Um estudo sobre a aprendizagem de números irracionais no ensino médio

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

Um estudo sobre a apreciação do raciocínio matemático na formação inicial de professores

The present work focused on developing teaching activities that would provide to the student in initial teacher training, improving the ability of mathematical reasoning and hence a greater appreciation of the concepts related to the golden section, the irrational numbers, and the incommensurability the demonstration from the reduction to the nonsensical. This survey is classified itself as a field one which data collection were inserted within a quantitative and qualitative approach. Acted in this research, two classes in initial teacher training. These were teachers and employees of public schools and local governments, living in the capital, in Natal Metropolitan Region - and within the country. The empirical part of the research took place in Pedagogy and Mathematics courses, IFESP in Natal - RN. The theoretical and methodological way construction aimed to present a teaching situation, based on history, involving mathematics and architecture, derived from a concrete context - Andrea Palladio s Villa Emo. Focused discussions on current studies of Rachel Fletcher stating that the architect used the golden section in this village construction. As a result, it was observed that the proposal to conduct a study on the mathematical reasoning assessment provided, in teaching and activity sequences, several theoretical and practical reflections. These applications, together with four sessions of study in the classroom, turned on to a mathematical thinking organization capable to develop in academic students, the investigative and logical reasoning and mathematical proof. By bringing ancient Greece and Andrea Palladio s aspects of the mathematics, in teaching activities for teachers and future teachers of basic education, it was promoted on them, an improvement in mathematical reasoning ability. Therefore, this work came from concerns as opportunity to the surveyed students, thinking mathematically. In fact, one of the most famous irrational, the golden section, was defined by a certain geometric construction, which is reflected by the Greek phrase (the name "golden section" becomes quite later) used to describe the same: division of a segment - on average and extreme right. Later, the golden section was once considered a standard of beauty in the arts. This is reflected in how to treat the statement questioning by current Palladio s scholars, regarding the use of the golden section in their architectural designs, in our case, in Villa Emo

O uso pedagógico de uma seqüência didática para a aquisição de algumas idéias relacionadas ao conceito de números complexos

The aim of the present work is to contribute to the teaching-learning process in Mathematics through an alternative which tries to motivate the student so that he/she will learn the basic concepts of Complex Numbers and realize that they are not pointless. Therefore, this work s general objective is to construct a didactic sequence which contains structured activities that intends to build up, in each student s thought, the concept of Complex Numbers. The didactic sequence is initially based on a review of the main historical aspects which begot the construction of those numbers. Based on these aspects, and the theories of Richard Skemp, was elaborated a sequence of structured activities linked with Maths history, having the solution of quadratic equations as a main starting point. This should make learning more accessible, because this concept permeates the students previous work and, thus, they should be more familiar with it. The methodological intervention began with the application of that sequence of activities with grade students in public schools who did not yet know the concept of Complex Numbers. It was performed in three phases: a draft study, a draft study II and the final study. Each phase was applied in a different institution, where the classes were randomly divided into groups and each group would discuss and write down the concepts they had developed about Complex Numbers. We also use of another instrument of analysis which consisted of a recorded interview of a semi-structured type, trying to find out the ways the students thought in order to construct their own concepts, i.e. the solutions of the previous activity. Their ideas about Complex Numbers were categorized according to their similarities and then analyzed. The results of the analysis show that the concepts constructed by the students were pertinent and that they complemented each other this supports the conclusion that the use of structured activities is an efficient alternative for the teaching of mathematics

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

A difícil aceitação dos números negativos: um estudo da teoria dos números de Peter Barlow (1776-1862)

The present study seeks to present a historico-epistemological analysis of the development of the mathematical concept of negative number. In order to do so, we analyzed the different forms and conditions of the construction of mathematical knowledge in different mathematical communities and, thus, identified the characteristics in the establishment of this concept. By understanding the historically constructed barriers, especially, the ones having ontologicas significant, that made the concept of negative number incompatible with that of natural number, thereby hindering the development of the concept of negative, we were able to sketch the reasons for the rejection of negative numbers by the English author Peter Barlow (1776 -1862) in his An Elementary Investigation of the Theory of Numbers, published in 1811. We also show the continuity of his difficulties with the treatment of negative numbers in the middle of the nineteenth century

Construção das capacidades organizacionais de tecnologia da informação no contexto dos sistemas institucionais integrados de gestão da UFRN

The IT capability is a organizational ability to perform activities of this role more effectively and an important mechanism in creating value. Its building process (stages of creation and development) occurs through management initiatives for improvement in the performance of their activities, using human resources and IT assets complementary responsible for the evolution of their organizational routines. This research deals with the IT capabilities related to SIG (integrated institutional management systems), built and deployed in UFRN (Universidade Federal do Rio Grande do Norte) to realization and control of administrative, academic and human resources activities. Since 2009, through cooperative agreements with federal and educational institutions of direct administration, UFRN has supported the implementation of these systems, currently involving more than 30 institutions. The present study aims to understand how IT capabilities, relevant in the design, implementation and dissemination of SIG, were built over time. This is a single case study of qualitative and longitudinal nature, performed by capturing, coding and analysis from secondary data and from semi-structured interviews conducted primarily with members of Superintenência de Informática, organizational unit responsible for SIG systems in UFRN. As a result, the technical, of internal relationship and external cooperation capabilities were identified as relevant in the successful trajectory of SIG systems, which have evolved in different ways. The technical capacity, initiated in 2004, toured the stages of creation and development until it reached the stage of stability in 2013, due to technological limits. Regarding the internal relationship capability, begun in 2006, it toured the stages of creation and development, having extended its scope of activities in 2009, being in development since then. Unlike the standard life cycle observed in the literature, the external cooperation capability was initiated by an intensity of initiatives and developments in the routines in 2009, which were decreasing to cease in 2013 in order to stabilize the technological infrastructure already created for cooperative institutions. It was still identified the start of cooperation in 2009 as an important event selection, responsible for changing or creating trajectories of evolution in all three capacities. The most frequent improvements initiatives were of organizational nature and the internal planning activity has been transformed over the routines of the three capabilities. Important resources and complementary assets have been identified as important for the realization of initiatives, such as human resources technical knowledge to the technical capabilities and external cooperation, and business knowledge, for all of them, as well as IT assets: the iproject application for control of development processes, and the document repository wiki. All these resources and complementary assets grew along the capacities, demonstrating its strategic value to SINFO/UFRN

