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

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

Possibilidades de exploração da história da ciência na formação do professor de matemática: mobilizando saberes a partir da obra de Nicolau Copérnico de revolutionibus orbium coelestium

This study aims to analyze the implications that the knowledge of an important work for the History of Science, De revolutionibus orbium coelestium , by Nicholas Copernicus, can bring for the formation of Mathematics professors. The study focuses on Book I of Copernicus s work, where, in the final part, is found the Table of the Subtense Straight Lines in a Circle, a true sine table constructed by the author. The study considers two theoretical references, the History of Science and of Mathematics, in the professor s formation searched amongst others in Miguel and Miorm, Brito, Neves and Martins, and Radford, and the necessary teaching knowledge professors mst have, on the basis of Gauthier, Schulman and Imbernón amongst others, through which it is established a net of knowledge grouped in dimensions such as mathematical, psycho pedagogical, cultural and practical diversity, that guide the study analysis. In the search for more necessary elements to enrich the analysis, beyond the theoretical research in Book I, it is carried through, with under graduation pupils, future Math professors, the construction of a sine table following the project used in De revolutionibus . The study still makes a description of the life and work of Nicholas Copernicus, detaching the historical context where the author lived and the conceptions about the Universe existing at that time. The research reveals that the studied work is an important source of culture, able to provide to the Mathematics professor in formation, beyond the conceptual and procedural mathematical knowledge, a cultural knowledge that allows him to be opened to the knowledge of other areas that not his specific area, and so to acquire knowledge about the world history, the development of sciences and of the society

Círculo de ação-reflexão-ação: uma possibilidade praxiológica para a prática pedagógica da formação problematizadora de professores

Considering the dialogue as a gnosiological act and teachers as a researchers of their own practice, this thesis deals with the contribution of Paulo Freire thoughts to teacher s formation process. The study was made over an intervention carried out at a regular Pedagogy Course, however directed to teachers on duty inside a program called PROFOMAÇÃO (Special program for professional formation on Basic Education) promoted by Universidade do Estado do Rio Grande do Norte (UERN). From Freire s ideas of problematizing education, action and reflection dialectics, conscientization and from the analysis of the course itself, I support the idea that the dynamics of collective construction of knowledge- three pedagogical moments (ANGOTTI, DELIZOICOV e PERNAMBUCO) when intermediated by individual reflection, provided by written register, permits the development of three important dimensions of knowledge about pedagogical practice; observation and selfobservation; understanding the theories witch grounds the action; and theorization. By these means, initial and permanent teacher s formation could materialize its political commitment in a concrete action of collective and participative act of conscientization and transformation of the reality of pedagogical practice at school ground, developing itself as a truly circle of action and reflection

Como se fora brincadeira de roda: a ciranda da ludopoiese para uma educação musical humanescente

The present work concerns an auto-ethnographic study based on life experiences and reflections of an educator at Escola Viva Preschool and Elementary-Middle School, located in the city center of Natal, Rio Grande do Norte. As a cognitive model of operation, we use the metaphor of the Circle Dance. The objective of this study is to identify, interpret and describe the ludopoetics that are achieved through a Musical Education program, which we denominate, Humanescent. The data of this investigation was derived from the music making by Preschool and Elementary-Middle School students at Escola Viva during 2007, 2008 and 2009, from which 20 learners were selected to form the corpus, along with the description and interpretation of photos of their experiences and sand tray scenes. We justify the methodological systemization of the research based on our own pedagogical practice, which supports Musical Education in the schools based on the principals of Embodiment, Autopoesis and Flow. The methodological systemization was developed through an Action Research model and on the concepts of Systemic Development, with the goal of re-reading the context investigated through the structuring of categories of Ludopoesis: Self-esteem, Self-territory, Self-connectivity, Self-realization and Selfworth. We used an observant-participant research approach with regard to the perception of emergent knowledge, the surroundings, the experience lived and the contextual and vibration of the circumstances. Besides this, we used projection to interpret the experiences lived, in the form of drawings, short poems, letters or sand tray scenes as symbolic interpretations of experience. In the unfolding of the Ludopoetic Process (Selfesteem, Self-territory, Self-connectivity, Self-realization and Selfworth) we draw conclusions about the relevance of the ludic musical experience, which foments the formation of the self based on music learning, and which is demonstrated in the Embodiment of the learners. In the auto-formative process (of learners and educators) we observe the importance of pedagogical work based on Musical Humanescent Education that gives value to the music making path to the construction of music and performance in play, creativity, and sensibility. The experience of making music in a playful way allows for organization of the self and its autonomous production in the joy of living within a ludopoetic process. These findings highlight the educator as in a permanent state of selfformation, which generates moments of flow. However, in Musical Humanescent Education, music is learned collectively, doing a circle dance, experiencing love, fostering an expansion of the creative spirit, and giving recognition to playfulness as a necessary condition for education and to the value of music made with the true nature and sensibilities of the educators

