Aprendizagens algébricas e o desenvolvimento do pensamento algébrico em alunos do 8º ano

A todos os alunos deve ser proporcionada uma aprendizagem da álgebra que promova o desenvolvimento da linguagem e do pensamento algébrico, no entanto este é um dos temas da matemática relativamente ao qual os alunos continuam a apresentar muitas dificuldades. Este estudo tem como objetivo compreender como os alunos de 8.º ano aprendem álgebra e, em particular, como desenvolvem o seu pensamento algébrico. Tendo em conta a complexidade deste objetivo, houve a necessidade de centrar o estudo em duas questões: (a) Que dificuldades manifestam os alunos na aprendizagem da álgebra? (b) De que forma a atividade matemática do aluno pode influenciar a aprendizagem da álgebra e o desenvolvimento do pensamento algébrico? A investigação seguiu uma metodologia qualitativa, no paradigma interpretativo, e incide no trabalho desenvolvido pelos alunos de uma turma de 8.º ano da qual a investigadora é professora. A recolha de dados baseou-se na observação direta dos comportamentos dos alunos, que foram registados através de anotações, da gravação de áudio e vídeo de algumas aulas e, ainda, em documentos produzidos pelos alunos. Procurou-se evidenciar os momentos onde ocorreram as principais aprendizagens e o desenvolvimento do pensamento algébrico. A experiência decorre ao longo do desenvolvimento dos tópicos de Funções e Equações e baseia-se na aplicação de um diversificado número de tarefas. As propostas de trabalho escolhidas pretendem proporcionar aos alunos experiências significativas para a aprendizagem da álgebra, promover o trabalho em grupo e a discussão na turma. Os resultados mostram que é necessário compreender as dificuldades que os alunos apresentam na álgebra, para lhes poder proporcionar uma aprendizagem contextualizada e com significado. Ao longo deste estudo foram muitas as dificuldades apresentadas pelos discentes, mas também se verificaram aprendizagens algébricas significativas que contribuíram para o desenvolvimento da linguagem e do pensamento algébrico nos mesmos.

Gestão híbrida em cooperativa de crédito: uma análise a partir do interesse, participação, satisfação e expectativa dos cooperados da COOPERUFPA

The globalization of markets has confirmed for the processes of change in organizations both in structure and in management. This dynamic was also observed in credit unions because they are financial institutions and are under the rules of the Brazil´s Financial System. Given the context of organizational changes in the financial capital has played the traditional management reform is urgent. In organizations credit unions, given its dual purpose, because in the same organizational environment and capitalism coexist cooperative whose logics are antagonistic, but can live through the balance between instrumental rationality and substantive rationality in credit unions. Based on this concept a new form of management should be thought to be able to accommodate the demand of cooperative, community, government and the market. Hybridization has been observed in management practices` COOPERUFPA into dimensions financial, social and solidarity participation with a trend in paradigmatic form of hybrid management, in that it directly or indirectly affect the management decisions in the credit union. The hybrid management is a trend that has been setting the basis for societal transformation, so that credit unions promote actions of welfare oriented cooperative members and the community around the same time that attend the dynamics of market globalization. These actions, in the context of hybrid management should be implemented by COOPERUFPA from the sociability of the remains and the wide diffusion of solidarity culture between cooperative partnership as a way to recover their participation in trade relations, financial and the social collective developement. For the members of COOPERUFPA financial interest is evidenced in greater relevance for the social interest given its dominant relationship as "mere customer" of the credit union, however, the proactive participation of the life of the cooperative credit union is one of its expectative among of participation of to share power in decisions by general meetings. This passivity`s cooperator of the COOPERUFPA in defending the ideals overshadowed the spread of cooperative principles and values of cooperation among them. Thus his conception for COOPERUFPA in the financial dimension, social and solidarity democracy, performed transversely. The COOPERUFPA for not developing an education policy for the cooperation among its members, contributed to a process of collective alienation of cooperative ideals, since the cooperative do not understand the reality that surrounds them as members of an organization whose mission is to social and financial sustainability of its members

Combater as secas e defender as florestas a natureza nos desafios da ciência e da técnica para modernizar o Brasil (1889 a 1934)

