Submitted by Rosivalda Pereira (mrs.pereira@ufma.br) on 2017-08-25T20:24:28Z No. of bitstreams: 1 JandersonFreitas.pdf: 2087995 bytes, checksum: e49b1008df3093f81aeb841870a06df9 (MD5) / Made available in DSpace on 2017-08-25T20:24:28Z (GMT). No. of bitstreams: 1 JandersonFreitas.pdf: 2087995 bytes, checksum: e49b1008df3093f81aeb841870a06df9 (MD5) Previous issue date: 2017-05-08 / The paper presents problem solving using Graph Theory and Euler’s Theorem. The research performs specific activities in high school involving graphs in various applications of the Euler relation as a problem solving method with Graph Theory. The relationship of Euler is presented in a Geometric view and by the graphs planning. The research proposes a link between the students ’daily problems with the modeling of problem situations by the Graph Theory, specifically the planar graphs solved with the implementation of Euler’ s Theorem focused on the teaching of basic mathematics. Applications of Graph Theory are shown in solving problems with the bridges of the city of Barra do Corda and the students’ school life. / O trabalho apresenta a resolução de problemas utilizando a Teoria dos Grafos e o Teorema de Euler. Uma pesquisa que executa atividades específicas no ensino médio envolvendo grafos em várias aplicações da relação de Euler como método de resolução de problemas com Teoria dos Grafos. A relação de Euler é apresentada em uma visão Geométrica e pela planificação dos grafos. Propondo um elo entre os problemas do cotidiano dos alunos com a modelagem de situações problema pela Teoria dos Grafos, especificamente os grafos planares resolvidos com a implementação do Teorema de Euler voltado ao ensino de matemática básica. São mostradas aplicações da Teoria dos Grafos na resolução de problemas com as pontes da cidade de Barra do Corda e da vida escolar dos alunos.

Made available in DSpace on 2014-06-11T19:24:50Z (GMT). No. of bitstreams: 0 Previous issue date: 2008-02-27Bitstream added on 2014-06-13T20:32:18Z : No. of bitstreams: 1 proenca_mc_me_bauru.pdf: 1462830 bytes, checksum: 518c15b861d67ff8aa5024e7c4385c2f (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / O objetivo da pesquisa foi analisar o conhecimento declarativo de alunos do ensino médio sobre polígnos e poliedros em termos de seus atributos difinidores, das relações subordinadas e supra-ordenadas e de seus exemplos e não-exemplos. A concepção teórica utilizada foi o modelo de formação de conceitos de Klausmeier e Goodwin (1977). Os participantes foram 253 alunos do ensino de uma escola de rede oficial pública de ensino de Bauru, que responderam, na primeira fase, um questionário, uma prova matemática, um testes de atributos definidores, um teste de exemplos e não-exemplos e um teste de relações subordinadas e supra-ordenadas. Na segunda fase, foram selecionados, aleatoriamente, três alunos com média abaixo de cinco pontos e três alunos com média igual ou superior a cinco pontos para participarem de uma entrevista. Os resultados coletados na primeira fase, analisados quantitativamente, mostram que no teste de atributos definidores a nota média foi de 6,03, sendo que não houve diferença significativa entre as séries (p=0,084). No teste de exemplos e não-exemplos a nota média 5,59 refletiu o desempenho dos participantes e não foram encontradas diferenças significativas entre as séries (p=0,057). Em relação ao teste de relações subordinadas e supra-ordenadas a nota média dos participantes foi 5,64, sendo que a nota média obtida pela primeira série diferiu significativamente da nota média obtida pela terceira série (p=0,024). Em relação aos dados da segunda fase, analisados qualitativamente, alguns participantes pensavam, de maneira equivocada, sobre os atributos definidores de polígnos e de poliedros. Os atributos irrelevantes não interferiam na identificação das figuras selecionadas do teste de exemplos e não-exemplos como exemplos polígnos. / The objective of this reseach was to analyse the declarative konowledge of students from Elementary School Teaching about polygons and polyhedrons in terms of their defining atributes, the subordinate relations and supraordinate and their examples and no-exemples. The theoretical conception used was the model of formation from Klausmeier and Goodwin (1977)'s concepts. The participants were 253 students from Elementary School Teaching of one school of the Oficial Public Network from Bauru, who answered, in the first phase one questionnaire, one math test, one test of defining attributes, one test of examples and no-examples and one test of subordinate relations and supraordinate. In the second phase, three students were randomly selected with the average below five points and three students with equal average or higher to five points who participated in an interview. The collected results in the first phase, quantitatively analysed, showed that in the test of defining attributes, the average grade was 6,03, so there was no significative difference among the series (p=0,084). In the test of examples and no-examples the average grade 5,59 reflected the performance of the participants and no significative differences were found among the series (p=0,057). In the relation to the test of subordinate relations ans supraordinate the average grade of the participants was 5,64, so the average obtained by the first grade had no significative difference from the average obtained by the third grade (p=0,024). In relation to the data of the second phase, qualitativety analysed, some participants thought wrongly about the defining attributes of polygons and polyhedrons. The irrelevants attributes did not interfere in the identification of the selected pictures of the test of examples and no-examples as polygons examples.

Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2015-01-14T13:35:24Z No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Dissertação - Helen Kássia Coelho Gontijo - 2014.pdf: 1533837 bytes, checksum: 06babe56caa781b8fdc2bc90de1a2947 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-01-14T14:11:25Z (GMT) No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Dissertação - Helen Kássia Coelho Gontijo - 2014.pdf: 1533837 bytes, checksum: 06babe56caa781b8fdc2bc90de1a2947 (MD5) / Made available in DSpace on 2015-01-14T14:11:25Z (GMT). No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Dissertação - Helen Kássia Coelho Gontijo - 2014.pdf: 1533837 bytes, checksum: 06babe56caa781b8fdc2bc90de1a2947 (MD5) Previous issue date: 2014-07-25 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This work is based on the study of the polyhedrons and the Euler's Theorem, by applying strategies of teaching using the concrete material, provoking improvements in the reasoning and in the geometrical perception the Euler's Theorem. Not mentioning a bit of history of tracks already made by several mathematicians who have contributed to the study of geometry, where the ideas previously applied by them teach us and help every day. Going to the presentation of a few concepts and de nitions about polyhedrons, as well as the demonstration that exist only ve polyhedrons of Plato. We've tried to expose the demonstration of the Euler's Theorem, through two researchers, Adrien Marie Legendre and of the professor Zoroastro Azambuja Filho, considering them very interesting and easy to understand. However, in the perspective that going from the concrete one is an alternative to improve the quality of teaching, it has been selected the activity Geometry of cutting soaps , which is in an article of Ana Maria Kale , see at [10], and Geometry of straws , at [9], which are based on work experiences of the same author. Before the new technologies we have opted for the mathematical software Poly, available on http://www.peda.com/poly which allows a better visualization of polyhedrons of di cult construction. All these activities have been presented to the students of the second grade in the Secondary Education to verify the Euler's Theorem through concrete experiences, obtaining this way a useful and creative geometrical knowledge, conquering the students' participation and interest. / Este trabalho baseia-se no estudo dos Poliedros e o Teorema de Euler, aplicando estratégias de ensinar usando o material concreto, desencadeando melhoras no raciocínio e na percepção geométrica do Teorema de Euler. Não deixando de mencionar um pouco da história de caminhos já trilhados por vários matemáticos que contribuíram para o estudo da geometria, onde as ideias anteriormente aplicadas por eles nos ensinam e ajudam no dia-a-dia. Partindo então para apresentação de alguns conceitos e de nições sobre Poliedros, bem como a demonstração de que só existem cinco poliedros de Platão. Buscamos expor a demonstração do Teorema de Euler, por dois pesquisadores, Adrien Marie Legendre e do professor Zoroastro Azambuja Filho, considerando-as bem interessantes e de fácil compreensão. Contudo, na perspectiva de que partir do concreto é uma alternativa para melhorar a qualidade de ensino, foi selecionada a atividade Geometria dos cortes de sabão , que se encontra em um artigo de Ana Maria Kale , veja em [10] e Geometria de Canudos , em [9], que são fundamentados em experiências de trabalho da mesma autora. Frente às novas tecnologias optamos pelo uso do software matemático Poly, disponível em http://www.peda.com/poly, que permite uma melhor visualização de poliedros de difícil construção. Todas estas atividades foram apresentadas para os alunos do 2o ano do Ensino Médio para a veri cação do Teorema de Euler através de experiências concretas, obtendo assim um conhecimento geométrico criativo e útil, conquistando a participação e interesse dos estudantes.

