Aprendizagem significativa: uma proposta de ensino e aprendizagem da geometria euclidiana espacial no ensino médio

This dissertation is a research based on the Meaningful Learning Theory, with students from the second year of High School, in the city named Capinzal do Norte, state of Maranhão. The pedagogic approach of this research focuses on what to do and how to do so students can better grasp knowledge inherent to the Euclidean Special Geometry in a more meaningful and changing way, also that information may be kept longer in their brain, so it can last longer in the present and future. The methodological strategy adopted was the research-action, followed by the constant observance of a researcher on the matter with the purpose to ensure consistent results, which come from the use of a variety of data collector instruments, such as: Concept Maps, manipulatives, educational softwares and application of evaluative tests, besides the observations made throughout the process of investigation and the diagnosis itself. It is all due to the fact that we rely on the premise that knowledge is assimilated in particular and idiosyncratic ways, which means each and every student learns in different ways and in different periods of time. That is why it is so important to develop diversified methodologies to the same subject. This research adds to the other ones related to the theoretical frameworks of the Meaningful Learning Theory, of Concept Maps, of the use of technology on the educational process and of manipulatives, which purpose is to connect their common dots. This pedagogical intervention also focuses on the construction of the educational orientations with applicability directly on class, directed specially by the Mathematics teacher of the basic education, who might use them during your teaching practice. Such guidelines established here as an educational product aim to follow the Theory's assumptions that serves as basis to this research, thus becoming an educational element with a relevant significance. The results, with which we are faced, proved overwhelming to the proposed objectives in terms of learning, which were evident in the construction of Conceptual Maps, as well as in the use of Concrete Materials, in addition to serving as a motivational element to participating students of research. The results obtained are indeed reliable in terms of learning, considered the expected goals, and made us certain that the way we have approached the subject is consistent with a holistic education and that at the same time values the tiniest details, which are fundamental to all the learning-teaching process.

Geometrias não-eucludianas como anomalias: implicações para o ensino de geometria e medidas

This present research the aim to show to the reader the Geometry non-Euclidean while anomaly indicating the pedagogical implications and then propose a sequence of activities, divided into three blocks which show the relationship of Euclidean geometry with non-Euclidean, taking the Euclidean with respect to analysis of the anomaly in non-Euclidean. PPGECNM is tied to the line of research of History, Philosophy and Sociology of Science in the Teaching of Natural Sciences and Mathematics. Treat so on Euclid of Alexandria, his most famous work The Elements and moreover, emphasize the Fifth Postulate of Euclid, particularly the difficulties (which lasted several centuries) that mathematicians have to understand him. Until the eighteenth century, three mathematicians: Lobachevsky (1793 - 1856), Bolyai (1775 - 1856) and Gauss (1777-1855) was convinced that this axiom was correct and that there was another geometry (anomalous) as consistent as the Euclid, but that did not adapt into their parameters. It is attributed to the emergence of these three non-Euclidean geometry. For the course methodology we started with some bibliographical definitions about anomalies, after we ve featured so that our definition are better understood by the readers and then only deal geometries non-Euclidean (Hyperbolic Geometry, Spherical Geometry and Taxicab Geometry) confronting them with the Euclidean to analyze the anomalies existing in non-Euclidean geometries and observe its importance to the teaching. After this characterization follows the empirical part of the proposal which consisted the application of three blocks of activities in search of pedagogical implications of anomaly. The first on parallel lines, the second on study of triangles and the third on the shortest distance between two points. These blocks offer a work with basic elements of geometry from a historical and investigative study of geometries non-Euclidean while anomaly so the concept is understood along with it s properties without necessarily be linked to the image of the geometric elements and thus expanding or adapting to other references. For example, the block applied on the second day of activities that provides extend the result of the sum of the internal angles of any triangle, to realize that is not always 180° (only when Euclid is a reference that this conclusion can be drawn)