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

As geometrias urbana e isoperimétrica: uma alternativa de uso em sala de aula

The main goal of the present study is to propose a methodological approach to the teaching of Geometry and, in particular, to the construction of the concepts of circle (circumference) and ellipse by 7th and 8th grade students. In order to aid the students in the construction of these concepts, we developed a module based on mathematical modeling, and both Urban Geometry (Taxicab Geometry) and Isoperimetric Geometry. Our analysis was based on Jean Piaget's Equilibrium Theory. Emphasizing the use of intuition based on accumulated past experiences, the students were encouraged to come up with a hypothesis, try it out, discuss it with their peers, and derive conclusions. Although the graphs of circles and ellipses assume different shapes in Urban and Isoperimetric Geometry than they do in the standard Euclidian Geometry, their definitions are identical regardless of the metric used. Thus, by comparing the graphs produced in the different metrics, the students were able to consolidate their understanding of these concepts. The intervention took place in a series of small group activities. At the end of the study, the 53 seventh grade and the 55 eighth grade students had a better understanding of the concepts of circle and ellipse

Recent Studies on Neoechinorhynchus curemai Noronha, 1973 (Acanthocephala: Neoechinorhynchidae), in Prochilodus lineatus Valenciennes, 1836, from Volta Grande Reservoir, MG, Brazil

O presente trabalho estudou a helmintofauna do curimbatá, Prochilodus lineatus Valenciennes, 1836, do reservatório de Volta Grande, MG, Brasil. Foram analisados 18 peixes com comprimento médio de 46,7 ± 1,1 cm e peso médio de 1.674,8 ± 75,6 g, sendo que 15 apresentaram acantocéfalos no intestino com prevalência de 83,3%. O helminto foi identificado como Neoechinorhynchus curemai Noronha, 1973 (Acanthocephala: Neoechinorhynchidae), que diferiu das outras espécies descritas pelas dimensões dos caracteres e pela morfologia. da descrição original de N. curemai difere pelas maiores dimensões dos testículos, pela glândula de cimento alongada, pela presença de núcleos nos lemniscos, pelas dimensões dos ovos e pelos maiores ganchos da probóscide presentes na segunda e na terceira fileiras nos machos e na primeira fileira nas fêmeas. Foi observada menor porcentagem ocupada pelo sistema reprodutivo em relação ao tronco da fêmea. A observação dos parátipos de N. curemai de Noronha (1973) mostrou grande semelhança com os do presente trabalho. Este fato complementa a descrição do helminto em outra localidade.