Orientador: Nelson Antonio Pirola / Banca: Odalea aparecida Viana / Banca: Regina Maria Pavanello / Resumo: O objetivo da pesquisa foi analisar o conhecimento declarativo de alunos do ensino médio sobre polígnos e poliedros em termos de seus atributos difinidores, das relações subordinadas e supra-ordenadas e de seus exemplos e não-exemplos. A concepção teórica utilizada foi o modelo de formação de conceitos de Klausmeier e Goodwin (1977). Os participantes foram 253 alunos do ensino de uma escola de rede oficial pública de ensino de Bauru, que responderam, na primeira fase, um questionário, uma prova matemática, um testes de atributos definidores, um teste de exemplos e não-exemplos e um teste de relações subordinadas e supra-ordenadas. Na segunda fase, foram selecionados, aleatoriamente, três alunos com média abaixo de cinco pontos e três alunos com média igual ou superior a cinco pontos para participarem de uma entrevista. Os resultados coletados na primeira fase, analisados quantitativamente, mostram que no teste de atributos definidores a nota média foi de 6,03, sendo que não houve diferença significativa entre as séries (p=0,084). No teste de exemplos e não-exemplos a nota média 5,59 refletiu o desempenho dos participantes e não foram encontradas diferenças significativas entre as séries (p=0,057). Em relação ao teste de relações subordinadas e supra-ordenadas a nota média dos participantes foi 5,64, sendo que a nota média obtida pela primeira série diferiu significativamente da nota média obtida pela terceira série (p=0,024). Em relação aos dados da segunda fase, analisados qualitativamente, alguns participantes pensavam, de maneira equivocada, sobre os atributos definidores de polígnos e de poliedros. Os atributos irrelevantes não interferiam na identificação das figuras selecionadas do teste de exemplos e não-exemplos como exemplos polígnos. / Abstract: The objective of this reseach was to analyse the declarative konowledge of students from Elementary School Teaching about polygons and polyhedrons in terms of their defining atributes, the subordinate relations and supraordinate and their examples and no-exemples. The theoretical conception used was the model of formation from Klausmeier and Goodwin (1977)'s concepts. The participants were 253 students from Elementary School Teaching of one school of the Oficial Public Network from Bauru, who answered, in the first phase one questionnaire, one math test, one test of defining attributes, one test of examples and no-examples and one test of subordinate relations and supraordinate. In the second phase, three students were randomly selected with the average below five points and three students with equal average or higher to five points who participated in an interview. The collected results in the first phase, quantitatively analysed, showed that in the test of defining attributes, the average grade was 6,03, so there was no significative difference among the series (p=0,084). In the test of examples and no-examples the average grade 5,59 reflected the performance of the participants and no significative differences were found among the series (p=0,057). In the relation to the test of subordinate relations ans supraordinate the average grade of the participants was 5,64, so the average obtained by the first grade had no significative difference from the average obtained by the third grade (p=0,024). In relation to the data of the second phase, qualitativety analysed, some participants thought wrongly about the defining attributes of polygons and polyhedrons. The irrelevants attributes did not interfere in the identification of the selected pictures of the test of examples and no-examples as polygons examples. / Mestre