As geometrias urbana e isoperimétrica: uma alternativa de uso em sala de aula

The main goal of the present study is to propose a methodological approach to the teaching of Geometry and, in particular, to the construction of the concepts of circle (circumference) and ellipse by 7th and 8th grade students. In order to aid the students in the construction of these concepts, we developed a module based on mathematical modeling, and both Urban Geometry (Taxicab Geometry) and Isoperimetric Geometry. Our analysis was based on Jean Piaget's Equilibrium Theory. Emphasizing the use of intuition based on accumulated past experiences, the students were encouraged to come up with a hypothesis, try it out, discuss it with their peers, and derive conclusions. Although the graphs of circles and ellipses assume different shapes in Urban and Isoperimetric Geometry than they do in the standard Euclidian Geometry, their definitions are identical regardless of the metric used. Thus, by comparing the graphs produced in the different metrics, the students were able to consolidate their understanding of these concepts. The intervention took place in a series of small group activities. At the end of the study, the 53 seventh grade and the 55 eighth grade students had a better understanding of the concepts of circle and ellipse

Pecolação em uma rede multifractal

In this work we present the principal fractals, their caracteristics, properties abd their classification, comparing them to Euclidean Geometry Elements. We show the importance of the Fractal Geometry in the analysis of several elements of our society. We emphasize the importance of an appropriate definition of dimension to these objects, because the definition we presently know doesn t see a satisfactory one. As an instrument to obtain these dimentions we present the Method to count boxes, of Hausdorff- Besicovich and the Scale Method. We also study the Percolation Process in the square lattice, comparing it to percolation in the multifractal subject Qmf, where we observe som differences between these two process. We analize the histogram grafic of the percolating lattices versus the site occupation probability p, and other numerical simulations. And finaly, we show that we can estimate the fractal dimension of the percolation cluster and that the percolatin in a multifractal suport is in the same universality class as standard percolation. We observe that the area of the blocks of Qmf is variable, pc is a function of p which is related to the anisotropy of Qmf

Calculando distância em geometria espacial usando material manipulável como recurso didático

This work presents a proposal for introducing the teaching of Geometry Space study attempts to demonstrate that the use of manipulatives as a teaching resource can be an alternative learning facilitator for fixing the primitive concepts of geometry, the postulates and theorems, position relationships between points, lines and planes and calculating distances. The development makes use of a sequence of activities aimed at ensuring that students can build a more systematic learning and these are divided into four steps

Arquitetura da (in)segurança: estudando relações entre configuração espacial, artifícios de segurança e violência urbana no bairro Manaíra, João Pessoa, Paraíba

João Pessoa, the capital city of the state of Paraíba (Northeast Brazil), is reputed throughout the country as a quiet place, although it has been acquiring, over the past years, an urban character with social implications similar to those of major metropolitan Brazilian areas. The new situation is evident by the social inequalities, with the creation of confined spaces, which segregate and cause enclosure of the inhabitants, leading to death the public space. This study correlates accessibility in spatial structure with two types of crime data, burglary and robbery, recorded in 2008 and 2009, by the Secretaria de Segurança da Paraíba (The government agency public in charge of safety), in the district of Manaíra, an upper middle class neighborhood, which has, in recent times, been considered one of the most violent areas in João Pessoa. Sought to understand connections between these events and morpho-social aspects of the built environment, where examined the spatial properties, such as accessibility of the urban net, the presence of control measures, the safety of buildings and their uses. Spatial properties were also validated by the observation of pedestrian flows at strategic points of the study area. It was concluded that the presence of intense flows helps to attract potential thieves, physical security and control offers little protection

Aparências da forma e forma do espaço: análise da configuração espacial de residências unifamiliares dos anos 1970 em João Pessoa PB

