This thesis deals with the mathematical knowledge of the geometry, which were used in the Gothic period. This is mainly the knowledge that was reflected in the architecture. It is also concerned with the geometrical modeling of the Gothic architectural elements using computer systems of dynamic geometry and potential use of these figures in the mathematics, because the visible connection between theory and practice is very good motivation. The thesis briefly introduces characteristic features of the Gothic style and also describes the historical background that enabled the rise of this new style. This work shows closer also how Gothic building was technically built up. Part of this work is dynamic geometric computer models, which were made with using the gathered information. The interactivity of these models helps students to get better insight into the principles of Gothic architecture elements and also into geometric relationships used in these elements.

Esta tese consiste em uma Metodologia para reusar ou criar objetos de a-prendizagem (OA) de Matemática, usando combinação de ferramentas de autoria. As teorias de Gagné e de Wiley foram usadas para dar suporte ao planejamento do sequenciamento das interações de aprendizagem, na construção desses OAs. As estratégias de aplicação desses objetos estão baseadas no ciclo de Kolb, que suge-re que o aprendizado ocorre se houver a compreensão da experiência e como esta se transforma, envolvendo um ciclo composto de quatro etapas constituído por ex-periência concreta, observação reflexiva, conceituação abstrata e experimentação ativa. O trabalho descreve a implantação desta metodologia realizada através de um Curso de Capacitação para professores municipais e estaduais de Santa Maria - RS, no qual aprenderam a construir OAs usando a metodologia proposta. Ao final da capacitação cada professor dessa amostra, analisou o desenvolvimento de seu pró-prio objeto e os OAs dos seus pares, através de um questionário. Esses dados fo-ram analisados estatisticamente pelo Teste de Hipótese da Proporção, chegando-se a conclusão que os professores de Matemática aprendem facilmente usar e combi-nar as ferramentas de autoria para criar OAs de acordo com a metodologia proposta. Também foi avaliado se esses OAs criados atendem critérios de sequenciamento e de reflexão. / This thesis is the construction of a methodology that combines ready and reusable Learning Objects (LO), creating and completing parts of these LOs, using a combina-tion of authoring software. The theories of Gagné and Wiley will support the se-quencing of instruction, construction of Los. The implementation strategies for apply-ing these LOs will follow the Kolb cycle’s, which suggests that learning occurs if there is an understanding of the experience and it’s transformation, involving a four stages cycle: concrete experience, reflective observation, abstract conceptualization and active experimentation. The paper describes the implementation of this methodology conducted through a training course for local teachers and state of Santa Maria - RS, during which they learned to build LOs using the proposed methodology. At the end of training each teacher in the sample, analyzed the development of its own object and review the LOs of their peers, through a questionnaire. These data were statisti-cally analyzed by Hypothesis Test of Proportion, reaching the conclusion that the mathematics teachers learn to use and easily combine authoring tools to create LOs according to the proposed methodology. We also assessed whether these meet cri-teria established LOs sequencing and reflection.

