Obstáculos superados pelos matemáticos no passado e vivenciados pelos alunos na atualidade : a polêmica multiplicação de números inteiros

In Mathematics literature some records highlight the difficulties encountered in the teaching-learning process of integers. In the past, and for a long time, many mathematicians have experienced and overcome such difficulties, which become epistemological obstacles imposed on the students and teachers nowadays. The present work comprises the results of a research conducted in the city of Natal, Brazil, in the first half of 2010, at a state school and at a federal university. It involved a total of 45 students: 20 middle high, 9 high school and 16 university students. The central aim of this study was to identify, on the one hand, which approach used for the justification of the multiplication between integers is better understood by the students and, on the other hand, the elements present in the justifications which contribute to surmount the epistemological obstacles in the processes of teaching and learning of integers. To that end, we tried to detect to which extent the epistemological obstacles faced by the students in the learning of integers get closer to the difficulties experienced by mathematicians throughout human history. Given the nature of our object of study, we have based the theoretical foundation of our research on works related to the daily life of Mathematics teaching, as well as on theorists who analyze the process of knowledge building. We conceived two research tools with the purpose of apprehending the following information about our subjects: school life; the diagnosis on the knowledge of integers and their operations, particularly the multiplication of two negative integers; the understanding of four different justifications, as elaborated by mathematicians, for the rule of signs in multiplication. Regarding the types of approach used to explain the rule of signs arithmetic, geometric, algebraic and axiomatic , we have identified in the fieldwork that, when multiplying two negative numbers, the students could better understand the arithmetic approach. Our findings indicate that the approach of the rule of signs which is considered by the majority of students to be the easiest one can be used to help understand the notion of unification of the number line, an obstacle widely known nowadays in the process of teaching-learning

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

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

Chloramphenicol restores the polymorphonuclear accumulation in carrageenin-induced pleurisy in diabetic rats

Investigou-se o efeito do succinato de cloranfenicol (30 mg/kg, a cada 12 h, durante 4 dias, IP) sobre o acúmulo de leucócitos polimorfonucleares (PMN) na pleurisia induzida pela carragenina (150 mig) em ratos (Wistar, machos, 180-230 g, n = 12) diabéticos (40 mg/kg de aloxana, IV). O antibiótico produziu aumento de 36% no número de PMN (p<0,05) migrados para a cavidade pleural de animais normais. O estado diabético provocou redução de 45% dos PMN (p<0,05) acumulados no exsudato pleural de animais não tratados com o antibiótico. Por outro lado, animais diabéticos tratados com succinato de cloranfenicol apresentaram resposta de PMN que não diferiu estatisticamente do observado em animais controle, não tratados. A contagem total e diferencial dos leucócitos circulantes realizada antes e 4 h depois da aplicação da carragenina não diferiu estatisticamente entre os grupos.

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

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.

Caracterização de matérias-primas regionais e desenvolvimento de formulações de massas cerâmicas para porcelanato

Initially concentrated in some poles at the South and Southeast regions of Brazil, the ceramic tiles industry became wide during the 80 s decade, with a disconcentration industrial and regional pulverization. The competitiveness in the ceramic tiles internal and external consumers markets, it has debtor the industries to invest in sophisticated products each time more, either in design or the technology, but, mainly, in its final properties. Amongst the diverse types of ceramic coating, the porcelanato if has detached had to its process of technological production and excellent characteristics techniques. The Porcelanato is currently the material for coatings that presents the best technical and aesthetic features when compared with others ceramics found on the market. The chemical composition and the others raw materials characteristics have an importance that must to be ally to the inherent characteristics of fabrication process, essentially those related to the cycle of burning. This work had as purpose to develop formularizations of ceramic mass for production of porcelanato without glass coating, pertaining to the group BIa (text of absorption of water ≤ 0.5%) and with resistance superior mechanics 35MPa from raw materials characterized. The ceramic raw materials selected to the development of this study (A1 and A2 clays, feldspate, talc and quartz) were submitted to the following tests: X-ray fluorescence - chemical analysis determination; X-ray diffraction - Analysis of the stages mineralogics; Laser granulometry - size distribution of particles; and Differential thermal analysis - thermal behavior. Were performed tests of absorption of water, lineal retraction of it burns, apparent specific mass and rupture tension the flexing. The results had evidenced that the formularizations that had the A1 clay and talc on its composition were efficient for the porcelanato production remaining their technological characteristics inside of the intervals of variation desired by the Norms of the ABNT