Submitted by Clebson Anjos (clebson.leandro54@gmail.com) on 2015-11-03T18:43:36Z No. of bitstreams: 1 arquivototal.pdf: 42429990 bytes, checksum: 73b94c005d54caae39822d3081337167 (MD5) / Approved for entry into archive by Clebson Anjos (clebson.leandro54@gmail.com) on 2015-11-03T19:05:57Z (GMT) No. of bitstreams: 1 arquivototal.pdf: 42429990 bytes, checksum: 73b94c005d54caae39822d3081337167 (MD5) / Made available in DSpace on 2015-11-03T19:05:57Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 42429990 bytes, checksum: 73b94c005d54caae39822d3081337167 (MD5) Previous issue date: 2014-06-13 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work we study the principle of the Deductive and Experimental Geometry trated in the High School. We begin the work with a set of axioms of the Plane Geometry, and we follows the work studing some topics of the Spacial Geometry. To illustrate some definitions and results ao long of the work, some solids are constructed with paperboard, straw and etc. / Neste trabalho estudamos os princípios da geometria dedutiva e experimental tratada no Ensino Fundamental e Médio. Iniciamos o trabalho com um conjunto de axiomas da geometria plana, e seguimos o mesmo estudando alguns tópicos da geometria espacial. A fim de ilustrar algumas definições e resultados discutidos ao longo do trabalho, alguns sólidos são construídos com cartolina, isopor, canudos e etc.

The thesis is destined mainly for high school teachers and students of descriptive geometry. Above all it deals with the intersection and the construction of pyramids and prisms in projections. Students can meet with these phenomena at high schools during lessons of descriptive geometry. The constructions of the intersections of figures are demonstrated on solved tasks. The tasks are processed in graphic programmes GeoGebra and Cabri 3D prospering from the following advantages and facilities of these programmes: a stepping of the construction, a contour accentuation or a secretion of auxiliary lines etc. Besides these solved tasks, there are also some unsolved tasks for practice at the ends of chapters. The introductory chapter contains definitions and characters of common polyhedrons and regular (Platonic) figures. The thesis consists of web sites, a printed version and an enclosed printed version in .pdf format.

Title: Educational environment additive polygons and polyhedrons Summary: The main intention of the work is to introduce a new mathematical educational environment that would be especially attractive for pupils in the grades 6. -9., but also in the secondary schools, universities or primary schools The work consists of six parts. In the introduction are mentioned the reasons that led me to choose this topic. The second chapter describes the theoretical basis of the work. The third section describes in detail the environment of additive polygons, both its aspects - mathematical and educational one. Analogously, as it is in the third chapter, is processed the fourth chapter that is dedicated to the environment of additive polyhedrons. The fifth chapter is devoted to the linking of the environment of additive polygons and polyhedrons into the linear algebra. In conclusion are provided further opportunities of work with this environment.

狄氏分配(Dirichlet distribution)可視為高維度的貝他分配，其應用範圍包括貝氏分析的共軛先驗分配，多變量資料建模。當狄氏分配參數α_1=⋯=α_(n+1)=1時，可視為在n維空間的單體(simplex)均勻分配。高維度空間的不規則區域均勻分配有很多的應用，例如：在不規則區域中物種調查的方區抽樣和蒙地卡羅模擬(Monte Carlo Simulation)常需要多面體的均勻亂數，利用狄氏分配可更迅速的生成不規則區域的均勻亂數。本論文主要是評估由Cheng et al. (2012) 設計的R統計軟體套件“rBeta2009” [8]，並探討如何利用此套件中的狄氏分配演算法來生成其他多變量分配，如：(i)反狄氏分配(Inverted Dirichlet distribution) (ii) Liouville分配，以及(iii)由線性限制式所圍成的多面體空間之均勻分配。本文也利用電腦模擬的方式驗證本文介紹之方法比現有的電腦軟體中的演算法有效率(以電腦執行時間來看)。 / Dirichlet distributions can be taken as a high-dimensioned version of beta distributions, and it has many applications, such as conjugate prior distribution in bayesian Inference and construction of the model of multivariate data. When the parameters of Dirichlet distributions are α_1=⋯=α_(n+1)=1, it can be regarded as uniform distribution within a n-dimensioned simplex. High-dimensioned uniform distribution in irregular domains has various applications, such as species surveys in quadrats sampling and Monte Carlo simulation, which often need to generate uniform random vectors over polyhedrons. With Dirichlet distributions, it is more efficient to generate uniform random vectors in irregular domain. This article evaluated the module in R, “rBeta2009” [8], originally designed by Cheng et al. (2012), and discusses how to generate other multivariate distributions by using the Dirichlet algorithm in the package, including generation of (i) Inverted Dirichlet random vectors (ii) Liouville random vectors, and (iii) uniform random vectors over polyhedrons with linear constraints. The article also verified that the method is more efficient than the older package in R. (by comparing the CPU time.)