Caminhos em Grafos: uma experiência no Ensino Médio

Abstract

The aim of this work is to describe an experience using problems on paths in Graphs with students of the first year of high school from two schools through a case study. There were 48 students from two schools, one located in Resende and another in Quatis, in Rio de Janeiro. The Basic Theory of Graphs initially has simple and intuitive concepts which may be used as powerful tools for solving various kinds of optimization problems. Many of the problems are present in the universe of students, such as the way Google Maps draws the shortest path between the starting point and destination, the procedure that can be used for a GPS to calculate a route, the path that optimizes the work a postman who has to go through several streets (without repetition) and return to the headquarters of the post office, among others. Bring real problems into the classroom is a challenge to the teacher, and solve them with simple techniques in the classroom is an even greater challenge, and this work attempts to perform a little experiment in which this dual task is conducted with some simple techniques from Graphs applied to the students everyday problems. Four basic 50-minute classes are held on Graphs and are taught some of their techniques. But before the classes, two tests are performed: a motivational test (based on Gontijo test) that assesses how students study and enjoy mathematics, and a test involving problems from the universe of the students that could be solved with graphs techniques, but also with what students already know from high school. After the classes, a new motivational test evaluates how much they enjoyed the activities with graphs and a new content test is performed, now being permitted to use the graphs techniques. Finally a survey was made on the results obtained by observing the improvement obtained by the students involved in the process and which had more difficulty, thus completing the experience.