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

Números complexos: uma proposta de mudança metodológica para uma aprendizagem significativa no ensino médio

This work presents a proposal of a methodological change to the teaching and learning of the complex numbers in the Secondary education. It is based on the inquiries and difficulties of students detected in the classrooms about the teaching of complex numbers and a questioning of the context of the mathematics teaching - that is the reason of the inquiry of this dissertation. In the searching for an efficient learning and placing the work as a research, it is presented a historical reflection of the evolution of the concept of complex numbers pointing out their more relevant focuses, such as: symbolic, numeric, geometrical and algebraic ones. Then, it shows the description of the ways of the research based on the methodology of the didactic engineering. This one is developed from the utilization of its four stages, where in the preliminary analysis stage, two data surveys are presented: the first one is concerning with the way of presenting the contents of the complex numbers in math textbooks, and the second one is concerning to the interview carried out with High school teachers who work with complex numbers in the practice of their professions. At first, in the analysis stage, it is presented the prepared and organized material to be used in the following stage. In the experimentation one, it is presented the carrying out process that was made with the second year High school students in the Centro Federal de Educação tecnológica do Rio Grande do Norte CEFET-RN. At the end, it presents, in the subsequent and validation stages, the revelation of the obtained results from the observations made in classrooms in the carrying out of the didactic sequence, the students talking and the data collection

Da cozinha ao terreiro em Mutamba da Caieira (RN) : cotidiano, espaço doméstico e sociabilidade

In this work we thought about the social use of the domestic space and, specifically, the space destined to the preparation of food. The kitchen is a creative space of social relationships. There the families exchange daily interaction with the neighbors, in a collective of the space reserved to the making of food. Our empiric research was in the Mutamba da Caieira community, located in the county of Assu (RN). The data was collected through the etnographic method aided by the photographic resources. In the discussion, we delimitated at the house three types of kitchens: one reserved to the family, another kitchen in the terrace and yet another kitchen in the yard. They are kitchens that link amongst themselves with activities and differentiated temporalities. In the daily social exchange, the kitchen imposes itself as a social space through the conditions that it offers for the production of the foods, the circulation of domestic objects, the communication of knowledge around the cookery, operating a group of symbolic and ritual actions combined with appropriate techniques for the transformation of the foods. The study reveals that the domestic chores accomplished amon relatives and friends form webs of intracommunitary relationships in the use of the three kitchens, and that the social network is updated in a singular moment that usually happens in the community, the Game of Pacará

O Sangyo em Dolls: um encontro do Bunraku com Takeshi Kitano

This work aims to investigate the relationship between the Bunraku theater and the film Dolls (2002), by the Japanese director Takeshi Kitano. To do so, it was initially done a theoretical study of this theater, detailing its key elements, and thus allowing a direct analysis of the film to be made. The main objective here was to reveal the film‟s connections with the Bunraku. The Sangyo refers to the simultaneous presence of three arts in the Bunraku theater: the narrative, the music and the manipulation of puppets. In Dolls, the director Takeshi Kitano presents a narrative through three different stories, all built with references to the Bunraku. As in the theater the three distinct arts harmonize on stage, in Dolls three separate stories will perform in harmony within the film. By confronting the Bunraku Theater with the film Dolls, the intention is to establish the connections between the scenic language of the Bunraku, the dramaturgy of Chikamatsu and also the cinema of Kitano. These connections allow to the understanding of how characteristics of a secular art, governed by strong rules and conventions, can be presented again through another language: the cinematic language and its particular set of codes and conventions

Simulação de fluxo de fluidos em meios porosos desordenados uma análise de efeito de escala na estimativa da permeabilidade e do coeficiente de arrasto

