Submitted by Bruna Rodrigues (bruna92rodrigues@yahoo.com.br) on 2016-09-14T11:48:45Z No. of bitstreams: 1 DissMCM.pdf: 4167196 bytes, checksum: 2c2cab88912171633575dbfd411acd9d (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-09-15T13:04:39Z (GMT) No. of bitstreams: 1 DissMCM.pdf: 4167196 bytes, checksum: 2c2cab88912171633575dbfd411acd9d (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-09-15T13:04:47Z (GMT) No. of bitstreams: 1 DissMCM.pdf: 4167196 bytes, checksum: 2c2cab88912171633575dbfd411acd9d (MD5) / Made available in DSpace on 2016-09-15T13:04:59Z (GMT). No. of bitstreams: 1 DissMCM.pdf: 4167196 bytes, checksum: 2c2cab88912171633575dbfd411acd9d (MD5) Previous issue date: 2015-08-21 / Não recebi financiamento / The main objective of this work is to make students understand the mathematical foundations for the operation of Global Positioning System (GPS). The research was done in a school in the state of São Paulo with students of the second year of high school and the analysis was done in a qualitative as well as quantitative manner. Two sheets of directed activities, were used so students were induced to understand what happens at the intersection of spherical surfaces and this was carried out in three stages. During the first activity, students reviewed the circles of intersection of ideas, both geometrically and algebraically. In the second activity, these ideas were enlarged to spheres. The operation of the GPS was exposed in the activity three using PowerPoint slides, so goal that students learned a little about the history of the GPS creation and its operation, and the central theorem of this work: "If four spherical surfaces intersect and their centers are not coplanar, then this intersection is a single point." The Didactic Engineering was the methodology used for the survey. The result indicates that although many students present difficulties during the activities, everyone understood the mathematical principles behind the GPS operation. / O principal objetivo desse trabalho é fazer com que os alunos entendam os fundamentos matemáticos para o funcionamento do Sistema de Posicionamento Global (GPS). A pesquisa foi feita numa escola no interior do Estado de São Paulo, com alunos do 2o ano do Ensino Médio e a análise dos resultados foi feita de maneira qualitativa e também quantitativa. Por meio de duas folhas de atividades dirigidas, os alunos foram induzidos a entenderem o que acontece na intersecção de superfícies esféricas. Durante a primeira atividade, os alunos revisaram as ideias de intersecção de circunferências, tanto geometricamente como algebricamente. Na segunda atividade, estas ideias foram extrapoladas para esferas. O funcionamento do GPS foi exposto na atividade três, por meio de slides em Power Point, com o objetivo de que os alunos aprendessem um pouco sobre a história da criação do GPS, do seu funcionamento e sobre o teorema central desse trabalho: “Se quatro superfícies esféricas se intersectam e seus centros são não coplanares, então essa intersecção consiste de um único ponto”. A Engenharia Didática foi a metodologia utilizada para a pesquisa. O resultado final indica que, apesar de muitos alunos apresentarem dificuldades durante as atividades, todos entenderam os princípios matemáticos por trás do funcionamento do GPS.