Submitted by Erika Demachki (erikademachki@gmail.com) on 2018-07-04T17:13:10Z No. of bitstreams: 2 Dissertação - Resende Pereira De Sousa - 2018.pdf: 9297175 bytes, checksum: 56cfc048e28cb8b738bb46b824f8e8e2 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2018-07-05T10:49:46Z (GMT) No. of bitstreams: 2 Dissertação - Resende Pereira De Sousa - 2018.pdf: 9297175 bytes, checksum: 56cfc048e28cb8b738bb46b824f8e8e2 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2018-07-05T10:49:46Z (GMT). No. of bitstreams: 2 Dissertação - Resende Pereira De Sousa - 2018.pdf: 9297175 bytes, checksum: 56cfc048e28cb8b738bb46b824f8e8e2 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2018-06-29 / The current situation of the low level of learning of Mathematics in Basic Education motivated the accomplishment of this research, realized in a municipal school located in the rural zone of the Municipality of Catalão. Involving 8th grade students, children of peasants, with little contact with technological devices. This research aims to find answers about the possible contribution of the use of new technologies, as a tool, as a pedagogical didactic resource, for learning in mathematics classes. The purpose was to verify if the use of technologies in Education contributes to an improvement in the teaching and learning process in Basic Education. A methodological proposal that includes the use of Communication and Information Technologies in mathematics classes, in the search to provide an increase of motivation, a greater involvement of the students with the content taught, so that they leave the condition of mere spectators, from simple receivers of information, to the condition of learners, active participants in the construction of knowledge. The activities were planned in order to use the Dynamic Geometry software - GeoGebra - allowing in some situations to associate activities in room with material simple concrete, such as paperboard, styrofoam board, toothpicks, etc. At times students were led to build, investigate, discover, raise hypotheses and check if some properties held even with shape changes and measurements in the figures. From this investigation the properties were a_rmed or denied. After our study, we conclude that the simple fact of including technological resources does not guarantee the quality of learning. However, if some questions are observed, such as a planning of the actions that take into account the reality of the students, the available resources and the mastery of the teacher about the technologies used,the contribution is enormous, because such resources promote motivation and student involvement, thus contributing to the achievement of a satisfactory learning of the concepts of geometry. In this way, it can be seen that such methodology contributed to the process of teaching and learning mathematics in Basic Education, from the motivation and the involvement presented by the students, as well as from the learning, diagnosed through activities developed in the computer, using GeoGebra, and the resolution of exercises in the classroom, when applying this methodology. / A atual situação do baixo nível de aprendizagem de Matemática na Educação Básica motivou a realização dessa pesquisa, realizada numa escola municipal situada na zona rural do Município de Catalão. Envolvendo alunos do 8o ano, filhos de camponeses, com pouco contato com os aparatos tecnológicos. Esta pesquisa se propôs a buscar respostas sobre a possível contribuição do uso de novas tecnologias, como ferramenta, como recurso didático pedagógico, para a aprendizagem nas aulas de matemática. A finalidade foi verificar se o uso das tecnologias na Educação contribui para uma melhoria no processo ensino e aprendizagem na Educação Básica. Uma proposta metodológica que inclui o uso das Tecnologias de Comunicação e Informação nas aulas de matemática, na busca de proporcionar um aumento da motivação, um maior envolvimento dos alunos com os conteúdos ministrados, de forma que deixem a condição de meros expectadores, de simples receptores de informação, para a condição de aprendizes, participantes ativos da construção do conhecimento. As atividades foram planejadas de forma a utilizarem o software de Geometria Dinâmica _ GeoGebra _ permitindo em algumas situações associar atividades em sala com material concreto simples, como cartolina, placa de isopor, palitos, etc momentos em que os alunos eram levados a construir, investigar, descobrir, levantar hipóteses e verificar se algumas propriedades se mantinham mesmo com modificações de forma e medidas nas figuras. Dessa investigação as propriedades eram afirmadas ou negadas. Após o desenvolvimento dessa pesquisa, concluiu-se que o simples fato de incluir os recursos tecnológicos não garante melhoria na qualidade da aprendizagem. Contudo, se observadas algumas questões, como um planejamento das ações que leva em consideração a realidade dos alunos, os recursos disponíveis e o domínio do professor sobre as tecnologias utilizadas, a contribuição é enorme, pois tais recursos promovem uma motivação e um envolvimento dos alunos, contribuindo assim para a concretização de uma aprendizagem satisfatória dos conceitos de geometria. Dessa forma percebe-se que tal metodologia contribuiu com o processo de ensinar e aprender matemática na Educação Básica, a partir da motivação e do envolvimento apresentados pelos alunos, bem como da aprendizagem, diagnosticada através de atividades desenvolvidas no computador, utilizando o GeoGebra, e da resolução de exercícios na sala de aula, por ocasião da aplicação dessa metodologia.