In the first decades of 20th century the just instituted Brazilian Republic faced the challenge to modernize the country. Considering that the progress was associated with the exhaustion of the forest reserves and with climatic changes, two big issues were seen as fundamental: To Fight the Droughts and To Defend the Forests; headed by professionals who were dedicated to these ideals. This research starts from the premise that these were the main challenges enforced by nature to the Brazilian development; the general objective was delimited in the search to understand the meaning and the conception of the natural world by this group of professionals who faced the shock between modernizing the country and conserving its natural resources. Aiming to contribute with the construction of the Brazilian environmental history and to bring historical elements to the debate about the environment in the country, the author concentrates his attention to the analyses, the discussions and the actions that preceded the regulation on the use of natural resources and the implementation of the environmental legislation in Brazil, occurred in 1934. The investigation uses as methodological basis the theoretical directions of environmental history, using sources of data still little explored and valued. In such way, it is taken as starting point some published papers about this subject during the period between 1889 and 1934 in two technical magazines the Revista Brazil Ferro-Carril and the Revista do Club de Engenharia. National engineering played a basic role in this process while arguing, projecting and constructing the development. The formulated proposals, after being divulged, had fomented the interchange with other professionals and had favored the advance of ambient questions in Brazil, in the sense to preserve natural resources, to construct more harmonic relations between the society and the nature and to equate the development with the environment preservation

Da escala médica de saúde à experiência social do saudável :diálogo entre os espaços dos bares e das academias fisiculturistas na cidade do Natal-RN

Currently, we attend a reverence of concepts ahead as health, life, youth and body. In we widen amount the ideals concerned to the healthful life, to the quality of life, the longevity and joviality and the extremities of the body represented by the illness, for the virus infection, the physical deficiency and the aging. Of the historical shades of the plague, of the hunger and the war that gagged the defenseless individual and its body, in the current days we increase the search for a full and powerful life, independent of a religious imaginary to predict the epidemic curse, the threat represented for the sick people and the incarnate divine anger in the death; or of medical science presented in the spaces of the technology and the physiology, being left fragile the social and psychological dimensions of the human confined to the patient issue and, finally, the commanded urban health politics in quantitative goals of hygienic cleaning, of the medical techniques and the education citizen. For beyond these instances, emerges in our days a plural, close and biographical agreement well of the body and welfare. On the other hand, an understanding of the healthful life and well-being that more certifies the presence of something the one that clear landmarks amongst normality and the irregularity, the esteem and the destructive vice: it has a projection of healthful life measures without conceptual models of body and health under the doctor-scientific standard occidental. This thematic one will confide in way to the enclosure for spaces to the muscles and fitness exercises and the bars from the city of Natal, in the state of Rio Grande do Norte, Brazil, while comprehensive interchange concerning as the individual comes dealing with the notion the body and health and, mainly, if perceiving inside of its body and its health. Amongst these two spaces of typical leisure of the modern urban phenomenon, the hedonism bodily with its muscles and salience and one another form of hedonism in the fruition of allowed drugs will be across itself in a dialogue about which social s relationships are really in game in an imaginary construction amongst an doctor-aesthetic ideal of health and the social and subjective experience in the option for a healthful life

Quão romance é minha vida amorosa! : namoro virtual e narrativas

This research aims to acknowledge the virtual dating phenomenon. The research deals with this phenomenon in Orkut, a social networking website. Thus, it considers debates and forums that were present in a Brazilian Orkut online community called Conheci meu amor pela internet (I met my love through the Internet). As a staring point the research dealt with issues such as: what are the debates about? How can we deal with practices that question their own dating process? According to the initial hypothesis, these debates reveal different contemporary social aspects: 1) they emerge as a response to demands on behalf of a society that is rather reflexive. This reflexive element is fundamental for the constitution of the self 2) these debates work as support elements in social relations that are built upon this sphere. In this context, individuals write about themselves and constitute themselves as real individuals that acquire a sense as subjects; and 3) people discuss online dating as form reconstructing former experiences. Empirical analysis demonstrates that these forums and polls present themselves as a social phenomenon that allows a particular form of self presentation on the internet. In order for these subjects to present themselves they built their own self narratives. What is possible to acknowledge considering these narratives is that there is a predominance of the element of intrigue that is further solved and demonstrate a satisfactory result. These narrators then choose online dating situation that present happy endings and happiness that are associated to romantic ideals that are worthwhile being shown. The contents present in these narratives are dealt with by the research. Thus, this work defends the thesis that the online dating narratives are a mixture of facts and fiction once all experiences deal with romantic imaginary as well as personal dating experience. Thus, the research is an attempt to understand what goes on the forums and debates that deal with the fictionalized and dramatized daily experiences in the performances that are similar to games. This is possible due to the fact that there is use of romantic fables and concrete experiences realized by online dating

