Quando as professoras se encontram para estudar matemática: saberes em movimento

This text results of a research in an Education Doctorate about teachers, professional background, formation, teaching knowledge and abilities. In this text, it s described the history of a study group in mathematics education composed by teachers who teach mathematics in the 2nd cycle of Ensino Fundamental (5th year of schooling), all belonging to the same school of the municipal public schools network. It presents the trajectory of the collaborative group, in all particularities, singularities, and the constant search to become collaborative. This trajectory was marked by the stories of it s participants in the ceaseless path to constitute teachers, by the sharing of knowledge, by the process of collaboration, by the thinking about the teaching practice, and by the personal and professional improvement of the teachers that form the group. The interpretative and qualitative research had as its investigation field the study group. The data supplied by the collect instruments indicate us that the collaboration between the teachers, the access to specific knowledge of mathematics area, the reflections about the teaching practice in a given context, are paths that lead to and make possible the re-elaboration of the teaching skills by teachers that teach mathematics to the first years

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

Não é que eu sei ser professora!: formação continuada e construção do currículo da matemática para o ciclo de alfabetização

Esta dissertação investiga como a prática da formação continuada em Matemática dos professores do Núcleo de Educação da Infância/Colégio de Aplicação (NEI/CAp) tem possibilitado a construção do currículo da Matemática para o ciclo de alfabetização nessa instituição. Assumimos os princípios metodológicos da abordagem qualitativa com ênfase na pesquisa colaborativa. Privilegiamos atividades de formação continuada organizadas em sessões de estudos e reflexões sobre a prática pedagógica que envolveram todos os partícipes. Para a construção dos dados realizamos a escolha de instrumentos e procedimentos metodológicos como a entrevista individual e as sessões reflexivas de videoformação e de estudo. Com a intensão de responder a questão central da pesquisa definimos duas categorias de interpretação: a formação continuada em Matemática dos professores do NEICAp dos anos iniciais do Ensino Fundamental e a construção do currículo da Matemática dos anos iniciais do Ensino Fundamental nesta escola. Constatamos que a prática da formação continuada em Matemática acontece dentro da própria instituição e tem como interesse, além da formação permanente dos seus professores, o desenvolvimento da escola e a aprendizagem dos alunos. Avaliamos que por meio de estudos e reflexões sobre as práticas docentes, análises de propostas pedagógicas de Secretarias de Educação e de outros documentos oficiais do Ministério da Educação, em momentos de formação continuada em contextos vivenciadas pelos professores do NEI/CAp, vem sendo possível construir o currículo desta instituição e, consequentemente, a sua proposta curricular, na qual privilegiamos a área da Matemática

A Proficiência escritora em matemática trabalhada nos livros didáticos dos 4º e 5º anos do ensino fundamental

Universidade Federal do Rio Grande do Norte

Automedicação e guarda de medicamentos por universitários das áreas de saúde e tecnologia

This study aimed to compare self-medication and domestic drug storage among undergraduate students in the areas of health and technology. This is a descriptive study of cross-sectional type and quantitative approach, conducted in a Public University of Natal, Rio Grande do Norte, Brazil. The sample consisted of 300 students of the third year of undergraduate courses at the Center for Health Sciences and Technology Center, selected through a simple random sample. The project was authorized by the Ethics Committee of Federal University of Rio Grande do Norte (CAAE 0137.0.051.000-10). Data collection lasted twelve months and was conducted during the period of study participants, in the university environment. The instrument for data collection was a structured questionnaire consisting of open and closed questions. For data analysis, we used descriptive statistics and applied Fisher s exact test and Chi-square test with adopted level of significance α=5% and 10%. For the variables that correlated with self-medication (p<0.05), we subsequently calculated the odds ratios and confidence intervals. The prevalence of undergraduate students who performed self-medication in the 15 days prior to the collection accounted for 33.7% and, by analyzing each knowledge area, we verified was a higher prevalence of self-medication among students in the technological area (37.3%). The analysis of the socio-demographic characteristics of the participants in this practice revealed a significant difference between the knowledge areas in the income and self-medication variables (p=0.005). General analgesics and antipyretics (N02) represent the therapy group most used in self-medication (57.4%), especially acetaminophen (28.7%), and the main health situations that motivated this practice related to pain, especially headaches (48.5%). Regarding the indication of the drugs used, the majority of students self-medicated themselves on their own (71.3%). As regards to the in-home drug storage, most of the participants had a home pharmacy (88%). By analyzing the socioeconomic characteristics, the variables medical service and home medicine presented a significant difference (p=0.002). General 10 analgesics and antipyretics constituted the medicinal products most found in the home pharmacies, especially acetaminophen. The main room used for the drug storage was the kitchen (36.4%), most students kept these products in boxes of different materials (38.6%) and the medicines stored at home of most of the participants were not easily accessible to children (75%). The results reinforce the need to develop strategies, from the reality found, aiming to encourage and implement educational and preventive activities with undergraduate students on the importance of proper self-medication and in-home drug storage. Despite the sample in our study is relatively small, not representative for the whole country, we believe that, at national level, the panorama of the subject does not present major differences