Assuming that the form of a building shell and its content the spatial form are distinct dimensions of architecture - however indivisible and interdependent -, this study focus, in the light of the Social Logic of Space (HILLIER; HANSON, 1984), on the intrinsic properties through which domestic space was structured in a sample of single-family dwellings built in João Pessoa (PB) during the 1970s - when the vocabulary of modern architecture still prevailed in Brazil though sharing the urban scene with other architectural trends -, in order to investigate regularities or divergences underlying their conception. These dwellings were originally classified (ARAÚJO, 2010a) in five categories defined according to the form of their building shells and to their prevailing construction techniques: (1) Brazilian modern legacy (considered as truly Brazilian modern style); (2) Paulista architecture (that refers to the modern production of São Paulo, Brazil, from the 1950s through the 1970s); (3) experiences of rationalization and prefabrication ; (4) experiences of adaptation to the climate (referring to a design strongly influenced by the hot and humid climate of North-eastern Brazil); and (5) hybrid (to account for a kind of stylistic hybridism that includes formal attributes, which evoke our colonial past). This study aims to determine, through the analyses of nineteen cases that represent each category, whether this taxonomy corresponds to distinct modes of spatial configuration. This research therefore proposes an approach to the classification of domestic architecture based on topological properties. The dwellings spatial organization was represented, quantified and analyzed, their spatial properties explored in consonance with one another and with the literature. Results pointed out that there is no evidence of a reciprocal relationship between the formal look of the built shells and their respective spatial structures

Geografia da dominação: um estudo sobre a organização espacial da terra do sal (Macau-RN)

This work aims to understand the spatial organization in the Town of Macau, State of Rio Grande do Norte, Brazil. This approach focus on bringing back the history of the town, the main personages responsible for the construction of this place, denominated "social agents", as well as its social processes and the spatial forms derived from them. As the personages and their practices were identified, it was found out the existence of a driving force for structuring, interlocking, and maintaining the actions carried out by the social agents during the time. Such actions were materialized in the urban space: "the social segregation". The social segregation takes place as a specific geography of domination. The outcome of those owning the best areas" and ways of accessibility in the urban space, varies from the enrichment by property valorization, because of the concentration of public investments of infrastructure, to the comfort of easily reaching all the daily needs related to the displacements in the urban space. In the latter case, such facility has contributed to improve life quality. While one takes advantage of the location in the urban space, others are negatively affected by the same process. This research identified the salina worker as the weakest element of this social structure, occupying the urban periphery of the town of Macau. Such area is characterized by the lack of services and urban equipment in opposition to the center of the town, the locus of elite. This way, it is established the most known segregation pattern: center x periphery, in which the space acts as a mechanism of segregation

Plásticos reforçados a base de tecidos híbridos: efeitos da anisotropia e geometria normativa na caracterização mecânica e da fratura

As most current studies, reinforced plastics have been, in recent years, a viable alternative in building structural elements of medium and large, since the lightness accompanied by high performance possible. The design of hybrid polymer composites (combination of different types of reinforcements) may enable structural applications thereof, facing the most severe service conditions. Within this class of composite materials, reinforced the underlying tissues hybrid high performance are taking space when your application requires high load bearing and high rigidity. The objective of this research work is to study the challenges in designing these fabrics bring these materials as to its mechanical characterization and fracture mechanisms involved. Some parameters associated with the process and / or form of hybridization stand out as influential factors in the final performance of the material such as the presence of anisotropy, so the fabric weave, the process of making the same, normative geometry of the specimens, among others. This sense, four laminates were developed based hybrid reinforcement fabrics involving AS4 carbon fiber, kevlar and glass 49-E as the matrix epoxy vinyl ester resin (DERAKANE 411-350). All laminates were formed each with four layers of reinforcements. Depending on the hybrid fabric, all the influencing factors mentioned above have been studied for laminates. All laminates were manufactured industrially used being the lamination process manual (hand-lay-up). All mechanical characterization and study of the mechanism of fracture (fracture mechanics) was developed for laminates subjected to uniaxial tensile test, bending in three and uniaxial compression. The analysis of fracture mechanisms were held involving the macroscopic, optical microscopy and scanning electron microscopy

Análise de agrupamentos dos dados de DFA oriundos de perfis elétricos de indução de poços de petróleo

