Une déformation isomonodromique d'une sphère épointée est une famille de connexions logarithmiques plates sur cette dernière ayant toutes, à conjugaison globale près, la même représentation de monodromie. Ces objets sont paramétrés par les solutions d'une certaine famille d'équations aux dérivées partielles, les systèmes de Garnier, qui sont équivalents dans le cas de la sphère à quatre trous aux équations de Painlevé VI. L'objet des travaux présentés ici est de construire de nouvelles solutions algébriques des ces systèmes dans le cas de la sphère à cinq trous. Dans une première partie, nous classifions les déformations isomonodromiques algébriques obtenues par restriction aux droites d'une connexion logarithmique plate sur le plan projectif complexe dont le lieu polaire est une courbe quintique. On obtient ainsi deux nouvelles familles de solutions algébriques du système de Garnier associé. Dans une deuxième partie, nous exploitons le fait qu'une déformation isomonodromique algébrique correspond à une orbite finie sous l'action du groupe modulaire sur la variété des caractères de la sphère à cinq trous pour obtenir de nouveaux exemples de telles orbites. Nous employons pour ce faire la convolution intermédiaire sur les représentations de groupes libres développée par Katz Enfin, nous décrivons une généralisation partielle de ce procédé au cas d'un tore complexe à deux trous. / We call isomonodromic deformation any family of logarithmic flat connections over a punctured sphere having the same monodromy representation up to global conjugacy. These objects are parametrised by the solutions of a particular family of partial differential equations called Garnier systems, which are equivalent to the Painlevé VI equations in the four punctured case. The purpose of this thesis is to construct new algebraic solutions of these systems in the five punctured case. First, we give a classification of algebraic isomonodromic deformations obtained by restricting to lines some logarithmic flat connection over the complex projective plane whose singular locus is a quintic curve. We obtain two new families of algebraic solutions of the associated Garnier system. In a second part, we use the fact that any algebraic isomonodromic deformation corresponds to a finite orbit under the mapping class group action on the character variety of the five punctured sphere to obtain new examples of such orbits. We do this by using Katz's middle convolution on representations of free groups. Finally, we give a partial generalisation of this procedure in the case of a twice punctured complex torus.

Le pseudo-groupe de Malgrange d'un champ de vecteurs défini sur une variété est la sous-pro-variété de l'espace des jets de biholomorphismes locaux de cette variété obtenue en prenant la clôture de Zariski des flots du champ de vecteurs. Une équation différentielle ordinaire d'ordre 2 définit un champ de vecteurs sur une variété de dimension 3. Le pseudogroupe de Malgrange de ce dernier est de type différentiel d'ordre inférieur ou égal à 2. Une équation différentielle ordinaire d'ordre 2 est dite irréductible si ses solutions générales ne peuvent pas être exprimées à l'aide de solutions d'équations algébriques, différentielles linéaires ou différentielles d'ordre 1. Si le type différentiel du pseudo-groupe de Malgrange d'une équation d'ordre 2 est exactement 2 alors cette dernière est irréductible. Nous donnons plusieurs définitions du pseudo-groupe de Malgrange d'un champ de vecteurs équivalentes à la définition originale donnée par Bernard Malgrange. La définition du premier paragraphe nous permet d'appliquer un théorème de semi-continuité de la dimension des clôtures de Zariski des feuilles d'un feuilletage holomorphe de Philippe Bonnet. Nous obtenons le résultat suivant concernant les équations différentielles ordinaires dépendant de paramètres. Si le type différentiel du pseudo-groupe de Malgrange de l'équation spécialisée en une valeur des paramètres est à exactement 2 alors il en sera de même pour les pseudo-groupes de Malgrange de l'équation spécialisée en des valeurs générales des paramètres. Une première application de ce résultat est de redémontrer l'irréductibilité des équations de Painlevé pour des valeurs générales des paramètres. Une seconde application est de déterminer complètement les pseudo-groupes de Malgrange de ces équations pour des valeurs générales des paramètres. Les définitions du pseudo-groupe de Malgrange et les résultats de spécialisations s'adaptent aux équations aux q-différences. En appliquant ces résultats aux équations de Painlevé discrètes, nous obtenons le pseudo-groupe de Malgrange de ces dernières pour des valeurs générales des paramètres. / The Malgrange pseudogroup of a vector field on a variety is the sub-pro-variety of the jet space of local biholomorphisms of this variety obtained by taking the Zariski closure of the flow of the vector field. A second-order ordinary differential equation defines a vector field on a variety of dimension 3. The differential type of the Malgrange pseudogroup of this one is at most 2. A second-order ordinary differential equation is said to be irreductible if its general solutions can not be expressed using solutions of algebraic equations, linear differential equations or differential equations of order 1. If the differential type of the Malgrange pseudogroup of a second-order differential equation is exactly 2 then the latter is irreductible. We give several definitions of the Malgrange pseudogroup of a vector field which are equivalent to the original definition given by Bernard Malgrange. The definition of the first paragraph leads us to apply a semi-continuity theorem of the dimension of the Zariski closure of the leaves of a holomorphic foliation given by Philippe Bonnet. We obtain the following result about the ordinary differential equations which depend on parameters. If the differential type of the Malgrange pseudogroup of the equation specialized in one value of parameters is exactly two then it will be the same for the Malgrange pseudogroup of the equation specialized in a general value of parameters. A first application of this result is an other proof of the irreductibility of the Painlevé equations for general value of parameters. A second application is to fully determined the Malgrange pseudogroups of this equations for general value of parameters. The definitions of the Malgrange pseudogroup of a vector field and the specialisation results can be adapted the q-difference equations. By applying this results to the discret Painlevé equations, we fully determined the Malgrange pseudogroup of the latters for general value of parameters.

