La représentation en perspective s'appuie sur plusieurs choix pour l'enseignement : mode de représentation, code d'écriture et de lecture pour combler la perte d'information dans le passage de trois dimensions à deux dimensions, approche pour enseigner le passage d'un objet géométrique de l'espace à un dessin. Notre étude questionne ces choix dans les deux systèmes éducatifs français et vietnamien et leurs effets sur l'apprentissage des élèves. En nous plaçant dans le cadre de la Théorie anthropologique du didactique, nous avons étudié les rapports institutionnel et personnel d'élèves français et vietnamien à l'objet « représentation en perspective ».Pour le premier (rapport institutionnel), nous avons caractérisé les modes de représentation et leurs approches mathématiques, puis nous avons élaboré les praxéologies de références relatives à l'objet « représentation en perspective ». Les technologies et théories de ces praxéologies s'appuient sur les règles de représentation du dessin en perspective (règles de conservation et de non conservation, règles de la troisième dimension, règles pour un dessin « bien informé ») que nous avons explicitées. Ensuite, nous avons utilisé ce modèle de référence pour l'analyse des programmes et des manuels ce qui nous a permis de mettre en évidence les points spécifiques de l'enseignement de la représentation en perspective en France et au Viêt-Nam. Enfin, nous avons formulé des hypothèses sur les règles implicites du contrat didactique, en tant que constituants des technologies des praxéologies personnelles de la représentation en perspective. Ces règles portent sur la troisième dimension et sont spécifiques à certains solides.Pour le deuxième (rapport personnel), nous avons fait passer aux élèves un questionnaire sur un type de tâches concernant la lecture d'un dessin. Ce questionnaire permet de mettre à l'épreuve les hypothèses précédentes et de mettre en lumière les praxéologies personnelles du passage d'un objet géométrique de l'espace à un dessin (technologie/théorie personnelle). / Perspective representation is based on several choices for teaching: mode of representation, code writing and reading to fill the information loss in the passage of three-dimensional object to two-dimensional object, approach to teaching the passage of a geometry object in space to a drawing. Our study poses questions for the choices in French and Vietnamese educational systems and their effects on student studying. By using the anthropological theory of didactics, we studied the institutional relation and personal relation of French and Vietnamese students for "perspective representation" object. For the first objective (institutional relation), we characterized the modes of representation and approaches mathematics, then we established the praxeologies of reference on the "perspective representation" object. The technologies and theories of the praxeologies are based on perspective representation's rules of drawings (rules of conservation and non-conservation, rules of the third dimension, rules for a "well informed" drawing) that we explicited. By applying the model of reference to analyze the programs and textbooks, we clarified the specific points of teaching the perspective representation in France and Vietnam. Finally, we established hypotheses about the implicit rules of the didactic contract, as the constituents of technologies of personal praxeologies, of perspective representation. These rules are based on the third dimension and specific to certain solids. For the second objective (personal relation), we designed a questionnaire for the students on a task type so-called reading a drawing. The questionnaire is used to check the mentioned hypotheses and to clarify the personal praxeologies of the passage from a geometric object in space to a drawing (personal technology / theory).

