Submitted by MARCIA ROVADOSCHI (marciar@unifra.br) on 2018-08-20T17:09:11Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertacao_NadiaRobertaQuainiBresolin.pdf: 2962274 bytes, checksum: 08e27819aea17dfb2d8c955d8761f265 (MD5) / Made available in DSpace on 2018-08-20T17:09:11Z (GMT). No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertacao_NadiaRobertaQuainiBresolin.pdf: 2962274 bytes, checksum: 08e27819aea17dfb2d8c955d8761f265 (MD5) Previous issue date: 2016-11-30 / This research aimed to investigate how the GeoGebra software can provide the development of creative, intuitive and visual abilities in the statement of theorems of synthetic geometry. The research was carried out with five students of the first year of high school in a state school of Rio Grande do Sul. This is a qualitative research carried out in the computer lab; data collection was obtained through the records of the constructions carried out by students and analyzed existing protocols in the software itself. The investigative activities, developed in workshop mode, consisted of four specific theorems of plane geometry, chosen at random and feasible to be offered to students of elementary school. The research results showed that the activities provided through the GeoGebra software, the development of creativity, the use of intuitive thinking and visualization as a way of analyzing the operation of ideas in the formulation of conjectures, which contributed to the construction of theorems, providing meaningful learning. Also, it indicates synthetic geometry as a way to perform logical statements of theorems, developing reasoning skills and justifications. In turn, the results showed that the use of GeoGebra software, used in construction, was key to achieving the goals in the research. / Este trabalho de pesquisa teve como objetivo investigar de que forma o software GeoGebra pode proporcionar o desenvolvimento de habilidades criativas, intuitivas e visuais na demonstração de teoremas de Geometria Sintética. A investigação foi realizada com cinco alunas do primeiro ano do Ensino Médio de uma Escola Estadual do Rio Grande do Sul. Trata-se de uma pesquisa de cunho qualitativo realizada em laboratório de informática; a coleta de dados foi obtida pelos registros das construções realizadas pelas estudantes e analisados os protocolos existentes no próprio software. As atividades investigativas, desenvolvidas na modalidade de oficina, consistiram de quatro teoremas específicos de Geometria Plana, escolhidos aleatoriamente e viáveis de serem propostos aos estudantes da escola básica. Os resultados da investigação demonstraram que as atividades propostas oportunizaram, por meio do software GeoGebra, o desenvolvimento da criatividade, o uso do pensamento intuitivo e a visualização como forma de analisar a exploração de ideias na formulação de conjecturas, o que contribuiu para a construção dos teoremas, propiciando uma aprendizagem significativa. Além disso, indica Geometria Sintética como uma forma de realizar demonstrações lógicas de teoremas, desenvolvendo habilidades de argumentação e justificativas. Por sua vez, os resultados mostraram que o uso do software GeoGebra, utilizado nas construções, foi fundamental para atingir os objetivos propostos na pesquisa.

A thesis submitted in fulfilment of the requirements for the degree of DOCTOR OF PIIILOSOPHY in the SCHOOL OF SCiENCE EDUCATION (MATHEMATICS) UNIVERSITY OF THE WITWATERSRAND / Cognitive gender differences in mathematics, which were noted in past research have latterly been found to be declining. but are still observed at secondary school level in the field of spatial skills and geometry. However, due to divergent geometry curricula and the multidimensional nature of spatial skills, results from gender studies have led to broad conclusions being drawn from investigations which were affected by random elements. Research results have been influenced by imbalanced representation of the two gender groups in samples and also by differential gender exposure to previous mathematical experience. Both these limitations in research have produced outcomes reflecting negatively On females. Internationally divergent geometry curricula are a result of the traditional synthetic approach to the teaching of Euclidean geometry falling Into disfavour in western countries. Thus, Euclidean geometry has been largely overlooked in current educational research and the cognitive processes such as deductive reasoning, proof writing and hypothesis testing, have received scant attention within geometry teaching over the past decade. The standardized system in most South African secondary schools coupled with a uniform core curriculum for mathematics lends itself to an advantageous environment for empirical studies in mathematics performance. The present gender investigation involved almost an equal number of males and females from 5' selected secondary schools near Johannesburg in South Africa. Performance in Euclidean geometry was evaluated for possible gender differences by means of multiple choice and open ended questions. In keeping with most existing research, mean differences were compared. No statistically significant gender difference in mean performance on Euclidean geometry was found. Further analysis at item level was undertaken for the multiple choice component of the test instrument by means of the one dimensional three parameter logistic model in Item Response Theory, This model, is considered to be very sensitive in identifying differences at different ability levels -a shortcoming in existing research. Four out of a total of twenty Euclidean geometry items, were identified as producing differential gender performance. Similar gender tendencies were observed for all four items. The performance was in favour of most males for each of these items. Females of lower ability (as measured by the item) did not perform as well as males of similar ability level. In all four Cases females of higher ability surpassed males of a corresponding ability level. Perceptual difficulties in females were more pronounced than in males for some of the items. / AC 2018