Estudo das propriedades termofísicas com variação da expansibilidade de compósito desenvolvido com matriz PUR-NOP e carga funcional de argilomineral

In this study were conducted experimental procedures for determination of variation of the expandability of rigid polyurethane foam (PUR) from a natural oil polyol (NOP), specifically the Castor oil plant, Ricinus communis, pure and additions of the vermiculite in phase dispersed in different percentage within a range from 0% to 20%, mass replacement. From the information acquired, were defined the parameters for production of bodies of test, plates obtained through controlled expansion, with the final volume fixed. Initially, the plates were subjected to thermal performance tests and evaluated the temperature profiles, to later be extracted samples duly prepared in accordance with the conditions required for each test. Was proceeded then the measurement of the coefficient of thermal conductivity, volumetric capacity heat and thermal diffusivity. The findings values were compared with the results obtained in the tests of thermal performance, contributing to validation of the same. Ultimately, it was investigated the influence that changes in physical-chemical structure of the material had exerted on the variation of thermophysical quantities through gas pycnometry, scanning electron microscopy (SEM) combined with energy dispersive X-ray fluorescence spectroscopy (EDXRF), infrared spectroscopy using Fourier transform (FTIR), thermogravimetric analysis (TGA) and differential thermal analysis (DTA). Based on the results obtained was possible to demonstrate that all load percentage analyzed promoted an increase in the potential expansion (PE) of the resin. In production of the plates, the composites with density near at the free expansion presented high contraction during the cure, being the of higher density adopted as definitive standard. In the thermal performance tests, the heating and cooling curves of the different composites had presented symmetry and values very close for lines of the temperature. The results obtained for the thermophysical properties of composites, showed little difference in respect of pure foam. The percentage of open pores and irregularities in the morphology of the composites were proportionate to the increment of vermiculite. In the interaction between the matrix and dispersed phase, there were no chemical transformations in the region of interface and new compounds were not generated. The composites of PUR-NOP and vermiculite presented thermal insulating properties near the foam pure and percentage significantly less plastic in its composition, to the formulation with 10% of load

Incorporação de cinzas da casca de café na produção de placas cerâmicas para revestimento

Brazil is the world s leading coffee producer. In 2008, 45.99 million of 60 kg bags of benefited coffee were produced. In the process of improvement 50% is grain and 50% is husk, thus, 1.38 million tons of coffee husk are produced annually. The husk is used as combustible in the drying and improvement ovens in the coffee farms, generating ash as residue. These ashes contain a high concentration of alkaline metals and earth metals, mainly K2O and CaO. This work studies the use of this residue in the ceramic tiles industry, as fluxing agents in substitution to the feldspar. Ten mixtures with equal ratios of clay and kaolin, proceeding from Bahia and the residue (varying from 30 to 5%) were defined and produced in uniaxial tool die of 60x20mm with approximately 5 mm of thickness and 45MPa compacting pressure. The samples were fired in four different temperatures: 1100 °C, 1150 °C, 1185 °C and 1200 °C during 60 minutes and characterized by means of X-ray fluorescence, X-ray diffraction, gravimetric thermal analysis and differential thermal analysis. The results of water absorption, apparent porosity, linear shrinkage, XRD, dilatometry, flexural strength and SEM were also analysed. The test specimen with addition of 10% of ash fired in 1200 °C resulted in 0.18% water absorption and 40.77 MPa flexural strength, being classified as porcelain stoneware tiles according to ABNT, UNI and ISO norms

