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[en] A TAXICAB FOR EUCLID: A NON EUCLIDEAN GEOMETRY IN BASIC EDUCATION / [pt] UM TAXI PARA EUCLIDES: UMA GEOMETRIA NÃO EUCLIDIANA NA EDUCAÇÃO BÁSICACARLOS AUGUSTO GOMES LOIOLA 11 August 2015 (has links)
[pt] A dissertação em tela foi desenvolvida com o intuito de proporcionar ao
professor de matemática uma introdução ao estudo das Geometrias Não
Euclidianas, um assunto carente em nossas salas de aulas tanto do Ensino Básico
como das Licenciaturas em Matemática. Em consonância com os Parâmetros
Curriculares Nacionais, são historicamente construídos os conhecimentos
matemáticos apresentados para discutir o Quinto Postulado dos Elementos de
Euclides e para apresentar a descoberta de novas geometrias. Para ser apresentada
de forma mais detalhada, foi escolhida uma Geometria Não Euclidiana que pode
ser facilmente entendida e contextualizada por alunos do Ensino Médio: a
Geometria do Táxi. Tal geometria, além de possibilitar ligações com outros
conteúdos do Ensino Básico também é um modelo para a geografia urbana,
oferecendo ao alunado a possibilidade de interação com questões motivadoras,
interdisciplinares e próximas do seu cotidiano. É apresentada uma sugestão de
dinâmica que compara os conceitos das distâncias euclidiana e do táxi além de
discutir a definição de circunferência e sua representação tanto na Geometria
Euclidiana como na Geometria do Táxi. Além disso, alguns resultados da
aplicação da referida dinâmica em turmas do 3o. ano do Ensino Médio do C.E.
Professor Ney Cidade Palmeiro, localizado na cidade de Itaguaí no Rio de Janeiro,
também são relatados. Pretende-se que este trabalho seja mais uma contribuição
para o aprimoramento da formação continuada dos professores das escolas de
ensino básico no país. / [en] The present dissertation was developed with the intention of providing the
mathematics teacher an introduction to the study of Non Euclidean Geometry, one
lacking subject in our classrooms as much as the basic education and
undergraduate mathematics. In line with the National Curriculum Parameters,
mathematical knowledge presented to discuss the Fifth Postulate of Euclid s
Elements, and to present the discovery of new geometries are historically
constructed. To be presented in more details, we choose a non Euclidean
Geometry that can be easily understood and contextualized by high school
students: the Taxicab Geometry. This geometry, in addition to allowing
connections with other content of basic education, such geometry is a model for
urban geography, offering the pupils the opportunity to their everyday issues. A
suggested activity to be developed in the classroom by students who compares the
concepts of taxi distance and euclidean distance and besides discussing the
definition of a circle and its representation in both Euclidean Geometry as in the
Taxi appears. Futhermore, some results of implementing this activity in class 3rd.
year of high school the Colégio Estadual Professor Ney Cidade Palmeiro, located
in Itaguaí in Rio de Janeiro, are also reported. It is intended that this work is a
futher contribuition to the improvement of continuing education of teachers of
primary schools in the country.
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A Study On Problem Posing-Solving in the Taxicab Geometry and Applying Simcity Computer GameAda, Tuba, Kurtulus, Aytaç 10 April 2012 (has links) (PDF)
Problem-posing is recognized as an important component in the nature of mathematical thinking
(Kilpatrick, 1987). More recently, there is an increased emphasis on giving students opportunities with
problem posing in mathematics classroom (English& Grove, 1998). These research has shown that
instructional activities as having students generate problems as a means of improving ability of
problem solving and their attitude toward mathematics (Winograd, 1991). In this study, teaching
Taxicab Geometry which is a non-Euclidean geometry is aimed to mathematics teacher candidates by
means of computer game-Simcity- using real life problems posing. This studies’ participants are forty
mathematics teacher candidates taking geometry course. Because of using Simcity computer game,
this game is based on Taxicab Geometry. Firstly, students had been given Taxicab geometry theory
for two weeks and then seperated six each of groups. Each of groups is wanted to posing problem and
solving from real life problems at Taxicab geometry. In addition to, students applied to problem
solving at Simcity computer game. Studens were model into Simcity game. They founded ideal city,
healty village, university campus, holiday village, etc. interesting of each others.
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A Geometria do Taxista como ferramenta de consolidação de conteúdosPavani, Victor Vaz January 2017 (has links)
Orientadora: Profa. Dra. Sinuê Dayan Barbero Lodovici / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Mestrado Profissional em Matemática em Rede Nacional, 2017. / É comum realizarmos revisões de conteúdos com os alunos com o objetivo de sanar
dúvidas e consolidar conceitos. Neste trabalho, apresentamos a Geometria do Taxista,
uma geometria que difere da Geometria Euclidiana na maneira de medir as distâncias.
Pela proximidade com a Geometria Euclidiana, propusemos cinco atividades que possibilitarão a apresentação desse conteúdo, a revisão e a consolidação de muitos temas
abordados nos diversos anos que antecedem o ensino superior. Esperamos que este
trabalho contribua para o aprendizado de alunos e professores. / It¿s a quite usual practice to review some mathematics topics on the middle and,
mainly, high school, several times in order to consolidate math¿s fundamental concepts
among the students. In the present work, we present the Taxicab Geometry, a geometry
which differs from the usual Euclidean Geometry on the way one can measure
distances. Due to the close relationship with the Euclidean Geometry, we propose
some activities that provide us a nice revision and consolidation exercise on several geometric
and algebraic topics relevant to undergraduate students aspirants. We deeply
hope that this work can contribute someway to the teachers¿ and students¿ learning
process.
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A Study On Problem Posing-Solving in the Taxicab Geometry and Applying Simcity Computer GameAda, Tuba, Kurtulus, Aytaç 10 April 2012 (has links)
Problem-posing is recognized as an important component in the nature of mathematical thinking
(Kilpatrick, 1987). More recently, there is an increased emphasis on giving students opportunities with
problem posing in mathematics classroom (English& Grove, 1998). These research has shown that
instructional activities as having students generate problems as a means of improving ability of
problem solving and their attitude toward mathematics (Winograd, 1991). In this study, teaching
Taxicab Geometry which is a non-Euclidean geometry is aimed to mathematics teacher candidates by
means of computer game-Simcity- using real life problems posing. This studies’ participants are forty
mathematics teacher candidates taking geometry course. Because of using Simcity computer game,
this game is based on Taxicab Geometry. Firstly, students had been given Taxicab geometry theory
for two weeks and then seperated six each of groups. Each of groups is wanted to posing problem and
solving from real life problems at Taxicab geometry. In addition to, students applied to problem
solving at Simcity computer game. Studens were model into Simcity game. They founded ideal city,
healty village, university campus, holiday village, etc. interesting of each others.
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