Accurate information about tree volume in tropical vegetation formations is critical for the identification of potential areas for sustainable timber production, carbon estimation and biodiversity conservation. Difficult access and the cost of obtaining a large number of samples needed for accurate wood volume and biomass determination are often barriers for carrying out inventories and studies in natural forests in Brazil. Therefore, the development of more efficient techniques of mensuration in tropical forests is an important mechanism for conservation, management and production advancement. The main purposes of this thesis are: introducing a new method for quantifying vertical and horizontal structures by using principal component analysis (PCA); developing two different approaches of volume modeling, one based on DBH and another based on crown area; proposing a new taper equation for native vegetation in three different formations; and estimating upper section diameters to become the geometric form method useful in natural vegetation in Brazil and reducing dependence on destructive measurements. / Informações corretas sobre o volume de árvores em formações de vegetação natural são fundamentais para a identificação de áreas potenciais para produção madeireira sustentável, estimativa de carbono e conservação da biodiversidade. Dificuldade de acesso e altos custos na obtenção de amostras necessárias para estimativas precisas de volume e biomassa são barreiras frequentes na condução de inventários e estudos florestais no Brasil. Dessa forma, o desenvolvimento de técnicas mais eficientes de mensuração em florestas tropicais é um importante mecanismo para o avanço da conservação, manejo e produção. Os principais objetivos deste trabalho foram: introduzir um novo método de quantificação das estruturas vertical e horizontal por meio do uso de análise de componentes principais (ACP); desenvolver modelos volumétricos baseados em DAP e modelos baseados em área de copa; propor uma nova função de afilamento aplicada a três diferentes formações vegetais; e estimar alturas em que deverão ter diâmetros medidos ao longo da árvore para tornar o método geométrico útil em formações naturais no Brasil, e reduzindo a necessidade de mensurações que requerem o abatimento das árvores.

Die Habilitationsschrift beschäftigt sich mit der Einbeziehung von Elementen der 3D-Computergrafik in den Unterricht der analytischen Geometrie in der Sekundarstufe II. Vorrangiges Ziel dabei ist, den Unterricht praxisnäher, anschaulicher und attraktiver zu gestalten. Im Bereich des Computereinsatzes im Mathematikunterricht weist die 3D-Computergrafik die Besonderheit auf, dass sie sowohl als Unterrichtsgegenstand als auch als Hilfsmittel für die Visualisierung und für experimentelles Arbeiten von Bedeutung ist. Grundlagen der in der vorliegenden Arbeit angestellten Überlegungen und unterbreiteten Vorschläge bilden einerseits eine Analyse der analytischen Geometrie als schulischer Lerninhalt einschließlich der dabei verfolgten Ziele (Kapitel 1) sowie andererseits die mathematischen Grundlagen der 3D-Computergrafik und ihrer Anwendungen (Kapitel 2). Basierend auf diesen beiden Aspekten werden in Kapitel 3 Potenzen und Ziele des Einsatzes dreidimensionaler Grafiksoftware und der Thematisierung mathematischer Grundlagen der Computergrafik im Stoffgebiet Analytische Geometrie herausgearbeitet. Es wird begründet, dass die Einbeziehung von Elementen der 3D-Computergrafik wesentlich dazu beitragen kann, den Intentionen des Unterrichts in analytischer Geometrie gerecht zu werden und den oft formalen Charakter der Behandlung dieses Themas zu überwinden sowie geometrische Betrachtungsweisen in den Vordergrund zu rücken. In Kapitel 4 erfolgt eine Konkretisierung dieser Überlegungen zu Unterrichtsvorschlägen für die Einbeziehung von Elementen der 3D-Computergrafik in das Stoffgebiet anhand einer Reihe von Gegenstandsbereichen. Erfahrungen aus Unterrichtsprojekten, die auf der Grundlage einiger der in Kapitel 4 entwickelten Konzepte durchgeführt wurden, sind Gegenstand von Kapitel 5. / The book is concerned with possibilities for using the potential of 3D computer graphics in mathematics education in grammar schools, especially in the subject analytic geometry, to improve student''s understanding and motivation. Computer graphics can be used as a tool for visualization of ideas and thoughts and can be also considered as a teaching subject because its mathematical foundations are closely related to the classical contents of mathematics education in grammar schools. Proposals, which are developed in the book, are based both on an analysis of history, aims and problems of teaching analytic geometry (chapter 1) and mathematical foundations of 3D computer graphics and its applications (chapter 2). Based on both aspects potencies and