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

Reflexões e contribuições para o ensino de gravitação clássica no nível médio

The subject of Classic Gravitation is part of the actual curriculum for High School in Brazil, and it is taught in the first year of that education level. This master thesis presents a research regarding the subject Classic Gravitation in High School. This research was based in two complementary guidelines of research and action. The first guideline was the analysis of 21 didactic books of physics which are the more frequently used in High School, in the city of Natal/RN. The second guideline, worked after being verified the most common deficiencies presents in the didactic books, was the elaboration, followed by a practical application, of a course suggesting how to approach that subject in the classroom. The Parâmetros Curriculares Nacionais para o Ensino Médio (National Curricular Parameters for High School PCNEM) defend that Classic Gravitation is very important in the student s formation and that its study helps the comprehension of many nature s phenomena. Because of this vision of that subject by the PCNEM, the 21 analyzed books were separated in two groups: the first one, containing 10 books, was edited before the spreading of PCNEM, and the second, with 11 books, after that spreading. Whatever the group to which the didactic books belonged, the great majority of them let that subject in a second plan; two of them even suggesting, in the teacher s orientations, that the subject Gravitation can be suppressed in case of insufficient time . These analyses points that the PCNEM had produced no changes in the conception of the authors that wrote books regarding that subject. To analyze the didactic books, we elaborated a script which was used as an analysis tool, in which we put in evidence the relative importance of the historic and philosophic contextualization of the subject, the quotidian experience of the students and the interdisciplinary approach, among other aspects. It became evident that the didactic books give very little emphasis to historic aspects of the knowledge construction, to the relations with the day-by-day questions and to the interdisciplinary character of the subject Gravitation. It calls attention the non concordance among the authors opinions regarding the necessary previous knowledge or prerequisites the students should fulfill in order to begin to study Gravitation. The course we elaborated was given to a group of teachers as well as to students. In those courses we treated theoretical and practical aspects and emphasized historical questions and the ones which are related to people s daily life. The course for teachers was realized as an extra-mural activity of the UFRN and was given by the author of this thesis at the Escola Estadual Francisco Ivo Cavalcanti (a state public school in Natal/RN). There were 23 teachers present, from several public schools and several fields of knowledge. The thesis supervisor and the master degree s colleagues of the author acted as collaborators , reporting the participants opinions and speeches. The course to the students, on the other hand, had the participation of 300 regular students who belonged to 6 different 1st year classes of the High School Escola Marista de Natal (RN), in which the author acts as a physics teacher. The student s course was realized as part of the regular curriculum activities, in which three classes stood under the responsibility of the author and other three classes in charge of another Marista s teacher, who participated as a collaborator . The teacher s course as well as the students one were given in two stages, with five hours each. The first stage was divided in two moments, the first one focused on the survey of the spontaneous conceptions about gravitation, in which we worked basically with experiments of free throwing and pendulum, and the second one focused in theoretical presentations and quarrels about universe s models. In the second stage of the course we improved the study of Kepler s laws and the Newton s Universal Gravitation law, and we used as motivating tools some practices involving the construction of the solar system in scale. As instruments for evaluating both courses we used questionnaires and reported the speeches with participants opinions, beyond usual written evaluations in the course for the students. The teachers who participated in the course showed very good wills in realizing interdisciplinary practices; nevertheless, according their own speeches, they frequently came across the difficulty of how to do . From the experience we had in both courses, we conclude that the approach we propose hear to the teaching of the subject Classic Gravitation , supported on the tripod theory, practice and historical and philosophical aspects, is viable and effective. One hopes that this research may contribute in the formation of a opinion, among the teachers, concerning how to approach the subject of Classic Gravitation, and may offer suggestions in order those who want to apply that approach may develop classroom practices aiming to improve the teaching of that subject, which has a singular importance in the formation of High School students

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

Contribuições da investigação em sala de aula para uma aprendizagem das secções cônicas com significado

In this work, the didactical possibilities of investigation use in classroom, through an experience with high school students from Federal Center of Technological Education of Paraíba, as well as the study of conic sections were analysed. In order to fulfill our goals the theoretical conceptions concerning the meaninful learning in conection with the investigation of mathematics history were taken into account. The classroom research occurred by means of activities which encouraged the learner to investigate his own concepts on the conic sections. The results of the proposed activities showed the effectiveness and the efficiency of such a methodology as regards the making up of the required knowledge. They also reveal that the investigation in the classroom guides the ones involved, in this process, to have a wider look at the origins, the methods used and the several representations presented by mathematics that certainly lead, specially the students, to a meaninful learning

Elaboração e aplicação de uma estratégia de ensino sobre os conceitos de calor e de temperatura

