Obstáculos superados pelos matemáticos no passado e vivenciados pelos alunos na atualidade : a polêmica multiplicação de números inteiros

In Mathematics literature some records highlight the difficulties encountered in the teaching-learning process of integers. In the past, and for a long time, many mathematicians have experienced and overcome such difficulties, which become epistemological obstacles imposed on the students and teachers nowadays. The present work comprises the results of a research conducted in the city of Natal, Brazil, in the first half of 2010, at a state school and at a federal university. It involved a total of 45 students: 20 middle high, 9 high school and 16 university students. The central aim of this study was to identify, on the one hand, which approach used for the justification of the multiplication between integers is better understood by the students and, on the other hand, the elements present in the justifications which contribute to surmount the epistemological obstacles in the processes of teaching and learning of integers. To that end, we tried to detect to which extent the epistemological obstacles faced by the students in the learning of integers get closer to the difficulties experienced by mathematicians throughout human history. Given the nature of our object of study, we have based the theoretical foundation of our research on works related to the daily life of Mathematics teaching, as well as on theorists who analyze the process of knowledge building. We conceived two research tools with the purpose of apprehending the following information about our subjects: school life; the diagnosis on the knowledge of integers and their operations, particularly the multiplication of two negative integers; the understanding of four different justifications, as elaborated by mathematicians, for the rule of signs in multiplication. Regarding the types of approach used to explain the rule of signs arithmetic, geometric, algebraic and axiomatic , we have identified in the fieldwork that, when multiplying two negative numbers, the students could better understand the arithmetic approach. Our findings indicate that the approach of the rule of signs which is considered by the majority of students to be the easiest one can be used to help understand the notion of unification of the number line, an obstacle widely known nowadays in the process of teaching-learning

Método de avaliação do gerenciamento de resíduos em canteiro de obras da construção civil : proposta baseada em empresas construtoras da cidade de Natal-RN

According to great concern between the developed industrial activities and resultant impacts over the environment, an association of several factors have occurred, procedures to the efficient management of the rotation between economical development and the environment have been improved. A research in field have been realized inside building sites of companies in order to provide knowledge about the implemented and accomplish actions according to the resolution from CONAMA nº307. Trough the interview among the representations of the companies and photographic survey in loco, such as, what makes the companies implement this management, reutilization and recycling, transport and disposition. The present study had as objective: analyze the insertion of the used tools to residuals management, proposing improvements, in a way that it can be easily identified during the procedures execution in the building sites of the building companies of the city of Natal/RN. To reach the goal, in the first place a revision of the pertinent literature was performed; there for, it can be seen the relation between residues management and environment sustainability, once it happens in a continued way it may prevent the waste and reduces the risk that the activities way bring to the employees, community and environment; once found the great difficult faced with regard to labors, material, equipment, project, planning, costumer s interference, furnisher. And still, it could be verified wich materials generate greater indexes of residues in the works and the main occurrences of waste and loss. However a greater transparency is needed coming from the high administration in the commitment with the continued actions, to make it so, there must be a cultural change inside the company. There for there will be a greater productivity and quality of the under taking such as costumer s satisfaction

Environmental adaptation of the source of the subbasin of Rico Stream, Monte Alto - SP, Brazil

Este trabalho teve como principal objetivo definir padrões fotográficos que representem o uso e a ocupação do solo da cabeceira de drenagem do Córrego Rico, localizada no Município de Monte Alto, Estado de São Paulo, para fins de adequação ambiental no que tange à legislação florestal brasileira. O mapeamento foi realizado utilizando técnicas de sensoriamento remoto e interpretação visual da imagem World View, seguida da digitalização da rede de drenagem e vegetações (naturais e agrícolas) no AutoCad, com auxílio de documentos e trabalho de campo. A área de estudo apresenta uma superfície de 2.141,53 ha, e os resultados permitiram constatar que a principal cultura é a cana-de-açúcar, com 546,34 ha, seguida de pastagens, com 251,22 ha, culturas perenes, com 191,71 ha, Eucalipto, com 57,31 ha, e a cebola, com 49,52 ha da área total, confirmando o avanço dos canaviais na região. A área possui 375,04 ha de áreas de preservação permanente (APPs), e desta superfície verificou-se que apenas 72,17 ha (19,24%) encontram-se compostos por vegetação arbórea ou mata, e destas 302,87 ha precisam ser enriquecidos e reflorestados com vegetação nativa da região, de acordo com legislação vigente. Os dados de área possibilitam futuras propostas de modelos de adequação ambiental para a microbacia, de acordo com a legislação ambiental vigente.