CAPES / Organizou-se esta dissertação a partir da constatação de que teoremas de matemáticos como Matthew Stewart e Heron são pouco empregados nas aulas de matemática do ensino fundamental e médio. As contribuições desses matemáticos no cálculo das cevianas e da área de triângulos podem simplificar a solução de muitos problemas. Como ponto de partida, elaborou-se uma atividade extraclasse contendo quatro questões centradas no Teorema de Stewart e aplicou-se a mesma a três turmas do ensino m´edio do CPM-PR. A partir da análise dos resultados dessa atividade, definiu-se a pesquisa bibliográfica, a estrutura do texto e a organização de uma coleção de problemas aplicados. / This dissertation was organized from the observation that mathematical theorems as Stewart’s theorem and Heron’s theorem are rarely used in mathematics classes in middle and high schools. The contributions of these mathematicians in calculating cevians and area of triangles can simplify the solution of many problems. As a starting point, we prepared one extracurricular activity containing four questions centered on Stewart’s theorem and applied the same in three high school classes of CPM-PR. From the analysis of the results of this activity, we defined the literature, the text structure and organization of a collection of applied problems.

No abstract. / Thesis (M.Ed.)-University of KwaZulu-Natal, Durban, 2011.

Acompanha: Manual de utilização do kit de materiais manipuláveis para o ensino de geometria plana para uma aluna com surdocegueira / Objetiva-se analisar as contribuições de atividades com materiais manipuláveis adaptados na elaboração de conceitos de geometria plana por alunos com surdocegueira. Para isso, desenvolveu-se uma pesquisa aplicada com abordagem qualitativa descritiva, como estudo de caso. O estudo foi levado a efeito em uma turma do 9° ano do Ensino Fundamental de uma escola da rede estadual de ensino de Guarapuava - PR. Para a efetivação da pesquisa, fundamentou-se o ensino da matemática, a utilização de materiais manipuláveis e a elaboração de conceitos, inclusão escolar, surdocegueira e o seu processo de ensino e aprendizagem. Inicialmente, entrevistou-se a Pedagoga, a professora de Matemática, o intérprete de Libras e a aluna surdocega. Por meio das entrevistas, compreendeu-se o contexto escolar e como acontece o processo de ensino e aprendizagem, principalmente, na disciplina de matemática. Após a etapa das entrevistas, foi aplicada uma avaliação inicial a todos os alunos da turma, com 14 perguntas. Após análise do teste, selecionaram-se atividades que envolveram geometria plana e confeccionaram-se os materiais necessários para a aplicação. Houve também as adaptações nos materiais, de modo a suprir as necessidades da aluna com surdocegueira. Na etapa seguinte, houve a intervenção pedagógica, na qual todos os alunos participaram desenvolvendo atividades que utilizavam o mesmo material adaptado para a aluna com surdocegueira, sendo assim, não houve distinção entre as atividades e os materiais utilizados pela aluna com surdocegueira e os demais alunos. Esse material foi denominado de “Kit de Materiais Manipuláveis Adaptados”, que é composto por uma coletânea de atividades selecionadas pela pesquisadora. As etapas da formação dos conceitos de Galperin (2009a) serviram de base para a intervenção pedagógica, que demonstrou grande progresso dos alunos na elaboração dos conceitos de geometria plana. Com a aplicação de teste final, após a intervenção pedagógica, verificou-se que os resultados foram positivos, visto que a aluna com surdocegueira teve um aproveitamento inicial de 53%, passando para 92% no teste final. O desempenho da turma passou de 54% no teste inicial para 81% no teste final, após a intervenção pedagógica. Os resultados da pesquisa evidenciam que estratégias de ensino com objetivos bem traçados contribuem para que os alunos, com deficiência ou não, se apropriem do conteúdo escolar, no caso da pesquisa eles elaboraram conceitos matemáticos. / This research intends to analyses the contributions activities with adapted manipulable materials in formulation of plane geometry concepts by students with deafblindness. For this, an applied research with qualitative descriptive approach, characterizing this as a case study was developed. The study happened in a class of 9th year of Elementary School at a state education school, in Guarapuava - PR. In order to actualize the research, the mathematics teaching, the use of manipulable materials and concepts elaboration, school inclusion, deafblindness and its teaching and learning process were substantiated. Initially, the school pedagogue, the Math professor, the Libras interpreter and the student with deafblindness were interviewed. By the interviews, the school inclusive context and how the teaching and learning process is made were understood, principally, in Mathematics. After interviews step, an initial test, composed by fourteen questions, was aplied for all students in the class. After the analyses of the test, were selected some activities involving plane geometry and the needed material to the application of this activities was made. There were, also, adaptations in the material, in order to meet the needs of the student with deafblindness. In the next step, there was the pedagogical intervention, in which all students participated developing activities using the same adapted material made for the student with deafblindness, therefore, there wasn’t distinctions between the activities and materials used by the student with deafblindness and the other students. This material was denominated “Adapted Manipulable Materials Kit”, that is composed by a collection of activities selected by the researcher. The steps of concepts formation of Galperin (2009a) were the base to the pedagogical intervention, that demonstrate great progress of the students in the plane geometry concepts formulation. By the application of final test, after the pedagogical intervention, were found positive results, since the student with deafblindness had an initial school achievement of 53%, passing to 92% in the final test. The performance of the class went from 54% in the initial test to 81% in the final test, after the pedagogical intervention. The research results evidence that teaching strategies with well-designed goals contribute to that students, with deficiency or not, appropriate the scholar content, in this case, they elaborated mathematical concepts.

