Uma sequencia didática para o ensino da resolução da equação do 2. grau : adequação para o uso com professores

The present study aims to check whether the use of activities mediated by the History of Mathematics can contribute to improve the understanding of resolution the 2nd degree equation for teachers and undergraduates that reproduce methods of solving such equations, uncritically, without domain of the justifications for their actions. For this, we adapted a didactic sequence with activities that aims to cause a rediscovery of resolutive formula of 2nd degree equation through the method known as cut and paste. Finally, we presented the activity module containing the didactic sequence used during the study, as suggestion for use in the classroom, by the math teacher

Utilizando processos geométricos da história da matemática para o ensino de equações do 2º grau

The present work had as principal objective to analyze the, 9th grade students understanding about the solutions of an equation of the 2° degree, using geometric processes of the History of the Mathematics. To do so, the research had as base the elaboration and application of a group of teaching activities, based on Jean Piaget's construtivism. The research consisted of a methodological intervention, that has as subjects the students of a group of 9th grade of the State School José Martins de Vasconcelos, located in the municipal district of Mossoró, Rio Grande do Norte. The intervention was divided in three stages: application of an initial evaluation; development of activities‟ module with emphasis in constructive teaching; and the application of the final evaluation. The data presented in the initial evaluation revealed a low level of the students' understanding with relationship to the calculation of areas of rectangles, resolution of equations of the 1st and 2nd degrees, and they were to subsidize the elaboration of the teaching module. The data collected in the initial evaluation were commented and presented under descriptive statistics form. The results of the final evaluation were analyzed under the qualitative point of view, based on Richard Skemp's theory on the understanding of mathematical concepts. The general results showed a qualitative increase with relationship to the students' understanding on the mathematical concepts approached in the intervention. Such results indicate that a methodology using the previous student‟s knowledge and the development of teaching activities, learning in the construtivist theory, make possible an understanding on the part of the students concerning the thematic proposal

Qualidade de vida de pessoas com úlcera venosa: associação dos aspectos sociodemográficos, de saúde, assistência e clínicos da lesão

Venous ulcer (VU) is a lower limbs injury resulting from inadequate return of venous blood in feet or legs. Although it is not a deadly disease, it causes chronic wounds, which seriously undermine patients´ quality of life (QOL) and sometimes leads to drastic family, social, economic and psychological changes. In this sense, there are several aspects that may influence the venous ulcers patients´ QOL. The study´s objective aimed on the association of socio-demographic and health, health care and clinical injury on UV patients‟ QOL. Analytical studies, which consider the complexity of factors involved in changes in UV patients‟ QOL has a cross-sectional and quantitative approach. The HUOL Ethics Committee approved this project (n.279/09). The collection of data lasted a period of 3 months in 2010 and it took place at the clinic of Angiology at Hospital Universitário Onofre Lopes (HUOL). The data sample consisted of 60 patients treated by UV angiologists in the HUOL Surgical Clinic. The results were analyzed with SPSS 15.0 by descriptive and inferential statistics. The study was based on UV patients that were predominantly female, average age of 61.4 years, that had low education level and low family income, with occupations requiring long periods of standing or sitting, but mostly retired, unemployed or laid off due to the disease and/or due to chronic diseases associated with the UV. The study took also into consideration patients that used inappropriate products, that were improperly treated by a professional caregiver, that lacked of adequate guidance and compression therapy, that performed no lifting of the lower limbs and regular exercise, that the time of injury were greater than or equal to six months, that were missing specific laboratory tests. The study‟s reference were on recurrent lesions, medium to large lesions area, bed of the lesion (injuries) with fibrin and/or necrosis, with amount of exudate with medium to large, odorless and no signs of infection, with tissue loss between 1st and 2nd degree, without collecting swab or biopsy and with pain. In general, QOL of researched individuals were considered low, the maximum score was 69 points, which the areas that were mostly influenced were the total scores of QOL functional capacity (0.021), emotional (0.000) and social functioning (0.080). Of the 60 individuals, 53.3% had scores between 40 and 69 points in SF-36, and they had the best scores in sociodemographic and health variables (ρ = 0.049). In respect to the assistance and injury characteristics, patients who scored between 40 and 69 points in SF-36 had better scores on these characteristics. By combining the socio-demographic variables, health, and handling characteristics of the injury, we observed a significant difference (ρ = 0.032) when linking them with the QOL total scores. When analyzing separately the domains of the SF-36 scores on the quality of life, we find that the areas that showed statistical significance were functional ability (ρ = 0.035), appearance (ρ = 0.019), emotional (ρ = 0.000), and mental health (ρ = 0.050). Among the socio-demographic characteristics studied, gender and marital status contributed more to the reduction of QOL and among the variables of assistance and the injury, orientation, reference and area of UV contributed the most. By analyzing these five variables all together in accordance with the overall score obtained in the quality of life, we found a significant correlation (ρ = 0.002); with 6.23 times more chances of patients have better QOL in the presence of these five positive factors. By conducting the Mann Whitney U test between all the five demographic variables, health, and clinical care, we found that this combination also proved to be significant (ρ = 0.006). Therefore, patients with these five variables positive tend to have a better QOL. Based on these results, we reject the null hypothesis (H0) and accept the alternative hypothesis (H1) proposed in this study because we noted that the QOL of patients with UV is associated with sociodemographic and health, health care and clinical aspects of the injury

