No description available.

CAPES / Com o intuito de desmistificar o estudo de Trigonometria, propõe-se fazer o estudo bibliográfico do seu surgimento e dos povos que deram suas contribuições, permitindo que ela se desenvolvesse ao longo do tempo. Aborda-se aqui algumas das formas de apresentar funções trigonométricas sob diferentes representações. Nesse sentido, ´e discutida a teoria de Raymond Duval, sobre os Registros de Representação Semiótica, que passaram a ser evidenciados nas duas últimas décadas. Tal fato é descrito a fim de evidenciar que o aprendizado de um objeto matemáticos só é possível quando o educando consegue visualizar o trânsito da informação matemática entre formas diferentes de representação. Para facilitar o transito de um objeto matemático entre as diferentes formas de representação, optou-se pela construção do material manipulável. Com o objetivo de obter a opinião de docentes referente a utilização do mesmo como ferramenta facilitadora do trânsito de informações de um objeto matemático, foi elaborada uma oficina. Nela demonstra-se que podemos visualizar diferentes relações trigonométricas de formas diferentes. Os envolvidos foram auxiliados na construção e instrução de uso do material manipulável. Com os dados coletados junto aos participantes dessa oficina, o pesquisador buscou testar a eficácia dessa metodologia de trabalho aplicando oficina semelhante a alunos de segundo ano do Ensino Médio, obtendo bons resultados. Os resultados da pesquisa apontaram que, tanto docentes como discentes passaram a fazer cálculos e evidenciar relações trigonométricas na forma geométrica que, até então, eram conhecidas por alguns deles somente de forma algébrica. / With the intention to demystify the study about Trigonometry, it proposes to the bibliographic study of the appearance of the people who gave their contributions allowing to develop over the times. We also discuss here some ways to demonstrate trigonometric functions in different representations. In this sense is enhanced the theory of Raymond Duval, on semiotics registers representation, which became evident in the last two decades . Such fact is described an evidence that it is only possible the learning of mathematical object , when the student can visualize the process using different forms of representations. To facilitate the transit of a mathematical object , we have opted for the construction of a manipulable material. Both the students and teachers started to make calculations and demonstrate the different ratios between geometric shapes and trigonometric that were only known to some as algebraically. In order to get the teacher´s opinion about the use of manipulable material to make easy the information about mathematical object, a workshop was developed . It has shown that they can see different functions in different ways and were assisted in the construction and instruction of this manipulable material. With the data collected from this workshop participants , the researcher decided to test the effectiveness of this methodology , applying a similar workshop to the students of the second year of high school, getting good results.

The high school pass rate, for mathematics, in South Africa is very low. This is particularly so in trigonometry functions. One of the possible factors leading to this is the traditional method of teaching and learning. This study was undertaken to determine whether the use of Information and Communication Technology (ICT) would influence students’ learning of trigonometry functions. In order to answer this question the teaching and learning instructions developed were based on activity theory (AT) and action, process, object, and schema (APOS) theory. The study followed a non-equivalent control group, quasi-experimental design with a pre- post-test approach. Since it was not possible to randomly select participants for the study, intact groups were used. There were two groups: a control and an experimental one. Both groups wrote a standardized achievement pre-test to establish their comparability at the beginning of the study. While the control group was taught in the traditional way (grade 10-12 syllabus), the experimental group used the software Geogebra. The computer software (Geogebra) and the South African grade 10-12 syllabus for trigonometry functions were used during the lessons of the experimental group. At the end of the study, a similar post-test was administered on both groups to measure the comparative effects of either of the teaching methods on the performance of students. A t-test independent sample statistical analysis was performed on the findings using a statistics package, SPSS. The results of this investigation indicated that the use of the computer software, Geogebra, in the teaching and learning of trigonometry functions improved the performance of the Grade 12 students. / Mathematics Education / M. Sc. (Mathematics Education)

