Reflexões sobre a construção e evolução de conceitos geométricos nas séries intermediárias do ensino fundamental

This thesis represents a didactic research linked to the Post-graduation Programme in Education of the Universidade Federal do Rio Grande do Norte which aimed to approach the construction of the geometrical concepts of Volume of the Rectangular Parallelepiped, Area and Perimeter of the Rectangle adding a study of the Area of the Circle. The research was developed along with students from the 6th level of the Elementary School, in a public school in Natal/RN. The pedagogical intervention was made up of three moments: application of a diagnostic evaluation, instrument that enabled the creation of the teaching module by showing the level of the geometry knowledge of the students; introduction of a Teaching Module by Activities aiming to propose a reflexive didactic routing directed to the conceptual construction because we believed that such an approach would favor the consolidation of the learning process by becoming significant to the apprentice, and the accomplishment of a Final Evaluation through which we established a comparison of the results obtained before and after the teaching intervention. The data gathered were analyzed qualitatively by means of a study of understanding categories of mathematical concepts, in addition to using descriptive statistics under the quantitative aspect. Based on the theory of Richard Skemp, about categorization of mathematical knowledge, in the levels of Relational and Instrumental Understanding were achieved in contextual situations and varied proportions, thus enabling a contribution in the learning of the geometrical concepts studied along with the students who took part in the research. We believe that this work may contribute with reflections about the learning processes, a concern which remained during all the stages of the research, and also that the technical competence along with the knowledge about the constructivist theory will condition the implementation of a new dynamics to the teaching and learning processes. We hope that the present research work may add some contribution to the teaching practice in the context of the teaching of Mathematics for the intermediate levels of the Elementary School

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 inclusiva e formação continuada: contribuições dos casos de ensino para os processos de aprendizagem e desenvolvimento profissional de professores

This study focuses on processes of learning and professional development experienced by elementary school teachers who have students with special educational needs in their classrooms. Cases and case methods can be used as methodological resource to articulate the continued training of teachers in an inclusive perspective. This research-intervention adopted a constructive-collaborative model for continued teachers formation. The main objective was to investigate the possible contributions of teaching cases, while investigative and formative strategies, for the processes of learning and professional development of teachers who work in the regular school. The data were collected by means of analytical activities, drafting collective discussion and teaching cases, having eight teachers as participants in a regular public school, located in the municipality of Natal/RN, Brasil. The theoretical reference covers the inclusive education, teaching learning, teachers professional development, the knowledge base for teaching and teaching cases as a resource for continued teachers formation in an inclusive perspective. The results indicated that teaching cases allowed description and analysis of educational practices developed by regular education teachers and adoption of reflective processes about situations reported and on their own pedagogical actuation, achieving indications of changes. It also indicates the contribution of cases for the clarification, systematization and extension of professional knowledge about inclusive education process as well as for involvement by the teachers of the study in a pedagogical thinking process. The lessons learned are related mainly to own role as teachers of regular education, to the role of professional support and specialized institutions faced to school inclusion. The analyses showed the methodological option was suitable to develop a schoolcentric training process, allowing teachers to seek in their actual environment alternatives for construction of a new logic of teaching that encloses diversity. The conclusion is that the cases, while bringing educational situations closer to the reality experienced by teachers in their daily professional role, causes relevant improvement on teachers education, because it offers training in conjunction with the experience and knowledge that teachers already have

Educação inclusiva e formação continuada: contribuições dos casos de ensino para os processos de aprendizagem e desenvolvimento profissional de professores