Investigação histórica nas aulas de matemática: avaliação de duas experiências

This study reflects on some procedural aspects about the development of mathematics learning from the experience with investigative activities concerning the resolution of second degree equation, which was tested a proposal for education, supported the use of texts in history of mathematics. The survey was conducted in two stages, taking the first-served basis for the second, which was carried out with a study group remainder of the first experiment. The intention was to investigate how the group participant, known as the study group, involved in the implementation of activities of research in mathematics, supported the use of the history of mathematics. Based on the results achieved during the study, it was possible to understand that the activities of research enable the development of students, range of learning mathematics and the development of skills and expertise for research as a vehicle for construction of their mathematical knowledge. This approach proposed research into the classroom is important, both for prospective teachers of mathematics and for students from elementary school, bringing a new phase for mathematical education that will come to schools

Aceitação e uso de ambiente virtual de aprendizagem no contexto de um curso de capacitação para servidores públicos

This study aimed to examine how students perceives the factors that may influence them to attend a training course offered in the distance virtual learning environment (VLE) of the National School of Public Administration (ENAP). Thus, as theoretical basis it was used the Unified Theory of Acceptance and Use of Technology (UTAUT), the result of an integration of eight previous models which aimed to explain the same phenomenon (acceptance/use of information technology). The research approach was a quantitative and qualitative. To achieve the study objectives were made five semi-structured interviews and an online questionnaire (websurvey) in a valid sample of 101 public employees scattered throughout the country. The technique used to the analysis of quantitative data was the structural equation modeling (SEM), by the method of Partial Least Square Path Modeling (PLS-PM). To qualitative data was the thematic content analysis. Among the results, it was found that, in the context of public service, the degree whose the individual believes that the use of an AVA will help its performance at work (performance expectancy) is a factor to its intended use and also influence its use. Among the results, it was found that the belief which the public employee has in the use of a VLE as a way to improve the performance of his work (performance expectation) was determinant for its intended use that, in turn, influenced their use. It was confirmed that, under the voluntary use of technology, the general opinion of the student s social circle (social influence) has no effect on their intention to use the VLE. The effort expectancy and facilitating conditions were not directly related to the intended use and use, respectively. However, emerged from the students speeches that the opinions of their coworkers, the ease of manipulate the VLE, the flexibility of time and place of the distance learning program and the presence of a tutor are important to their intentions to do a distance learning program. With the results, it is expected that the managers of the distance learning program of ENAP turn their efforts to reduce the impact of the causes of non-use by those unwilling to adopt voluntarily the e-learning, and enhance the potentialities of distance learning for those who are already users

Estimativas de mortalidade para a região nordeste do Brasil em 2010: uma associação do método demográfico equação geral de balanceamento, com o estimador bayesiano empírico