Submitted by Emanuel Varela Cardoso (emanuel.varela@ufcg.edu.br) on 2018-11-12T17:19:37Z No. of bitstreams: 1 CARLOS ANDRÉ CARNEIRO DE OLIVEIRA – DISSERTAÇÃO (PPGMat) 2014.pdf: 2129969 bytes, checksum: 19715b30880dbcde6347a169b0fdbdec (MD5) / Made available in DSpace on 2018-11-12T17:19:37Z (GMT). No. of bitstreams: 1 CARLOS ANDRÉ CARNEIRO DE OLIVEIRA – DISSERTAÇÃO (PPGMat) 2014.pdf: 2129969 bytes, checksum: 19715b30880dbcde6347a169b0fdbdec (MD5) Previous issue date: 2014-04 / Este trabalho apresenta um estudo sobre o ensino da trigonometria no ensino médio, contemplando as recomendações sobre esse conteúdo encontradas nos Parâmetros Curriculares Nacionais e uma breve análise desses conteúdos em alguns dos livros recomendados pelo Guia de Livros Didáticos de Matemática - PNLP 2012. Destacando a formação do conceito de radiano; a extensão das razões trigonométricas seno, cosseno e tangente definidas no triângulo retângulo para as funções Trigonométricas de domínio real, além das demonstrações geométricas das fórmulas da adição e da subtração de arcos das funções seno, cosseno e tangente. Apresenta, também, uma sequência didática, com atividades contemplando os conteúdos destacados acima. As atividades foram elaboradas tendo como referência a teoria da aprendizagem significativa e adaptadas ao uso do software GeoGebra. / This work presents a study on the teaching of trigonometry in high school, in accordance with the recommendations about this subject found in National Curriculum Guidelines (Parâmetros Curriculares Nacionais) and a analysis of the content of some of the books recommended by the Mathematics Textbook Guide - PNLP 2012. It highlight the formation of the concept of radian; the extension of trigonometric ratios sine, cosine and tangent defined in the triangle for Trigonometric functions of real field, in addition to the geometrical proofs of the formula of addition and subtraction arches functions sine, cosine and tangent. It also presents a didactic sequence, with activities covering the highlighted contents above. The activities were developed with reference to the meaningful learning theory and adapted to the use of GeoGebra software.

Made available in DSpace on 2015-03-26T14:00:07Z (GMT). No. of bitstreams: 1 texto completo.pdf: 1720802 bytes, checksum: 1ba4dd33cf192fc803d93c63726a8a5f (MD5) Previous issue date: 2014-03-17 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The following study addresses the theme of auxiliary tools in the teaching and learning of the sine, cosine and tangent functions. Focused on math activities for students in the first year of high school, which investigates the effectiveness of using tools as scientific calculators, theodolites, trigonometric board and GeoGebra software in the teaching and learning of the sine, cosine and tangent functions in basic education. Aimed to make the teaching of trigonometry more meaningful through the manipulation of basic tools. This work is based on the resolution of problem situations aimed at calculating inaccessible measures, measures of the acute angles of a right triangle and the measurements of sine, cosine and tangent of these angles. Still having the use of plotting and analyzing graphs of the sine, cosine and tangent functions in the Cartesian coordinate system. We analyzed how relevant the use of these tools in trigonometry class and especially in the teaching and learning of the sine, cosine and tangent functions. This study indicates that the use of these tools can result in significant advances in the teaching and learning of the sine, cosine and tangent functions in basic education, and in addition to making a challenge to its use by math teachers and researchers. / O presente trabalho abordou o tema ferramentas auxiliares no ensino e aprendizagem das funções seno, cosseno e tangente. Teve como foco atividades de matemática para alunos do primeiro ano do Ensino Médio, que investiga a eficácia da utilização das ferramentas calculadora científica, teodolito, prancha trigonométrica e o software GeoGeobra no ensino e aprendizagem das funções seno, cosseno e tangente na educação básica. Teve como objetivo tornar o ensino de trigonometria mais significativo através da manipulação de ferramentas básicas. Este trabalho valeu-se da resolução de situações problemas que visavam o cálculo de medidas inacessíveis, medidas dos ângulos agudos de um triân- gulo retângulo e as medidas do seno, cosseno e tangente destes ângulos. Tratou-se ainda da plotagem e análise dos gráficos das funções seno, cosseno e tangente no sistema de coordenadas cartesianas. Analisou o quanto é relevante o uso destas ferramentas nas aulas de trigonometria e em especial no ensino e aprendizagem das funções seno, cosseno e tangente. Este estudo indica que o uso destas ferramentas pode resultar em avanços significativos no ensino e aprendizagem das funções seno, cosseno e tangente na educação básica, além de tornar um desafio a sua utilização por professores de matemática e pesquisadores.

Made available in DSpace on 2014-12-17T15:04:45Z (GMT). No. of bitstreams: 1 FranciscoCanindeO.pdf: 417601 bytes, checksum: 726fac10e6cb100b537429348f244630 (MD5) Previous issue date: 2006-06-14 / This study analyses the difficulties that teachers of high school face in the process of the teaching of trigonometry through activities in a construtivist focus. It contains a review of some publications and dissertations related with the study of trigonometry elaborated in the last years by several authors. It resorts to the study of teaching engineering as an instrument used in the research. It also presents a set of activities which will serve as sample to other teachers of mathematics; and points ways for the overcome of the difficulties found / Este estudo analisa as dificuldades que os professores do ensino m?dio enfrentam no processo de ensino de trigonometria atrav?s de atividades dentro de um enfoque construtivista. Ele cont?m uma revis?o de algumas publica??es e disserta??es relacionadas com o estudo da trigonometria elaborada nos ?ltimos anos por diversos autores. Recorre ao estudo da Engenharia Did?tica como uma ferramenta utilizada na pesquisa. Apresenta, tamb?m, um conjunto de atividades o que servir? de amostra para outros professores de matem?tica; e aponta caminhos para supera??o das dificuldades encontradas