Simulação computacional da interação fluido-estrutura em bombas de cavidades progressivas

The pumping through progressing cavities system has been more and more employed in the petroleum industry. This occurs because of its capacity of elevation of highly viscous oils or fluids with great concentration of sand or other solid particles. A Progressing Cavity Pump (PCP) consists, basically, of a rotor - a metallic device similar to an eccentric screw, and a stator - a steel tube internally covered by a double helix, which may be rigid or deformable/elastomeric. In general, it is submitted to a combination of well pressure with the pressure generated by the pumping process itself. In elastomeric PCPs, this combined effort compresses the stator and generates, or enlarges, the clearance existing between the rotor and the stator, thus reducing the closing effect between their cavities. Such opening of the sealing region produces what is known as fluid slip or slippage, reducing the efficiency of the PCP pumping system. Therefore, this research aims to develop a transient three-dimensional computational model that, based on single-lobe PCP kinematics, is able to simulate the fluid-structure interaction that occurs in the interior of metallic and elastomeric PCPs. The main goal is to evaluate the dynamic characteristics of PCP s efficiency based on detailed and instantaneous information of velocity, pressure and deformation fields in their interior. To reach these goals (development and use of the model), it was also necessary the development of a methodology for generation of dynamic, mobile and deformable, computational meshes representing fluid and structural regions of a PCP. This additional intermediary step has been characterized as the biggest challenge for the elaboration and running of the computational model due to the complex kinematic and critical geometry of this type of pump (different helix angles between rotor and stator as well as large length scale aspect ratios). The processes of dynamic generation of meshes and of simultaneous evaluation of the deformations suffered by the elastomer are fulfilled through subroutines written in Fortan 90 language that dynamically interact with the CFX/ANSYS fluid dynamic software. Since a structural elastic linear model is employed to evaluate elastomer deformations, it is not necessary to use any CAE package for structural analysis. However, an initial proposal for dynamic simulation using hyperelastic models through ANSYS software is also presented in this research. Validation of the results produced with the present methodology (mesh generation, flow simulation in metallic PCPs and simulation of fluid-structure interaction in elastomeric PCPs) is obtained through comparison with experimental results reported by the literature. It is expected that the development and application of such a computational model may provide better details of the dynamics of the flow within metallic and elastomeric PCPs, so that better control systems may be implemented in the artificial elevation area by PCP

Estudo da viabilidade técnica do uso das argilas da região do agreste potiguar para produção de peças cerâmicas: caracterização e formulação

In recent decades, ceramic products have become indispensable to the technological development of humanity, occupying important positions in scientific production and consequently in industrial production. One area of the economy that continues to absorb large amounts of the products of this sector is Construction. Among the branches of the ceramic industry, there are the red ceramic industry which is traditionally the basis of that economic sector. Among the reasons for which the red ceramic industry became popular in the country, and specifically in Rio Grande do Norte, is the abundance of this raw material, easily found throughout the national territory. However, it appears that the red ceramic industry has deficiencies in technology and skilled labor, resulting in the production of ceramic goods with low added value. Among the factors that determine the quality of the ceramic products red has the proper formulation of the ceramic mass, the conformation and the firing temperature. Thus, the overall goal of this work is to study the mineralogical and technological properties, two clays from the region of the Wasteland Potiguar industrial ceramist. Therefore, the raw materials were characterized by analysis of Xray diffraction (XRD) analysis, X-ray fluorescence (XRF), particle size analysis (FA), scanning electron microscopy (SEM), optical microscopy (OM ), plasticity index (PI), thermal gravimetric analysis (TGA) and differential thermal analysis (DTA). The technological properties of the material were analyzed by water absorption tests (AA%) porosity (% PA), the linear shrinkage (RT%), apparent density (MEA), loss on ignition (PF%) and flexural strength three points (TRF)

Síntese e caracterização de tungstatos de cério e estrôncio para fins catalíticos