Esta tese consiste em uma Metodologia para reusar ou criar objetos de a-prendizagem (OA) de Matemática, usando combinação de ferramentas de autoria. As teorias de Gagné e de Wiley foram usadas para dar suporte ao planejamento do sequenciamento das interações de aprendizagem, na construção desses OAs. As estratégias de aplicação desses objetos estão baseadas no ciclo de Kolb, que suge-re que o aprendizado ocorre se houver a compreensão da experiência e como esta se transforma, envolvendo um ciclo composto de quatro etapas constituído por ex-periência concreta, observação reflexiva, conceituação abstrata e experimentação ativa. O trabalho descreve a implantação desta metodologia realizada através de um Curso de Capacitação para professores municipais e estaduais de Santa Maria - RS, no qual aprenderam a construir OAs usando a metodologia proposta. Ao final da capacitação cada professor dessa amostra, analisou o desenvolvimento de seu pró-prio objeto e os OAs dos seus pares, através de um questionário. Esses dados fo-ram analisados estatisticamente pelo Teste de Hipótese da Proporção, chegando-se a conclusão que os professores de Matemática aprendem facilmente usar e combi-nar as ferramentas de autoria para criar OAs de acordo com a metodologia proposta. Também foi avaliado se esses OAs criados atendem critérios de sequenciamento e de reflexão. / This thesis is the construction of a methodology that combines ready and reusable Learning Objects (LO), creating and completing parts of these LOs, using a combina-tion of authoring software. The theories of Gagné and Wiley will support the se-quencing of instruction, construction of Los. The implementation strategies for apply-ing these LOs will follow the Kolb cycle’s, which suggests that learning occurs if there is an understanding of the experience and it’s transformation, involving a four stages cycle: concrete experience, reflective observation, abstract conceptualization and active experimentation. The paper describes the implementation of this methodology conducted through a training course for local teachers and state of Santa Maria - RS, during which they learned to build LOs using the proposed methodology. At the end of training each teacher in the sample, analyzed the development of its own object and review the LOs of their peers, through a questionnaire. These data were statisti-cally analyzed by Hypothesis Test of Proportion, reaching the conclusion that the mathematics teachers learn to use and easily combine authoring tools to create LOs according to the proposed methodology. We also assessed whether these meet cri-teria established LOs sequencing and reflection.

Submitted by MARCOS LEANDRO TEIXEIRA DE OLIVEIRA (marcosteixeira@ufv.br) on 2018-07-26T12:59:07Z No. of bitstreams: 1 texto completo.pdf: 2498223 bytes, checksum: c49ec93b270afd4d6651cef879c3ccce (MD5) / Made available in DSpace on 2018-07-26T12:59:07Z (GMT). No. of bitstreams: 1 texto completo.pdf: 2498223 bytes, checksum: c49ec93b270afd4d6651cef879c3ccce (MD5) Previous issue date: 2018-04-06 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Este trabalho ter ́a um enfoque nas Curvas Planas no Ensino Médio com uma perspectiva literária de aprofundamento teórico e de sugestão pedagógica. Introduziremos as noções de curvas planas com definições, teoremas e apresentaremos algumas curvas parametrizadas no plano, tais como: Elipse, Hipérbole, Ciclóide, Lemniscata de Bernoulli, dentre outras, para tanto, recorreremos ao GeoGebra. Além disso, utilizando os conceitos de geometria diferencial, vamos representar várias curvas regulares com mesmo traço, através da mudança de parâmetro e demonstraremos o conceito de Curvaturas, apresentando a fórmula de Frenet para curvas parametrizadas pelo comprimento do arco. Com intuito de demonstrar o Teorema de Jordan, forneceremos uma ideia geral de topologia, incluindo definições e resultados básicos, além de algumas noções de espaços métricos, funções e caminhos conexos, a fim de facilitar a execução e compreensão do teorema. Por fim, usando a propriedade de separação de polígonos no plano, iremos apresentar e demonstrar o Teorema de Jordan, que se enuncia: “Uma curva de Jordan separa o plano em duas regiões, uma limitada e outra ilimitada, sendo o traço da curva a fronteira comum das duas regiões” de fácil compreensão mas possui uma demonstração complexa. Como intervenção em sala de aula, apresentaremos uma proposta de atividades envolvendo parametrização e construção de curvas planas no GeoGebra / This paper will have a focus on the Flat Curves in High School with