Do encantamento dos números à realidade dos fatos: conciliação entre os balanços patrimonial e social da ALUNORTE

The social balance is turning into an instrument capable of identifying the Organizational Commitment socio-environmental. The objective of the Social Balance is to present the application of company resources on socio-environmental investments internally and externally. The research was developed based on the Balance Social and Sheet from Alumina North Brazil S / A, ALUNORTE, for fiscal years 2008 and 2009, with the purpose of describing the finding of the Balance Social and Sheet from ALUNORTE about social responsibility. To validate the proposal were doing comparisons between accounting and financial datas from Alunorte and Y.Yamada, in order to highlight what they say and indicators confirm the privileges of the first against second

O city marketing em Natal/RN e a construção da imagem da cidade

The growing importance of tourism in overall economic activity worldwide has favored the intensification of competition among cities that seek to create environments attractive to tourists and potential investors. It has been common practice to import characteristics of the business environment in the public management of cities. The city marketing is a key tool used by public leaders to promote a linkage between the tourism image and urban image and involves, in addition to promoting the image of the city, the planning of interventions in urban space, trying to formulate a positive image of the city able to facilitate the deployment of capital. This research seeks to understand the nature of city marketing as part of contemporary urban management and analyzes how is its application in decisions concerning the promotion of tourism in Natal/RN. The approach of this research is qualitative, exploratory and descriptive, in which respondents were the main leaders of two of the official tourism site, the Empresa Potiguar de Promoção Turística and the Secretaria Municipal de Turismo e Desenvolvimento Econômico. It was found that there is a strong articulation of public power with private enterprise in the design and conduct of the actions of urban marketing, that from the survey data show that the behavior of target markets provide guidelines for taking strategic decisions relating to tourism. Sun and sea are some key elements explored to form the image of Natal and to authorize the sale of the city as a tropical paradise. However, there is an increase in the diversification of tourism products, seeking to increase flow to the segments of ecotourism, adventure, business and culture. It s also growing the use of local culture as a tourism product, however, the cultural representation focuses on superficial values and does not bring to light the social and historical richness that the city has. Public authorities use the city marketing strategies as a means able to maximize the attractiveness of Natal urban space to investors, business groups and tourists. It can be observed that urban managers seek solutions that can continuously increase the tours, which often manifests in interventions that focus the tourist areas of the city, in oposition of those who do not contribute to a positive reading of the city, which ultimately generate the worsening of spacial and social inequalities

Aqui o nativo é o caboclo... : O processo de construção da identidade cabocla em Mirandas/RN

Ce travaille de dissertation (Master) est le résultat de trois ans de travaille auprès de Mirandas, endroit situé à 22 kilomètres de la ville de Caraúbas, région ouest de l Etat du Rio Grande do Norte. Pendant cette période, on a compris que les habitants de Mirandas se identifient et sont identifiés pour les autres comme des caboclos , catégorie de classification que dans le discours courant, soit à Mirandas ou dans la siège de la municipalité, a des rapports avec la vision que les tous premiers habitants de Mirandas sont venus de la ville du Cabo , dans l Etat de Pernambuco. Et pourtant ; l usage qu a été fait de cette version a fini pour cacher des éléments qui ont défini l identité de Mirandas, tel comme la probable descendance indigène que parfois est actionnée dans les narratives qui montrent des rapports entre les portugais et des femmes indiens qu ont été pris à casco de cavalo (cheval) . (MACÊDO, 2010; CAVIGNAC, 2003). Donc, cette ethnographie porte à la lumière des éléments que sont utilisés pour les mirandenses pour définir leur identité. Cette identité peut être bien visualisé a partir des éléments que les caboclos font des signes diacritiques (BARTH, 1998; OLIVEIRA, 1976), bien comme des rapports établis entre les habitants de Mirandas et ces de Caraúbas. Des rapports qui ont rendu possible les manifestations d affinité et de conflits et que, donc, nous aide à entendre comme cette identité se réactualise dans ces rapports d union et opposition que les mirandenses construisent avec les caraubenses. Cela arrive dans les rapports territoriaux, économiques et de façon plus marquante, dans les rapports religieux.

Arte, prazer e bisturi: construção corporal através da body modification

In view of a field research carried out by a team connected to the universe of body modification, it is possible to discern some uses and meanings linked to these forms of body interventions. Body modification or body change is part of the circuit of piercings and tattoos, although they are socially less thinned and more extreme, like scarifications, subcutaneous implants, bifurcated tongues, surfaces and body suspensions. The aim of this paper is to cast an anthropological glance on these practices, joining at the same context all the subjects involved with these techniques, placing them inside the same relational focus and capturing their journeys and trajectories. The discussions are concentrated on the notion of body building and urban life style. Ideas as personal distinctness and prestige imitation are also present in this universe, as well as matters attached to genre, pleasure, art, and to the so-called alternative circuit . This way, the ethnography so far presented here, reveals the complex and contemporaneous character of these practices of body markings in which the body appears as the central element in the experiences of the subjects of this study