This study focuses on processes of learning and professional development experienced by elementary school teachers who have students with special educational needs in their classrooms. Cases and case methods can be used as methodological resource to articulate the continued training of teachers in an inclusive perspective. This research-intervention adopted a constructive-collaborative model for continued teachers formation. The main objective was to investigate the possible contributions of teaching cases, while investigative and formative strategies, for the processes of learning and professional development of teachers who work in the regular school. The data were collected by means of analytical activities, drafting collective discussion and teaching cases, having eight teachers as participants in a regular public school, located in the municipality of Natal/RN, Brasil. The theoretical reference covers the inclusive education, teaching learning, teachers professional development, the knowledge base for teaching and teaching cases as a resource for continued teachers formation in an inclusive perspective. The results indicated that teaching cases allowed description and analysis of educational practices developed by regular education teachers and adoption of reflective processes about situations reported and on their own pedagogical actuation, achieving indications of changes. It also indicates the contribution of cases for the clarification, systematization and extension of professional knowledge about inclusive education process as well as for involvement by the teachers of the study in a pedagogical thinking process. The lessons learned are related mainly to own role as teachers of regular education, to the role of professional support and specialized institutions faced to school inclusion. The analyses showed the methodological option was suitable to develop a schoolcentric training process, allowing teachers to seek in their actual environment alternatives for construction of a new logic of teaching that encloses diversity. The conclusion is that the cases, while bringing educational situations closer to the reality experienced by teachers in their daily professional role, causes relevant improvement on teachers education, because it offers training in conjunction with the experience and knowledge that teachers already have

Avaliar na alfabetização: uma reflexão sobre as dificuldades docentes

Our work leads up to the context of evaluation during alphabetization process as a moment of an educational action cycle that requires planning, teaching and learning of reading and writing. It aimed to research the difficulties lived by teachers of a public elementary school during the specific task of evaluating children in the alphabetization process. This qualitative research took place as a case study at Emília Ramos Municipal School, in Natal, capital city of Rio Grande do Norte State, Brazil. Semi-structured interview and questionnaire were used as fact-gathering proceedings. Two pedagogical advisers and seven teachers formed the group of research subjects. All of them worked with elementary school first cycle classes, in that school, in the year of 2003. The analysis shows that teachers difficulties concern to theoretic questions of conceptual and methodological orders, although these questions indicate an important knowledge of teachers about alphabetization and evaluation. Our reflection about these problems articulates two points: alphabetization and evaluation. Concerning alphabetization, we took reference on Psychogenetic studies of Ferreiro and Teberosky (1985) which emphasizes fundamental points for a coherent evaluation practice: a) objective knowledge is not a beginning data; it is a construction process, which the learner does not conquest step by step on a linear way; b) objective knowledge acquisition happens through a global re-construction, and some of them may seem mistakes if we consider conventional writing but these mistakes are constructive and necessary. We also took reference on Interactionist-constructivist theory. Here, Vygotsky (1984) proposes that writing must be specially understood as language, symbolical activity, cultural practice. So, acquisition of writing process, as language learning, must be understood as a development of abilities relative to symbolical and communicative activity of sense production. On this way, Hoffmann (1994) advises that is necessary to overtake current evaluation practices, limited by their terminality character, only pointing right or wrong questions. According to a new paradigm, valuation appears as one of the mediations by which teachers must indicate re-ordination of pupil s knowledge, and re-organize their own practices too. The comprehensions of these questions plays decisive part in order to overtake our difficulties in evaluating. Besides, it points a way to build a coherent valuate practice, with an emancipating character and able to create new teaching-and-learning situations, leading to a better alphabetization Pedagogy

Um estudo sobre a aprendizagem de números irracionais no ensino médio

The present study describes theoretical practical relationships between development and application of activities in Mathematics education. It s proposed a methodological approach to Mathematics in the first grade of Ensino Médio, supported by an experiment involving Irrational Numbers education by using constructive activities, applied obeying an educational sequence. Constructivism is used as an important theoretical reference in teaching learning process of Mathematics. The methodological intervention was done with two classes of students of the first grade of Ensino Médio, in two public schools, a state one and a federal one, located on the city of Natal, Rio Grande do Norte. The development, application and testing of the activities used on this experiment led us to think more profoundly about the value of constructivism ideas and understand that the use of activities that obey an educational sequence favors the learning. It s also discussed the research results, commented on a way to contribute to the advances of the proposal and it s more constant use. The participation and testing of the students were analyzed and judged using Skemp s Instrumental Understanding and Relational Understanding concepts. The results of the research were considered good, so we believe this methodological intervention can be used more frequently in the classes of Ensino Médio and also be applied to teachers in courses of initial education and continuous formation

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

Valorização do servidor no Programa Nacional de Humanização: estudo em um hospital universitário