goals of the use of three-dimensional graphics software and the treatment of mathematically based working principles of computer graphics in mathematics education are worked out in chapter 3. It is justified that the inclusion of elements of 3D computer graphics can essentially contribute to the intentions of the instruction in analytic geometry and to overcome the often formal character of the treatment of this topic as well as moving geometrical approaches into the foreground. In chapter 4, these considerations are substantiated and concepts and suggestions for the inclusion of elements of computer graphics into a variety of subject areas are developed. Experiences from instruction projects in analytic geometry classes, that were carried out some of the concepts developed in chapter 4 on the basis, are object of chapter 5.

Made available in DSpace on 2016-04-27T16:57:02Z (GMT). No. of bitstreams: 1 Marcia Varella.pdf: 5652142 bytes, checksum: 5d52ae8ee1cbd69935aed388298b43b5 (MD5) Previous issue date: 2010-11-25 / Secretaria da Educação do Estado de São Paulo / This study aims to analyze how the authors of teaching materials of high school have organized tasks proposals with proofs and demonstrations on content proposed of Analytic Geometry on 3rd series of high school. With a view to proposing some thoughts in this respect, we analyze the collections of textbooks approved by the National Program of textbook for high school (PNLEM/2009) and the notebooks bimonthly adopted by the Education Secretary of the State of São Paulo (SEESP/2009), made available to students and teachers, distinctly. We judge the relevance in analyzing these materials because we act in the public network of State of São Paulo aiming contributions that may occur. The analysis of these materials was carried out considering the tasks proposed on the content Analytic Geometry, limited to studying the equation of a line. The theoretical contribution that substantiate our analyses followed the assumptions of Anthropological Theory of didactic Yves Chevallard (1999) that focuses the study of praxeological organization mathematics and didactics designed for teaching and learning of Mathematics and the work of Nicolas Balacheff (1988), which aims to study the typology of proofs produced by students. Supported by this theoretical, we realize our analyses with the purpose of responding to our question: Which mathematics and didactics organizations involving proofs and demonstration are proposed for didactics materials of high school, on content Analytic Geometry? Answering this question, we developed a qualitative research with approach documentary and from survey bibliographic we might have idea of problems involved in the teaching and learning of proofs and demonstrations on mathematical content, both in elementary and high school. The analysis of these materials confirmed two of our research hypotheses and showed that the work with proofs and demonstrations in didactics materials was not abandoned, but the clarity of the terms belonging to deductive system is unsatisfactory for understanding of what is demonstration in Mathematics / O presente estudo tem como objetivo analisar como os autores de materiais didáticos do Ensino Médio organizaram as tarefas propostas envolvendo provas e demonstrações no conteúdo Geometria Analítica para a 3ª. série do Ensino Médio. Com o intuito de propor algumas reflexões a esse respeito, decidimos analisar as coleções de livros didáticos aprovadas pelo Programa Nacional do Livro Didático para o Ensino Médio (PNLEM/2009) e os cadernos bimestrais adotados pela Secretaria da Educação do Estado de São Paulo (SEESP/2009), disponibilizados para alunos e professores, distintamente. Julgamos a pertinência de analisar conjuntamente esses materiais por atuarmos na rede pública estadual paulista, visando às contribuições que vierem a ocorrer. A análise desses materiais foi realizada considerando as tarefas propostas sobre o conteúdo Geometria Analítica, limitado ao estudo da equação de uma reta. O aporte teórico que fundamentou nossas análises seguiu os pressupostos da Teoria Antropológica do Didático de Yves Chevallard (1999), que focaliza o estudo das organizações praxeológicas Matemática e didática pensadas para o ensino e aprendizagem da Matemática, e o trabalho de Nicolas Balacheff (1988), que visa ao estudo da tipologia de provas produzidas por alunos. Apoiado por esse referencial teórico efetivamos nossas análises com o intuito de responder à nossa questão de pesquisa: Quais organizações Matemáticas e didáticas envolvendo prova e demonstração são propostas por materiais didáticos do Ensino Médio, no conteúdo Geometria Analítica? Visando a responder a esta questão, desenvolvemos uma pesquisa qualitativa com enfoque documental, e a partir do levantamento bibliográfico pudemos ter ideia da problemática envolvida no ensino e na aprendizagem de provas e demonstrações em conteúdos matemáticos, tanto no Ensino Fundamental quanto no Ensino Médio. A análise desses materiais confirmou duas de nossas hipóteses de pesquisa e nos revelou que o trabalho com provas e demonstrações em materiais didáticos não foi abandonado, porém a clareza dos termos pertencentes ao sistema dedutivo é insatisfatória no que diz respeito à compreensão do que seja passível de demonstração em Matemática

