Cadeias de Markov - Uma sequência didática para o ensino médio

Abstract

A Markov chain is a stochastic process obtained by the loss of memory. In other words, it is a random time-dependent process that satisfies the Markov property, which is characterized by predictions for future states based on the present state and independent of past states. The chains of Markov have applications in several topics of Physics, Economics, Biology, game theory, etc. This study involves the contents of matrices and probability. Since these contents are part of Basic Education, there are the possibility of an initial study of its concepts through some examples and applications in the 2 year of High school. Thus, in order to present interesting applications of mathematics and motivate students in their learning, this work presents a didactic sequence proposal, that is, a set of activities planned for the group study, with a duration of two class hours. Students will have the opportunity to note that the lines of reasoning used in problem solving are very similar, although the themes of each problem are completely different. Such a situation shows the character of generalization of Mathematics, which makes use of the same tool to solve problems of different origins.