Globos e mapas ao alcance das mãos : ensino de matemática numa perspectiva de alfabetização funcional na EJA

The following dissertation has as its main advantage the privilege of visualizing the literacy processes through the angle of the functional perspective, which does not see the literary process as a practice solely based on the decoding of alphabetical codes, and then allows for the opening of ample spaces for the allocation of mathematical skills in the realms of the functional literacy. The main object of this study was to investigate which are the contributions that a sequence of activities and of methodologies developed for the teaching of Geometry could provide for a part of the functional literacy process in mathematics of youngsters and adults of EJA, corresponding to the acquisition or to the improvement of skills related to the orientation capacity. The focus of the analyses consisted in the practice of these activities with the young and adult students of an EJA class belonging to a municipal public school of Natal/RN. The legacies of Paulo Freire about the redimensioning of the role of the teacher, of the students, of the knowledge and of their connections within the teaching-learning process, prevailed in the actions of the methodology implemented in the classroom and, especially, in the establishing of dialogic connections with the students, which directed all the observations and analyses regarding the collected information. The results indicated that the composition of articulations between the teaching of mathematics and the exploration of maps and the earth globe enabled the creation of multidisciplinary learning environments and situations, where we could observe, gradually, the development of procedures and attitudes indicating the evolution of space-visual type skills

Reflexões sobre a construção e evolução de conceitos geométricos nas séries intermediárias do ensino fundamental

This thesis represents a didactic research linked to the Post-graduation Programme in Education of the Universidade Federal do Rio Grande do Norte which aimed to approach the construction of the geometrical concepts of Volume of the Rectangular Parallelepiped, Area and Perimeter of the Rectangle adding a study of the Area of the Circle. The research was developed along with students from the 6th level of the Elementary School, in a public school in Natal/RN. The pedagogical intervention was made up of three moments: application of a diagnostic evaluation, instrument that enabled the creation of the teaching module by showing the level of the geometry knowledge of the students; introduction of a Teaching Module by Activities aiming to propose a reflexive didactic routing directed to the conceptual construction because we believed that such an approach would favor the consolidation of the learning process by becoming significant to the apprentice, and the accomplishment of a Final Evaluation through which we established a comparison of the results obtained before and after the teaching intervention. The data gathered were analyzed qualitatively by means of a study of understanding categories of mathematical concepts, in addition to using descriptive statistics under the quantitative aspect. Based on the theory of Richard Skemp, about categorization of mathematical knowledge, in the levels of Relational and Instrumental Understanding were achieved in contextual situations and varied proportions, thus enabling a contribution in the learning of the geometrical concepts studied along with the students who took part in the research. We believe that this work may contribute with reflections about the learning processes, a concern which remained during all the stages of the research, and also that the technical competence along with the knowledge about the constructivist theory will condition the implementation of a new dynamics to the teaching and learning processes. We hope that the present research work may add some contribution to the teaching practice in the context of the teaching of Mathematics for the intermediate levels of the Elementary School

Práticas etnomatemáticas no Liceu do Paracuri :a propósito dos ornamentos geométricos da cerâmica

The present study analyzes the ethnomatematics practices presents in the creation of the geometric ornaments of the icoaraciense ceramic, originated and still practiced in the neighborhood of Paracuri, District of Icoaraci, belonging to Belém, capital of the State of Pará/Brasil. The object of our study was centered at the workshops supplied by the artisans master of the School of Arts and Occupations, Master Raimundo Cardoso. Referred school provides to its students, formation at fundamental level as well professional formation, through vocational workshops that help to maintain alive the practice of the icoaraciense ceramic. Our interest of researching that cultural and vocational practice appeared when we got in touch with that School, during the development of activities of a discipline of the degree course of mathematics. In order to reach our objective, we accomplished, initially, a research about the icoaraciense ceramic historic, since the first works with the clay until to the main characteristics of that ceramic. Soon afterwards, we discussed on ethnomatematics, culture, knowledge, cognition and mathematical education. At the end, we analyzed the creation of the geometric ornaments of the icoaraciense ceramic, considering the proportion concepts, symmetry and some geometry notions, that are used by the artisans when they are ornamenting the pieces of that ceramic. We verified that, in spite of the artisans, usually, do not demonstrate to possess a bit of domain on the mathematical concepts that they are working with, for instance, the ones of translaction symmetry, rotation and reflection, they demonstrate full safety in the use of those concepts, as well as the capacity to recognize them, even if in a singular specific and very peculiar way, what opens the possibility of a partnership among mathematics teachers and master-artisans of the archeological ceramic and icoaraciense workshops