Gestão de centros históricos: uma avaliação da política de requalificação urbana de Natal/RN

From the second half of the century XX, in many Brazilian cities, the "historic centers" stop being the most densely populated areas of the city, accumulate degradation of the built environment and its functions have physical, social and economic resignified when also intensified interventions in these same centers Historic focused its redevelopment. This work aims to reflect on the experience of urban regeneration in the historic center of Natal, addressing the strategies adopted in the implementation of public policies and how these improve the effectiveness of actions, processes and outcomes for which turn the management of the historic center in question. In Natal, is identified in the neighborhoods of the Upper Town and Ribeira, the historic city center, a large distortion of their ancient architectural complex, the use of sub-urban infrastructure and emptying in the evenings and weekends. Shares redevelopment of the historic center of Natal are considered late, it is only recently that these neighborhoods were objects of policies and projects generally aimed at enhancing the cultural attraction of the area, and not always, it can be said that they have relevance in development process of the city. Added to this, there is the slowness of the interventions, although the zoning as an area of historic preservation has been done for over two decade. In Natal, the ideas of sustainable development articulated a proposed redevelopment of its historic center is still far from being achieved, but on the other hand, the latest phase of implementation of plans and projects in the area, indicating the intention to transform practical experience in the formulations and proposals in relation to these ideals

A relação histórica entre democracia e liberalismo. Um diálogo crítico com Norberto Bobbio.

This work seeks to examine the historical relationships established between liberalism and democracy, questioning the apparent inseparability between the two ideologies. Methodologically construct a hypothetical dialogue with the Italian thinker Norberto Bobbio, one of the most important systematizers of liberal democracy, defending a theoretical and conceptual complementarity between the two ideologies. Following the Bobbio theoretical propose, it presents the political contributions of classical liberalism that the Italian thinker identify as logical and axiological antecedent of the modern democracy, naturalizing and universalizing the principles and ideals of classical liberalism. Going counter, it problematizes the political contributions of classical liberalism, emphasizing the tension between liberal theory and its practice, between the declared political principles and their translation into concrete historical reality, reserving rights and freedoms to property minority and severe restrictions to the majority. The critical analysis of classical liberalism allows questioning the privilege position that Bobbio reserves to the liberalism in the democracy history, to restore the important contribution of illiberal politics currents in the civil, political and social rights history, advocating the democracy with its social character, inclusive and participatory

O princípio constitucional do desenvolvimento sustentável: análise da sua concretização no Estado do Rio Grande do Norte

The Article 225 of Constitution of the Federative Republic of Brazil in its main body, stipulates that everyone is entitled to ecologically balanced environment and the use of common people and essential to the healthy quality of life, should be imposed on public authorities and the community the duty to defend it and preserve it for present and future generations. Following a universal trend, the letter raised the Brazilian environment the category of one of those values ideals of social order, dedicating it, along with a constitution of rules sparse, a chapter, itself, which definitely, institutionalized the right to healthy environment as a fundamental right of the individual. The national public policies and state should be in line with modern theories of Sustainable Development, outlined within the international society, and certainly instruments that should be made effective through the mobilization of civil society as a whole. The implementation of Human Rights, in fact, depends on a strong political action and not just a legal problem. Thus, this work of theoretical-descriptive nature we will address various dimensions of sustainable development, such as environmental education, water, sanitation, health and sustainable development plans, evaluating its current stage in our state