a literary perspective of theoretical deepening and pedagogical suggestion. We will introduce the notions of flat curves with definitions and theorems and present some curves parameterized in the plane, such as: Ellipse, Hyperbole, Cycloid, Lemniscate of Bernoulli, among others, and for this we will resort to GeoGebra. Beyond that, using the concepts of the differential geometry, we will represent several regular curves with the same trace, through the parameter change and we‘ll demonstrate the concept of Curvatures, presenting the Frenet formula for parameterized curves by the length of the arc. In order to demonstrate the Jordan Theorem, we will provide a general idea of topology, including basic definitions and results, as well as some notions of metric spaces, functions and connected ways, in order to facilitate the execution and understanding of the theorem. Finally, using the property of separation of polygons on flat, we will present and demonstrate the Jordan Theorem, which enunciates: ”A Jordan curve separates the flat into two regions, one limited and one unlimited, being the trace of the border curve, common of the two regions” It‘s easy to understand but has a complex demonstration. As a classroom intervention, we‘ll present a proposal of activities involving parameterization and construction of flat curves in GeoGebra

Submitted by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2018-08-03T15:52:36Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertação_Mirna_Final.pdf: 22678722 bytes, checksum: b13ceaad015697aaad286862e44f47ed (MD5) / Approved for entry into archive by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2018-08-03T15:52:55Z (GMT) No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertação_Mirna_Final.pdf: 22678722 bytes, checksum: b13ceaad015697aaad286862e44f47ed (MD5) / Made available in DSpace on 2018-08-03T15:52:55Z (GMT). No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertação_Mirna_Final.pdf: 22678722 bytes, checksum: b13ceaad015697aaad286862e44f47ed (MD5) Previous issue date: 2018-04-27 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This paper deals with the results of the research entitled "Fraction Teaching with GeoGebra software". The same was done in three classes of the 6th year of elementary public school in the city of Manaus. The rational numbers are presented in fractional form and decimal, however, in our research we focus only on rational numbers in the fractional form, because it is pointed out by teachers, according to research, as one of the more complex to teach and learn in the math of the early grades. Decided on the mathematical content to be approached, we have resolved, in our action research, to use tools technologies, because we recognize their potential in the teaching and learning process, learning to do so, to outline the main objective of the research, to describe the influence of GeoGebra software in the learning of rational numbers among 6th grade students Elementary School. Although the research focused on the potential of GeoGebra in the classroom, it was not the only technological resource used. In the course of the work, we will explain the use we made of the Moodie platform for the organization of the Fraction course that we do at school. In Chapter 1, we describe the theory of learning which supported our action at school, the methodology, as well as the mathematical contents addressed in the sessions. In Chapter 2 we deal with the analysis of the results of the research, but before this we talk about field research, tests 01 and 02, the use of the Moodie platform, the details of the didactic sequences developed in the sessions, the intervention through the results of the diagnosis and, finally, the analysis of tests 01 and 02, as well as the general about the results question by question. Chapter 03 is dedicated to our conclusions and Chapter 04 we reserve the opportunity to discuss new questions that have arisen in the course of the research and that we express in the topic "Future works". Research has brought answers to our inquiries, because through the analysis of the data we can verify that the GeoGebra software is a tool with a lot of potential to contribute to the teaching and learning Fraction content. We hope that the discussions discussed in this paper can contribute to the reflection on the teaching and learning of rational numbers in the fractional form and that reach their greater objective: to contribute to the improvement in the Mathematics. / Este trabalho trata dos resultados da pesquisa intitulada "Ensino