Memórias midiatizadas: percepções sobre ciência reconfiguradas a partir do consumo midiático

This piece focuses on the issue of media in the contemporary context, taking for its object the sociocultural phenomenon of mediatization‟, understood as the dilution of media culture in the everyday life, according to the perspective from Fausto Neto (2008) e Sodré (2002). This phenomenon is viewed from the angle of reception, that is, one that considers the individuals as pro-actives in this dynamic. The media culture is perceived as a fundamental element in the process of social structuring, and also is taken as a symbolic arm of great importance for the elaboration of the notion of reality as it interferes with the flow of information. Thus, we emphasize the process of symbolic consumption that we do with media content (Canclini, 1999), through a dynamic of appropriation and reframing, given from the interweaving of the meanings proposed with extra-media elements, recaptured from the perspective of mediations, by Barbero (2006), which concerns the articulation of the contents we appropriate from media with interactions from other social practices. We also consider the dimension of memory according to Sarlo (2007) and Halbwachs (2004) in order to, through speeches made in its scope, reach empirically the phenomenon of mediatization‟, and overlapping it, the media consumption on a specific theme, "science". Nevertheless, in terms of field work, we use the technique of in-depth interviews, so that the speech of our interviewers was our corpus. Through their narratives, speeches considered by us as memory-related, we visualize the dynamics of media consumption on given topic. At the level of conclusions, we realize that mediatization‟ as a phenomenon occurred, but its flows and orders showed discontinuities and pluralities not initially conceived; regarding the consumption of science through media, we see hybrid perceptions by our respondents, that is, one that include both elements aligned with the positivist conception of science - which we consider to be the view of science proposed by the media and elements that would contradict this view

Sentidos e perspectivas atribuídos por crianças à sua condição de estar para adoção

Considering the Brazilian current context, where many children are in institutional shelter waiting for adoption, the aim of this study was to know the meaning that sheltered children (whose families had already lost their custody or were in the process of losing it, at the moment of the field work) gave to their adoption condition. The research was carried out with three children in the shelter where they lived, in Natal, Rio Grande do Norte, Brazil. The field work took six months approximately. In order to meet the objective of this research, individual procedures were structuralized using figures and drawing material. With these procedures the children could speak directly or indirectly about the application of the legal measure of institutional shelter, about their lives before the application of this legal measure and what happened since then, and their original families and future perspectives. The content of the procedures was tape recorded and registered in the field work diary. The analysis of the corpus occurred with the Thematic Content Analysis, considering the theoretical methodological perspective of the Net of Meanings approach. The analysis of the corpus showed the ambiguity of the children, who consider good to live in the institution where they are, recognizing the responsibility of the original caregivers for their sheltered condition and, at the same time, they miss their relatives and wish to be with them. The subjects recognize the perspective of adoption and imagine it in a positive way. However, when the children were questioned about what could happen to them in the future, they said that they did not know, expressing uncertainty concerning their destinations

Significados de família para crianças em abrigo

This research explores the meanings of family for institutionalized children. It identifies, more specifically, how the relationship between the child and his/ her family is. The field work was developed at a municipal shelter in Natal/RN, which houses children aged between 7 and 11 years old. The subjects of research consisted of three children: two boys and one girl. Besides age-group criterion, which facilitates the use of oral language and the procedures, we took into consideration another selection criterion: children whose family configurations were similar. In order to achieve the objectives, we used toys, pictures, collages and semi-structured interviews. Data were examined under the Thematic Content Analysis, with three thematic categories previously chosen: Configuration of geographic area, family composition and family s internal dynamics. Among the results, we highlight that, for children, the concept of family is based essentially on existence of affection ties, regardless of kinship. Through this study, we hope to contribute to the discussion on the rights of institutionalized children, concerning their need of experiencing family life and living in community

Turismo e pobreza: percepções dos guias de turismo, moradores e não moradores que trabalham na favela da Rocinha Rio de Janeiro