One of the greatest challenges of demography, nowadays, is to obtain estimates of mortality, in a consistent manner, mainly in small areas. The lack of this information, hinders public health actions and leads to impairment of quality of classification of deaths, generating concern on the part of demographers and epidemiologists in obtaining reliable statistics of mortality in the country. In this context, the objective of this work is to obtain estimates of deaths adjustment factors for correction of adult mortality, by States, meso-regions and age groups in the northeastern region, in 2010. The proposal is based on two lines of observation: a demographic one and a statistical one, considering also two areas of coverage in the States of the Northeast region, the meso-regions, as larger areas and counties, as small areas. The methodological principle is to use the General Equation and Balancing demographic method or General Growth Balance to correct the observed deaths, in larger areas (meso-regions) of the states, since they are less prone to breakage of methodological assumptions. In the sequence, it will be applied the statistical empirical Bayesian estimator method, considering as sum of deaths in the meso-regions, the death value corrected by the demographic method, and as reference of observation of smaller area, the observed deaths in small areas (counties). As results of this combination, a smoothing effect on the degree of coverage of deaths is obtained, due to the association with the empirical Bayesian Estimator, and the possibility of evaluating the degree of coverage of deaths by age groups at counties, meso-regions and states levels, with the advantage of estimete adjustment factors, according to the desired level of aggregation. The results grouped by State, point to a significant improvement of the degree of coverage of deaths, according to the combination of the methods with values above 80%. Alagoas (0.88), Bahia (0.90), Ceará (0.90), Maranhão (0.84), Paraíba (0.88), Pernambuco (0.93), Piauí (0.85), Rio Grande do Norte (0.89) and Sergipe (0.92). Advances in the control of the registry information in the health system, linked to improvements in socioeconomic conditions and urbanization of the counties, in the last decade, provided a better quality of information registry of deaths in small areas

O Curso Normal de 1º Ciclo em Assu/RN (1951-1971)

The aim of this research is the analysis of the history of the Normal Course in the 1st period in Assu, Rio Grande do Norte, since its foundation by the state law no. 621, de 06 December 1951 until its demise, with the implementation of the Course of the Magisterium, by Federal Law 5692 from August 11, 1971. The goal is to answer how it was constituted the operation and the educational practices of this institution, teacher trainers, throughout its existence. For this, we analyze the institution's documents in focus interviews, legislation, of the education, newspapers and books of the season, guiding itself by the studies of Chartier (1991), Elias (2001), Certeau (2001), Frago (1995), Magalhães (2005) and Julia (2001). When dealing with an educational institution, the central category of analysis is the school culture, in which supported the cutting of specific categories of study: the entrance into the Normal Course, the conferring of a degree, the "Normalista Week‖ in Assu and formative elements. The Normal Course from 1st cycle formed teachers in a basic level, differing themselves from schools of teacher education of 2nd Cycle. It was founded in Assu as Regional Training Course and called Ginásio Normal in 1961.In the temporal cut studied, 279 women and 07 men were graduated as Regents of Elementary School, demonstrating a school attended virtually by women. In the narrative, it is restored to the inclusion of female students in the Normal Course, focusing on the processes of registration and the admission exams, graduation events, imbued with discourses on the social role of the teacher and the Party Normalista Week, which valued the sense of belonging with of students to the profession. Through theater plays in the school, of practices forming behaviors and stages of female students in elementary school, training elements are reassembled, demonstrating the discourse of modern education intermingled with the Christian Catholic values of the culture for female education. The reconstruction of the historical identity of this institution sometimes close, sometimes unique, when confronted with other schools of teacher training brings a contribution to the setting of the history of schooling in the state of Rio Grande do Norte

De solutione problematum diophanteorum per números integros : o primeiro trabalho de Euler sobre equações diofantinas

The present dissertation analyses Leonhard Euler´s early mathematical work as Diophantine Equations, De solutione problematum diophanteorum per números íntegros (On the solution of Diophantine problems in integers). It was published in 1738, although it had been presented to the St Petersburg Academy of Science five years earlier. Euler solves the problem of making the general second degree expression a perfect square, i.e., he seeks the whole number solutions to the equation ax2+bx+c = y2. For this purpose, he shows how to generate new solutions from those already obtained. Accordingly, he makes a succession of substitutions equating terms and eliminating variables until the problem reduces to finding the solution of the Pell Equation. Euler erroneously assigns this type of equation to Pell. He also makes a number of restrictions to the equation ax2+bx+c = y and works on several subthemes, from incomplete equations to polygonal numbers