The main goal of this work was to produce nanosized ceramic materials of the family of the tungstates (tungstates of cerium and strontium), and test them for their catalytic activity in processes involving the transformation of methane (CH4). The methodology used for the synthesis of the ceramic powders involved the complexation combining EDTA-citrate. The materials characterization was performed using simple and differential thermogravimetry, x-ray diffraction, transmission electron microscopy, and energy dispersive spectroscopy (EDS). The microstructure analysis was performed using the refinement by the Rietveld method, and the crystallite size and distribution of the materials was elucidate by the Scherrer and Williamson-Hall methods. The conditions of the synthesis process for the three envisaged materials (SrWO4, SrWO4 using tungsten oxide concentrate as raw material, and Ce2(WO4)3) were adjusted to obtain a single phase crystalline material. The catalytic tests were carried out in the presence of methane and synthetic air, which is composed of 21% O2 and 79% N2. The analysis of the conversion of the reaction was done with the aid of an fourier transform infrared device (FTIR). The analysis showed that, structurally, the SrWO4 produced using raw materials of high and poor purity (99% and 92%, respectively) are similar. The ideal parameters of calcination, in the tested range, are temperature of 1000 °C and time of calcination 5 hours. For the Ce2(WO4)3, the ideal calcination time and are temperature 15 hours and 1000°C, respectively. The Williamson-Hall method provided two different distributions for the crystallite size of each material, whose values ranged between the nanometer and micrometer scales. According to method of Scherrer, all materials produced were composed of nanometric crystallites. The analyses of transmission electron microscopy confirmed the results obtained from the Williamson- Hall method for the crystallite size. The EDS showed an atomic composition for the metals in the SrWO4 that was different of the theoretical composition. With respect to the catalytic tests, all materials were found to be catalytically active, but the reaction process should be further studied and optimized.

Incorporação de resíduo de perfuração em matriz cerâmica: estabilização por solidificação

One of the waste generated during the drilling of oil wells are gravel which are impregnated of drilling fluid. This residue consists of highly toxic chemicals, including toxic metals. This study suggests an alternative process to the treatment of this waste, by incorporating it the form of raw material in the ceramic matrix , and by solidification and stabilize the metals present, Aluminum (Al), Iron (Fe), Manganese (Mn) and Zinc (Zn). The raw materials were characterized by the techniques of X ray fluorescence (FRX), X ray diffraction (DRX), laser granulometry (GL), thermogravimetry (TG) and differential thermal analysis (ADT). To evaluate the percentage of gravel effect the environmental and technological properties were obtained from formulations containing 0, 10 and 20 % by weight of gravel in the ceramic matrix. After sintering at temperatures 1080, 1120 and 1160 °C, the samples were tested for water absorption, the linear shrinkage firing, voltage of rupture and solubility. The results obtained showed that the stabilization by solidification, is a viable alternative to safe disposal of waste drilling. Ceramics products can be used in the manufacture of solid bricks

A modelagem matemática como alternativa de ensino e aprendizagem da geometria na educação de jovens e adultos

This is work itself insert in the mathematics education field of the youth and adult education to aim to practitioners of the educational action into the mathematics area performing to with this is teaching kind, adopting to as parameter the Mathematics Molding approach. The motive of the research is to draw up a application proposal of the molding mathematics as teaching and learning geometry alternative in the youth and adult education. The research it develops in three class of the third level (series 5th and 6th) of he youth and adults education in the one school municipal from the Natal outskirts. Its have qualitative nature with participating observation approach, once performing to directly in to research environment as a mathematics teacher of those same classes. We are used questionnaires, lesson notes and analyses of the officials documents as an basis of claim instruments. The results indicates that activity used the mathematic moldings were appreciated the savoir-faire of the student in to knowledge construction process, when search develop to significant learning methods, helping to student build has mathematics connections with other knowledge areas and inside mathematics himself, so much that enlarges your understanding and assist has in your participation in the other socials place, over there propitiate to change in student and teacher posture with relation to mathematic classroom dynamics

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)