Análise do processo judicial eletrônico (PJe) sob os parâmetros da discursividade processual e do acesso democrático à justiça

The conceptions of the judicial function, the process and the factors of legitimacy of the norm of decision are changed according to the model of State (liberal, social democratic and constitutional). The right of access to justice, likewise, follows the ideals present in constitutional movements experienced in different historical moments. The deficit of legitimacy of the judiciary is recurring subject of study in the doctrine, especially in the face of democratic standards that permeate the current paradigm of state. Under the process law, the essential element for the distinction of the states based on the rule of law (formal and material) and the democratic constitutional state lies in the democratic guarantee of participation to the litigants in the process of elaborating the norm of decision. The concern about the participatory democracy and the concretion of fundamental rights has as presupposition the conception of popular sovereignty. Keeping this effort in mind, the civil procedure cannot be oblivious to such considerations, especially when it justifies its constitutional conformation from the institutionalization of discourse within the procedural field (democratic principle) and of the democratization of access to justice, leading to the necessary contestation of the theory of instrumentality of the process. The democratic prospects of civil procedure and the concern about the legitimacy of the rule of decision cannot be moved away from the analysis of the judicial function and the elements that influence the legal suit s progress. The computerization of the judicial process entails extensive modification in the way the judicial function is developed, in view of automation of activities held, of the eliminating of bureaucratic tasks, manual and repetitive, and of streamlining the procedure. The objective of this study is to analyze the dogmatic changes and resulting practices from the implementation of the Judicial Electronic Process (JEP), prepared by the National Council of Justice, under the parameters of procedural discourse and democratic access to justice. Two hypotheses are raised, which, based on a bibliographic-documentary, applied and exploratory research, are contested dialectically. The expansion of publicity of procedural acts and the facilitating of communication and practice of such acts are elements that contribute to the effective participation of the recipients of the norm of decision in its making process and, therefore, the democratic principle in the procedural field. Ensuring access (to the parts) to the case files and reasonable duration of the process along with the preservation of its founding principles (contradictory, legal defense and isonomy) are essential to ensure democratic access to justice within the virtual system

Direito fundamental à saúde: parâmetros e alternativas para sua concretização no Brasil

If, on one hand, only with the 1988 Federal Constitution the right to health began to receive the treatment of authentic fundamental social right; on the other, it is certain since then, the level of concretization reached as to such right depicts a mismatch between the constitutional will and the will of the rulers. That is because, despite the inherent gradualness of the process of concretization of the fundamental social rights, the Brazilian reality, marked by a picture of true chaos on public health routinely reported on the evening news, denatures the priority status constitutionally drew for the right to health, demonstrating, thus, that there is a clear deficit in this process, which must be corrected. This concern regarding the problem of the concretization of the social rights, in turn, is underlined when one speaks of the right to health, since such right, due to its intimate connection with the right to life and human dignity, ends up assuming a position of primacy among the social rights, presenting itself as an imperative right, since its perfect fruition becomes an essential condition for the potential enjoyment of the remaining social rights. From such premises, this paper aims to provide a proposal for the correction of this problem based upon the defense of an active role of the Judiciary in the concretization of the right to health as long as grounded to objective and solid parameters that come to correct, with legal certainty, the named deficit and to avoid the side effects and distortions that are currently beheld when the Judiciary intends to intervene in the matter. For that effect, emerges as flagship of this measure a proposition of an existential minimum specific to the right to health that, taking into account both the constitutionally priority points relating to this relevant right, as well as the very logic of the structuring of the Sistema Único de Saúde - SUS inserted within the core of the public health policies developed in the country, comes to contribute to a judicialization of the subject more in alignment with the ideals outlined in the 1988 Constitution. Furthermore, in the same intent to seek a concretization of the right to health in harmony with the constitutional priority inherent to this material right, the research alerts to the need to undertake a restructuring in the form of organization of the Boards of Health in order to enforce the constitutional guideline of SUS community participation, as well as the importance of establishing a new culture budget in the country, with the Constitution as a compass, pass accurately portray a special prioritization directed constitutional social rights, especially the right to health