Made available in DSpace on 2018-06-27T19:13:24Z (GMT). No. of bitstreams: 2 Guilherme Baggio Marin.pdf: 4379487 bytes, checksum: ec8b50d0e4b6a00e653571cf516dfb91 (MD5) Guilherme Baggio Marin.pdf.jpg: 3797 bytes, checksum: bd8774219b0438142a96f5e67a7dd6a5 (MD5) Previous issue date: 2013-09-27 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This study aimed to investigate the contributions of the software Cabri 3D in the viewing of flat sections in the cube, made by high school students of a private school in Santa Maria, Rio Grande do Sul state. This Research has an investigative methodology, and the data collected is qualitative in nature, so the researcher should analyze and present the results. A group of 29 students of the 3rd year, all from the same class, volunteered for this study. Ten activities were prepared, where students performed sections in the cube using pencil and paper, then these same activities performed using the software Cabri 3D, so we could compare the results. The first three ones consisted in obtaining triangular regions, scalenon, isosceles and equilateral. The following three regions involved four sides to reach regions of six sides, increasing the difficulty of the buildings and the views. In each activity, students recorded, initially, their justifications on paper. Later, in the realization with the use of Cabri 3D, feature of the software itself, was used to type along with the building with the reasoning of the building. This research shows the advantages of using the software in the visualization of plane sections obtained from a cube by planes that intersect its edges. As a product of this master professional dissertation, we designed a Power Point tutorial addressing to the topic of the study proposed. / Este trabalho teve como objetivo investigar as contribuições do software Cabri 3D na visualização de seções planas no cubo, realizadas por alunos do ensino médio de uma escola particular de Santa Maria RS. A pesquisa tem a metodologia da investigação, e os dados coletados são de natureza qualitativa, cabendo ao investigador analisar e apresentar os resultados. Um grupo de 29 alunos do 3º ano, todos de uma mesma turma, foi voluntário para essa pesquisa. Foram elaboradas dez atividades, onde os alunos realizaram seções planas no cubo utilizando lápis e papel, posteriormente realizaram essas mesmas atividades usando o software Cabri 3D, dessa forma conseguimos comparar os resultados. As três primeiras consistiram na obtenção de regiões triangulares, escalena, isósceles e equiláteras. As três seguintes envolviam regiões de quatro lados até chegar a regiões de seis lados, aumentando o grau de dificuldade das construções e visualizações. Em cada atividade os alunos registraram, inicialmente, suas justificativas em papel. Posteriormente, na realização com o uso do Cabri 3D, utilizaram recurso do próprio programa para digitar junto à construção a argumentação da construção realizada. A pesquisa comprovou as vantagens do uso do software na visualização das seções planas obtidas em um cubo por planos que interceptam suas arestas. Como produto dessa dissertação de mestrado profissional, foi elaborado um tutorial em Power Point abordando o tema de estudo proposto.

The subject of diploma thesis is cycle of paintings, animation and video. This work is based on the operation system error. I focusing on well know phenomen of freezing computer and follow layering of system windows over themselves. Due to an error may arise aesthetic shape, which may refer to geometric abstraction. On this phenomenon interested me especially the elementary aspects of painting, building space on surface, geometry, movement and shape.

Made available in DSpace on 2016-04-27T16:58:49Z (GMT). No. of bitstreams: 1 ADRIANA MARIA COZZOLINO.pdf: 4568146 bytes, checksum: 0e32b55df54f9d137d6bfb0530e21ca9 (MD5) Previous issue date: 2008-12-19 / Secretaria da Educação do Estado de São Paulo / This work is inserted in the context of teaching-learning Spatial Geometry in Basic Education, in particular, teaching Perspective by High School students and the relations between three-dimensional objects and their representations in the plain. We have used the dynamic geometry environment, CABRI 3D, considering the limitations existing of the paper and pencil environment. The difficulties of students in relation to three-dimensional representations into two-dimensional environment, were researched by Parzysz (1988, 1989, 1991, 2001), and our work was basis in his theoretical Geometry presuppositions. Our aim is verify how the education of the perspective can help students to change or to articulate different points of view of three-dimensional geometric object. Besides, to notice how CABRI 3D can contribute with them, so that they