It is at the work environment where value of the health professional is realized, according to the National Humanization Policy (PNH) from a Pediatric Hospital connected to an institution of higher education. Among the guiding principles of PNH it is highlighted the commitment to the democratization of labor relations and enhancement of health professionals, stimulating the continuing education process. For this research, a qualitative approach was chosen, using a semistructured interview as a tool to collect data. In a perspective of identifying the appreciation and humanization into interpersonal relations between workers, information from the theory of communicative action of Habermas was analyzed, considering cultural values goes beyond the practice in action, where the prospects of moral arguments in the universal truisms of life pervade original cultural moral, cognitive and expressive, imbued on ethics. This reasearch had the collaboration 29 employees with a regular contract labor to a teaching hospital in Natal, Brazil. The data was obtained through interviews which all participants signed a consent term. After data analysis the results shows the existance of a satisfaction of all workers on performing duties. The workers perceive its role valorization through kudos received as a consequence of a work done, others believe that it occurs when the institution or the group itself is concerned to enhance the work. Thus, in general, they feel valued. Regarding the interpersonal relationship, the most highlighted point was the fact that in the employees versus general directors item, respondents indicated the existence of a distance between these two categories, which can affect a participatory management. Therefore, the results of this study showed the necessity to develop actions that provide a healthy work environment. The joint guidelines of the PNH and the Employee Health Care Policy, represent some directions with some similarities in their purpose to the theory of communicative action, where there is a mutual respect, tolerance and coexistence of differences, considering the constructive conflict among health workers within the perspective of communication and interaction among individuals

A construção da ponte metálica sobre o Rio Pontengi: aspectos históricos, construtivos e de durabilidade - Natal/RN, Brasil (1912-1916) - estudo de caso

It is a case study that reports the construction of metal truss bridge in the river Potengi in Natal, Rio Grande do Norte, between the years 1912 and 1916. From testimonials on steel bridges in Brazil and worldwide including foundations. Documentary research from procurement of projects and contracts was performed. A chronology of construction, with a description of the equipment used and its original budget with the Brazilian government. Still, we used interviews and surveys with experimental sampling / testimonies, laboratory tests. This study aims to analyze historically and technically the Bridge over the River Potengi, emphasizing primarily the construction process, the qualities and characteristics of the materials used and the technological, chemical, mineralogical and microstructural properties of cement and concrete used in its construction. Taking as conclusions that cements pozolônicos ensured a good durability to the concrete in a hundred-year period and that the solution employed with the compressed air caissons was right

Conversor CC/CA de alta freqüência baseado em inversores ressonantes com comutação seqüencial para excitação de uma tocha indutiva a plasma térmico

This work describes the study, the analysis, the project methodology and the constructive details of a high frequency DC/AC resonant series converter using sequential commutation techniques for the excitation of an inductive coupled thermal plasma torch. The aim of this thesis is to show the new modulation technique potentialities and to present a technological option for the high-frequency electronic power converters development. The resonant converter operates at 50 kW output power under a 400 kHz frequency and it is constituted by inverter cells using ultra-fast IGBT devices. In order to minimize the turn-off losses, the inverter cells operates in a ZVS mode referred by a modified PLL loop that maintains this condition stable, despite the load variations. The sequential pulse gating command strategy used it allows to operate the IGBT devices on its maximum power limits using the derating and destressing current scheme, as well as it propitiates a frequency multiplication of the inverters set. The output converter is connected to a series resonant circuit constituted by the applicator ICTP torch, a compensation capacitor and an impedance matching RF transformer. At the final, are presented the experimental results and the many tests achieved in laboratory as form to validate the proposed new technique

Antena de microfita com substrato metamaterial

This paper presents a theoretical and numerical analysis of the parameters of a rectangular microstrip antenna with metamaterial substrate. The metamaterial (MTM) theory was applied along with Transverse Transmission Line (LTT) method to characterize substrate quantities and obtain the general equations of the electromagnetic fields. A study on metamaterial theory was conducted to obtain the constructive parameters, which were characterized through permittivity and permeability tensors to arrive at a set of electromagnetic equations. Electromagnetic principes are used to obtained parameters such as complex resonance frequency, bandwidth and radiation pattern were then obtained. Different metamaterial and antenna configurations were simulated to miniaturize them physically and increase their bandwidth, the results of which are shown through graphics. The theoretical computational analysis of this work proved to be accurate when compared to other studies, and may be used for other metamaterial devices. Conclusions and suggestions for future work are also proposed