Taxa de absorção atmosférica sobre as cidades de Botucatu-SP e Rio de Janeiro-RJ

O segundo satélite da Missão Espacial Completa Brasileira (SCD2/MECB) foi colocado em órbita em 23 de Outubro de 1998 e carrega a bordo um experimento de células solares. Célula solar de silício é um dispositivo semicondutor, que pode medir a intensidade da radiação visível e parte da radiação infravermelha (400-1100 nm). O experimento permite medir simultaneamente a insolação direta e parte da radiação solar que é refletida pela Terra para o espaço. Os dados do experimento célula solar são transmitidos em tempo real pela telemetria do satélite e recebidos pela estação terrestre em Cuiabá, MT-Brasil (16°S; 56°W). Este fato limita a cobertura espacial para um círculo sobre a América do Sul. O albedo planetário é obtido dentro desta cobertura e seus valores podem ser agrupados em períodos temporais (anual, sazonal ou mensal), ou podem ser estudados para várias localizações (latitude e longitude) durante a vida do satélite. O coeficiente de transmissão atmosférica ou índice de claridade (Kt), medido em estações meteorológicas na superfície da Terra, junto com o valor medido simultaneamente do albedo planetário, permite calcular o coeficiente de absorção atmosférica (Ka). O método desenvolvido neste trabalho para avaliar Ka considera que o albedo planetário é composto por duas partes: uma refletividade local e uma refletividade não local. Considerando este novo conceito, é definida uma taxa de absorção atmosférica (denominada Ra) que é a razão entre Ka e a potência de irradiância solar líquida, que não atravessou a atmosfera (100%-Kt). A taxa de absorção atmosférica assim definida é independente da cobertura de nuvens. O histograma de freqüência de Ra mostra os valores de 0,86±0,07 e 0,88±0,09 sobre as cidades de Botucatu-SP e do Rio de Janeiro-RJ, durante os anos de 1999 até 2006, respectivamente.

Ocorrência e variabilidade genética do Tomato severe rugose virus em tomateiro e pimentão no Estado de São Paulo

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Sob a égide de Afrodite: o espaço feminino em O Despertar, de Kate Chopin

Departing from the theoretical principle of the feminine text as a palimpsest that holds subtextual meanings which, in permanent interaction with the textual surface, disarticulate the oppositional and hierarchical backgrounds of patriarchy, this essay intends to offer a general overview on the narrative instance of space in The Awakening, the most important work by Kate Chopin one of the highlights of Realism in the United States, with the intention to show how the space is itself plenty of and at the same time disseminates into the other narrative elements some inter-dictions to gainsay patriarchy. We intend, in this perspective, to develop an analysis of the space and its subtextual inter-relationships displayed in the symbolic implications of the water, the sea, the circle, and the feminine subjectivity awakening of the work's protagonist.

Espaço e subjetividade: estudo com ribeirinhos

Nesta pesquisa, investigamos as transformações vividas por uma comunidade afetada pela construção de uma usina hidrelétrica no rio Paraná. Utilizando procedimentos da etnografia, realizamos várias visitas à comunidade, reassentada numa vila planejada e construída para substituir a antiga vila que foi submersa. Estabelecemos contatos com os moradores mais antigos e produzimos, com eles, diálogos entabulados em situações diversas, como em visitas às próprias casas e rodas de conversa ocorridas nas calçadas. Nas falas dos ribeirinhos, a mudança do espaço é sentida como algo negativo, em todos os planos da vida. Ressentem-se da perda do rio, da pesca farta, da caça realizada nas matas, das terras férteis cultivadas nas barrancas, da socialidade e de toda produção de subjetividade que mantinham naquele lugar marcado pela proximidade com o rio e suas águas.

Slogans políticos em campanhas eleitorais no Rio Grande do Norte: a mídia na disputa ideológica.

To the observe the periods of electoral campaigns, we can realize sharply the abundance of political propaganda that announces the candidates, their campaign record, their proposed and everything that can carry them to the victory in the urns. The propaganda is today an essential tool in the votes dispute, in consequence of this, there is, in Brazil, the increasing participation of the Politics Parties in seminars of electoral marketing. They are varied strategies of the media used in the divulging of the candidacies, among them the slogan. Instigated by the explicit relation media/political, this work intends to investigate the ideologies (values) announced by the slogans of political propaganda that circulated in electoral periods. Thus, we base on the theory of the Circle of Bakhtin, who considers the statement as unit of the verbal communication, and that conceives the language as phenomenon dialogical, and, too, in the conceptions of alien words, social voices and dialogical relations formulated by the referred theory. We use, for better to comprehend, the slogan as strategy mediatic, of the classical study done by Olivier Reboul concerning the slogan; and, like starting point of a conception about ideology, studied John Thompson to comprehends the ideological phenomenon. Our corpus it constitutes of 14 political slogans announced in the campaigns for mayor of the cities in Natal and Mossoró, both located in Rio Grande do Norte s state, Brazil, in 1996, 2000 and 2004. For the analysis of these slogans, we consider the social-historical context in which were announced, being contemplated the linguistic and discursive aspect, according to the following methodological order: the identification of alien words (interdiscours); the social voices and the kinds dialogical relations established; and, finally, the ideology announced by the statement. This way, we can arrive to the conclusion that in the electoral context occurs a true ideologies war , in other words, in the political game of an electoral campaign, the slogans announces different values, which vary in several factors function, for example, the historicity, the subject that enunciates, the discursive positionings.