A dinâmica do pensamento geométrico :aprendendo a enxergar meias verdades e a construir novos significados

This work is a case study to investigate the dynamics of the historians thought as they produce a knowledge about the history of the area measurement systems as forms of historical expressions and representations. We refer to some of the ideas of David Bohm (1989, 1992, 1994, 1996) to support our theoretical understanding about the operation of thought. We chose a period that is recognized by the theorists as the origin of the geometrical thought -embracing the knowledge developed by the Egyptians, Babylonians, Chinese, Hindus, Greeks and Romans- and is referred to as containing a cycle in the development of this knowledge, described as beginning, apogee and decline. We assume this history, as told by the theorists, as a version that we organize and tell with the help of three sets of categories. The first refers to the elements that take part in the measurement practices; the second refers to the historians understanding about the development of the scientific knowledge. This exercise allowed us to extract the theorists main beliefs, that we criticized in the light of the knowledge about Cubação (Dal Pian, 1990). We stress the importance of the methodological approach adopted in this study to the teaching of Geometry and its history

Um estudo sobre a aprendizagem de alguns conceitos algébricos e geométricos

The objective of the present work was develop a study about the writing and the algebraic manipulation of symbolical expressions for perimeter and area of some convex polygons, approaching the properties of the operations and equality, extending to the obtaining of the formulas of length and area of the circle, this one starting on the formula of the perimeter and area of the regular hexagon. To do so, a module with teaching activities was elaborated based on constructive teaching. The study consisted of a methodological intervention, done by the researcher, and had as subjects students of the 8th grade of the State School Desembargador Floriano Cavalcanti, located on the city of Natal, Rio Grande do Norte. The methodological intervention was done in three stages: applying of a initial diagnostic evaluation, developing of the teaching module, and applying of the final evaluation based on the Mathematics teaching using Constructivist references. The data collected in the evaluations was presented as descriptive statistics. The results of the final diagnostic evaluation were analyzed in the qualitative point of view, using the criteria established by Richard Skemp s second theory about the comprehension of mathematical concepts. The general results about the data from the evaluations and the applying of the teaching module showed a qualitative difference in the learning of the students who participated of the intervention

Caracterização morfológica de plantas de rambutan

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Balancing guava nutrition with liming and fertilization

A resposta da goiabeira à calagem e à adubação pode ser monitorada por análises de tecido vegetal. O perfil nutricional é definido em relação a padrões de teores de nutrientes. No entanto, os teores de nutrientes-padrão são constantemente criticados por não considerarem as interações que ocorrem entre nutrientes e por gerarem tendências numéricas, decorrentes da redundância dos dados, da dependência de escala e da distribuição não normal. As técnicas de análise composicional de dados podem controlar esses dados tendenciosos, equilibrando os grupos de nutrientes, tais como os envolvidos na calagem e na adubação. A utilização das relações log isométricas (ilr) ortonormais, sequencialmente dispostas, evita tendências numéricas inerentes aos dados de composição. Os objetivos do trabalho foram relacionar o balanço de nutrientes dos tecidos vegetais com a produção de goiabeiras em pomares de 'Paluma' diferentemente corrigidos e adubados, e ajustar os atuais padrões de nutrientes com a faixa de equilíbrio das goiabeiras mais produtivas. Um experimento de calagem de sete anos e três, experimentos de três anos com doses de N, P2O5 e K2O, foram conduzidos em pomares de goiabeiras 'Paluma' em um Latossolo Vermelho-Amarelo. Os teores de N, P, K, Ca e Mg na planta foram monitorados anualmente. Selecionaram-se os balanços [N, P, K | Ca, Mg], [N, P | K], [N | P] e [Ca | Mg] para separar os efeitos da calagem (Ca-Mg) e dos fertilizantes (N-K) nos balanços de macronutrientes. Os balanços foram mais influenciados pela calagem do que pela fertilização. A produtividade das goiabeiras e seu balanço nutricional permitiram a definição de faixas de equilíbrio de nutrientes e sua validação com as faixas de concentrações críticas atualmente utilizadas no Brasil e combinadas em coordenadas ilr.