This project refers to a study somewhat controversial , as in focusing less recognized and valued hand, although the dynamics of tourism pass to take another view , you can not beforehand consider favorable or unfavorable . Analyzes the phenomenon related to conception or perception of poverty from tourism residents and non residents of the Favela of Rocinha in Rio de Janeiro tourist guides . It is a subject to an object of research somewhat controversial , but about which there is already an academic and scientific concern and deserves an investigator look. Fits as a qualitative study whose methodological procedure based on interviews and participant observation , and the geographic divisions chosen the Rocinha slum , for its expressiveness and for being a pioneer in this type of tourism , had to conducting fieldwork lasting six months, which was accompanied by at least four hours walking work of sixteen tour guides, eight residents and eight non- residents in the community, working for different travel agencies and tourism. End of each tour, all tour guides answered a semi-structured questionnaire, containing nineteen questions. Most respondents tour guides authorized record interview, which has made it possible to analyze the speech through spoken language. In tourism, foreign tourists are the main target, although rarely also count with the participation of domestic tourists. Notes that the relationship between poverty and slums, from the perceptions of tourist guides residents better reflects the reality of favela residents compared with non residents guides, since they fully know all the intricacies and better the difficulties they have endured and still go, when it comes to the issue of stigmatization respect, by which has suffered by Brazilian society, in relation to live in slums, and have your dwelling place as a tourist attraction. While presenting the social reality of Rocinha consistently during his work, the non residents guides worry about being as natural as possible with tourists as much as the locals show slum, in the same way they avoid authorize tourists to take compromising photos and that will expose the intimacy of community residents . Concludes that, while recognizing the importance of elevation to the rank of tourist attraction and its promising prospects, requires attention and priority, given the greater precariousness of the human condition in relation to the prime areas in which it operates tourism should be a vector of development, not a masking of reality

Dinâmica da paisagem na Microbacia do Riacho Cajazeiras no semiárido potiguar

The semi-arid Northeast region are coming through changes since its formation causing changes in the landscape and increased degradation. The economic dynamics which was established at the Potiguar semiarid had for a long time settled in livestock, subsistence agriculture and cotton, however, these economies decline from the year 1970. Thus, the Potiguar spaces are undergoing by a process of space reordering marked by the growth of agricultural activities and the process of urbanization. In the Potiguar western region these changes weaken significantly transform the landscape. In these areas, the process of urbanization and agricultural activities have caused changes in the hinterland landscape changing the natural dynamics of the caatinga biome that has been subject to negative interference with the indiscriminate removal of vegetation. In this case, the specific study area of the watershed of Cajazeiras Creek located in the cities of Pau dos Ferros, Água Nova, Encanto and Rafael Fernandes, changes in the landscape has led to degradation and environmental fragility. From this perspective, the research objective is to assess the dynamics of the landscape of the watershed of Cajazeiras Creek, semiarid region of the state of Rio Grande do Norte, identifying the degrading factors, the most degraded areas and/or susceptible to degradation and environmental fragility. The research investigated the phenomena of light geosystems theory that emphasizes the integration of elements in shaping the landscape. During this reporting period, it was carried out exploratory and bibliographical research, and geoprocessing techniques to assess the social and environmental conditions of the researched area and its environmental fragility. To do so, first, it was made an multitemporal analisis on the basis of the years 1984, 1996 and 2009 demonstrating that the dynamics of use and land cover in the watershed of Cajazeiras Creek showed a significant change in the landscape, especially in the caatinga vegetation. This has been recovering in various areas of the watershed, especially in its upper course in the mountains of Bom Sera, in Encanto city. The analysis showed the need to develop policies and programs for the maintenance, restoration and preservation of the caatinga vegetation of the river network and of water bodies. In addition, it was identified the most degraded areas of the watershed, environmental fragility and potential emerging that take into account the landscape components such as climate, topography, geology, pedology, geomorphology and the use and occupation of the soil in an integrated manner. The results show that the landscape of the watershed has medium and high environmental fragility throughout its area, especially on the banks of the river network provided by the use and occupation of the soil in an inadequate way with the environmental conditions of the watershed

Zoneamento geoambiental como subsídio ao planejamento territorial municipal: estudo de caso para Currais Novos/RN

This paper presents the master plan and geoenvironmental zoning natures as instruments of environmental planning and management. The discussion of territory environmental planning is guided by two directions: at first the environmental elements involved in planning and the another is the implementation of these instruments at the municipal territory. To analyze the planning directed of the municipal territory we consider the fragments of its, represented by country and urban. The master plan inside of the Estatuto da Cidade (City Statute) and the geoenvironmental zoning are directed to territorial environmental planning. Regarding of the master plan the first challenge has been the spacial area that the plan can cover. It is necessary to prepare master plans that could include all the territory. The environmental zoning are directed for the territory totality.In this sense, the geoenvironmental zoning of the Currais Novos was done in the totality of the municipal territory and guided by the environmental physics variables. The geoenvironmental zoning sets in a planning and ordering of the territory instrument based in the landscape analysis. Therefore grounded in the Geosystems‟s Theory this work has like a main objective to propose a geoenvironmental zoning for the Currais Novos Municipality in RN. So, was used an analysis technique suggested for Bardin (2010) and the Currais Novos‟s physical environment characterization through of the fieldwork and cartographic data vectorization, beyond the image‟s treatment SRTM. The geoenvironmental systems definitions were based in the suggestion of Cestaro, et al. (2007) support in Bertrand (1968). For both were identified five geoenvironmental systems: Borborema Plateau, Residual plateau, Chapada da Serra de Santana, semiarid river valley and lagoon valley and eleven geoenvironmental subsystems: Borborema Plateau Western Slope, Isolated Massif of the Borborema Plateau, Residual Crest, Residual Massif, Erosional Scarp of the Chapada, flat top plateau, fluvial plains, temporary river of the semiarid and ornamental water or sluice