Otimização Topológica com Termo-elasticidade Utilizando Elementos Tri3

This work proposes a formulation for optimization of 2D-structure layouts submitted to mechanic and thermal shipments and applied an h-adaptive filter process which conduced to computational low spend and high definition structural layouts. The main goal of the formulation is to minimize the structure mass submitted to an effective state of stress of von Mises, with stability and lateral restriction variants. A criterion of global measurement was used for intents a parametric condition of stress fields. To avoid singularity problems was considerate a release on the stress restriction. On the optimization was used a material approach where the homogenized constructive equation was function of the material relative density. The intermediary density effective properties were represented for a SIMP-type artificial model. The problem was simplified by use of the method of finite elements of Galerkin using triangles with linear Lagrangian basis. On the solution of the optimization problem, was applied the augmented Lagrangian Method, that consists on minimum problem sequence solution with box-type restrictions, resolved by a 2nd orderprojection method which uses the method of the quasi-Newton without memory, during the problem process solution. This process reduces computational expends showing be more effective and solid. The results materialize more refined layouts with accurate topologic and shape of structure definitions. On the other hand formulation of mass minimization with global stress criterion provides to modeling ready structural layouts, with violation of the criterion of homogeneous distributed stress

Determinação de dados de equilíbrio de fases para sistemas aquosos com eletrólitos

In the present work are established initially the fundamental relationships of thermodynamics that govern the equilibrium between phases, the models used for the description of the behavior non ideal of the liquid and vapor phases in conditions of low pressures. This work seeks the determination of vapor-liquid equilibrium (VLE) data for a series of multicomponents mixtures of saturated aliphatic hydrocarbons, prepared synthetically starting from substances with analytical degree and the development of a new dynamic cell with circulation of the vapor phase. The apparatus and experimental procedures developed are described and applied for the determination of VLE data. VLE isobarics data were obtained through a Fischer s ebulliometer of circulation of both phases, for the systems pentane + dodecane, heptane + dodecane and decane + dodecane. Using the two new dynamic cells especially projected, of easy operation and low cost, with circulation of the vapor phase, data for the systems heptane + decane + dodecane, acetone + water, tween 20 + dodecane, phenol + water and distillation curves of a gasoline without addictive were measured. Compositions of the equilibrium phases were found by densimetry, chromatography, and total organic carbon analyzer. Calibration curves of density versus composition were prepared from synthetic mixtures and the behavior excess volumes were evaluated. The VLE data obtained experimentally for the hydrocarbon and aqueous systems were submitted to the test of thermodynamic consistency, as well as the obtained from the literature data for another binary systems, mainly in the bank DDB (Dortmund Data Bank), where the Gibbs-Duhem equation is used obtaining a satisfactory data base. The results of the thermodynamic consistency tests for the binary and ternary systems were evaluated in terms of deviations for applications such as model development. Later, those groups of data (tested and approved) were used in the KijPoly program for the determination of the binary kij parameters of the cubic equations of state original Peng-Robinson and with the expanded alpha function. These obtained parameters can be applied for simulation of the reservoirs petroleum conditions and of the several distillation processes found in the petrochemistry industry, through simulators. The two designed dynamic cells used equipments of national technology for the determination of VLE data were well succeed, demonstrating efficiency and low cost. Multicomponents systems, mixtures of components of different molecular weights and also diluted solutions may be studied in these developed VLE cells

Determinação de Dados de Equilíbrio Líquido-Vapor para Sistemas Hidrocarbonetos e Desenvolvimento de uma Nova Célula Dinâmica

