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

Educação matemática, ciência e tradição: tudo no mesmo barco

Les connaissances de la tradition et position de la Science dehors pour un non-hiérarchique dialoguez qui frappe pour les distinguer mais ils sont undésavouer inséparable étant donné les compléments ils composent. Cet essai assume la possibilité de ce roi de dialogue dans un place spéciale: la classe. Sur ce qui vient au connaissance de la tradition, le centre remarquable est pour la construction de bateaux du travail manuel, una pratique culturellement déployé dans la ville d'Abaetetuba, dans le État de Pará, Brésil. En revanche, la Science est concentrée par le le contenu d'école a adopté dans l'Ensino Fundamental (École primaire). La construction du dialogue est faite en utilisant des activités de l'enseignement qui accentuez des aspects géométriques (solide, géométrique, angles et symétries) aussi bien que par information qui implique le tableau, poésie, histoire, géographie et physique - les deux inspiré dans le chiffre de bateau résumé dans un CD-ROM interactif. Les activités ont eu lieu dans D'Escola Ensino Pedro Teixeira Fondamental (Abaetetuba-Pa), avec étudiants du 6e niveau (plus spécifiquement avec un groupe de 13 étudiants) d'août à octobre2004. Ethnomathématiques et transdisciplinarité sont le support théorique sous-jacent du projet. Dans résumé, c'est possible pour dire que l'interaction entre Science et Tradition, à travers activités au-delà lesquelles vont le le contenu a restreint à mathématiques d'école, contribuées à,: identifiez le contenu a appris pas sur dans série antérieure; renouveler le rôle joué par école dans ses fonctions didactique pédagogiques; réduire le isolement entre information passée historique et les étudiants présent culturel; indiquer des obstacles à l'érudition des mathématiques intéresser aux aspects cognitifs et behavioristes; et provoquer un participation affective qui rôle principal à la qualité d'apprendre l'école contenu aussi bien que les connaissances de la tradition

Os ateliês (auto)formativos na constituição do sujeito docente da educação matemática

The object of study of this thesis is the use of (self)training workshops as a fundamental process for the constitution of the teaching subject in mathematics education. The central purposes of the study were to describe and analyze a learning process of mathematics teachers supported by the training-research methodology, which procedures have been affected with the practice of (self)training workshops as a way of collaborating to the constitution of the teaching subject in Mathematics Education. The survey was conducted with a group of teachers in the city of Nova Cruz, Rio Grande do Norte through a process of continued education realized in the training workshops having as main goal the realization of the group s (self)training sessions in order to lead participants to the extent of their autonomy in their personal and professional transformations. The results obtained in the formative processes have shown the need to develop activities of mathematics teaching as a contribution to overcome the conceptual difficulties of the teachers, apart from their (self)reflections about themselves and the educational processes in which they belong. The results raised some propositions about (self)training workshops that may be incurred in practices to be included in the curriculum frameworks or materialize as a strategy of pedagogical work in training courses for teachers of mathematics. Also, they can constitute an administrative and educational activity to be instituted in the public schools of Basic Education

Um estudo sobre o estágio supervisionado na formação inicial de professores de matemática na Bahia

This work arose from our concerns with the issues of teacher training for early childhood education. From the difficulties encountered as a novice teacher in elementary, we deem important to research training needs of these professionals. Thus, we define the objective of this research to investigate the training needs of novice teachers teaching Early Childhood Education/Elementary school. Our work fits in Educational Research Qualitative Approach, and its construction procedures of the semistructured interview data and document analysis. Our empirical field was made up of schools in the metropolitan region of Natal / RN, offering kindergarten / elementary school. The subjects are five teachers who act as holder of the elementary school class and have 0-3 years of teaching practice, characterizing the second Huberman (2007) as novice teachers. Data analysis, based on principles of content analysis, three themes emerged: Beginner Teaching Professor in Early Childhood Education / Preschool; Reasons explaining the difficulties Faculty / Formative Needs Teaching and Training in Early Childhood Education / Elementary school, from the Training Needs Analysis, with their respective categories, subcategories, contributing to our understanding of the subject matter. The entry into the profession is marked by mixed feelings of euphoria and fear, where there seems to be a "clash" with reality. The difficulties are related to the planning / execution of activities, meet the individual needs of learning and assessment of children. As a strategy to overcome the difficulties the teachers exercise the action-reflection-action in their practices and seek continuous updates in the theoretical and methodological framework of early childhood education. The reasons that define these difficulties may be related to the teacher, school, family, and students of these institutions. In experiencing these difficulties has outlined the need for teacher training, among which stand out studies on ethics in teaching with children, the concept of children and their childhoods, peculiarities of teaching / learning in preschool, toys and legal determinations on early childhood education, multi-language and expressions in early childhood education, specific content areas of knowledge, among others. Furthermore, studies on the theoretical as Piaget, Vigotsky, Maria Carmen Barbosa and Emily Smith. For these professionals to be a professional early childhood education is: like children, be patient and careful, have specific theoretical and practical training for teachers in kindergarten, being able to improvise with seriousness and competence and get updates on continuing education. The surveys, together with the authors and teachers, to confirm our understanding that the training needs of beginners may be related to shortcomings in the initial and continuing education