de Fração com o Software GeoGebra". A mesma foi realizada em três turmas do 6° ano do ensino fundamental de uma escola pública na cidade de Manaus. Os números racionais se apresentam na forma fracioná-ria e decimal, porém, em nosso trabalho de pesquisa focamos apenas os números racionais na forma fracionária, por ser apontado por professores, segundo pesquisas, como um dos temas mais complexos de ensinar e de aprender na matemática das séries iniciais. Decididos sobre o conteúdo matemático a ser abordado, resolvemos, em nossa pesquisa ação, utilizar ferramentas tecnológicas digitais, por reconhecermos o potencial das mesmas no processo de ensino e de aprendizagem, para tanto, traçamos como objetivo principal da pesquisa, descrever a influência do software GeoGebra na aprendizagem dos números racionais entre os estudantes do 6° ano do Ensino Fundamental. Apesar da pesquisa ter tido como foco verificar o potencial do GcoGebra na sala de aula, ele não foi o único recurso tecnológico utilizado. No decorrer do trabalho, explicitaremos o uso que fizemos da plataforma Moodle para a organização do curso Fração que realizamos na escola. No Capítulo 01, descrevemos os objetivos, a teoria de aprendizagem que respaldou nossa ação na escola, a metodologia, bem como os conteúdos matemáticos abordados nas sessões. No Capítulo 02 tratamos da análise dos resultados da pesquisa. mas antes disso discorremos sobre a pesquisa de campo, os testes 01 e 02, o uso da plataforma Moodle, o detalhamento das sequências didáticas desenvolvidas nas sessões, a intervenção mediante os resultados do diagnóstico e por fim a análise dos testes 01 e 02, bem como as considerações gerais a cerca dos resultados questão por questão. O Capítulo 03 destinamos às nossas conclusões e o Capítulo 04 reservamos para discorrermos sobre novas perguntas que surgiram no decorrer da pesquisa e que expressamos no tópico "Trabalhos futuros". A pesquisa trouxe respostas às nossas indagações, pois por meio da análise dos dados pudemos constatar que o software GeoGebra é uma ferramenta com muito potencial para contribuir com a melhoria do ensino e aprendizagem do conteúdo Fração. Esperamos que as discussões expostas nesse trabalho possam contribuir para a reflexão acerca do ensino e aprendizado dos números racionais na forma fracionária e que alcancem seu objetivo maior: contribuir para a melhoria no ensino da Matemática.

Submitted by Karem Dantas (karem.c.dantas@gmail.com) on 2018-10-08T13:33:57Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Teorema de Pick.pdf: 18162866 bytes, checksum: b5924b5d514e4978acc23fddace5a5cb (MD5) / Approved for entry into archive by Marcos Roberto Gomes (mrobertosg@gmail.com) on 2018-10-08T14:49:39Z (GMT) No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Teorema de Pick.pdf: 18162866 bytes, checksum: b5924b5d514e4978acc23fddace5a5cb (MD5) / Approved for entry into archive by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2018-10-09T17:15:54Z (GMT) No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Teorema de Pick.pdf: 18162866 bytes, checksum: b5924b5d514e4978acc23fddace5a5cb (MD5) / Made available in DSpace on 2018-10-09T17:15:54Z (GMT). No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Teorema de Pick.pdf: 18162866 bytes, checksum: b5924b5d514e4978acc23fddace5a5cb (MD5) Previous issue date: 2018-06-20 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The purpose of this project is Pick’s Theorem, which is about of the calculation of simple polygons with vertices in the points of mesh grid at the plane. The theorem let us to calculate the area using counting, analyzing the points in the edge and the interior of the polygon at the mesh grid. We going to talk about a little bit of Georg Alexander Pick history, beyond the necessary observations to understand the theorem’s demonstration and complexity. At last, we going to show you Pick’s Theorem activities, in the Geoboard and on the GeoGebra software as didactic resources for classroom. / O foco deste trabalho é o Teorema de Pick. Esse teorema se refere ao cálculo de áreas de polígonos simples com vértices nos pontos de uma malha quadriculada no plano, o teorema permite calcular a área usando contagem, analisando os pontos do bordo e do interior do polígono em uma malha quadriculada. Apresentaremos um pouco da história de Georg Alexander Pick, além de observações necessárias para se compreender a demonstração do teorema e sua extensão. Finalmente mostramos atividades com o teorema de Pick no Geoplano e no software GeoGebra como recursos didáticos para a sala de aula.