In the present work are established initially the fundamental relationships of thermodynamics that govern the equilibrium between phases, the models used for the description of the behavior non ideal of the liquid and vapor phases in conditions of low pressures. This work seeks the determination of vapor-liquid equilibrium (VLE) data for a series of multicomponents mixtures of saturated aliphatic hydrocarbons, prepared synthetically starting from substances with analytical degree and the development of a new dynamic cell with circulation of the vapor phase. The apparatus and experimental procedures developed are described and applied for the determination of VLE data. VLE isobarics data were obtained through a Fischer's ebulliometer of circulation of both phases, for the systems pentane + dodecane, heptane + dodecane and decane + dodecane. Using the two new dynamic cells especially projected, of easy operation and low cost, with circulation of the vapor phase, data for the systems heptane + decane + dodecane, acetone + water, tween 20 + dodecane, phenol + water and distillation curves of a gasoline without addictive were measured. Compositions of the equilibrium phases were found by densimetry, chromatography, and total organic carbon analyzer. Calibration curves of density versus composition were prepared from synthetic mixtures and the behavior excess volumes were evaluated. The VLE data obtained experimentally for the hydrocarbon and aqueous systems were submitted to the test of thermodynamic consistency, as well as the obtained from the literature data for another binary systems, mainly in the bank DDB (Dortmund Data Bank), where the Gibbs-Duhem equation is used obtaining a satisfactory data base. The results of the thermodynamic consistency tests for the binary and ternary systems were evaluated in terms of deviations for applications such as model development. Later, those groups of data (tested and approved) were used in the KijPoly program for the determination of the binary kij parameters of the cubic equations of state original Peng-Robinson and with the expanded alpha function. These obtained parameters can be applied for simulation of the reservoirs petroleum conditions and of the several distillation processes found in the petrochemistry industry, through simulators. The two designed dynamic cells used equipments of national technology for the determination Humberto Neves Maia de Oliveira Tese de Doutorado PPGEQ/PRH-ANP 14/UFRN of VLE data were well succeed, demonstrating efficiency and low cost. Multicomponents systems, mixtures of components of different molecular weights and also diluted solutions may be studied in these developed VLE cells

Teoria cinética não extensiva: efeitos físicos em gases e plasmas

The standard kinetic theory for a nonrelativistic diluted gas is generalized in the spirit of the nonextensive statistic distribution introduced by Tsallis. The new formalism depends on an arbitrary q parameter measuring the degree of nonextensivity. In the limit q = 1, the extensive Maxwell-Boltzmann theory is recovered. Starting from a purely kinetic deduction of the velocity q-distribution function, the Boltzmann H-teorem is generalized for including the possibility of nonextensive out of equilibrium effects. Based on this investigation, it is proved that Tsallis' distribution is the necessary and sufficient condition defining a thermodynamic equilibrium state in the nonextensive context. This result follows naturally from the generalized transport equation and also from the extended H-theorem. Two physical applications of the nonextensive effects have been considered. Closed analytic expressions were obtained for the Doppler broadening of spectral lines from an excited gas, as well as, for the dispersion relations describing the eletrostatic oscillations in a diluted electronic plasma. In the later case, a comparison with the experimental results strongly suggests a Tsallis distribution with the q parameter smaller than unity. A complementary study is related to the thermodynamic behavior of a relativistic imperfect simple fluid. Using nonequilibrium thermodynamics, we show how the basic primary variables, namely: the energy momentum tensor, the particle and entropy fluxes depend on the several dissipative processes present in the fluid. The temperature variation law for this moving imperfect fluid is also obtained, and the Eckart and Landau-Lifshitz formulations are recovered as particular cases

Avaliação clínica do efeito da irradiação pós-opratória do laser de baixa intensidade na cicatrização de gengivoplastias em humanos

Many studies have been made to understand the process of tissular cicatrization, as well as the possible effects of laser therapy in the wound healing. However, the influence of low frequency laser irradiation in the repairing process is not completely understood. Our study has the purpose to assess clinically the effect of postoperative irradiation of the low frequency laser in humans, and the gingival repairing process postgingivoplasty performed with the extern bevel technique. Twenty-four patients with inflammatory gingival hyperplasia were enrolled in this study, which did not reduce with basic periodontal procedures, and patients with melanin pigmentation, with esthetic indications. After surgery the test group, randomly selected by a drawing, received laser application with energy density of 4 J/cm2, immediately after surgery and each 48 hours, during a week, with a total of 4 sections. The control group did not receive irradiation. The visual clinical analyses were performed by a single blind examiner, in the 2nd, 4th, 6th, 8th, 15th and 21st days post surgery. For statistic analyses of the data was used a Q-square test. Concerning the color, the results showed a better wound healing during days 6 to 8. when assessed the degree of progress of surgical wound, the results showed that the test group had a better cicatrization compared with the control group in the 2nd, 6th, 8th and 15th days post surgery, and at the 21st day both groups had the same results. Our results confirm that the laser had clinical influence in the repairing process after gingivoplasty surgery during days 2 to 15 post surgery