A contribuição de Diké na formação do Emílio ou o papel da jurisdição constitucional na concretização do direito social à educação

The fundamental social right to education has a lengthy constitutional argument, having been declared as a right to everyone in the Title dedicated to the fundamental rights and warrants and, later, scrutinized in the Social Order Chapter exclusively devoted to this theme, where specific rights are guaranteed and fundamental duties are imposed to family, society, and state. In that which concerns education, the 1988 Constitution is the result of a historical-normative process which, since the days of the Lusitanian Empire wavering between distinct levels of protection warrants in some way the educational process. Nevertheless, not even the State s oldest commitment to education has been fully achieved, namely, the annihilation of illiteracy. Even as other fundamental social rights, education is inflicted with the lack of effective political will to reach its fulfillment, and this is reflected in the production of doctrine and jurisprudence which reduce the efficacy of these rights. The objective of this work is to analyze what part is to be played by the constitutional jurisdiction in the reversal of this picture in regards to the fulfillment of the fundamental social right to education. Therefore it is indispensable to present a proper conception of constitutional jurisdiction its objectives, boundaries and procedures and that of the social rights in the Brazilian context so as to establish its relationship from the prism of the right to education. The main existing obstacles to the effective action of constitutional jurisdiction on the ground of social rights are identified and then proposals so as to overcome them are presented. The contemplative and constructive importance of education in the shaping of the individual as well as its instrumental relevance to the achievement of the democratic ideal through the means of the shaping of the citizen is taken into account. The historical context which leads to the current Brazilian educational system is analyzed, tracing the normative area and the essential content of the fundamental right to education aiming to delineate parameters for the adequate development of the constitutional jurisdiction in the field. This jurisdiction must be neither larger nor narrower than that which has been determined by the Constitution itself. Its activity has been in turns based on a demagogic rhetoric of those fundamental rights which present a doubtful applicability, or falling short of that which has been established showing an excessive reverence to the constituent powers. It is necessary to establish dogmatic parameters for a good action of this important tool of constitutional democracy, notably in regards to the fundamental social right to education, for the sake of its instrumental role in the achievement of the democratic ideals of liberty and equality

Padre Miguelinho :o intelectual, o professor, o revolucionário - vozes que se fazem ouvir

This research work worries in building the history of the natalense priest Miguel Joaquim of Almeida Castro, Miguelinho, I don't just eat one of the heroes and martyrs of the Revolution From Pernambuco of 1817, as bill the traditional history, but also the educated man, the intellectual and the admired teacher. The studied period understands the beginning of the century XIX, when priest Miguelinho comes back to Brazil, coming of Portugal, to assume teacher's occupation in the Seminar of Olinda, and it ends in the year of 1817, marked by the Revolution From Pernambuco, one of the most important movements in the fight for the liberation of Brazil of the Portuguese domain. Miguelinho, one of the leaders of the Revolution, that also reached the provinces of Paraíba and of Rio Grande do Norte, it was executed by the real troops. Like this, he tries to understand the Priest's conflicting relationship, while representative clergyman, of a Church that almost obtained a religious monopoly, and your ideals per centuries more gone back to a social and economical order of Illumines, that even certain point condemned the attitude of the own Church. The objective, then, is to understand through the path of priest's Miguelinho life, not only the intellectual, the teacher and the revolutionary, but the representation of your political and pedagogic-educational ideas in a die historical moment and the creation of the republican myth, looking for the plurality of an universe that seeks, per times, to flee of our theoretical context