The present study provides a methodology that gives a predictive character the computer simulations based on detailed models of the geometry of a porous medium. We using the software FLUENT to investigate the flow of a viscous Newtonian fluid through a random fractal medium which simplifies a two-dimensional disordered porous medium representing a petroleum reservoir. This fractal model is formed by obstacles of various sizes, whose size distribution function follows a power law where exponent is defined as the fractal dimension of fractionation Dff of the model characterizing the process of fragmentation these obstacles. They are randomly disposed in a rectangular channel. The modeling process incorporates modern concepts, scaling laws, to analyze the influence of heterogeneity found in the fields of the porosity and of the permeability in such a way as to characterize the medium in terms of their fractal properties. This procedure allows numerically analyze the measurements of permeability k and the drag coefficient Cd proposed relationships, like power law, for these properties on various modeling schemes. The purpose of this research is to study the variability provided by these heterogeneities where the velocity field and other details of viscous fluid dynamics are obtained by solving numerically the continuity and Navier-Stokes equations at pore level and observe how the fractal dimension of fractionation of the model can affect their hydrodynamic properties. This study were considered two classes of models, models with constant porosity, MPC, and models with varying porosity, MPV. The results have allowed us to find numerical relationship between the permeability, drag coefficient and the fractal dimension of fractionation of the medium. Based on these numerical results we have proposed scaling relations and algebraic expressions involving the relevant parameters of the phenomenon. In this study analytical equations were determined for Dff depending on the geometrical parameters of the models. We also found a relation between the permeability and the drag coefficient which is inversely proportional to one another. As for the difference in behavior it is most striking in the classes of models MPV. That is, the fact that the porosity vary in these models is an additional factor that plays a significant role in flow analysis. Finally, the results proved satisfactory and consistent, which demonstrates the effectiveness of the referred methodology for all applications analyzed in this study.

Influência das mudanças climáticas na estrutura funcional da comunidade fitoplanctônica em um reservatório da região do semiárido

The Brazilian Northeast is the most vulnerable region to climatic variability risks. For the Brazilian semi-arid is expected a reduction in the overall rates of precipitation and an increase in the number of dry days. These changes predicted by the IPCC (2007) will intensify the rainfall and droughts period that could promote the dominance of cyanobacteria, thus affecting the water quality of reservoirs, that are most used for water supply, in the semi-arid. The aim of this study was to evaluate the effects of increasing temperature combined with nutrient enrichment on the functional structure of the phytoplankton community of a mesotrophic reservoir in the semi-arid, in the worst case scenario of climate change predicted by the IPCC (2007). Two experiments were performed, one in a rainy season and another in the dry season. In the water sampled, nutrients (nitrate and orthophosphate) were added in different concentrations. The microcosms were submitted to two different temperatures, five-year average of air temperature in the reservoir (control) and 4°C above the control temperature (warming). The results of this study showed that warming and nutrient enrichment benefited mainly the functional groups of cyanobacteria. During the rainy season it was verified the increasing biomass of small functional groups of unicellular and opportunists algae such as F (colonial green algae with mucilage) and X1 (nanoplanktonic algae of eutrophic lake systems). It was also observed an increasing in total biomass, in the richness and diversity of the community. In the dry season experiment there was a greater contribution in the relative biomass of filamentous algae, with a replacement of the group S1 (non-filamentous cyanobacteria with heterocytes) for H1 (filamentous cyanobacteria with heterocytes) in nutrient- enriched treatments. Moreover, there was also loss in total biomass, species richness and diversity of the community. The effects of temperature and nutrients manipulation on phytoplankton community of reservoir Ministro João Alves provoked changes in species richness, the diversity of the community and its functional composition, being the dry period which showed the highest susceptibility to the increase in the contribution of potentially toxic cyanobacteria with heterocytes

A Poética do corpo no mito e na dança butô: por uma educação sensível

The thesis presents the body poetry and its inscribing in the myth and Butô dance. The argumentation highlights the sensitive dimension present in these itineraries, as a possibility to operate the emergency of knowing inscribed in the body, bringing a kind of rationality that links the fragments, that allows the knowing to break through the barriers of disciplinary isolation, that abandons the certainties and goes through the ways of creation and that gives the body new space and time, featuring epistemological elements, ethical and esthetical, that can permit a sensitive education. All along the way, we comprehend by sensitive education, a education that considers the relinking of logical, analogical, symbolic and artistic knowledge and therefore reconsiders the own act of knowing as a continuous and inconcluded process. That sensitive education is also understood as retaking the body experience, its sensitive nature, as well as being meaningful to reading the world. It includes the body memory, its history and creativity, opening it to innovation, change, sense amplification and dialogue with other bodies and world, because it is within them. It is about an investigation of phenomenologic nature, that dialogues philosophy and art, pointing breakdowns of this reflection foe the body and education studies. We find it necessary to notice the body language, that allows one to think through movements, articulate a thought that is risen from articulations, guts and all the body. This incarnated reason starts the expressive body action, that makes us move to mean, communicate, inaugurate senses. Among these senses, we present a possibility of approach of the elements of Butô dance teaching and physical education, as ways of sensitive education showings of body poetry