Made available in DSpace on 2014-12-17T15:05:02Z (GMT). No. of bitstreams: 1 AnaPPNS_DISSERT.pdf: 1944801 bytes, checksum: f5fc6e6c19f0d79eea29adb6c0b36b1e (MD5) Previous issue date: 2013-07-24 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / Esta disserta??o teve como objetivo discutir a import?ncia do uso de fontes hist?ricas em uma abordagem interdisciplinar para uso em sala de aula. Essa abordagem interdisciplinar de conhecimento que nos propomos fazer envolveu no??es de trigonometria, astronomia b?sica e as hist?rias desses campos, a filosofia natural, a Educa??o Matem?tica e a leitura e an?lise de textos antigos. A fonte hist?rica trabalhada aqui foi o Almagesto, de Ptolomeu, especificamente os cap?tulos 10 e 11 do Livro I. Os cap?tulos referidos tratam da constru??o da tabela de cordas que ser? a base para o mapeamento dos c?us feito por Ptolomeu nos 12 livros seguintes que comp?em o Almagesto. Procurou-se compreender a constru??o da tabela de cordas, de Ptolomeu analisando n?o s? a produ??o matem?tica em si, mas tamb?m o contexto hist?rico, filos?fico e as principais caracter?sticas astron?micas presentes na obra. Ao final foi elaborado um caderno de atividades voltado para professores formados e/ou em forma??o, para que esses profissionais possam se sentir motivados a utilizar a Hist?ria da Matem?tica como ferramenta pedag?gica de ensino e aprendizagem matem?tica

Submitted by (lucia.rodrigues@ufrpe.br) on 2017-03-29T14:39:03Z No. of bitstreams: 1 Tetsuo Usui.pdf: 2577747 bytes, checksum: 9114b8620e50bf459a5b0f41ed172e08 (MD5) / Made available in DSpace on 2017-03-29T14:39:03Z (GMT). No. of bitstreams: 1 Tetsuo Usui.pdf: 2577747 bytes, checksum: 9114b8620e50bf459a5b0f41ed172e08 (MD5) Previous issue date: 2014-08-25 / This work aims to establish a connection among Mathematics with Geography and Astronomy. In this perspective it aims to encompass an interdisciplinary approach in understanding the geographical concepts of the globe, as well as the concepts inherent in the celestial sphere underlying the theoretical foundations of Euclidean Geometry, in order to present a logical and deductive structure of Geometry and Trigonometry in that sphere. This work complements the existing gap between the subjects of Geography and Mathematics in High School because it gives Mathematical supports to the lines (parallels and meridians) and geographic coordinates. Being therefore useful for undergraduate Mathematics students, the same way that teachers of Mathematics and Geography from High School and Elementary Education. Moreover, it also contemplates the sky watchers who wish to have a look at Astronomy from a point of view of Greek antiquity, since the study of Spherical Trigonometry was totally linked to the celestial study. / O presente trabalho tem como objetivo principal estabelecer uma conexão da Matemática com a Geografia e a Astronomia. Nesta perspectiva visa contemplar uma abordagem interdisciplinar na compreensão dos conceitos geográficos do globo terrestre, assim como, dos conceitos inerentes à esfera celeste acoplados na fundamentação teórica de Geometria Euclidiana, a fim de apresentar uma estrutura lógica e dedutiva da geometria e da trigonometria na esfera. O trabalho complementa a lacuna existente entre as disciplinas de Geografia e Matemática do Ensino Médio, pois fundamenta matematicamente, as linhas (paralelos e meridianos) e coordenadas geográficas. Sendo, portanto, útil para alunos de Graduação de Licenciatura em Matemática, da mesma forma que aos professores de Matemática e Geografia do Ensino Médio e Fundamental. Além disso, também contempla aos observadores do céu que queiram olhar a astronomia de um ponto de vista da antiguidade grega, pois o estudo da trigonometria esférica estava totalmente vinculado ao estudo celestial.

Given a hyperbolic surface, the set of all closed geodesics whose length is minimal form a graph on the surface, in fact a so called fat graph, which we call the systolic graph. The central question that we study in this thesis is: which fat graphs are systolic graphs for some surface -we call such graphs admissible. This is motivated in part by the observation that we can naturally decompose the moduli space of hyperbolic surfaces based on the associated systolic graphs. A systolic graph has a metric on it, so that all cycles on the graph that correspond to geodesics are of the same length and all other cycles have length greater than these. This can be formulated as a simple condition in terms of equations and inequations for sums of lengths of edges. We call this combinatorial admissibility. Our first main result is that admissibility is equivalent to combinatorial admissibility. This is proved using properties of negative curvature, specifically that polygonal curves with long enough sides, in terms of a lower bound on the angles, are close to geodesics. Using the above result, it is easy to see that a subgraph of an admissible graph is admissible. Hence it suffices to characterize minimal non-admissible fat graphs. Another major result of this thesis is that there are infinitely many minimal non-admissible fat graphs (in contrast, for instance, to the classical result that there are only two minimal non-planar graphs).

No description available.