Evolução geodinâmica e condicionamento estrutural dos terrenos Piancó-Alto Brígida e Alto Pajeú, domínio da zona transversal, NE do Brasil

This thesis aims to advance in the geological knowledge of the region comprising the Piancó-Alto Brígida (TPAB) and Alto pajeú (TAP) terranes, in the Transversal Zone Domain (Borborema Province, NE Brazil), with the main objective of understanding the geodynamic evolution and the structural framework of these units. To reach this objective, and besides field work and interpretation of traditional aerial photographs, other tools were employed like of remote sensing products (Landsat 7 ETM+, aeroradiometrics, aeromagnetics and topographical images), lithogeochemical (whole rock) analyses and geochronological dating (U-Pb in zircon), besides integration with literature data. In the area, several precambrian geological units outcrop, represented in the TAP by the paleoproterozoic Serra Talhada and Afogados da Ingazeira complexes, Riacho Gravatá Complex (metavolcano-sedimentary sequence of Stenian-Tonian age) and Cariris Velhos orthogneisses (of Tonian age). The TPAB comprises the Santana do Garrote (lower unit) and Serra do Olho d'Água (upper unit) formations of the Cachoeirinha Group (Neoproterozoic III), besides the Piancó orthogneisses and Bom Jesus paragneisses; the latter correspond to an older (basement ?) block and a possible high grade equivalent of the Cachoeirinha Group (or Seridó Group ?), respectively. Several Brasiliano-age plutons occur in both terranes.The aeromagnetic data show the continuity, at depth, of the main shear zones mapped in the region. The Patos, Pernambuco, Boqueirão dos Cochos, Serra do Caboclo, Afogados da Ingazeira/Jabitacá and Congo-Cruzeiro do Nordeste shear zones reach depths greater than to 6-16 km. The aeromagnetic signature of other shear zones, like the Juru one, suggests that these structures correspond to shallower crustal features. The satellite images (Landsat 7 ETM+) and aerogamaspectrometric images discriminate different geological units, contributing to the mapping of the structural framework of the region. The Serra do Caboclo Shear Zone was characterized as the boundary/suture between the TPAB and TAP. This structure is an outstanding, pervasive feature that separates contrasting geological units, such as the Neoproterozoic III Cachoeirinha Group in the TPAB and the Riacho Gravatá Complex and the Cariris Velhos metaplutonics, of Stenian-Tonian age, in the TAP. Occupying different blocks, these units are not found in authoctonous relations, like unconformities and intrusive contacts. Concerning the Cariris Velhos (ca. 1,0 Ga old) event is recorded by radiometric ages of the Riacho Gravatá Complex metavolcanics and intrusive augen and orthogneisses, all of them displaying geochemical affinities of arc or collisional settings. A structural signature of this event was not recorded in the region, possibly due to its low grade/low strain style, obliterated by the overprinting of younger, higher grade/high strain Brasiliano-age fabrics.The first tectonic event (D1) observed in the Cariris Velhos lithotypes presents contractional kinematics with transport to the NW. Neoproterozoic III geochronologic dates, obtained in late-D1 granitoids, imply a Brasiliano age (ca. 610-600 Ma) for this deformation event. The second tectonic event (D2) characterized in the region corresponds to the Brasiliano transcurrent kinematics of the outstanding shear zones and associated granitoid plutons. The geochronological (U-Pb in zircon) data obtained during this thesis also confirms the occurrence of the Cariris Velhos magmatic suite in the TAP, as well as the Neoproterozoic III age to the Cachoeirinha Group in the TPAB. The TAP (Riacho Gravatá Complex, augen and orthogneisses) is interpreted as a continental arc possibly accreted to a microcontinent during the Cariris Velhos (Stenian-Tonian) event. Later on, this terrane collided with the TPAB at the beginning of the Brasiliano orogeny (D1 contractional deformation), and both domins were reworked by the transcurrent shear deformation of the D2 event

Sistemas orbitais e aéreos aplicados à análise multi-escala da tectônica rúptil atuante na borda sudeste da Bacia do Parnaíba