Ateliês de história e pedagogia da matemática: contribuições para a formação de professores que ensinam matemática nos anos iniciais

This paper presents a discussion about the use of the History of Mathematics as an educational resource and conceptual mediator in the formation of teachers who teach mathematics in the years of elementary school. It was a qualitative action method, in order to show the importance of holding workshops of History and Pedagogy of Mathematics as contribution to overcome the conceptual difficulties of teaching and teachers regarding the content covered in the course of education and afterwards they have to teach in the early of elementary school. We assume that understanding the historical, social and cultural comprehension as a conceptual and didactic focus effectively nurture the pursuit of a teaching and learning of mathematics students safe and justified in order to contribute to overcoming the difficulties of teaching and learning usually occurred in the classroom of the early years. In this sense, we organized a study group formed by students of Bachelors in Education and Mathematics at the University of Piauí. We developed five training workshops in History and Pedagogy of Mathematics, with a workload of 20 hours each and four follow-up sessions and advicement, totalizing 180 hours. The purpose of workshops was to develop studies on the History of Mathematics that could support the formation of a conceptual and didactic group with a view to prepare teaching materials and activities based on information drawn from undertaken historical studies .The products designed were used in formation of the group itself and will later be used in training teachers of public school in Teresina, in the form of workshop of History and Pedagogy of Mathematics in order to overcome problems arising from teaching and conceptual this education degree in Education Based on the obtained informations it was possible to suggest new referrals procedural level of education and university extension that may contribute to the reorientation of initial and continuing training of teachers in the early years elementary school

Geometria e simetria nas rendas de bilro: contribuições para matemática escolar

A tese tem como objetivo descrever e analisar características e princípios dos padrões das rendas de bilro de modo a estabelecer relações com a Matemática escolar, principalmente, no que se refere aos tópicos como Geometria, simetria, isometria, área, perímetro, entre outros. Desse modo, elaboramos atividades didáticas, com base na Matemática explorada nos padrões da criação da renda de bilro, visando concretizar um exercício investigatório nas aulas de Matemática, de modo que, sejam estabelecidas relações conceituais entre a prática investigada e os conteúdos da Matemática escolar. Para satisfazer esses objetivos, buscamos apoio metodológico na pesquisa bibliográfica, do tipo documental em catálogos como o da Professora Valdelice Girão (1984) e também o de Dawson (1984). Realizamos também a pesquisa empírica durante as visitas ao Museu do Ceará e ao Centro das Rendeiras na Prainha, em Aquiraz, no Ceará. Para realizar as atividades didáticas, apoiamo-nos em Mendes (2009). Consideramos relevante essa abordagem de ensino porque pressupõe a experiência direta do aprendiz com situações reais vivenciadas, nas quais a abordagem instrucional é centrada no aluno. Desse modo, concluímos que para o ensino de conteúdos como Geometria, simetria, isometria, relação entre perímetro e área, entre outros que são abordados na Educação Básica, os modelos decorrentes da criação renda de bilro e outros modelos já descritos na tradição cearense podem ser usados como artefato cultural na criação de atividades didáticas

Os jogos com regras na perspectiva do desenho universal: contribuições à educação matemática inclusiva

To think about a school that is for everyone has been a challenge for many people connected to education worldwide demanding from researchers of each level of knowledge an association to such effort. The study presented on this paper unites itself to the voices, movements and researches of these scholars, seeking to contribute on building possibilities on which mathematics can be thought and worked on schools in order for every student to learn, whether they have some sort of deficiency, disorders, syndromes or not. This essay has the goal to investigate the possibilities of inclusive pedagogical practices mediated by math games with rules, developed and used throughout the Universal Design perspective; a qualitative research took place with a collaborative methodology that involved managers, teachers and students from a public school situated on the city of Natal/Brazil. On the investigation math games with rules were developed and made according to the Universal Design concept, starting from initial studies which articulated theoretical groundings to the reality of school and the teacher s conceptions. After that, classes using these tools were planned collectively which oriented inclusive pedagogical practices of classes from the 1st to the 4th year of elementary school. Throughout the process many instruments such as: tape recording, video footages, notes from the researcher; the teachers and the students were used for constant work evaluation and also to record the research data. In the end, the data indicated effective contributions of the mediated pedagogical practices by games with rules under the perspective of Universal Design for Inclusive Mathematics Education