Análise e otimização de superfícies seletivas de Frequência utilizando redes neurais artificiais e algoritmos de otimização natural

The bidimensional periodic structures called frequency selective surfaces have been well investigated because of their filtering properties. Similar to the filters that work at the traditional radiofrequency band, such structures can behave as band-stop or pass-band filters, depending on the elements of the array (patch or aperture, respectively) and can be used for a variety of applications, such as: radomes, dichroic reflectors, waveguide filters, artificial magnetic conductors, microwave absorbers etc. To provide high-performance filtering properties at microwave bands, electromagnetic engineers have investigated various types of periodic structures: reconfigurable frequency selective screens, multilayered selective filters, as well as periodic arrays printed on anisotropic dielectric substrates and composed by fractal elements. In general, there is no closed form solution directly from a given desired frequency response to a corresponding device; thus, the analysis of its scattering characteristics requires the application of rigorous full-wave techniques. Besides that, due to the computational complexity of using a full-wave simulator to evaluate the frequency selective surface scattering variables, many electromagnetic engineers still use trial-and-error process until to achieve a given design criterion. As this procedure is very laborious and human dependent, optimization techniques are required to design practical periodic structures with desired filter specifications. Some authors have been employed neural networks and natural optimization algorithms, such as the genetic algorithms and the particle swarm optimization for the frequency selective surface design and optimization. This work has as objective the accomplishment of a rigorous study about the electromagnetic behavior of the periodic structures, enabling the design of efficient devices applied to microwave band. For this, artificial neural networks are used together with natural optimization techniques, allowing the accurate and efficient investigation of various types of frequency selective surfaces, in a simple and fast manner, becoming a powerful tool for the design and optimization of such structures

Uso de renderização volumétrica e realidade virtual para problemas de percolação na engenharia

In the recovering process of oil, rock heterogeneity has a huge impact on how fluids move in the field, defining how much oil can be recovered. In order to study this variability, percolation theory, which describes phenomena involving geometry and connectivity are the bases, is a very useful model. Result of percolation is tridimensional data and have no physical meaning until visualized in form of images or animations. Although a lot of powerful and sophisticated visualization tools have been developed, they focus on generation of planar 2D images. In order to interpret data as they would be in the real world, virtual reality techniques using stereo images could be used. In this work we propose an interactive and helpful tool, named ZSweepVR, based on virtual reality techniques that allows a better comprehension of volumetric data generated by simulation of dynamic percolation. The developed system has the ability to render images using two different techniques: surface rendering and volume rendering. Surface rendering is accomplished by OpenGL directives and volume rendering is accomplished by the Zsweep direct volume rendering engine. In the case of volumetric rendering, we implemented an algorithm to generate stereo images. We also propose enhancements in the original percolation algorithm in order to get a better performance. We applied our developed tools to a mature field database, obtaining satisfactory results. The use of stereoscopic and volumetric images brought valuable contributions for the interpretation and clustering formation analysis in percolation, what certainly could lead to better decisions about the exploration and recovery process in oil fields

Análise e síntese de antenas e superfícies seletivas de frequência utilizando computação evolucionária e inteligência de enxames

