This thesis deals with the description of constructive approach to teaching mathematics in the third grade of primary school. Teaching mathematics is focused on geometry, specifically on one way of introducing the area of the scalene triangle which describes the relation between a side and its height and corresponding area. In the thesis I describe six particular lessons, their preparation, process of their realization and my own reflections. In these lessons, I analyse some cognitive phenomena as well as social relationships among pupils. Furthermore, I present a detailed examination of tasks from the final diagnostic test, in which I aim towards proving success of this method of teaching mathematics. After four years, I attempt to verify the permanency of the knowledge pupils gained in these particular lessons. I illustrate this by presenting analysis of additional exercises. The whole experimental process was led within the method of releasing parameter. Individual lessons were in accordance with given stages of this method, as described in specialised literature. I verified that the above mentioned method is applicable in teaching mathematics even in the third grade of the primary school. KEYWORDS teachingstyles, perimeter and area, square grid, polygon, method of releasing parameter

Submitted by Erika Demachki (erikademachki@gmail.com) on 2014-08-29T20:47:14Z No. of bitstreams: 2 Poliedros_E_Teorema_de_Euler.pdf: 4810573 bytes, checksum: f1f57ad45cfd7dc575fe3c3e963b24c6 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2014-08-29T20:47:14Z (GMT). No. of bitstreams: 2 Poliedros_E_Teorema_de_Euler.pdf: 4810573 bytes, checksum: f1f57ad45cfd7dc575fe3c3e963b24c6 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2014-03-21 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This work aims is to demonstrate the Euler's Theorem for polyhedra, given by the equation V 􀀀 A + F = 2, where V; A and F are the numbers of vertices, edges and faces, respectively, the polyhedron. A historical survey of the main characters who contributed to the theme was elaborated. De nitions and properties of polygons and polyhedra were given. The statements were constructed in three distinct ways. The rst by Cauchy, commented by Professor Elon Lages Lima. This statement is valid for any polyhedron homeomorphic to a sphere and has the path planning of the polyhedron withdrawing one of its faces. The second statement was prepared by the professor Zoroastro Azambuja Filho, valid for any convex polyhedron, and its path projection of the polyhedron on a plane and comparison of the internal angles of polygons with projection angles of the polygon faces. The third statements was presented by Legendre, also valid for any convex polyhedron, and its path in the projection of a spherical polyhedron surface. We use the Girard's Formula, the sum of the interior angles of a spherical triangle, to complete the demonstration. This work also suggests methods of applying the proof of Euler's Theorem in the classroom for high school students, and resolution of vestibular exercises involving the subject. / Este trabalho tem por objetivo a demonstra c~ao do Teorema de Euler para poliedros, dado pela equa ção V 􀀀 A + F = 2, onde V; A e F são os n úmeros de v értices, arestas e faces, respectivamente, do poliedro. Foi elaborada uma pesquisa hist orica dos principais personagens que contribuiram para o tema. Foram dadas de ni ções e propriedades de pol ígonos e poliedros. As demonstra ções foram constru ídas em três caminhos distintos. A primeira por Cauchy, comentada pelo professor Elon Lages Lima. Esta demonstra ção é v álida para qualquer poliedro homeomorfo a uma esfera e tem como caminho a plani fica ção do poliedro retirando-se uma de suas faces. A segunda demonstra c~ao foi elaborada pelo professor Zoroastro Azambuja Filho, v álida para qualquer poliedro convexo e tem como caminho a proje ção do poliedro num plano e a compara c~ao dos ângulos internos dos pol ígonos da proje ção com os ângulos dos pol gonos das faces. A terceira demonstra c~ao foi apresentada por Legendre, tamb ém v álida para qualquer poliedro convexo e tem como caminho a projeção do poliedro em uma superf ície esf érica. Utiliza-se a F ormula de Girard, da soma dos ângulos internos de um tri^angulo esf érico, para concluir a demonstra ção. Este trabalho tamb ém sugere metodologias de aplica ção da demonstração do Teorema de Euler em sala de aula, para alunos do Ensino M édio, e resolu ção de exercí cios de vestibulares envolvendo o tema.

This study compared the effect of the use of physical manipulative with self-metacognitive questioning versus manipulative without self-metacognitive questioning on the knowledge acquisition in polygons. Participants were 220 sixth grade students. A pretest, treatment and posttest two-group design was used. There were two treatment groups: manipulative with self-metacognitive questioning (MAN+META) and manipulative without self-metacognitive questioning (MAN) Three distinct knowledge tests were designed by the researcher: Declarative, conditional and procedural. Declarative knowledge test consisted of 18 multiple-choice questions. The conditional and procedural knowledge tests consisted of six and ten open-ended questions respectively. Mixed design analysis of variance results revealed that there is a significant effect for time but no group-by-time interaction effect suggesting that both groups responded equally well to treatment in the amount of change in their scores on the two outcome measures: pretests and posttests. A follow up analysis (paired t-test) was conducted to evaluate the impact of time on students&rsquo / pretest and posttest scores. The large effect size indicated that there was a statistically significant increase in scores of all three tests.