Padrões nutricionais para lavouras arrozeiras irrigadas por inundação pelos métodos da CDN chance matemática

Para o arroz irrigado, poucos trabalhos utilizam métodos de diagnose foliar desenvolvidos para as condições locais de clima, solo ou cultivares. O objetivo deste trabalho foi avaliar os métodos da Diagnose da Composição Nutricional e da Chance Matemática na definição dos padrões nutricionais de lavouras arrozeiras do Estado do Rio Grande do Sul. Resultados de produtividade de grãos e teores foliares de N, P, K, Ca, Mg, S, B, Cu, Fe, Mn, Zn e Mo de 356 lavouras arrozeiras cultivadas sob sistema de irrigação por inundação foram utilizados para a determinação das faixas de suficiência calculadas pelo método da Chance Matemática. As faixas de suficiência foram comparadas com valores críticos propostos pela literatura e com o intervalo de confiança do teor médio dos nutrientes em lavouras consideradas nutricionalmente equilibradas, identificadas pelo método Diagnose da Composição Nutricional. Observou-se pouca concordância entre os valores das faixas de suficiência indicados pelos métodos da Chance Matemática e da Diagnose da Composição Nutricional e os respectivos valores indicados na literatura. A faixa de teores foliares adequados, consistentes com maior produtividade média das lavouras arrozeiras, foi indicada ser de 23 a 28 g kg-1 para N; 11 a 14 g kg-1 para K; 1,4 a 2,0 g kg-1 para S; 6 a 12 mg kg-1 para B; e 70 a 200 mg kg-1 para Fe. Para os teores foliares de P, Ca, Mg, B, Cu, Mn e Zn e Mo nenhuma das faixas adequadas testadas indicou capacidade para distinguir as lavouras arrozeiras quanto à produtividade média.

Qualidade em serviços de saúde: uma contribuição à definição de um modelo paramétrico e padrão de qualidade do tempo agendado para consulta ambulatorial

This work presents a study in quality of health care, with focus on consulting appointment. The main purpose is to define a statistical model and propose a quality grade of the consulting appointment time. The time considered is that from the day the patient get the appointment done to the day the consulting is realized. It is used reliability techniques and functions that has as main characteristic the analysis of data regarding the time of occurrence certain event. It is gathered a random sample of 1743 patients in the appointment system of a University Hospital - the Hospital Universitário Onofre Lopes - of the Federal University of Rio Grande do Norte, Brazil. The sample is randomly stratified in terms on clinical specialty. The data were analyzed against the parametric methods of the reliability statistics and the adjustment of the regression model resulted in the Weibull distribution being best fit to data. The quality grade proposed is based in the PAHO criteria for a consulting appointment and result that no clinic got the PAHO quality grade. The quality grade proposed could be used to define priority for improvement and as criteria to quality control

Uma Fundamentação Intervalar Aplicada à Morfologia Matemática

This work present a interval approach to deal with images with that contain uncertainties, as well, as treating these uncertainties through morphologic operations. Had been presented two intervals models. For the first, is introduced an algebraic space with three values, that was constructed based in the tri-valorada logic of Lukasiewiecz. With this algebraic structure, the theory of the interval binary images, that extends the classic binary model with the inclusion of the uncertainty information, was introduced. The same one can be applied to represent certain binary images with uncertainty in pixels, that it was originated, for example, during the process of the acquisition of the image. The lattice structure of these images, allow the definition of the morphologic operators, where the uncertainties are treated locally. The second model, extend the classic model to the images in gray levels, where the functions that represent these images are mapping in a finite set of interval values. The algebraic structure belong the complete lattices class, what also it allow the definition of the elementary operators of the mathematical morphology, dilation and erosion for this images. Thus, it is established a interval theory applied to the mathematical morphology to deal with problems of uncertainties in images