The frequency selective surfaces, or FSS (Frequency Selective Surfaces), are structures consisting of periodic arrays of conductive elements, called patches, which are usually very thin and they are printed on dielectric layers, or by openings perforated on very thin metallic surfaces, for applications in bands of microwave and millimeter waves. These structures are often used in aircraft, missiles, satellites, radomes, antennae reflector, high gain antennas and microwave ovens, for example. The use of these structures has as main objective filter frequency bands that can be broadcast or rejection, depending on the specificity of the required application. In turn, the modern communication systems such as GSM (Global System for Mobile Communications), RFID (Radio Frequency Identification), Bluetooth, Wi-Fi and WiMAX, whose services are highly demanded by society, have required the development of antennas having, as its main features, and low cost profile, and reduced dimensions and weight. In this context, the microstrip antenna is presented as an excellent choice for communications systems today, because (in addition to meeting the requirements mentioned intrinsically) planar structures are easy to manufacture and integration with other components in microwave circuits. Consequently, the analysis and synthesis of these devices mainly, due to the high possibility of shapes, size and frequency of its elements has been carried out by full-wave models, such as the finite element method, the method of moments and finite difference time domain. However, these methods require an accurate despite great computational effort. In this context, computational intelligence (CI) has been used successfully in the design and optimization of microwave planar structures, as an auxiliary tool and very appropriate, given the complexity of the geometry of the antennas and the FSS considered. The computational intelligence is inspired by natural phenomena such as learning, perception and decision, using techniques such as artificial neural networks, fuzzy logic, fractal geometry and evolutionary computation. This work makes a study of application of computational intelligence using meta-heuristics such as genetic algorithms and swarm intelligence optimization of antennas and frequency selective surfaces. Genetic algorithms are computational search methods based on the theory of natural selection proposed by Darwin and genetics used to solve complex problems, eg, problems where the search space grows with the size of the problem. The particle swarm optimization characteristics including the use of intelligence collectively being applied to optimization problems in many areas of research. The main objective of this work is the use of computational intelligence, the analysis and synthesis of antennas and FSS. We considered the structures of a microstrip planar monopole, ring type, and a cross-dipole FSS. We developed algorithms and optimization results obtained for optimized geometries of antennas and FSS considered. To validate results were designed, constructed and measured several prototypes. The measured results showed excellent agreement with the simulated. Moreover, the results obtained in this study were compared to those simulated using a commercial software has been also observed an excellent agreement. Specifically, the efficiency of techniques used were CI evidenced by simulated and measured, aiming at optimizing the bandwidth of an antenna for wideband operation or UWB (Ultra Wideband), using a genetic algorithm and optimizing the bandwidth, by specifying the length of the air gap between two frequency selective surfaces, using an optimization algorithm particle swarm

Uma contribuição ao estudo das categorias internas e de sua proliferação em redes ARTMAP

ART networks present some advantages: online learning; convergence in a few epochs of training; incremental learning, etc. Even though, some problems exist, such as: categories proliferation, sensitivity to the presentation order of training patterns, the choice of a good vigilance parameter, etc. Among the problems, the most important is the category proliferation that is probably the most critical. This problem makes the network create too many categories, consuming resources to store unnecessarily a large number of categories, impacting negatively or even making the processing time unfeasible, without contributing to the quality of the representation problem, i. e., in many cases, the excessive amount of categories generated by ART networks makes the quality of generation inferior to the one it could reach. Another factor that leads to the category proliferation of ART networks is the difficulty of approximating regions that have non-rectangular geometry, causing a generalization inferior to the one obtained by other methods of classification. From the observation of these problems, three methodologies were proposed, being two of them focused on using a most flexible geometry than the one used by traditional ART networks, which minimize the problem of categories proliferation. The third methodology minimizes the problem of the presentation order of training patterns. To validate these new approaches, many tests were performed, where these results demonstrate that these new methodologies can improve the quality of generalization for ART networks

Mapeamento com Sonar Usando Grade de Ocupação baseado em Modelagem Probabilística

In this work, we propose a probabilistic mapping method with the mapped environment represented through a modified occupancy grid. The main idea of the proposed method is to allow a mobile robot to construct in a systematic and incremental way the geometry of the underlying space, obtaining at the end a complete environment map. As a consequence, the robot can move in the environment in a safe way, based on a confidence value of data obtained from its perceptive system. The map is represented in a coherent way, according to its sensory data, being these noisy or not, that comes from exterior and proprioceptive sensors of the robot. Characteristic noise incorporated in the data from these sensors are treated by probabilistic modeling in such a way that their effects can be visible in the final result of the mapping process. The results of performed experiments indicate the viability of the methodology and its applicability in the area of autonomous mobile robotics, thus being an contribution to the field

Um método para determinação da profundidade combinando visão estéreo e autocalibração para aplicação em robótica móvel