Tyrimai buvo atliekami 2008 ir 2010 m. pavasarį Padauguvos miško biosferos poligone, kurio plotas yra 5782 ha. Kiekvienais metais tyrimų metu buvo išskirta apie 500 apskaitos aikštelių, kuriose įvertinta žiemos ganyklų būklė. Nustatyta, kad elninių žvėrių žiemos ganyklų būklė yra gera. Taip pat tyrimų metu nustatyta trako ir pomiškio medelių gausa, skabymo intensyvumas ir jų dinamika per 2008 – 2010 metus. Stirnų populiacijos būklė yra gera, gyvenanti intensyvaus trikdymo teritorijoje. Taurjiųjų elnių populiacija šioje teritorijoje yra vertinama kaip perspektyvi. Briedžių tankis Padauguvos miško biosferos poligono teritorijoje yra permažas. Padauguvos miško biosferos poligono teritorijoje vyrauja Gryni lapuočių ir mišrūs lapuočių su spygliuočiais medynai, kurie sudaro 78,0 % nuo viso medyno medyno ploto. / Research performed in spring of 2008 and 2010 in Padauguva forest biosphere plygon, which covers 5782 ha. Each year around 500 sampling plots were intercepted to evaluate condition of winter pastures. It was estimated, that winter pastures are in good condition. It was estimated intensity and dynamics of deer browsing on undergrowth and understorey tree and shrub species during the 2008-2010 period. Condition of Roe deer population, living in high disturbance zone, is good. Population of Red deer, living in same territory, considered as perspective. Density of Moose Padauguva forest biosphere polygon is too low. Broadleaves and mixed broadleaved with coniferous stands dominates in Padauguva forest biosphere polygon. They compose 78,0% of total area of forest stand.

Polygon-based classification applied on the unitemporal SPOT4 XS, SPOT5 XS, IKONOS XS, QuickBird XS and QuickBird Pansharpaned (PS) images is described. The study site is an agricultural area located near Karacabey, Turkey covering an area of about 95 km2. The objective was to assess the effect of the spatial resolution on the polygon-based classification of agricultural crops. Both the post-polygon and pre-polygon classifications were carried out. In the post-polygon classification, first, the images were classified on per-pixel basis through a Maximum Likelihood classifier. Then, for each field, the model class was computed and the field was assigned the label of the model class. In the pre-polygon classification, first, the mean values were calculated for each field. Then, the per-pixel Maximum Likelihood Classification was carried out using the mean bands. The post-polygon classification of the SPOT4 XS and SPOT5 XS images produced an overall accuracy of 76,1% and 81,4%, respectively. The IKONOS XS image provided the highest overall accuracy of 88,6%. On the other hand, the QuickBird XS and QuickBird PS images provided the overall accuracies of 83,7% and 85,8%, respectively. For the pre-polygon classification, the overall accuracies of the SPOT4 XS and SPOT5 XS images were computed to be 65,2% and 69,8%, respectively. Similar to the post-polygon classification, the IKONOS image provided the highest overall accuracy of 81,8% while the SPOT5 XS image revealed slightly better results than the SPOT4 XS image. The overall accuracies of the QuickBird XS and PS images were found to be 78,6% and 82,1%, respectively.

Made available in DSpace on 2016-06-02T20:29:21Z (GMT). No. of bitstreams: 1 5048.pdf: 1543384 bytes, checksum: 76d92ce057a127fc38905223eccb4a8c (MD5) Previous issue date: 2013-03-21 / The presented work aims to allow students to infer about the different concepts by building Mathematicians luminaire. For this, occur following the development of a didactic, teaching methodology that consists in presenting the project to the students who undergo an initial production or initial assessment - production of texts, conversations, problems - from which different activities are performed, worked in modules on the topics. It is then rated the performance obtained through the production end. This methodology was applied to two classes of 2nd year of high school in a public school. The first step began with a presentation of the sequence followed by initial production, which allowed students to exhibit their knowledge of mathematics involved in the production end (luminaire). The proposal focuses on various topics from basic mathematics possible, through different methodologies, the resumption of constant content addressed thus enabling advances in the teachinglearning process. The topics taken up are observed in the plane geometry, which underlies the study of Space Geometry. The practice of mathematical modeling is used to rescue the concept of function with real meaning to students. The news was on account of the discovery of mathematics Barcode. And finally, the closing of the work took place with the presentation of the final production performed by students. / O trabalho apresentado tem como objetivo permitir ao aluno inferir sobre os diferentes conceitos Matemáticos através da construção de luminária. Para isso, ocorrerá o desenvolvimento de uma sequência didática, metodologia de ensino que consiste em apresentar o projeto aos alunos que são submetidos a uma produção inicial ou avaliação inicial produção de textos, conversas, problemas a partir da qual são realizadas atividades diferenciadas, trabalhadas em módulos sobre os assuntos propostos. Em seguida, é avaliado o desempenho obtido através da produção final. Esta metodologia foi aplicada em duas turmas de 2os anos do Ensino Médio de uma Escola Pública. A primeira etapa iniciou-se com uma apresentação da sequência seguida da produção inicial, que permitiu ao aluno expor seus conhecimentos acerca da Matemática envolvida na produção final (luminária). A proposta privilegia vários tópicos da Matemática básica possibilitando, através de metodologias diferenciadas, a retomada constante dos conteúdos abordados permitindo, assim, avanços no processo ensino-aprendizagem. As retomadas são observadas nos tópicos da Geometria Plana, o que embasa o estudo da Geometria Espacial. A prática da Modelagem Matemática é utilizada para resgatar o conceito de Função com significado real para os alunos. A novidade ficou por conta da descoberta da Matemática do Código de Barras. E por fim, o fechamento do trabalho deu-se com a apresentação da produção final realizada pelos alunos.