This piece of work has investigated the alternative conceptions shown by students of secondary school, concerned to the concepts of warmth and temperature, aiming the elaboration and application of a learning strategy as of the diagnose risen from the conceptions present in students. The learning strategy was built up by a sequence of activities that involve History of Science and experiments, put in a course that had as a base the proposal of the Group of Redevelopment of Physics Teaching (GREF). We have used as the conductor wire of our research the development of thermo dynamics since the development of the first thermo machines, passing by the Industrial Revolution and the evolution of concepts of warmth and temperature. The learning strategy was applied to a group of second grade of secondary school in a public school in Mossoró (RN). By doing these activities we tried to become the concepts, which are part of thermo dynamics, more meaningful to the students. We have estimated that the application of the strategy has represented some profits to the students of the group, concerning to learning of laws and concepts of thermo dynamics (specifically the concepts of warmth and temperature), as well as what it is referred to the overcoming of its initial conceptions

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

Investigação histórica na formação de professores de matemática: um estudo centrado no conceito de função

In this study we analyzed the development of a teaching experience, involving students with a bachelor s degree in mathematics from UFRN, based on the history of mathematics and mathematical investigations with the aim of contributing to the improvement of the teaching-learning of mathematics. The historical investigation tasks were planned and applied in the classroom, focusing on functional thought. The results obtained during the experience were described and evaluated based on authors who support the assumption of investigation and history as an alternative to the learning of mathematics. We emphasize that the material of analysis consisted of a work diary, audio recordings, questionnaires with testimony of the students involved, and, in addition, the assessment of the teacher of that subject. With regard to the mathematical content, the study was restricted to the concept of function, forms of representation and notation. It was evident that students showed great improvement with regard to the necessary formalization of the mathematical contents which were focused on, and to the active involvement of the students at different stages of the study. We can affirm that the completed study certainly represents significant contributions to an approach in the teaching-learning of functional thought

Uma abordagem histórica para o ensino do princípio da inércia

Placed in the field of Didactic of Science, this paper proposes an approach to the introduction of the History of Science in science education, at high school level. It was designed and implemented a series of activities regarding the history of the Principle of Inertia. The aim of this approach was to give more meaning to scientific education, while opening new avenues for a better understanding of the processes of construction of scientific knowledge. The preparation of the activities involved a study of the historical development of the concept of motion, from the Aristotelian physics through physical movement concepts at medieval period, from Galileo, Gassendi, Descartes, until the first law of Newton. The strategy of teaching was applied to three classes of high school (night period) of a state public school at the city of Natal (RN). The results indicated the difficulty of overcoming alternative conceptions about movement by students. Nevertheless, we consider that the implementation of this strategy of teaching both represented gains for the learning of students, and contributed to the resizing of pedagogical practices of the teacher-researcher

Controvérsias sobre a natureza da luz: uma aplicação didática

Researches in the field of Science Teaching have shown, in recent decades, that students from high school level have difficulties in understanding basic concepts of science, in general, and physics, in particular. The specific literature indicates, as a priority for a scientific education of better quality, a more structured understanding about science. This work proposes the introduction of elements of History and Philosophy of Science in high school as an aid to learning the concepts of optics, in general, and of aspects concerning the nature of science, specifically. Making use of historical episodes regarding the controversy on the nature of light, especially during the seventeenth and eighteenth centuries, as well as clippings of the history of optics in relation to the development of models that explain the process of vision, we formulated a teaching unit and implemented it on two night high school classes of a public school in the city of Parnamirim (RN). The unit involved, primarily, the reading of three historical texts containing written questions followed by a collective debate ("moot"). The results indicated some difficulties in overcoming the misconceptions related to the process of vision and the nature of light. Nevertheless, we believe that the teaching unit has succeeded in relation to the learning of most students, both in relation to a better understanding of science as well as concepts of optics

Educação científica no contexto pós-ontológico: por uma concepção plural de conhecimento e educação

The development of this work arises from the research of sociological and philosophical characters contemplating also other approaches which aims to answer the followingquestions: what is the responsibility of science teaching for the image one has about science? ; which scientific education should be designed for nowadays? . After considering the assumptions brought along by rationalism and the criticisms to the illuminist model proposed by sociology and philosophy of science, as well by the biology of the knowing process, going through discussions concerning post-modernity issues, one is given to understand that the image of science has become the central point of discussion in the last hundred years, including what concerns the area of science teaching, and that practically none of those discussions really reached natural science classes indeed. We adopt the term postontological to characterize the recent proposals on philosophy and sociology, because we evaluate that this term allows a better identification of the scientific realism crisis, which supports the existence of an ontological domain which science, and only science, is able to understand. One notices that the general public is not aware of those discussions, mainly if they are science teachers and students. So we believe that discussing the logic in which science is structured, the new understandings concerning the scientific undertaking, especially those of an externalist character, and the relationship between science and society, all of this contributes to build up a science teaching which contemplates a reflective contribution, besides allowing the inclusion of the study of other epistemologies in the educational practice. We argue that a revisionist posture seems to be the most appropriate for the contemporary scientific education, contemplating, besides the teaching of the usual science contents, discussions on the issues involving that knowledge, as well as respecting epistemologies alternative to the modern Western scientific one, in order one can work on the perception of local knowledge generated from other epistemological bases. We describe here practical activities we did involving teachers (short-term courses) and high-school students in an inland school in the Rio Grande do Norte state, in Brazil, as a way to demonstrate the possibility of interventions which can take those conceptions, discussions and changes to the classroom