Made available in DSpace on 2016-04-27T16:57:08Z (GMT). No. of bitstreams: 1 Denilson Goncalves Pereira.pdf: 7924777 bytes, checksum: 477a51645572c92238dd48b6a98b1d8e (MD5) Previous issue date: 2011-05-26 / Secretaria da Educação do Estado de São Paulo / The present work is part of a project that aims to examine how teaching proposal in the classroom can be organized and developed, exploring the everyday contexts in other areas of knowledge and of mathematics itself, with a view to building some expectations learning. Our research involves three mathematics teachers from public schools in São Paulo, each one with a class of Grade 3 High School, during the night, totaling 122 students. The guest teachers work in school EE Padre Anchieta located in Diadema (SP). The project aims to contribute to the professional development of teachers in a consistent manner which is intended to be his practice in the classroom, through a strategy of closely linking theory, teaching practice and research. Through the collaborative work and the hypothetical learning trajectory (HLT), we believe that teachers can reflect about their teaching practice, focusing on a teaching strategy in which the student is motivated to investigate and assign meaning to their learning autonomously. After the teachers know the whole project and the primary HLT by the teacher researcher, with assistance from teachers applicators, that develop a course in class. During this stage, the researcher observed and recorded with audio recordings and notes, teachers reported applicators, along with the protocols of the students, which occurred in each proposed activity, pointing out the mistakes, difficulties, interactions, assumptions that were questioned in elaboration of the trajectory and other observations / O presente trabalho faz parte de um projeto que tem por objetivo analisar o modo como podem ser organizadas e desenvolvidas propostas didáticas em sala de aula, explorando contextos do cotidiano, de diversas áreas de conhecimento e da Matemática, com vistas a contemplar algumas expectativas de aprendizagem. Nossa pesquisa envolve três professores de Matemática da rede pública estadual paulista, cada qual com uma turma da terceira série do Ensino Médio, período noturno, totalizando 122 alunos. Os professores convidados atuam na E.E. Padre Anchieta, localizada em Diadema. O projeto visa a contribuir para o desenvolvimento profissional dos professores de forma coerente com o que se pretende que seja sua prática em sala de aula, mediante uma estratégia de estreita articulação entre teoria, prática docente e pesquisa. Por meio de uma trajetória hipotética de aprendizagem (THA) e do trabalho colaborativo, acreditamos que o professor pode refletir sobre sua prática docente, privilegiando uma estratégia de ensino na qual o aluno seja motivado a investigar e atribuir significado a sua aprendizagem de forma autônoma. A THA preliminar foi elaborada pelo professor pesquisador, com a contribuição dos professores aplicadores, e cada um destes a desenvolveu em uma turma. Nessa etapa, o pesquisador fez observações e registro, por meio de gravações de áudio e anotações, enquanto os professores aplicadores relataram, junto com os protocolos dos alunos, o que ocorreu em cada atividade proposta, apontando os erros, dificuldades, interações, hipóteses que foram questionadas na elaboração da trajetória, além de outras observações

Made available in DSpace on 2016-04-27T16:57:36Z (GMT). No. of bitstreams: 1 Acylena Coelho Costa.pdf: 4495391 bytes, checksum: 036e84e7258e8b0ddf6bc886cce6222d (MD5) Previous issue date: 2015-04-24 / Universidade do Estado do Pará / This research aims to analyze how the authors of textbooks organized the activities proposed in relation to the study of Line and Planning for the teaching of Analytic Geometry in Space. Analyses of textbooks substantiate mainly on Anthropological Theory of the Didactic (TAD), with regard to praxeologias proposed by Chevallard (1999) and in didactic variables for the teaching of Analytic Geometry in Space established by Lebeau (2009). Based on the theoretical framework adopted we conducted a qualitative investigation of documentary type, based on a literature review on four textbooks Analytic Geometry devoted to higher education. The methodology used in our research was supported in manual analysis