[pt] Este trabalho apresenta um estudo comparativo de algumas representações em multi-resolução para linhas poligonais. São estudados as estruturas strip tree, arc tree e box tree, e suas variantes, comparando as velocidades de construção, de percorrimento (drawing), de operações de interseção e seleção (pick); e custo de armazenagem em memória. A comparação é feita usando bancos de dados cartográficos reais disponíveis na Internet. O objetivo do estudo é identificar técnicas e algoritmos adequados para exploração interativa de grandes bancos de dados cartográficos. / [en] This work presents a comparative study of some multiresolution representations for polygonal lines. We study the strip tree, the arc tree and the box tree data structures, comparing their performance for construction, drawing, intersection and selection; and memory storage costs. The comparation uses actual databases available in the Internet. The goal of this study is to identify techniques and algorithms for interactive exploration of large cartographic data bases.

Made available in DSpace on 2015-03-26T13:45:34Z (GMT). No. of bitstreams: 1 texto completo.pdf: 763497 bytes, checksum: 2a493cf586d69925a1022b40c47bd6f1 (MD5) Previous issue date: 2011-02-24 / In this paper we study a class of polygons on the Poincare disk, known as canonical Fricke polygon that are fundamental polygon related to a Fuchsian group, generating a surface of genus g. We rely on Article by Linda Keen [15], considering the case where the genus g > 0. Moreover, in order to apply the procedure adopted by Keen, we calculate the cycles and found the relationship of groups related to the tiles of the type {24λ + 4, 4} and {24λ − 12, 4}, which were originally obtained the tiles {12η − 8, 4} and {12η − 12, 4} given by Oliveira in [19]. Then we use a procedure developed by Agustini [1] to display the matrices associated with pairing functions coming this way to the vertices of the polygon associated key. / Neste trabalho fazemos um estudo de uma classe polígonos no disco de Poincaré, conhecidos como polígonos canônicos de Fricke, que são polígonos fundamentais relacionados a um grupo fuchsiano, gerador de uma superfície de gênero g. Nos baseamos no artigo de Linda Keen [15], considerando o caso em que o gênero g > 0. Além disso, com o intuito de aplicar o procedimento adotado por Keen, calculamos os ciclos e encontramos as relações do grupo relacionado aos ladrilhamentos de tipo {24λ +4, 4} e {24λ − 12, 4}, que originalmente foram obtidos dos ladrilhamentos {12η − 8, 4} e {12η − 12, 4} apresentados por Oliveira em [19]. Em seguida fazemos uso de um procedimento desenvolvido por Agustini [1] para exibir as matrizes associadas às funções de emparelhamento chegando desta maneira aos vértices do polígono fundamental associado.

Making 3D models with polygon modeling is the most common technique used for a 3D animated movie production, but there are also other good modeling techniques to work with. The aim of this thesis is to examine which of three chosen modeling technique is most appropriate to use for modeling a chair for a 3D animated movie production. I made three models of the same chair design and compared the results. The modeling technique used is polygon modeling, NURBS modeling and digital sculpting. A few factors were considered when I judged which one of the three techniques that was most suitable: The model's geometry, the workflow and the rendering (material and lightning). The three chairs were rendered in the same scene with the same lightning and settings. The results showed that the model's geometry and how smooth it is to work with the modeling technique matter most for judging which technique is the most appropriate. In addition, the results show that how the light falls and reflects the surface depends on how the geometry was placed on the model rather than which of the other modeling techniques that was used.

Aus der Einleitung: "Klassische VR/AR-Ausgabegeräte sind meist kopfgetragene Systeme oder 3D-Projektionsanlagen. In bestimmten Anwendungsfällen, zum Beispiel in der Wartung (Schreiber 2011) oder auch in Bauplanung und Bauausführung (Woodward 2011), verbieten sich diese Geräte aufgrund von Arbeitsschutzbestimmungen oder widrigen Einsatzbedingungen. Hier bieten sich Smartphones oder auf ähnlicher Technologie arbeitende Tablett-Computer als Alternative an, insbesondere dann, wenn stereoskopische Darstellung nicht benötigt wird."