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

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

Body art, existência e conhecimento :a percepção do corpo na Educação Física

In the Renaissance, the anatomy project a map of the body. Since then, the human body has been investigated for innumerable techniques, configuring new landscapes on the condition human being and the proper knowledge. In accordance with Merleau-Ponty (1975), All technique is body technique. It configures and extends the Metaphysical structure of our meat. In this direction, any intervention in the human body, a tattooing, a surgery or a performance, extends the perception and the directions of the existence of the subject. Merleau-Ponty (1975) still affirms, that all technique presents objective interventions. However, the body, ahead of these interventions, doesn t have to be considered only object, but subject that, from the interventions, attributes sensible and meanings through the movements, also being this its way of being in the world. Searching to extend this reflection on the discontinuities between the object body and the subject body, as well as, with the objective to reflect on the relation between the corporal techniques and the production of the subjectivity and the knowledge of the physical education, we reflect on the body art, as one technique of body that marks the exterior of the body, exteriorizing the subjectivity, to search new means to the body and that ahead of this, we believe being able to project innumerable directions for the corporal transformations in the contemporarily. As a method for our reflection in we will support them in the phenomenology. IT presents as a new ontology, in which distinction does not occur enters the operating paper of the citizen that knows and the influence of the known object. The phenomenological understanding of body will be able to contribute with the knowledge of the Physical Education, a time that gives us important arguments on the experience of the body in relation with the nature, the culture, history. To be a body is to be tied to a world that we do not possess completive, but that we do not cease to search it

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.

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

Cosmoeducação: uma abordagem transdisciplinar no ensino de astronomia

This work proposes a transdisciplinary approach that integrates transpersonal psychology exercises with astronomy teaching, seeking to allow one to reintegrate the sky in his/her daily life, expand his/her environmental awareness and eventually experiment the unity between human and cosmos. This proposal intends to collaborate with the supplying of education, which lacks initiatives of this kind, with the promotion of an integration of the scientific knowledge with the human experience that transcends the materialistic and fragmentary objectives of the current educational system. As a result of that lack, the teachers formation is also poor as for an integral and transdisciplinary approach. Besides, we also approached in this research the necessity to propose alternatives so that the educators may work in a more assertive way with the environmental and anthropological crisis in which we are living. Our working hypothesis is that the contents of astronomy, when they are dealt in a holisticanthropological focus and are related with transpersonal psychology practices, can come to be an efficient cultural-academic vehicle, capable of propitiating an expansion of consciousness and changes in the way one conceives the world. Such changes are necessary so that a more solidary, fair and ecologically balanced life may come to exist and prevail in the planet. Part of the collection of data was done through the ethnographic method, once an anthropological interpretation is inextricably associated with this kind of educational intervention, which will naturally include ethno-visions of the universe as well as specific cultural elements. In the beginning the scope of this research was a group of students attending the Astronomy assignment in an undergraduate Geography course (UFRN), in which we accomplished participant observation, half-open interviews and the first experimental practices mentioned. After the evaluation of the first data collected from that initial group, we elaborated an academic extension course, Laboratory in Cosmoeducation, and we offered it to teachers of the 1st and 2nd cycles of the fundamental level of the Alceu Amoroso Lima State School, located in the North Zone of Natal. We prized self-experimentation in that course, so that the teachers could enrich their repertoire of personal experiences, stimulating meditative reflections and eventual changes in the ways of conceiving the world and in their pedagogical practice. The transdisciplinary attitude permeated all our educational action, because this approach transcends the boundaries of disciplines, seeking essentially the integral development of the human being. The process has made us realize that the practice of looking at the sky , as a way of reintegrating it into daily life, provokes a process of expansion of the consciousness and of reintegration of the self in a wider level of environmental interrelation. According to the results, the occurrence of conceptual and existential changes of the world vision of the participant teachers was evident, reassuring ourselves of the idea that the interface between astronomy teaching and the practices of transpersonal psychology can contribute to the recovery of a holistic relationship between the human being and the cosmos and to inspire the arising of a more wide-ranging ethics, based on universal, impartial and sustainable values