will articulate the real image and its representations. Design Experiments was adopted as the methodology of this work. It was developed by Steffe and Thompson (2000), Doerr and Wood (2000), Cobb et al (2003) and Collins et al (2004). High School students of a private school of the state of São Paulo participated in this work. Their productions showed that the changes between the paper and pencil (static) environment and the dynamic geometry environment CABRI 3D, contributed so that the students mobilize and articulate knowledge between the image and its representations. Finally, we pretend that this work was used as a tool to enlarge the visualization capacity and to sensitize the look of the students for the representations perspective of three-dimensional objects / A presente pesquisa está inserida no contexto do ensino-aprendizagem da Geometria Espacial na Educação Básica, referindo-se, em particular, ao ensino da Perspectiva para alunos do Ensino Médio e as relações entre os objetos tridimensionais e suas representações no plano. Optamos por utilizar o ambiente de geometria dinâmica CABRI 3D, considerando as limitações no ambiente convencional papel e lápis. As dificuldades dos alunos com relação à representação plana de objetos espaciais são tratados por Parzysz (1988, 1989, 1991, 2001) e estes estudos serviram como referencial teórico para a nossa pesquisa. Procuramos verificar em que medida o ensino da perspectiva pode auxiliar o aluno a mudar ou articular diferentes pontos de vista sobre um objeto geométrico tridimensional e de que forma o CABRI 3D pode contribuir para que articulem a imagem real e suas representações. A metodologia utilizada foi o Design Experiments, fundamentada nos autores Steffe e Thompson (2000), Doerr e Wood (2000), Cobb et al (2003) e Collins et al (2004). Participaram do estudo alunos do Ensino Médio de uma escola particular da cidade de São Paulo. As produções dos alunos mostraram que as variações entre o ambiente papel e lápis (estático) e ambiente de geometria dinâmica CABRI 3D, contribuíram para que eles mobilizassem seus conhecimentos e articulassem entre a imagem e suas representações. Este trabalho foi utilizado como uma ferramenta para ampliar a capacidade de visualização e sensibilizar o olhar dos alunos para as representações em perspectiva, de objetos espaciais

Made available in DSpace on 2016-04-27T16:58:50Z (GMT). No. of bitstreams: 1 ELEN GOMES LEITE SANTIAGO DA SILVA.pdf: 6593196 bytes, checksum: d141853a76b9c54c71e895f7ce06b693 (MD5) Previous issue date: 2008-12-18 / Secretaria da Educação do Estado de São Paulo / This research work aims to investigate how the WebQuest Methods can collaborate in the development of Mathematic contents together with the high school students, using as basis the resources available on the Internet, featuring an activity of research and development. The WebQuest Method was developed by Bernie Dodge, professor of the University of San Diego in 1995. The WebQuest entitled "What a football ball has to do with mathematics?" has as central theme related to the shape of a football ball with the Archimedean Solid, part of the Geometry that is very little studied in the high school. This WebQuest activity has been apllied in a class of 32 students of the third year of a public school in São Paulo. Then it has applied to two classes of the second grade, with 20 students each, in a private school, also in São Paulo. Analyzing the conception and application of the WebQuest, the purpose was verifing whether this activity has some benefit in relation to the student learning confronting with the traditional way of presenting the same content (expository classes with blackboard and chalk).The support of this research, was performed connecting the spontaneous knowledge and scientific knowledge, once that the football ball is known by the most people. It also uses the concepts of how to do and understanding and collaborative work. From the analysis of the final products of the proposed tasks in the WebQuest and the answers to a questionnaire offered to students it can be concluded that knowledge can be built from the research made on the Internet, like this contributing to the development of contents of mathematics. It may be observed also in terms of motivation and interest, a considerable growth on the part of students, to achievement of studies on subjects of Mathematics using this feature (Internet), particularly the collaborative work developed by them / Este trabalho de pesquisa tem como objetivo investigar como a metodologia WebQuest pode colaborar para o desenvolvimento de conteúdos de Matemática junto a alunos do Ensino Médio, usando como base os recursos disponíveis na Internet, caracterizando uma atividade de pesquisa e elaboração. A metodologia