The main objective of this study is to apply recently developed methods of physical-statistic to time series analysis, particularly in electrical induction s profiles of oil wells data, to study the petrophysical similarity of those wells in a spatial distribution. For this, we used the DFA method in order to know if we can or not use this technique to characterize spatially the fields. After obtain the DFA values for all wells, we applied clustering analysis. To do these tests we used the non-hierarchical method called K-means. Usually based on the Euclidean distance, the K-means consists in dividing the elements of a data matrix N in k groups, so that the similarities among elements belonging to different groups are the smallest possible. In order to test if a dataset generated by the K-means method or randomly generated datasets form spatial patterns, we created the parameter Ω (index of neighborhood). High values of Ω reveals more aggregated data and low values of Ω show scattered data or data without spatial correlation. Thus we concluded that data from the DFA of 54 wells are grouped and can be used to characterize spatial fields. Applying contour level technique we confirm the results obtained by the K-means, confirming that DFA is effective to perform spatial analysis

Sistemas de informação geográfica e análise espacial de dados como ferramentas para determinação de agregação espacial de doenças: a hanseníase como modelo

This work demonstrates the importance of using tools used in geographic information systems (GIS) and spatial data analysis (SDA) for the study of infectious diseases. Analysis methods were used to describe more fully the spatial distribution of a particular disease by incorporating the geographical element in the analysis. In Chapter 1, we report the historical evolution of these techniques in the field of human health and use Hansen s disease (leprosy) in Rio Grande do Norte as an example. In Chapter 2, we introduced a few basic theoretical concepts on the methodology and classified the types of spatial data commonly treated. Chapters 3 and 4 defined and demonstrated the use of the two most important techniques for analysis of health data, which are data point processes and data area. We modelled the case distribution of Hansen s disease in the city of Mossoró - RN. In the analysis, we used R scripts and made available routines and analitical procedures developed by the author. This approach can be easily used by researchers in several areas. As practical results, major risk areas in Mossoró leprosy were detected, and its association with the socioeconomic profile of the population at risk was found. Moreover, it is clearly shown that his approach could be of great help to be used continuously in data analysis and processing, allowing the development of new strategies to work might increase the use of such techniques in data analysis in health care

Geometria e simetria nas rendas de bilro: contribuições para matemática escolar

A tese tem como objetivo descrever e analisar características e princípios dos padrões das rendas de bilro de modo a estabelecer relações com a Matemática escolar, principalmente, no que se refere aos tópicos como Geometria, simetria, isometria, área, perímetro, entre outros. Desse modo, elaboramos atividades didáticas, com base na Matemática explorada nos padrões da criação da renda de bilro, visando concretizar um exercício investigatório nas aulas de Matemática, de modo que, sejam estabelecidas relações conceituais entre a prática investigada e os conteúdos da Matemática escolar. Para satisfazer esses objetivos, buscamos apoio metodológico na pesquisa bibliográfica, do tipo documental em catálogos como o da Professora Valdelice Girão (1984) e também o de Dawson (1984). Realizamos também a pesquisa empírica durante as visitas ao Museu do Ceará e ao Centro das Rendeiras na Prainha, em Aquiraz, no Ceará. Para realizar as atividades didáticas, apoiamo-nos em Mendes (2009). Consideramos relevante essa abordagem de ensino porque pressupõe a experiência direta do aprendiz com situações reais vivenciadas, nas quais a abordagem instrucional é centrada no aluno. Desse modo, concluímos que para o ensino de conteúdos como Geometria, simetria, isometria, relação entre perímetro e área, entre outros que são abordados na Educação Básica, os modelos decorrentes da criação renda de bilro e outros modelos já descritos na tradição cearense podem ser usados como artefato cultural na criação de atividades didáticas