Uma educação tecida no corpo

In theory say the education as a knot of meanings made in the body. We take as a reference for demonstration of this argument the shows Folguedos, Guarnicê and Flor do Lírio and built within such spectacles cultural, symbolic and aesthetic meanings, which reveal the education woven in the body. Education that can happen not only in the formal space like the classroom or the university, but also in the area of art and the inclusion of individuals in the world of culture. So during the construction of the thesis we reflect on the following issues: what is the construction of culture and art that have in the Parafolclórico group? What way theses shows in their buildings bring significant elements that might compose an educational activity. How objectives sought asking the dichotomies present in the concepts of art and culture; critically systematize a work of artistic, cultural and educational production in the group, in addition to expanding the understanding of education, considering the body experiences. The phenomenological attitude of Merleau-Ponty, is a reference methodology of this study, which places the reference knowledge as a result of our experience in the world, our world lived. Thus, this study considers the experience of the researcher in the three shows in tariff, represented by scenes described, as a dancer and spectator. Therefore we understand that Folguedos, Guarnicê and Flor do Lírio in their artistic, aesthetic and cultural languages, allow many meanings that occur in the body, which invites the perception and extend the experience of the subject, demonstrating an education that allows sight and knowledge, seeking new sensations and experiences, we show our intimacy with the world, with the objects and with the other. The art is understood as virtuality, as a human creation that carries the reality and that allows many readings and experiences, each perception can recognize and know new horizons, having as base and material the culture. This entails the heterogeneous, is not closed but that individuals can interpret it entered and recognize the symbols they created the same way, confirming a unit. The art and culture show us significant evidences of an education woven in the body

Em nome da república: escolas e tradições modernas

Our research aims to analyze some institutions of primary education in so-called First Republic in Natal/RN, when they were considered high standard institutions on training, dissemination and creation of national identity and republican traditions. Thus, we investigated to try to understand the creation of the new man and the invention of new traditions to confirm the status of republican modernity in two schools in Natal, the Colegio Americano, a private one, and a standard model of school, Augusto Severo, which is a public one. As a basis we have the history of institutions to analyze, paying close attention to consider the use of imitation in cultural patrimony as well as the use of strategies to distinguish. The concept of ownership follows, for present purposes, their focus of study on observation of diverse and contrasting use of these cultural objects, texts, readings and ideas from research institutions. For analysis of the link which occurs within the school environment, in every period of its history, we used the concept of school culture as a set of rules and practices which define knowledge to teach and conduct the introject. A culture that incorporates the school to keep a set with other religious cultures, political and popular of its time and space. In this sense, the educational institutions which we studied while showing what kind of in this work by preparing cultures, codes, different practices, and specific individuals they have, they were in important locations to provide modern cultural appropriation as a strategy for educational innovation and a factor of rationality and efficiency which could be observed and controlled, so gradually the modern school education was organized to produce its own society. As a challenge of affirmation and incorporating diverse social experiences to produce the modern, civilized man of the Republican time, the school, as part of the social life, which is singular in its practices, not only the set of reforms, decrees, laws and projects, but also as expressions of concept about life and society in terms of material, symbolic and cultural symbols in the social context in modernization. We focused on these two schools, because inside the wide cultural and material status of the city, they were the first republic schools which had the goal of having men and woman together culturally , with a view to adapting them to the modern movement to make them civilized / educated / rational . On this view, we would emphasize that this statement needs a reinvention as a new way through what is made at the schools which production of new spaces, practices, rites and what represents school, making and expressing a new identity, modern, different of the old symbols of the Empire. For this, nothing better than the organization of schooling, emphasizing on educating the individual and his/her responsibilities with the order and progress. We need to understand the past as a result of conflicts, including strengths and limitations within the historical and social context, and the invention of tradition as a process of formalization and ritualization of acts which want to perpetuate, as a reference to a group identity. These are practices and social educative representations which support the understanding of pedagogical and educational ideas at this historical moment, making a new way of being and doing in the Republican universe

Formação e vivências: a representação social do ser professor em comunidades ribeirinhas do Vale do Juruá Acre