Uma fundamentação matemática para processamento digital de sinais intervalares

This work deals with a mathematical fundament for digital signal processing under point view of interval mathematics. Intend treat the open problem of precision and repesention of data in digital systems, with a intertval version of signals representation. Signals processing is a rich and complex area, therefore, this work makes a cutting with focus in systems linear invariant in the time. A vast literature in the area exists, but, some concepts in interval mathematics need to be redefined or to be elaborated for the construction of a solid theory of interval signal processing. We will construct a basic fundaments for signal processing in the interval version, such as basic properties linearity, stability, causality, a version to intervalar of linear systems e its properties. They will be presented interval versions of the convolution and the Z-transform. Will be made analysis of convergences of systems using interval Z-transform , a essentially interval distance, interval complex numbers , application in a interval filter.

Metodologia estatística na solução do problema do caixeiro viajante e na avaliação de algoritmos : um estudo aplicado à transgenética computacional

The problems of combinatory optimization have involved a large number of researchers in search of approximative solutions for them, since it is generally accepted that they are unsolvable in polynomial time. Initially, these solutions were focused on heuristics. Currently, metaheuristics are used more for this task, especially those based on evolutionary algorithms. The two main contributions of this work are: the creation of what is called an -Operon- heuristic, for the construction of the information chains necessary for the implementation of transgenetic (evolutionary) algorithms, mainly using statistical methodology - the Cluster Analysis and the Principal Component Analysis; and the utilization of statistical analyses that are adequate for the evaluation of the performance of the algorithms that are developed to solve these problems. The aim of the Operon is to construct good quality dynamic information chains to promote an -intelligent- search in the space of solutions. The Traveling Salesman Problem (TSP) is intended for applications based on a transgenetic algorithmic known as ProtoG. A strategy is also proposed for the renovation of part of the chromosome population indicated by adopting a minimum limit in the coefficient of variation of the adequation function of the individuals, with calculations based on the population. Statistical methodology is used for the evaluation of the performance of four algorithms, as follows: the proposed ProtoG, two memetic algorithms and a Simulated Annealing algorithm. Three performance analyses of these algorithms are proposed. The first is accomplished through the Logistic Regression, based on the probability of finding an optimal solution for a TSP instance by the algorithm being tested. The second is accomplished through Survival Analysis, based on a probability of the time observed for its execution until an optimal solution is achieved. The third is accomplished by means of a non-parametric Analysis of Variance, considering the Percent Error of the Solution (PES) obtained by the percentage in which the solution found exceeds the best solution available in the literature. Six experiments have been conducted applied to sixty-one instances of Euclidean TSP with sizes of up to 1,655 cities. The first two experiments deal with the adjustments of four parameters used in the ProtoG algorithm in an attempt to improve its performance. The last four have been undertaken to evaluate the performance of the ProtoG in comparison to the three algorithms adopted. For these sixty-one instances, it has been concluded on the grounds of statistical tests that there is evidence that the ProtoG performs better than these three algorithms in fifty instances. In addition, for the thirty-six instances considered in the last three trials in which the performance of the algorithms was evaluated through PES, it was observed that the PES average obtained with the ProtoG was less than 1% in almost half of these instances, having reached the greatest average for one instance of 1,173 cities, with an PES average equal to 3.52%. Therefore, the ProtoG can be considered a competitive algorithm for solving the TSP, since it is not rare in the literature find PESs averages greater than 10% to be reported for instances of this size.

