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

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.

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.

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

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

A formação inicial do professor de química e o uso das novas tecnologias para o ensino: um olhar através de suas necessidades formativas

La disertación, desarrollada en el Programa de PostGraduación en Enseñanza de las Ciencias Naturales y de la Matemática de la UFRN, estudia las necesidades formativas de licenciandos en Química sobre el uso de las nuevas tecnologías de la información y de las comunicaciones (NTIC), en especial, las relacionadas con la utilización de programas computacionales para la enseñanza de la química. En la actual sociedad del conocimiento, se torna imperativo la eclosión de nuevas formas de aprender y de enseñar, que requieren de nuevas concepciones del trabajo pedagógico. En ese sentido, se exige de los profesores el desarrollo de nuevas habilidades y competencias. El presente trabajo está comprometido con la búsqueda de elementos que puedan nortear los procesos formativos de profesores de química con el objetivo de contribuir con una mejor preparación de la formación inicial, tomando en cuenta sus necesidades de formación. Fue utilizado el cuestionario como instrumento de investigación para diagnosticar y caracterizar las necesidades fomativas, buscando establecer correlaciones entre diferentes variables que cacarterizan el estudio, con el fin de establecer semenazas y discrepancias entre las habilidades docentes en estudio y las necesidades formativas. Los analises de los datos tomo elementos de la estadistica descriptivo e inferencial, con analises multivariados, lo que posibilitó identificar las necesidades formativas. Los resultados muestran ue de forma general los licenciandos evaluan como de bajo, el grado de desarrollo de las habilidades para enseñar usando las NTIC, así como manifiestan sentir necesidades formativas en todas las habilidades referentes a esa esfera del trabajo docente

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