Práticas discursivas e relações afetivas na contemporaneidade: o caso dos verbos ficar e namorar no contexto do vestibular da UFRN

This work is inserted to Applied Linguistic studies, concerned to the understanding that language is a social practice, bringing a qualitative research, discussing essential aspects that involve the subject and his/her discursive practice: signification and valuation. Due to this, we have elected as subject study, the sense and values attributed to the verbs make out and date searched on the articles written in the Vestibular 2005 process promoted by the Universidade Federal do Rio Grande do Norte (UFRN), that had the following instruction: In a relationship, is it better make out , just date , or, both, make out and date ? This research is based on the Circle of Bakhtin s dialogic theory, as well as in the notions of instability in the affective relationships nowadays and in the individualization and multiplicity of contemporaneous subjectivity. Those papers are important to analyze the meaning and values that the verbs make out and date present, nowadays, as expressions of an affective relationship and how this situation can interfere in the positions of subjectivity in a formal instance as a vestibular. Those textual productions reflect those relationships, confronting temporary ones, whose discuss is marked, in general, by social voices that evaluate to make out negatively and to date positively

Um olhar dialógico sobre a atividade de revisão de textos escritos: entrelaçamento dizeres e fazeres

This research deals with the activity of text revision. It aims at understanding the work of the text reviewer, taking into consideration the professional experiences of the subjects who work in the area. It s theoretical basis comes from Bakhtin Circle, mainly the concept of verbal interaction formulated from reflections on language used in different spheres of human activities, which implies the notions of discourse genres, alterity, as well as exotopy. The methodology follows the tradition of the qualitative and interpretative research. The data is composed of the statements of text reviewers both in handbooks and interviews, as well as of the description of the researcher s own experience as text reviewer. The results indicate that the revision activity needs to be orientated by a dialogical conception of language, which takes into consideration the interaction between the reviewer and the author, aiming the text finalization

Vozes sociais em diálogo: uma análise bakhtiniana dos diários de leituras produzidos por alunos do ensino médio

The work aims to analyze high school students utterances, in reading diary discursive genre, starting from the language concept proposed by the Bakhtin Circle. The genre in question has peculiar characteristics which justify its choice for this work, especially with regard to subjectivity marks, that reveal, through the ideological clash, positions on various issues. From the utterances selected for the corpus, categories were created, during the research, according to the guidelines of Guba and Lincoln (2006), Mazzotti and Gewandsznajder (1998) and Amorim (2002), for whom the research in human sciences cannot be based on pre-established categories. We consider diary as a discursive genre (BAKHTIN, 2010a), which carries the characteristics of composition, style and content. Other concepts of the Circle, concerning to utterance, dialogical relations, social voices, responsiveness and exotopy also formed the basis for the study. Moreover, during the analysis of the utterances that compose the corpus of research, we used the concepts of discursive polemics (BAKHTIN, 2010b) and Framework (2010a). At the end of the research, we realized that the assessment situation of students, the fact that they are in an institution whose policy follows national documents, based on diversity and plurality, and live together in a classroom space where there are differences of social class, age, and finally, different realities, were not sufficient factors for this diversity be well accepted in their positions. Thus, their utterances bring voices that demonstrated a difficulty in accepting others that are different from themselves. In view of this, we conclude that teachers need to be prepared to handle these discourses, creating strategies for mediating these dissonant voices, with which must make contact every day at school