methodology developed by Chaachoua (2014a) analyzing the textbooks the following: time of writing, representation, structure, ecological analysis and praxeological analysis. For regards the praxeological analysis identified six types present in the analyzed manual tasks, namely to: determine the equation of the line in space, determining the straight condition of parallelism in space, to determine the alignment condition of points in space, present plane equation in space as a property of orthogonality, determine a plan characterized by two intersecting lines and characterize algebraically the parallelogram. Among the findings it can be inferred that the authors favor an algebraic modeling of mathematical objects, as well as the techniques adopted by them are situated in the field of Linear Algebra and Analytic Geometry / A presente pesquisa tem como objetivo analisar como os autores de livros didáticos organizaram as atividades propostas no que se refere ao estudo da Reta e do Plano para o ensino da Geometria Analítica no Espaço. As análises dos livros didáticos fundamentaram-se essencialmente na Teoria Antropológica do Didático (TAD), quanto às praxeologias, propostas por Chevallard (1999) e nas variáveis didáticas para o ensino da Geometria Analítica no Espaço estabelecidas por Lebeau (2009). Com base no referencial teórico adotado realizamos uma investigação de caráter qualitativo do tipo documental, partindo de um levantamento bibliográfico em quatro livros didáticos de Geometria Analítica destinados ao ensino superior. A metodologia adotada em nossa pesquisa foi subsidiada na metodologia de análise de manuais desenvolvida por Chaachoua (2014a) analisando nos livros didáticos os seguintes aspectos: momento da edição, representatividade, estrutura, análise ecológica e análise praxeológica. Em relação a análise praxeológica identificamos seis tipos de tarefas presentes nos manuais analisados, a saber: determinar a equação da reta no espaço, determinar a condição de paralelismo de retas no espaço, determinar a condição de alinhamento de pontos no espaço, apresentar a equação do plano no espaço como uma propriedade da ortogonalidade, determinar um plano caracterizado por duas retas secantes e caracterizar algebricamente o paralelogramo. Dentre os resultados encontrados é possível inferir que os autores privilegiam uma modelização algébrica dos objetos matemáticos, bem como as técnicas adotadas pelos mesmos encontram-se situadas no campo da Álgebra Linear e da Geometria Analítica

Orientador: Prof. Dr. Sinuê Dayan Barbero Lodovici / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Mestrado Profissional em Matemática em Rede Nacional - PROFMAT, 2014.

Submitted by Cássia Santos (cassia.bcufg@gmail.com) on 2016-08-10T13:40:03Z No. of bitstreams: 2 Dissertação - Vanessa Ribeiro Soares - 2016.pdf: 11844437 bytes, checksum: 03d509603ea96f2647ea2764aea87d17 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2016-08-10T13:42:09Z (GMT) No. of bitstreams: 2 Dissertação - Vanessa Ribeiro Soares - 2016.pdf: 11844437 bytes, checksum: 03d509603ea96f2647ea2764aea87d17 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2016-08-10T13:42:09Z (GMT). No. of bitstreams: 2 Dissertação - Vanessa Ribeiro Soares - 2016.pdf: 11844437 bytes, checksum: 03d509603ea96f2647ea2764aea87d17 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2016-05-30 / This work has the purpose contribute to the improvement in some teaching contents of analytic geometry and trigonometry in high school . The content work was based on the National Curriculum Parameters, highlighting de nitions, theorems and properties necessary for the development of student learning. The theme was chosen after a practical experience involving the Naval Battle game in order to reduce the students' di culties. The playful work, as the game, has a practical application that does the student become familiar with the content. That's an interesting way to propose problems and solutions involving the content. Thus becomes something attractive to the student and encourages creativity in nding problems solutions. / O trabalho tem como objetivo contribuir para o aprimoramento no ensino de alguns conteúdos de Geometria Analítica e Trigonometria no Ensino Médio. Dentro dos Parâmetros Curriculares Nacionais, trabalhamos o conteúdo destacando de nições, teoremas e propriedades necessárias para o desenvolvimento de aprendizagem do aluno. O tema foi escolhido depois de uma experiência prática envolvendo o jogo Batalha Naval a m de diminuir as di culdades dos alunos. O trabalho lúdico, como o jogo, tem uma aplicação prática que faz o aluno se familiarizar com os conceitos. É uma forma interessante de propor problemas e soluções envolvendo o conceitos. Assim se torna algo atrativo para o aluno e favorece a criatividade na busca de soluções para os problemas.