Being a teacher is a challenging task, driving action strategies that mobilize technical dimensions of being / doing teaching, but also affection. This research was conducted with teachers / students of the Special Program of formation for Teachers of Basic Education agricultural zone (PROFIR) developed by the Federal University of Acre in partnership with the State Department of Education (SEE) and City Halls of the region; locus typically Amazon and, in this research, comprises five municipalities in the Valley of Juruá - Acre. Northern Brazil. It Aims to capture the social representation of being a teacher in riverside communities. We performed this study from the Theory of Social Representations (MOSCOVICI, 1978, 1990, 2005a, 2005b, 2009, 2011) and (JODELET, 2001), from discussions on teacher formation (LDB No. 9394 of 1996). Work, among others, (TARDIF, 2004), (TARDIF; LESSARD, 2007), (NÓVOA, 1992, 1999), (ARROYO, 2007). We used as a methodological strategy, the multiple classification procedure (PCM), which is organized in two steps: Free Classification and Directed Classification, as well as semi-structured interviews, involving, thus, 137 teachers surveyed. For the analysis of the data, we appealed to software SPSS, version 13.0 for Windows, mapping the elements of the representational content through Multidimensional Analysis (MSA and SSA). Through the different strategies of analysis, we identified from the Free Classification, the regionalization: Beyond forest, teaching Attributes and Mobilized Attributes. With data of the Directed Classification, the analysis was based on the Theory of Facets (BILSKY, 2003) and (BUSCHINI, 2005) and we found: Reference of teacher; Negative Dimension and affective and technicians attributes. Finally, with the Analysis of Content (BARDIN, 2004) e (FRANK, 2005) and of the interviews the categories we found the categories: Urban relation versus agricultural, Knowledge in construction and possible bets. The report of the experiences along the edge of the rivers, in these different methodological strategies and of analysis, demonstrates the existence of symbolic and representational elements that influence and guide the educational conduct and actions of these teachers and that they are deeply anchored and objectified in technical and affective elements of the making teacher. They daily live deeply the concreteness of the Amazonian realism redesigning the Real and the symbolic one as a way to understand themselves as a teacher in adversity of this context. We also observed the historical, social and cultural local marks, framing, thus, the collective personality and generating its guides of action

CORPOREIDADE E A MELODIA DA EXPERIÊNCIA ESTÉTICA NA FORMAÇÃO HUMANESCENTE DE CANTORES-EDUCADORES

In order for this study to be developed, the central goal on our investigation was defined as analyzing and interpreting the aesthetical experiences meanings lived by singers-educators in the human formation. The interest for the aesthetical experience theme was built from my own experience for the last twelve years as a member of the School of Music Madrigal, the oldest group in the State Federal University, created for research and cultural extension with structural perspective which brings closer teachers, students and the outer community that comes from different social realities to face the challenge of combining the ability of singing, the corporeity involvement and the aesthetical experiences meanings. This paper points out the understanding of art as perceptive expression of human emotions, such as the creation of existential demand, the restructuring of oneself and the constructions which shape beauty. We seek a dense contribution of new challenges to the peculiar demand of human potential in terms of sensibility repertoire, of involvement, of expectation in magnifying the possibilities and the human and social competences. In the formation human process, we find a living field blooming with natural artistical possibilities, experimenting emotions and feelings shared in collective life, and bringing out impulses to unexpected ludic creation, establishing a powerful aesthetical ambience which highlights the symbolic and imaginary with the deepening of rich ludopoiese properties in several meanings. From the guiding principles of etnophenomenology we find structural and indispensable perspectives which contemplate values, desires, archtype images and ideas that impress originality and fertility to the study. On this path we understand the abundance of living moments of intense commitment, acquaintance, challenges, reunions and connections that stand out from fundamental aspects to freedom, autonomy, creativity and new discontinuities. This acknowledgement brings us closer to the enlighted fullness which makes us humans

Uma investigação histórica sobre os logaritmos com sugestões didáticas para a sala de aula

This study was conducted from a preliminary research to identify the conceptual and didactic approach to the logarithms given in the main textbooks adopted by the Mathematics teachers in state schools in the School of Natal, in Rio Grande do Norte. I carried out an historical investigation of the logarithms in order to reorient the math teacher to improve its educational approach this subject in the classroom. Based on the research approach I adopted a model of the log based on three concepts: the arithmetic, the geometric and algebraic-functional. The main objective of this work is to redirect the teacher for a broad and significant understanding of the content in order to overcome their difficulties in the classroom and thus realize an education that can reach the students learning. The investigative study indicated the possibility of addressing the logarithms in the classroom so transversalizante and interdisciplinary. In this regard, I point to some practical applications of this matter are fundamental in the study of natural phenomena as earthquakes, population growth, among others. These practical applications are connected, approximately, Basic Problematization Units (BPUs) to be used in the classroom. In closing, I offer some activities that helped teachers to understand and clarify the meaningful study of this topic in their teaching practice