WebQuest foi elaborada por Bernie Dodge, professor da Universidade de San Diego, em 1995. A WebQuest intitulada Bola de futebol tem a ver com a Matemática? tem como tema central relacionar o modelo de uma bola de futebol com os Sólidos Arquimedianos, parte da Geometria que é muito pouco estudada nas séries do Ensino Médio. Esta atividade WebQuest foi aplicada inicialmente em uma turma de 32 alunos do terceiro ano de uma escola da rede pública de São Paulo. Em seguida, foi aplicada para duas turmas do segundo ano do Ensino Médio, compostas de 20 alunos cada, de uma escola da rede particular, também em São Paulo. Ao analisar a concepção e aplicação da WebQuest, objetivou-se verificar se esta atividade apresenta algum benefício em relação ao aprendizado dos alunos confrontando com a forma tradicional de apresentação do mesmo conteúdo (aulas expositivas com lousa e giz). A fundamentação deste trabalho foi efetuada relacionando o conhecimento espontâneo e o conhecimento científico, uma vez que bola de futebol é de conhecimento da maioria das pessoas. Também utiliza os conceitos do fazer e do compreender e do trabalho colaborativo. A partir da análise feita dos produtos finais das tarefas propostas na WebQuest e das respostas a um questionário proposto aos alunos pode-se concluir que o conhecimento pode ser construído a partir da pesquisa realizada na Internet, colaborando assim para o desenvolvimento de conteúdos da Matemática. Pode-se notar também em termos de motivação e interesse, um crescimento considerável por parte dos alunos, para a realização de estudos sobre temas da Matemática utilizando-se desse recurso (Internet), em especial pelo trabalho colaborativo desenvolvido por eles

Made available in DSpace on 2016-04-27T16:59:00Z (GMT). No. of bitstreams: 1 Maria de Fatima Aleixo de Luna.pdf: 1631180 bytes, checksum: 605733c786ce49e5974e370a56c3d4ac (MD5) Previous issue date: 2009-11-26 / Secretaria da Educação do Estado de São Paulo / The aim of this research was to investigate the possibility of harmonizing constructivist learning perspective to the planning of education, in collaboration researcher and teacher in the particular geometry of space and check the performance of teachers of mathematics in relation to plan activities education, consistent with a constructivist view of learning. Part of the research project "construction of hypothetical learning trajectories and implementation of curricular innovations in mathematics in high school." The theoretical foundation was based on the works of Simon (1995) about hypothetical learning trajectories (HLT). The study was qualitative and involved three mathematics teachers from the public schools of Sao Paulo and his performances with 104 students in the second year of high school. From the stages of Mathematics developed by Simon, was elaborated HLTs, seeking proposing tasks that explore research, use of technology, everyday contexts and in other areas of knowledge and of mathematics itself. Data were collected through semi-structured interviews, questionnaires and observations at two different times: before and during the development of MASD. It was found that although the MASD are potentially rich in order to produce situations in which the teacher participates cogito is constantly (re) organization of school planning, it is understood that the HLT itself does not guarantee a constructivist learning perspectives. Thus, it was found, as already mentioned by different authors, the teacher plays a fundamental role in mediating the construction of knowledge of their students. The performance of teachers, it was considered that this path is still challenging in the sense of teachers' willingness to approach the world of research and continuing education, relying on different methodologies and didactic procedures. For students, it was felt that their involvement has become more promising, when participating in tasks that involve the use of technology and materials handling, particularly in relation to the concepts and procedures of the Space Geometry / O objetivo da presente pesquisa foi verificar a possibilidade de compatibilizar perspectivas construtivistas de aprendizagem com a planificação do ensino, em colaboração pesquisador e professor, no caso particular da Geometria Espacial e verificar a atuação do professor de Matemática no que se refere às atividades de planejamento de ensino, de forma compatível com uma perspectiva construtivista de aprendizagem. Faz parte do projeto de pesquisa denominado Construção de Trajetórias Hipotéticas de Aprendizagem e implementação de Inovações Curriculares em Matemática no Ensino Médio . A fundamentação teórica apoiou-se nas obras de Simon (1995) a respeito de Trajetórias Hipotéticas de Aprendizagem (THA). O estudo realizado foi de