Probabilidades imprecisas: intervalar, fuzzy e fuzzy intuicionista

The idea of considering imprecision in probabilities is old, beginning with the Booles George work, who in 1854 wanted to reconcile the classical logic, which allows the modeling of complete ignorance, with probabilities. In 1921, John Maynard Keynes in his book made explicit use of intervals to represent the imprecision in probabilities. But only from the work ofWalley in 1991 that were established principles that should be respected by a probability theory that deals with inaccuracies. With the emergence of the theory of fuzzy sets by Lotfi Zadeh in 1965, there is another way of dealing with uncertainty and imprecision of concepts. Quickly, they began to propose several ways to consider the ideas of Zadeh in probabilities, to deal with inaccuracies, either in the events associated with the probabilities or in the values of probabilities. In particular, James Buckley, from 2003 begins to develop a probability theory in which the fuzzy values of the probabilities are fuzzy numbers. This fuzzy probability, follows analogous principles to Walley imprecise probabilities. On the other hand, the uses of real numbers between 0 and 1 as truth degrees, as originally proposed by Zadeh, has the drawback to use very precise values for dealing with uncertainties (as one can distinguish a fairly element satisfies a property with a 0.423 level of something that meets with grade 0.424?). This motivated the development of several extensions of fuzzy set theory which includes some kind of inaccuracy. This work consider the Krassimir Atanassov extension proposed in 1983, which add an extra degree of uncertainty to model the moment of hesitation to assign the membership degree, and therefore a value indicate the degree to which the object belongs to the set while the other, the degree to which it not belongs to the set. In the Zadeh fuzzy set theory, this non membership degree is, by default, the complement of the membership degree. Thus, in this approach the non-membership degree is somehow independent of the membership degree, and this difference between the non-membership degree and the complement of the membership degree reveals the hesitation at the moment to assign a membership degree. This new extension today is called of Atanassov s intuitionistic fuzzy sets theory. It is worth noting that the term intuitionistic here has no relation to the term intuitionistic as known in the context of intuitionistic logic. In this work, will be developed two proposals for interval probability: the restricted interval probability and the unrestricted interval probability, are also introduced two notions of fuzzy probability: the constrained fuzzy probability and the unconstrained fuzzy probability and will eventually be introduced two notions of intuitionistic fuzzy probability: the restricted intuitionistic fuzzy probability and the unrestricted intuitionistic fuzzy probability

Estimação de Fasores para Proteção de Sistemas Elétricos Baseada em Mínimos Quadrados e Morfologia Matemática

This work proposes a new technique for phasor estimation applied in microprocessor numerical relays for distance protection of transmission lines, based on the recursive least squares method and called least squares modified random walking. The phasor estimation methods have compromised their performance, mainly due to the DC exponential decaying component present in fault currents. In order to reduce the influence of the DC component, a Morphological Filter (FM) was added to the method of least squares and previously applied to the process of phasor estimation. The presented method is implemented in MATLABr and its performance is compared to one-cycle Fourier technique and conventional phasor estimation, which was also based on least squares algorithm. The methods based on least squares technique used for comparison with the proposed method were: forgetting factor recursive, covariance resetting and random walking. The techniques performance analysis were carried out by means of signals synthetic and signals provided of simulations on the Alternative Transient Program (ATP). When compared to other phasor estimation methods, the proposed method showed satisfactory results, when it comes to the estimation speed, the steady state oscillation and the overshoot. Then, the presented method performance was analyzed by means of variations in the fault parameters (resistance, distance, angle of incidence and type of fault). Through this study, the results did not showed significant variations in method performance. Besides, the apparent impedance trajectory and estimated distance of the fault were analysed, and the presented method showed better results in comparison to one-cycle Fourier algorithm

Análise estatística das emissões de CO e HC produzidas por gases da exaustão veicular oriundos de gasolina, GNV e mistura álcool/gasolina