Estratégia de vida do peixe anual Hypsolebias antenori (Cyprinodontiformes: Rivulidae) do semiárido brasileiro

This work deals with the life strategy of an endangered annual fish, Hypsolebias antenori (Cyprinodontiformes: Rivulidae), of the Brazilian semiarid region. The eggs of these fish hatch at the onset of the rainy season, grows rapidly and they reproduce during the rainy season. When the water puddles dry out, the entire population dies. The resistant eggs which are buried in the bottom of the dried pools go through diapause stages, during which time the embryonic development becomes temporarily arrested. With the onset of the next rainy season, the eggs hatch and a new generation is formed. Specimens of H. antenori were captured during 2011 and 2013, in temporary water pools located in the hydrographic basin of river Jaguaribe in Ceará, Brazil. Sex ratio, the length-weight relationship, the growth type, first sexual maturity, anatomy and histology of the digestive tract, development of gonads, reproductive strategy, karyotypic pattern of the species, and the conservation status of H. antenori were investigated. The results of this study are presented in the form of eight articles. The first article is about the fish faunal composition of the hydrographic basins of Rio Grande do Norte, Brazil, wherein the record of H. antenori is included. The second article deals with the sex ratio, secondary sexual characteristics of males, the length-weight relationship and the type of growth. Males show a pattern of intense coloration with well developed fins. The sex ratio showed a significant predominance of females (1M:1.7 F). Males were larger in length and weight. The equation of weight and total length relationship was Wt=0.0271Lt3,8937, showing a positively allometric growth, indicating greater increase in weight than in length. The third article discusses the anatomy and histology of the digestive tract of H. antenori. It is considered as a generalist feeder with characteristics of omnivore, which utilizes different food sources. The fourth article discusses the stages and phases of gonad development and type of spawning of H. antenori. The fifth article is about the r reproductive strategy adopted by H. antenori which helps in successful reproduction over a short period of life. The sixth article deals karyotypic pattern of the species, constituting the first cytogenetic contribution to the genus. The seventh article discusses about the risk of extinction of this species which suffers a series of threats, such as, habitat loss through land use, deforestation, construction of reservoirs, pollution due to domestic and industrial sewage, besides pesticides and agrochemicals. Furthermore, decreasing rainfall and intensification of aridity due to global climate changes, interferes with the reproductive cycle. The eighth article deals with aggressive behavior adopted between males and among females during reproduction. All temporary water pools sampled during this study were in high degree of degradation, mainly due to human action. There is a great need for conservation measures to protect the populations of annual fish, including the creation of protected areas in the semiarid ephemeral aquatic environments of Brazil

Caracterização de poliacrilamida parcialmente hidrolisada em regime concentrado

A partially hydrolyzed polyacrylamide (HPAM) is a copolymer composed of acrylamide and sodium acrylate. Due to its wide range of applications there are different methods for its quantification and characterization in solution systems. Evaluation of C* is important to describe the transition from dilute to semi-dilute, behavior, when the solution will have its characteristic viscosity at concentrations above C*. This dissertation describes the determination of the critical concentration of overlap C* by potentiometry of partially hydrolyzed polyacrylamide - HPAM under acidic conditions. Based on the law of mass action and the proper treatment of the constant of aggregate formation, polymer molecular weight, degree of polymerization and hydrolysis were calculated. The inflection point was determined by the intersection of the resulting equation and mathematical development, statistically satisfy the experimental points relating the number of moles of monomers (n), equilibrium constant of formation of the entanglements (K*), pH, C* and acidity constant of the polymer (Ka). The viscometric parameters of C* showed a percentage difference compared to potentiometers. The results for the determination of C*, and degree of copolymerization molar mass proved to be a simple alternative for the characterization of polymers with protonated monomers and water soluble