Se presenta una actividad colaborativa de Matemática en la que los alumnos determinan las ecuaciones y las gráficas de cónicas y rectas; y reconocen las ventajas de usar un software como Winplot o Geogebra para obtener las gráficas, así como para realizar cambios de forma rápida.

This study investigated the use of an advanced technological development (free GeoGebra software) within the secondary educational setting in four relatively under-resourced schools in the Gauteng Province of South Africa. This advancement is viewed as having the potential to promote the teaching and learning of complex ideas in mathematics, even within traditionally deprived communities. The focus in this study was on the teaching and learning of transformation geometry at Grade 9 and attainment was reflected in terms of the van Hieles' levels of geometrical thinking. A mixed methods approach was followed, where data was collected through lesson observations, written tests and semi-structured interviews. Four Grade 9 teachers from four schools were purposively selected, while twenty-four mathematics learners (six from each school) in the Tshwane metropolitan region were randomly selected. The teachers' lesson observations and interview outcomes were coded and categorised into themes, and the learners' test scripts were marked and captured. The analysis of test scores was structured according to the van Hieles' levels of geometric thought development. As far as the use of GeoGebra is concerned, it was found that teachers used the program in preparation for, as well as during lessons; learners who had access to computers or android technology, used GeoGebra to help them with practice and exercises. As far as the effect of the use of GeoGebra is concerned, improved performance in transformation geometry was demonstrated. / Dissertation (MEd)--University of Pretoria, 2016. / Science, Mathematics and Technology Education / MEd / Unrestricted

This study is attempting to test the effectiveness of dynamic computer models such as GeoGebra and Desmos on high school students’ ability to understand key concepts with regards to the introduction of unit circle and the graphing of the sine and cosine functions. Algebra two high school students of varying ages were chosen and randomly placed into two groups. Both groups were given the same pre-assessment and an identical lesson. The two groups’ only difference occurred with the individual student practice portion of the lesson where one group did ‘traditional’ paper and pencil practice for graphing and solving while the other group used only computer models as their individual practice. Both groups were then reassessed by giving the same assessment again. Their levels of improvement were compared using standard statistical analysis and a mean comparison test. The results showed a statistically significant improvement in the student group that used the dynamic models versus the group that did not use the computer. The sample size was large enough to generate a confidence value of over 99% (99.3%) so we were able to reject the null hypothesis that there was no difference between the group results and accept the hypothesis that the student group that used the computer models improved by a statistically significant amount. The non computer group improved by 7.7 percent while the computer aided group improved by over 49 percent. This represented an 88 percent increase in the scores of the computer group when compared with the control group. I was able to definitively conclude that the dynamic software did have a significant and positive effect on the students' learning of the unit circle. It is hoped that this information will be used to help inform more effective instruction for high school and college students as they learn this topic. It also provides a strong argument for an increased emphasis on educating teachers to become more fluent in the use of dynamic models and software as both a demonstration tool and as an interactive tool for their students in a variety of math levels. These results may also have wider applications to many other math topics and math instruction in general.