CAPES / Este trabalho apresentará um breve histórico do desenvolvimento da Geometria, com foco no surgimento da sua organização na forma lógico-dedutiva efetuado por Euclides. Na sequência será discutida a situação do ensino e aprendizagem dos tópicos de geometria desde a antiguidade até os dias atuais, onde observaremos que a mesma não se dá sob a ótica lógico-dedutiva. Após essa contextualização, proporemos a realização de uma oficina de geometria para alunos do sexto ano do Ensino Fundamental, com vistas ao desenvolvimento do raciocínio lógico-dedutivo. Aplicada a oficina, foram observadas mudanças na organização do pensamento dos alunos participantes da pesquisa, favorecendo a compreensão dos conceitos e propriedades da geometria euclidiana plana. / This study will introduce a brief history of the Geometry development, focused in the appearing of the organization in the logical deductive structure achieved by Euclid. Following will be discussed the situation of the learning and teaching of geometry topics since antiquity until the present day, where we will notice that it does not happen with the logical-deductive perspective. After this contextualization, we will propose the realization of a geometry workshop for students of the sixth grade of elementary school, focusing to the development of logical-deductive reasoning. Applied to workshop, changes were observed in the organization of thought of the participating students in the research, furthering the understanding of the concepts and properties of flat euclidean geometry.

CAPES / Este trabalho apresentará um breve histórico do desenvolvimento da Geometria, com foco no surgimento da sua organização na forma lógico-dedutiva efetuado por Euclides. Na sequência será discutida a situação do ensino e aprendizagem dos tópicos de geometria desde a antiguidade até os dias atuais, onde observaremos que a mesma não se dá sob a ótica lógico-dedutiva. Após essa contextualização, proporemos a realização de uma oficina de geometria para alunos do sexto ano do Ensino Fundamental, com vistas ao desenvolvimento do raciocínio lógico-dedutivo. Aplicada a oficina, foram observadas mudanças na organização do pensamento dos alunos participantes da pesquisa, favorecendo a compreensão dos conceitos e propriedades da geometria euclidiana plana. / This study will introduce a brief history of the Geometry development, focused in the appearing of the organization in the logical deductive structure achieved by Euclid. Following will be discussed the situation of the learning and teaching of geometry topics since antiquity until the present day, where we will notice that it does not happen with the logical-deductive perspective. After this contextualization, we will propose the realization of a geometry workshop for students of the sixth grade of elementary school, focusing to the development of logical-deductive reasoning. Applied to workshop, changes were observed in the organization of thought of the participating students in the research, furthering the understanding of the concepts and properties of flat euclidean geometry.

This thesis aims to show that the notable points of the triangles are not limited to Incentro, circumcenter, Baricentro and Orthocenter which are the best known. In fact, the Encyclopedia of Triangle Centers (ETC), see [5], features over five thousand notable points. Are points with several interesting properties as we will see throughout this work. In addition to the points already mentioned will also present the points of Feuerbach, the Lemoine point, the point Gergonne, the Nagel point, the Spieker point and the points of Fermat. Will be also presented some important theorems, among them we highlight the Ceva theorem that will be used to prove the existence of several points mentioned. We realize that it is a matter of understanding that can be easily inserted into the basic education. / A presente dissertação tem como objetivo mostrar que os pontos notáveis dos triângulos não se resumem ao Incentro, Circuncentro, Baricentro e ao Ortocentro que são os mais conhecidos. Na verdade, a Encyclopedia of Triangle Centers (ETC), ver [5], apresenta mais de cinco mil pontos notáveis. São pontos com várias propriedades interessantes como veremos ao longo deste trabalho. Além dos pontos já citados apresentaremos também os pontos de Feuerbach, o ponto de Lemoine, o ponto de Gergonne, o ponto de Nagel, o ponto de Spieker e os pontos de Fermat. Serão apresentados também alguns teoremas importantes, entre eles podemos destacar o Teorema de Ceva que será usado para provar a existência de vários pontos citados. Podemos perceber que é um assunto de fácil compreensão que pode ser inserido no ensino básico.

University of Macau / Faculty of Education