The tectonics activity on the southern border of Parnaíba Basin resulted in a wide range of brittle structures that affect siliciclastic sedimentary rocks. This tectonic activity and related faults, joints, and folds are poorly known. The main aims of this study were (1) to identify lineaments using several remotesensing systems, (2) to check how the interpretation based on these systems at several scales influence the identification of lineaments, and (3) to contribute to the knowledge of brittle tectonics in the southern border of the Parnaíba Basin. The integration of orbital and aerial systems allowed a multi-scale identification, classification, and quantification of lineaments. Maps of lineaments were elaborated in the following scales: 1:200,000 (SRTM Shuttle Radar Topographic Mission), 1:50,000 (Landsat 7 ETM+ satellite), 1:10,000 (aerial photographs) and 1:5,000 (Quickbird satellite). The classification of the features with structural significance allowed the determination of four structural sets: NW, NS, NE, and EW. They were usually identified in all remote-sensing systems. The NE-trending set was not easily identified in aerial photographs but was better visualized on images of medium-resolution systems (SRTM and Landsat 7 ETM+). The same behavior characterizes the NW-trending. The NS-and EW-trending sets were better identified on images from high-resolution systems (aerial photographs and Quickbird). The structural meaning of the lineaments was established after field work. The NEtrending set is associated with normal and strike-slip faults, including deformation bands. These are the oldest structures identified in the region and are related to the reactivation of Precambrian basement structures from the Transbrazilian Lineament. The NW-trending set represents strike-slip and subordinated normal faults. The high dispersion of this set suggests a more recent origin than the previous structures. The NW-trending set may be related to the Picos-Santa Inês Lineament. The NS-and EW-trending sets correspond to large joints (100 m 5 km long). The truncation relationships between these joint sets indicate that the EW-is older than the NS-trending set. The methodology developed by the present work is an excellent tool for the understanding of the regional and local tectonic structures in the Parnaíba basin. It helps the choice of the best remote-sensing system to identify brittle features in a poorly known sedimentary basin

Dinâmica costeira entre as praias de Areia Preta e do Forte, Natal/RN

The coastal zone has been studied worldwide with a focus on the coastal erosion. In the present days, much of the world's coastlines are being affected by erosion, which causes great damage to the economy. This work had as study case the beaches of Areia Preta, Artistas, Meio and Forte located in Natal in Rio Grande do Norte. It shows as result the monitoring of the beach strip that makes possible to obtain quantitative and qualitative data, allows the study of the coastal dynamics of the beaches and the Recovery Project of the Areia Preta beach interference on adjacent beaches. This research was guided by the integrated analysis method on the systemic perspective. The pratical procedures adopted were: bibliographic research; fieldwork during eleven months (environmental characterization, collection of hydrodynamic data, topographic leveling, collection of sediments) and; sedimentological analysis of samples collected. By monitoring of the points A, B, C, D and E we were able to find the occurrence of the coastal erosion on their biggest part except by the C and D profiles. It was noted the need for the government to complete the hydraulic fill, as it made only 60% of the landfill planed. It was found that the spikes built on the beach of Areia Preta are preventing the natural transport of sediments that the longshore performs towards South-North. This interference is causing the lack of sediment on the beaches of Forte and Meio and their coastal erosion in consequence

Agricultura familiar integrada ao mercado: mediação política e transformações socioespaciais no assentamento rural Vale do Lírio/RN

It s an application about the development of the family agriculture integrated to the market in which is detected the development of the relation of partnership between settled of agrarian reform and the capitalist enterprise. It s shown initially, a conceptual discussion about family agriculture, watching the historical contexts that characterize the expropriation and subordination of the category. This way, the family agriculture is contextual zed in the moment of the modernization of the agriculture, he rising of the social tension in the area of the restructuration of production and the globalization. Finding to understand the agrarian question in Rio Grande do Norte, it s characterized the acting of the state in promoting agrarian reform politics and redistribution of lands. This way, the research demonstrate the reality of the settled of Vale do Lírio, with the partnership of the Caliman Company S. A. in this context, it s emphasized the social geographic transformation in the settler. This way it was realized the analysis of the survey of data in a lot of public department, and the research of the area with use of application form, in 90% percent of the researched group, with interviewing with the leaders of this group and with the manager of the Company. The research demonstrates an analysis of the reality lived by this group, in the perspective the interests of the government and the capital.

Diet of the ichthyofauna associated with marginal vegetation of a mangrove forest in southeastern Brazil

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Estratégias e modos reprodutivos de anuros (Amphibia) em uma poça permanente na Serra de Paranapiacaba, Sudeste do Brasil

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)