This work proposes a method to determine the depth of objects in a scene using a combination between stereo vision and self-calibration techniques. Determining the rel- ative distance between visualized objects and a robot, with a stereo head, it is possible to navigate in unknown environments. Stereo vision techniques supply a depth measure by the combination of two or more images from the same scene. To achieve a depth estimates of the in scene objects a reconstruction of this scene geometry is necessary. For such reconstruction the relationship between the three-dimensional world coordi- nates and the two-dimensional images coordinates is necessary. Through the achievement of the cameras intrinsic parameters it is possible to make this coordinates systems relationship. These parameters can be gotten through geometric camera calibration, which, generally is made by a correlation between image characteristics of a calibration pattern with know dimensions. The cameras self-calibration allows the achievement of their intrinsic parameters without using a known calibration pattern, being possible their calculation and alteration during the displacement of the robot in an unknown environment. In this work a self-calibration method based in the three-dimensional polar coordinates to represent image features is presented. This representation is determined by the relationship between images features and horizontal and vertical opening cameras angles. Using the polar coordinates it is possible to geometrically reconstruct the scene. Through the proposed techniques combination it is possible to calculate a scene objects depth estimate, allowing the robot navigation in an unknown environment

Novas configurações de monopólios planares quase-fractais para sistemas de comunicações móveis

The characteristic properties of the fractal geometry have shown to be very useful for the construction of filters, frequency selective surfaces, synchronized circuits and antennas, enabling optimized solutions in many different commercial uses at microwaves frequency band. The fractal geometry is included in the technology of the microwave communication systems due to some interesting properties to the fabrication of compact devices, with higher performance in terms of bandwidth, as well as multiband behavior. This work describes the design, fabrication and measurement procedures for the Koch quasi-fractal monopoles, with 1 and 2 iteration levels, in order to investigate the bandwidth behavior of planar antennas, from the use of quasi-fractal elements printed on their rectangular patches. The electromagnetic effect produced by the variation of the fractal iterations and the miniaturization of the structures is analyzed. Moreover, a parametric study is performed to verify the bandwidth behavior, not only at the return loss but also in terms of SWR. Experimental results were obtained through the accomplishment of measurements with the aid of a vetorial network analyzer and compared to simulations performed using the Ansoft HFSS software. Finally, some proposals for future works are presented

Antenas de microfita com patch quase-fractal para aplicações em Redes WPAN/WLAN

The microstrip antennas are in constant evidence in current researches due to several advantages that it presents. Fractal geometry coupled with good performance and convenience of the planar structures are an excellent combination for design and analysis of structures with ever smaller features and multi-resonant and broadband. This geometry has been applied in such patch microstrip antennas to reduce its size and highlight its multi-band behavior. Compared with the conventional microstrip antennas, the quasifractal patch antennas have lower frequencies of resonance, enabling the manufacture of more compact antennas. The aim of this work is the design of quasi-fractal patch antennas through the use of Koch and Minkowski fractal curves applied to radiating and nonradiating antenna s edges of conventional rectangular patch fed by microstrip inset-fed line, initially designed for the frequency of 2.45 GHz. The inset-fed technique is investigated for the impedance matching of fractal antennas, which are fed through lines of microstrip. The efficiency of this technique is investigated experimentally and compared with simulations carried out by commercial software Ansoft Designer used for precise analysis of the electromagnetic behavior of antennas by the method of moments and the neural model proposed. In this dissertation a study of literature on theory of microstrip antennas is done, the same study is performed on the fractal geometry, giving more emphasis to its various forms, techniques for generation of fractals and its applicability. This work also presents a study on artificial neural networks, showing the types/architecture of networks used and their characteristics as well as the training algorithms that were used for their implementation. The equations of settings of the parameters for networks used in this study were derived from the gradient method. It will also be carried out research with emphasis on miniaturization of the proposed new structures, showing how an antenna designed with contours fractals is capable of a miniaturized antenna conventional rectangular patch. The study also consists of a modeling through artificial neural networks of the various parameters of the electromagnetic near-fractal antennas. The presented results demonstrate the excellent capacity of modeling techniques for neural microstrip antennas and all algorithms used in this work in achieving the proposed models were implemented in commercial software simulation of Matlab 7. In order to validate the results, several prototypes of antennas were built, measured on a vector network analyzer and simulated in software for comparison