Atribuição de significado ao conceito de proporcionalidade: contribuições da história da matemática

This study is the result of a work which approaches the Mathematics History how source of the meaning s attribution in the proportionality concept. We adopt the methodology of the source qualitative and we work with a group of teachers from instruction s public system of the fundamental and medium level from Pocinhos City Paraíba. For the data collection, we use the field notes, the questionnaire, a sequence of activities and the interview semistructured like instruments. The study had how objective to know the significates attributeds to proportionality concept through of the activity mediate from Mathematics History, besides to investigate if a approach of the nature enables modification according to this sense. The results obtaineds though the data analysis indicate that the activities bring contributions which refer to achieve objectives. On the other hand they also showed that we have a long trajectory to be trailed in the meaning of to turn the Mathematics History a subsidy effective in the teachers practice, in view of the formation absence in the knowledge area, besides the necessity of the approach adequated of the Mathematics History in the didatics books of Mathematic

Atividades experimentais no ensino de biologia em escolas públicas do estado do Rio Grande do Norte, Brasil: caracterização geral e concepção de professores

Recent research has revealed that the majority of Biology teachers believe the practice of experimental activities as a didactical means would be the solution for the improvement of the Biology teaching-learning process. There are, however, studies which signal the lack of efficiency in such practice lessons as far as building scientific knowledge is concerned. It is also said that despite the enthusiasm on the teachers‟ part, such classes are rarely taught in high school. Several studies point pedagogical difficulties as well as nonexistence of a minimal infrastructure needed in laboratories as cause of low frequency in experimental activities. The poor teacher performance in terms of planning and development of classes; the large number of students per class; lack of financial stimulus for teachers are other reasons to be taken into account among others, in which can also be included difficulties of epistemological nature. That means an unfavorable eye of the teacher towards experimental activities. Our study aimed to clarify if such scenario is generalized in high schools throughout the state of Rio Grande do Norte Brazil. During our investigation a sample of twenty teaching institutions were used. They were divided in two groups: in the first group, five IFRN- Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Norte schools. Two of those in Natal, and the other three from the country side. The second group is represented by fifteen state schools belonging to the Natal metropolitan area. The objectives of the research were to label schools concerning laboratory facilities; to identify difficulties pointed by teachers when performing experiment classes, and to become familiar with the conceptions of the teachers in regarding biology experiment classes. To perform such task, a questionnaire was used as instrument of data collecting. It contained multiple choice, essay questions and a semi-structured interview with the assistance of a voice recorder. The data analysis and the in loco observation allowed the conclusion that the federal schools do present better facilities for the practice of experimental activities when compared to state schools. Another aspect pointed is the fact that teachers of federal schools have more time available for planning the experiments; they are also better paid and are given access a career development, which leads to better salaries. All those advantages however, do not show a significantly higher frequency regarding the development of experiments when compared to state school teachers. Both teachers of federal and state schools pointed infra-structure problems such as the availability of reactants, equipments and consumption supplies as main obstacle to the practice of experiments in biology classes. Such fact leads us to conclude that maybe there are other problems not covered by the questionnaire such as poor ability to plan and execute experimental activities. As far as conceptions about experimental activities, it was verified in the majority of the interviewees a inductive-empiric point of view of science possibly inherited during their academic formation and such point of view reflected on the way they plan and execute experiments with students

Construção e aplicação de uma sequência didática para o ensino de trigonometria usando software geogebra

The present study aims to analyze the potentialities and limitations of GeoGebra software on what concerns trigonometry s teaching and learning processes. Taking the present resources of public school from the state of Rio Grande do Norte, the research intends to answer the following question: Could we use the current conditions of public school and the Geogebra software to optimize the trigonometry s learning and teaching processes situation? . To make it a possible to answer the question above, a module of investigative activities was created and applied. The methodological intervention was made among second year High School students from a public school in Natal, RN. The theoretical reference of Mathematics Didactics was taken was a base, adopting the conceptions of Borba and Penteado (2001), Valente (1999) and Zulatto (2002, 2007) about the use of Information Technology (IT) on Mathematics classrooms. In order to create the investigative activities helped us to understand how the students make their constructions and their visual perception through the process of dragging images on the computer screen. Furthermore, the activities done with the GeoGebra software s resources facilitate the resolution of trigonometry situations