natureza qualitativa e envolveu três professores de Matemática da rede pública de São Paulo e suas atuações com 104 alunos da segunda série do Ensino Médio. A partir do Ciclo de Ensino de Matemática desenvolvido por Simon, elaborou-se THAs, buscando a proposição de tarefas que explorassem investigação, uso de tecnologia, contextos do cotidiano e em outras áreas de conhecimento e da própria Matemática. Os dados foram coletados por entrevistas semiestruturadas, questionário e observações em dois diferentes momentos: antes e durante o desenvolvimento das THAs. Verificou-se que, embora as THAs sejam potencialmente ricas, no sentido de produzir situações em que o professor cogite e participe constantemente da (re) organização do planejamento escolar, compreende-se que a THA por si só não garante uma aprendizagem sob perspectivas construtivistas. Desse modo, constatou-se, conforme já mencionado por diferentes autores, que o professor exerce papel fundamental na mediação da construção do conhecimento de seus alunos. Quanto à atuação do professor, considerou-se que esse caminho continua sendo desafiador, no sentido dos docentes estarem dispostos a aproximar-se do universo das pesquisas e formação continuada, apoiando-se em diferentes metodologias e procedimentos didáticos. Em relação aos estudantes, percebeu-se que seu envolvimento apresenta-se mais promissor, quando participa de tarefas que envolvem o uso de tecnologia e manipulação de materiais, particularmente, em relação aos conceitos e procedimentos da Geometria Espacial

Cette thèse se propose d’étudier la difficulté de l’estimation de la distance dans le cadre de la géométrie de l’espace visuel. En philosophie de la perception, cette thèse est d'abord discutée au plan épistémologique : comment savoir que cette distance n'est pas connue ou connaissable, quoique perçue et discutée. Les travaux de Berkeley nous servent de point de départ et fixent un cadre spéculatif, puisque Berkeley soutient en effet que le jugement porté sur la distance résulte entièrement de l'expérience, quoique cette distance ne puisse être vue phénoménalement. La thèse se propose d'examiner une question essentielle supportée par cette alternative centrale mais au plan ontologique cette fois : comme déterminer de quel type est la distance : est-elle inconsciemment visible ? tangible ? ou visible et tangible à la fois ? Peut-elle être une entité assignable dans un espace hyperbolique, ou sphérique, un espace strictement euclidien, ou hyperbolique et sphérique en même temps qu'euclidien ? Pour appuyer notre propos et notre recherche nous mettrons à l’épreuve différents textes et expériences en passant de Berkeley à I. Rock ou de T. Reid à M. Wagner. Notre but aura été d'explorer les limites argumentatives et de montrer ce qui est impliqué par ces différentes appréciations et assignations de la distance dans tel ou tel espace déterminé. A chaque fois s'affrontent la géométrie de l’espace visuel et l’optique physiologique, mais au sein d'un même débat de fond qui consiste à savoir comment définir philosophiquement l’estimation de la distance ? / This thesis examines the difficulties in estimating the geometrical distance of visual space. Submitted in the field of Philosophy of Perception, this thesis is first discussed from an epistemological standpoint: how does one know that this distance is unknown or unknowable despite being perceived and discussed. The various works of Berkeley serve as a point of depart and establish a speculative framework as Berkeley held that judgment of distance results entirely from experience despite the fact that this distance cannot be seen in a phenomenal way. This thesis examines an essential question supported by this central problem, this time from an ontological position: how is the type of distance to be determined: is it unconsciously visible?tangible? or both visible and tangible at the same time? Can it be categorized in a hyperbolic space, or spherical space, or a strictly Euclidean space, or hyperbolic and spherical at the same time as Euclidean? In support of the thesis and research, various texts and experiences have been examined and contrasted, including those of Berkeley and I. Rock as well as T. Reid and M. Wagner. The goal has been to explore the limits of argumentation and to show what is implicated by these different accounts and assignment of distance in one, versus another, determined space; additionally studying subjects including the experience of the alleys or the so-called the moon illusion, which appeared to be demonstrative examples. In each instance, geometry of visual space and physiological optics confront one another, but at the center of this same fundamental debate is the question of how to define the estimation of distance philosophically?