Caracterização de antenas planares com substrato metamaterial

This work presents a theoretical and numerical analysis for the radiation characteristics of rectangular microstrip antenna using metamaterial substrate. The full wave analysis is performed in the Fourier transform domain through the application of the Transverse Transmission Line - TTL method. A study on metamaterial theory was conducted to obtain the constructive parameters, which were characterized through permittivity and permeability tensors to arrive at a set of electromagnetic equations. The general equations for the electromagnetic fields of the antenna are developed using the Transverse Transmission Line - TTL method. Imposing the boundary conditions, the dyadic Green s function components are obtained relating the surface current density components at the plane of the patch to the electric field tangential components. Then, Galerkin s method is used to obtain a system of matrix equations, whose solution gives the antenna resonant frequency. From this modeling, it is possible to obtain numerical results for the resonant frequency and return loss for different configurations and substrates

Otimização Topológica com Termo-elasticidade Utilizando Elementos Tri3

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

Análise do desempenho térmico de sistema constutivo de concreto com EPS como agregado graúdo

In the last decades there was a concentrate effort of researchers in the search for options to the problem of the continuity of city development and environmental preservation. The recycling and reuse of materials in industry have been considerate as the best option to sustainable development. One of the relevant aspects in this case refers to the rational use of electrical energy. At this point, the role of engineering is to conceive new processes and materials, with the objective of reducing energy consumption and maintaining, at the same time the benefits of the technology. In this context, the objective of the present research is to analyze quantitatively the thermal behavior of walls constructed with concrete blocks which composition aggregates the expanded polystyrene (EPS) reused in the shape of flakes and in the shape of a board, resulting in a “light concrete”. Experiments were conducted, systematically, with a wall (considerate as a standard) constructed with blocks of ordinary concrete; two walls constructed with blocks of light concrete, distinct by the proportion of EPS/sand; a wall of ceramic bricks (“eight holes” type) and a wall with ordinary blocks of cement, in a way to obtain a comparative analysis of the thermal behavior of the systems. Others tests conducted with the blocks were: stress analysis and thermal properties analysis (ρ, cp e k). Based on the results, it was possible to establish quantitative relationship between the concentration (density) of EPS in the constructive elements and the decreasing of the heat transfer rate, that also changes the others thermal properties of the material, as was proved. It was observed that the walls of light concrete presents better thermal behavior compared with the other two constructive systems world wide used. Based in the results of the investigation, there was shown the viability of the use of EPS as aggregate (raw material) in the composition of the concrete, with the objective of the fabrication of blocks to non-structural masonry that works as a thermal insulation in buildings. A direct consequence of this result is the possibility of reduction of the consume of the electrical energy used to climatization of buildings. Other aspect of the investigation that must be pointed was the reuse of the EPS as a raw material to civil construction, with a clear benefit to reducing of environmental problems

Estudo térmico e de materiais de um compósito à base de gesso e EPS para construção de casas populares

A housing unit was built to study the thermal performance, and of material using a composite made of gypsum and EPS ground. We used two techniques of construction, using blocks, and filling on the spot. Two compositions of the composite were studied. The blocks were fixed using conventional mortar. In the technical of filling on the spot were used PET bottles up inside the walls to provide mechanical and thermal resistance. Compression tests were realized according to the ABNT standard of sealing bricks. It is going to be shown an analysis of the thermal comfort through the use of thermocouples placed on the walls of the building, internally and externally. The manufacturing viability of houses, using recyclable materials, through the use of composite materials proposed will be demonstrated. The constructive aspects showing the advantages and disadvantages of the technique used also will be broached. The block used presents structural functions and thermal insulating, is low cost and represents an alternative to the use of EPS and PET bottles which are materials that end up occupying much space in the landfills, giving than an ecologically correct use. The results of thermal analysis shows the thermal comfort provided by the composite by the obtainment of a difference between the internal and external surfaces of the walls more exposed to the sun around 7º C. The average temperature of the air inside the building, around 28.0 º C was below the zone of thermal comfort recommended for countries with hot weather