calculator application was used. The results of applying the didactic sequence were positive, the students enjoyed and felt motivated by the different activity, even with some difficulties and mathematical errors made by them. The use of the application contributed to the positive results, as it made the activity more attractive and provided a deeper understanding of the problem situation. Ultimately, the didactic sequence made it possible to show an application for the matrices content, making the Mathematics class more interesting and tangible.