A dimensão espacial e o proceder pedagógico

This research was conducted at the Post Graduate Program in Education at the Federal University of Rio Grande do Norte. It had the aim to understand the spatial conception associated with the pedagogical action. It promoted a historical-scientific approach to concepts of space to emphasize the spatiality from the geographical and educational theoretical referential. In it empiria situated in a university student universe, has utilized a quantitative measuring instrument as a subsidy to a qualitative dialogical analysis. It showed a synthetic framework arising from the interaction and the reflection focused into problems, challenges and potential of a pedagogical vision that considers the spatiality of teaching education. It seeks to promote delineations of paths pedagogical to a integrate approach of heterotopic space conception, as a necessary critical condition to the appropriation of social reality without doing the epistemological dichotomy, enhancing it signification to the learning academic teaching ambience; as well the scientific and teaching formation in the geography course

Análise e projeto de superfícies seletivas de frequência com elementos pré-fractais para aplicações em comunicações indoor

In this thesis, a frequency selective surface (FSS) consists of a two-dimensional periodic structure mounted on a dielectric substrate, which is capable of selecting signals in one or more frequency bands of interest. In search of better performance, more compact dimensions, low cost manufacturing, among other characteristics, these periodic structures have been continually optimized over time. Due to its spectral characteristics, which are similar to band-stop or band-pass filters, the FSSs have been studied and used in several applications for more than four decades. The design of an FSS with a periodic structure composed by pre-fractal elements facilitates the tuning of these spatial filters and the adjustment of its electromagnetic parameters, enabling a compact design which generally has a stable frequency response and superior performance relative to its euclidean counterpart. The unique properties of geometric fractals have shown to be useful, mainly in the production of antennas and frequency selective surfaces, enabling innovative solutions and commercial applications in microwave range. In recent applications, the FSSs modify the indoor propagation environments (emerging concept called wireless building ). In this context, the use of pre-fractal elements has also shown promising results, allowing a more effective filtering of more than one frequency band with a single-layer structure. This thesis approaches the design of FSSs using pre-fractal elements based on Vicsek, Peano and teragons geometries, which act as band-stop spatial filters. The transmission properties of the periodic surfaces are analyzed to design compact and efficient devices with stable frequency responses, applicable to microwave frequency range and suitable for use in indoor communications. The results are discussed in terms of the electromagnetic effect resulting from the variation of parameters such as: fractal iteration number (or fractal level), scale factor, fractal dimension and periodicity of FSS, according the pre-fractal element applied on the surface. The analysis of the fractal dimension s influence on the resonant properties of a FSS is a new contribution in relation to researches about microwave devices that use fractal geometry. Due to its own characteristics and the geometric shape of the Peano pre-fractal elements, the reconfiguration possibility of these structures is also investigated and discussed. This thesis also approaches, the construction of efficient selective filters with new configurations of teragons pre-fractal patches, proposed to control the WLAN coverage in indoor environments by rejecting the signals in the bands of 2.4~2.5 GHz (IEEE 802.11 b) and 5.0~6.0 GHz (IEEE 802.11a). The FSSs are initially analyzed through simulations performed by commercial software s: Ansoft DesignerTM and HFSSTM. The fractal design methodology is validated by experimental characterization of the built prototypes, using alternatively, different measurement setups, with commercial horn antennas and microstrip monopoles fabricated for low cost measurements

Estudo do efeito de dipolos em arranjos de antenas adaptativas de sistemas de comunicação DS-CDMA

This master dissertation introduces a study about some aspects that determine the aplication of adaptative arrays in DS-CDMA cellular systems. Some basics concepts and your evolution in the time about celular systems was detailed here, meanly the CDMA tecnique, specialy about spread-codes and funtionaly principies. Since this, the mobile radio enviroment, with your own caracteristcs, and the basics concepts about adaptive arrays, as powerfull spacial filter was aborded. Some adaptative algorithms was introduced too, these are integrants of the signals processing, and are answerable for weights update that influency directly in the radiation pattern of array. This study is based in a numerical analysis of adaptative array system behaviors related to the used antenna and array geometry types. All the simulations was done by Mathematica 4.0 software. The results for weights convergency, square mean error, gain, array pattern and supression capacity based the analisis made here, using RLS (supervisioned) and LSDRMTA (blind) algorithms