Euler e os números pentagonais

The present investigation includes a study of Leonhard Euler and the pentagonal numbers is his article Mirabilibus Proprietatibus Numerorum Pentagonalium - E524. After a brief review of the life and work of Euler, we analyze the mathematical concepts covered in that article as well as its historical context. For this purpose, we explain the concept of figurate numbers, showing its mode of generation, as well as its geometric and algebraic representations. Then, we present a brief history of the search for the Eulerian pentagonal number theorem, based on his correspondence on the subject with Daniel Bernoulli, Nikolaus Bernoulli, Christian Goldbach and Jean Le Rond d'Alembert. At first, Euler states the theorem, but admits that he doesn t know to prove it. Finally, in a letter to Goldbach in 1750, he presents a demonstration, which is published in E541, along with an alternative proof. The expansion of the concept of pentagonal number is then explained and justified by compare the geometric and algebraic representations of the new pentagonal numbers pentagonal numbers with those of traditional pentagonal numbers. Then we explain to the pentagonal number theorem, that is, the fact that the infinite product(1 x)(1 xx)(1 x3)(1 x4)(1 x5)(1 x6)(1 x7)... is equal to the infinite series 1 x1 x2+x5+x7 x12 x15+x22+x26 ..., where the exponents are given by the pentagonal numbers (expanded) and the sign is determined by whether as more or less as the exponent is pentagonal number (traditional or expanded). We also mention that Euler relates the pentagonal number theorem to other parts of mathematics, such as the concept of partitions, generating functions, the theory of infinite products and the sum of divisors. We end with an explanation of Euler s demonstration pentagonal number theorem

Nos tempos do blackout: cena musical, práticas urbanas e a ressignificação da Rua Chile, Natal-RN

This study aims to analyze the process of resignification of Chile Street, in Natal, from the development of a music scene in the late 1990s. Chile Street, as part of the Historic Centre of Natal, had its images constructed from the discursive practices and everyday life of its regular visitors, leading to a series of symbolic and imaging transformations throughout the twentieth century. Initially transformed into glamorous space as a result of urban actions of the new republic of Albuquerque Maranhão, in the early twentieth century, Ribeira and Chile Street, specifically, came to be seen as bohemian area, during the war time"; followed by a marginal phase, it was eventually transformed into the main rocker area of Natal, with the development of a musical scene in the second half of the 1990s. This music scene, its practices, economic interests, cultural events and identity ties created among their practitioners made Chile Street, "in the time of Blackout night club", an "alternative" space. As the historic centers, inserted in the logic of postmodern city marketing, both spaces are dynamic in their practices, as in their images, Chile Street also suffered changes in its meanings and symbols, around the year 2000 when the alternative-underground space became a pop space, where people from various parts of the city began attending its events and places, transforming it into a point of very heterogeneous sociability

Desvelando as teias de Pinóquio :concepções de família em jovens moradores de bairros periféricos

This thesis discusses family as a social and historical construction and concerns to the perceptions developed by the peripheral youth living in suburbs. It investigates the speeches of young boys and girls who take part in Engenho de sonhos a forum composed by a pool of eleven non-governmental organizations and UFRN which aim is the elaboration and execution of projects focusing local development of poor communities in violence and social exclusion context. Throughout interactive diagnosis seminars in five communities in West Side of Natal with six hundred teenagers, it was detected the need to work with family relationships. In order to build the methodological corpus a range variety of procedures were done such as: interviews, focal groups and psychosocial questionnaires with nine local young leaders. The purpose to understand data guided the research through the theory of social imagery and pointed out the following themes: conceptions, relationship, roles, family projects. Live stories of these young population reveals conflicts when it comes to the configuration of family ties, far from the family model stated by society. Family is also, in their perception, an important space to the development of affection, in experiences of all sorts, affecting personality development and determining behaviors in local contexts. The research concludes stating the urge to comprehend this academic work as a way to fight against symbolic and emotional poverty in family context producing discussions and critical reflection in a permanent relation between juvenile social vulnerability (characterized by lacks of all orders) and potential