Uma análise histórico-epistemológica do conceito de grupo

This work aims to analyze the historical and epistemological development of the Group concept related to the theory on advanced mathematical thinking proposed by Dreyfus (1991). Thus it presents pedagogical resources that enable learning and teaching of algebraic structures as well as propose greater meaning of this concept in mathematical graduation programs. This study also proposes an answer to the following question: in what way a teaching approach that is centered in the Theory of Numbers and Theory of Equations is a model for the teaching of the concept of Group? To answer this question a historical reconstruction of the development of this concept is done on relating Lagrange to Cayley. This is done considering Foucault s (2007) knowledge archeology proposal theoretically reinforced by Dreyfus (1991). An exploratory research was performed in Mathematic graduation courses in Universidade Federal do Pará (UFPA) and Universidade Federal do Rio Grande do Norte (UFRN). The research aimed to evaluate the formation of concept images of the students in two algebra courses based on a traditional teaching model. Another experience was realized in algebra at UFPA and it involved historical components (MENDES, 2001a; 2001b; 2006b), the development of multiple representations (DREYFUS, 1991) as well as the formation of concept images (VINNER, 1991). The efficiency of this approach related to the extent of learning was evaluated, aiming to acknowledge the conceptual image established in student s minds. At the end, a classification based on Dreyfus (1991) was done relating the historical periods of the historical and epistemological development of group concepts in the process of representation, generalization, synthesis, and abstraction, proposed here for the teaching of algebra in Mathematics graduation course

Mãe-esposa e professora: educadoras no final do século XIX

This text is organized through discussions undertaken in the area of the History of Education in Rio Grande do Norte, circumscribed to the History of Women from the first decades of the Brazilian Republic, and to the analysis of what was expected of this education. We examined representations of women in Natal, between 1889 and 1914, with the goal of configuring relations between the sexes with the emphasis on moral, intellectual and pedagogical aspects required of these women. As documental sources we utilized the educational, civil and criminal Legislation, on a National scope, as well as on a State and Municipal scope. We circumscribed our search to the newspaper A República, in which we found literature that circulated in Natal in the form of pamphlets, short stories and poetry, as well as other texts by authors that were part of the corpus of analysis of this study, located in public and private archives in Rio Grande do Norte, such as the Historical and Geographic Institute of Rio Grande do Norte (IHGRN) and the State Public Archive of Rio Grande do Norte (APE-RN). The use of the indexing method and the propositions of Cultural History were the appropriate theoretical-methodological framework to complete studies of this nature. This operational perspective permitted us to elaborate nuances about this time of transition from the 19th to the 20th Century, and to spotlight the fire of the women from this period. The basis of the argument that related women to maternity and domesticity, and within the ideals of abnegation and religious leadership, aligned to a demand coming from the increase in the quantity of schools for women, allocated women as the most appropriate for superior in educational performance in the country, based on its foundations: primary education. Beyond the universe of formal education, the other side of women appeared in republican politics. The mother-spouse and the institutionalization of domestic education associated the female gender with the role of educator at home as well. Be it in the public sphere, as a teacher, or in private, as mother-spouse, female care is perceived in this configuration, as an educational base that the Republic, and in transition, bequeathed to the Brazilian 20th Century

A obra de triangulis omnimodis libri quinque de Johann Müller Regiomontanus (1436 1476): uma contribuição para o desenvolvimento da trigonometria

Trigonometry, branch of mathematics related to the study of triangles, developed from practical needs, especially relating to astronomy, Surveying and Navigation. Johann Müller, the Regiomontanus (1436-1476) mathematician and astronomer of the fifteenth century played an important role in the development of this science. His work titled De Triangulis Omnimodis Libri Quinque written around 1464, and published posthumously in 1533, presents the first systematic exposure of European plane and spherical trigonometry, a treatment independent of astronomy. In this study we present a description, translation and analysis of some aspects of this important work in the history of trigonometry. Therefore, the translation was performed using a version of the book Regiomontanus on Triangles of Barnabas Hughes, 1967. In it you will find the original work in Latin and an English translation. For this study, we use for most of our translation in Portuguese, the English version, but some doubt utterance, statement and figures were made by the original Latin. In this work, we can see that trigonometry is considered as a branch of mathematics which is subordinated to geometry, that is, toward the study of triangles. Regiomontanus provides a large number of theorems as the original trigonometric formula for the area of a triangle. Use algebra to solve geometric problems and mainly shows the first practical theorem for the law of cosines in spherical trigonometry. Thus, this study shows some of the development of the trigonometry in the fifteenth century, especially with regard to concepts such as sine and cosine (sine reverse), the work discussed above, is of paramount importance for the research in the history of mathematics more specifically in the area of historical analysis and critique of literary sources or studying the work of a particular mathematician