Made available in DSpace on 2016-06-02T20:02:48Z (GMT). No. of bitstreams: 1 3164.pdf: 2079123 bytes, checksum: 784894d4279af30e5ff5b035c4f73ba1 (MD5) Previous issue date: 2010-04-08 / This work involves the construction of a virtual learning environment (AVA) on fundamental concepts of Analytical Geometry (GA) using GeoGebra resources to be applied in a room of the 1st year of a Bachelor's Degree in Mathematics from a private college. Throughout its history the teacher develops ways of presenting the ideas you want to convey and that is the essence of pedagogical reasoning. As a teacher of this subject, I note in my career and the exchange of experiences with other professionals, a common sense about the mechanization of techniques and lack of connection between algebra and geometry, as in this discipline. Reflecting, experiencing and telling me about this issue, I think much of this problem in a limited way that we present these ideas in our classes. The advent of information technology, especially software for dynamic geometry, can provide greater ease in viewing this connection. Motivated by the possibility of using dynamic geometry software in the teaching of GA, the use of Moodle to create an AVA and inspired by the discipline of Information Technology for Teaching Science and Mathematics, the curriculum component of the Masters in Teaching Professional Exact Sciences, idealized this work from the construction of the 3D viewer in GeoGebra and the creation of an AVA in Moodle. The AVA has been divided into four modules with the following basics of GA: points, vectors, lines and planes. These grounds were presented through Moodle resources in the form of theory, lesson and evaluation. The activities were conducted as semi-distance (in the computer lab school) and totally distance (in their students). We hope with this work is expanding the size that most students have to GA and the fundamental connection between algebra and geometry existing in this discipline, and encourage the use of technological resources as teaching tools. / Este trabalho consiste na construção de um ambiente virtual de aprendizagem (AVA) sobre conceitos fundamentais de Geometria Analítica (G.A.), utilizando recursos do Geogebra, para ser aplicado em uma sala do 1º ano de um curso de Licenciatura em Matemática de uma faculdade privada. Ao longo de sua trajetória o professor desenvolve formas de apresentar as ideias que deseja transmitir e essa e a essência do raciocínio pedagógico. Como professor desta disciplina, constato em minha trajetória e na troca de experiencias com outros profissionais da área, um senso comum a respeito da mecanização de técnicas e da falta de conexão entre a Álgebra e a Geometria, tao presente nesta disciplina. Refletindo, experimentando e me informando sobre essa questão, penso que grande parte dessa problemática esta na forma limitada com que apresentamos essas ideias em nossas aulas. O advento da informatica, em especial de softwares de geometria dinâmica, pode proporcionar uma maior facilidade para visualização desta conexão. Motivado pela possibilidade do uso de softwares de geometria dinâmica no ensino de G.A., do uso do Moodle para criação de um AVA e inspirado pela disciplina de Tecnologias da Informação para o Ensino de Ciências e Matemática, componente curricular do programa de Mestrado Profissional em Ensino de Ciências Exatas, idealizei este trabalho a partir da construção de visualizadores em 3D no Geogebra e da criação de um AVA no Moodle. O AVA foi dividido em quatro módulos com os seguintes fundamentos básicos de G.A.: pontos, vetores, retas e planos. Estes fundamentos foram apresentados através dos recursos do Moodle na forma de teoria, lição e avaliação. As atividades foram desenvolvidas na forma semipresencial (no laboratório de informatica da escola) e totalmente a distancia (na casa dos alunos). Esperamos com esse trabalho estar ampliando a dimensão que a maioria dos estudantes tem de G.A e a conexão fundamental entre a Álgebra e a Geometria existente nesta disciplina, alem de estimular o uso de recursos tecnológicos como ferramentas de ensino.