The vehicles are the main mobile sources of carbon monoxide (CO) and unburned hydrocarbons (HC) released into the atmosphere. In the last years the increment of the fleet of vehicles in the municipal district of Natal-RN it is contributing to the increase of the emissions of those pollutants. The study consisted of a statistical analysis of the emissions of CO and HC of a composed sample for 384 vehicles with mechanization Gasoline/CNG or Alcohol/Gasoline/CNG of the municipal district of Natal-RN. The tests were accomplished in vehicles submitted to Vehicular Safety's Inspection, in the facilities of INSPETRANS, Organism of Vehicular Inspection. An partial gases analyzer allowed to measure, for each vehicle, the levels of CO and HC in two conditions of rotation of the motor (900 and 2500 rpm). The statistical analysis accomplished through the STATISTICA software revealed a sensitive reduction in the efficiency of the converters catalytic after 6 years of use with emission average it is of 0,78% of CO and 156 (ppm) of HC, Which represents approximately 4 (four) times the amount of CO and the double of HC in comparison with the newest vehicles. The result of a Student s t-test, suggests strongly that the average of the emissions of HC (152 ppm), at 900 rpm, is 40% larger than at 2500 rpm, for the motor without load. This result reveals that the efficiency of the catalytic conversion is limited kinetically in low engine speeds. The Study also ends that when comparing the emissions of CO and HC considering the influence of the fuels, it was verified that although the emissions of CO starting from CNG are 62% smaller than arising from the gasoline, there are not significant differences among the emissions of HC originating from of CNG and of the gasoline. In synthesis, the results place the current criteria of vehicular inspection, for exhaust gases, in doubt, leading the creation of emission limits of pollutant more rigorous, because the efficiency of the converters catalytic is sensibly reduced starting from 6 years of use. It is also raised the possibility of modifications in the test conditions adopted by the current norms, specifically in the speed engine, have seen that in the condition without load the largest emission indexes were registered in slow march. That fact that allows to suggest the dismissal of the tests in high speed engine, reducing the time of inspection in half and generating economy of fuel

Extração do óleo e caracterização dos resíduos da borra de petróleo para fins de reuso

The petroleum industry, in consequence of an intense activity of exploration and production, is responsible by great part of the generation of residues, which are considered toxic and pollutants to the environment. Among these, the oil sludge is found produced during the production, transportation and refine phases. This work had the purpose to develop a process to recovery the oil present in oil sludge, in order to use the recovered oil as fuel or return it to the refining plant. From the preliminary tests, were identified the most important independent variables, like: temperature, contact time, solvents and acid volumes. Initially, a series of parameters to characterize the oil sludge was determined to characterize its. A special extractor was projected to work with oily waste. Two experimental designs were applied: fractional factorial and Doehlert. The tests were carried out in batch process to the conditions of the experimental designs applied. The efficiency obtained in the oil extraction process was 70%, in average. Oil sludge is composed of 36,2% of oil, 16,8% of ash, 40% of water and 7% of volatile constituents. However, the statistical analysis showed that the quadratic model was not well fitted to the process with a relative low determination coefficient (60,6%). This occurred due to the complexity of the oil sludge. To obtain a model able to represent the experiments, the mathematical model was used, the so called artificial neural networks (RNA), which was generated, initially, with 2, 4, 5, 6, 7 and 8 neurons in the hidden layer, 64 experimental results and 10000 presentations (interactions). Lesser dispersions were verified between the experimental and calculated values using 4 neurons, regarding the proportion of experimental points and estimated parameters. The analysis of the average deviations of the test divided by the respective training showed up that 2150 presentations resulted in the best value parameters. For the new model, the determination coefficient was 87,5%, which is quite satisfactory for the studied system

A matemática sob a ótica do Tarô: Uma experiência com a educação de jovens e adultos

La recherche de la formation des citoyens critiques et participatifs, dans le travail pédagogique avec les jeunes et les adultes, a besoin d un entraînement pédagogique qui va au delà de l attitude traditionnelle d'apprendre avec des méthodes mécaniques et arbitraires qui, en insistant excessivement sur l image du professeur, donnent priorité à l'enseignement, au détriment de l apprentissage. Dans ce sens, la présente étude, cherchant la possibilité de réalisation d'un travail alternatif pour l'enseignement des Mathématiques, dans une perspective transdisciplinaire, dans le sens de développer l apprentissage significatif des étudiants jeunes et adultes du Projet Croire, présente les résultats d'une recherche-intervention qui a utilisé les lettres du tarot comme ressource didactique en salle de classe. On prétend, avec cela, montrer cet instrument comme facilité d apprentissage de contenus des Mathématiques comme systèmes de numération, nombres entiers et géométrie, en amenant les Mathématiques dans une perspective historique et culturelle et donnant un traitement global à l'acte complexe d'apprendre. Dans ce travail, le jeune étudiant et l étudiant adulte est pris comme individu concret, prenant en considération les aspects cognitifs et les aspects d attitude de son apprentissage, ce qui est favorisé par la nature des lettres du tarot et par la compréhension adoptée, des mathématiques comme système symbolique