980 resultados para Concepções de Matemática
Resumo:
ades de natureza investigativa contribuem para a aprendizagem matemática de alunos do ensino secundário. O estudo incidiu sobre uma turma do décimo primeiro ano de escolaridade do curso de línguas e humanidades. Foram trabalhadas três atividades no âmbito do capítulo Modelos Populacionais. Estas foram desenvolvidas com o auxílio de tecnologia, nomeadamente, calculadora gráfica e computador através da exploração do software Graph 4.4.2, no sentido de motivar os alunos e facilitar a compreensão dos conteúdos abordados. Tendo em conta que um dos objetivos deste estudo é analisar as atitudes reveladas pelos alunos aquando da realização das propostas, os dados obtidos são constituídos essencialmente por pormenores descritivos de tal forma que foi aplicada uma metodologia de natureza qualitativa através da observação participante. A utilização da tecnologia motivou os alunos, que se mostraram desde logo entusiasmados com a realização das atividades. Foi também visível, ao longo da realização das propostas, o desenvolv
Resumo:
O presente trabalho foi elaborado no âmbito do Mestrado em Ensino da Matemática no 3º Ciclo do Ensino Básico e Secundário, da Universidade da Madeira, no ano letivo de 2012/2013. Tem como objetivo analisar e refletir sobre o trabalho implementado nas duas turmas do 8º ano que me foram atribuídas, incidindo sobre a motivação dos alunos face à presença de outros materiais além do típico caderno de exercícios e do manual na aula de matemática. Deste modo, relatarei algumas aulas onde foram propostas atividades com recurso a materiais manipuláveis, jogos e computadores. Esta pesquisa foi realizada com base numa avaliação qualitativa que incidiu sobre a observação direta do trabalho desenvolvido pelos alunos, através dos registos escritos e de gravações de vídeo e áudio de algumas aulas, de forma a poder transmitir com maior exatidão a postura e o empenho dos alunos no decurso destas atividades.
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O conteúdo de ciências no Ensino Fundamental dos ciclos I e II é ministrado por um professor polivalente com formação em Pedagogia. Sua formação deve possibilitar uma visão global do fenômeno educativo, o que implica a construção de conhecimentos múltiplos e contextualizados, porém com pouco aprofundamento. Este trabalho objetiva identificar as opiniões e dificuldades de licenciandos de Pedagogia a respeito dos conteúdos de Ciências nos dois primeiros ciclos do Ensino Fundamental, mediado por dois questionamentos: Com relação aos conteúdos de ciências ministrados no I e II ciclos, você os considera fácil ou difícil? Sendo solicitado que justificasse sua resposta; De acordo com seus conhecimentos sobre ciências, cite as principais dificuldades que você teria (tem/teve) em ensinar ciências nos ciclos I e II. Participaram do estudo 29 licenciandas da turma de Ensino das Ciências Naturais II do Curso de Pedagogia da Universidade Federal do Rio Grande do Norte. Com relação ao questionamento referente à consideração dos conteúdos de ciências, 52% das licenciandas consideraram fácil, 31% difícil e 17% não responderam a questão. Foram identificadas três categorias de respostas: processo de elaboração do planejamento (20,5% fácil e 20,5% difícil), nível de conhecimento dos alunos (7% fácil e 0% difícil) e natureza dos conteúdos abordados (14% fácil e 10,5% difícil). Foram classificadas três categorias distintas em relação às dificuldades em ensinar ciências: natureza dos conteúdos abordados (50%), aspectos metodológicos (25%), e conhecimento básico (25%). A análise dos resultados revelou que a principal dificuldade das licenciandas em Pedagogia quanto à aplicabilidade do ensino de ciências nos primeiros ciclos do Ensino Fundamental esta diretamente relacionada à falta de conhecimento básico destes conteúdos, que somente foram estudados por elas no Ensino Básico, indicando a necessidade de incorporação de abordagens de conteúdos de ciências no currículo do curso de Pedagogia.
concepções de administração e administrador em tempos de capitalismo flexível: uma abordagem crítica
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A tese trata de dois construtos sócio-históricos Administração e Administrador em face do capitalismo em sua fase flexível. Considerando as mudanças do capitalismo, o texto estabelece como objeto de estudo as concepções de Administração e Administrador, para o campo administrativo, na contemporaneidade. A tese é suportada por uma pesquisa de campo cujo objetivo foi compreender criticamente as concepções do campo administrativo sobre a Administração e o Administrador, em tempos de capitalismo flexível. Epistemologicamente, a pesquisa foi conduzida a partir da perspectiva crítica frankfurtiana, fundamentada em três pares categóricos dialéticos: (i) história versus naturalização; (ii) práxis social versus sistema; e (iii) alienação versus emancipação; privilegiando o pensamento crítico vinculado à primeira geração da Escola de Frankfurt. A literatura prevalente da área de Administração foi revisada mediada pelas duas questões ontológicas que suportam a tese: O que é Administração? e O que é Administrador? para autores como Taylor, Fayol, Drucker, Ohno, Deming, Champy e Mintzberg. Metodologicamente, foi realizada uma pesquisa integralmente qualitativa, com uso de três tipos de entrevistas: (i) entrevista narrativa com história de vida; (ii) entrevista com uso de elementos-estímulo; e (iii) entrevista narrativa ficcional. Para compreensão das narrativas, foi utilizada a técnica de análise hermenêutico-dialética. Os resultados indicam o predomínio da concepção pragmática-instrumental, no tocante à Administração, pela qual ela continua a ser pensada e discursada como uma ação tecnológica e teleológica, que utiliza saberes múltiplos e aprendizagens cambiantes como meios para alcance das finalidades do contexto organizacional mutante. Com relação ao Administrador, há a emergência da concepção estética para apresentá-lo, quando vinculado às organizações. Por esta concepção, há a migração do histórico estereótipo do Administrador controlador e vigilante para a representação do Administrador como um profissional performático. O segundo resultado, que se apresenta como o mais relevante em relação ao Administrador, é o da fuga da profissão. A partir dos pares categóricos dialéticos, esta tese propõe algumas sínteses provisórias críticas: (i) história-naturalização: os sujeitos tomam como naturais a organização empresarial e suas demandas, naturalizando as recentes mudanças que, entre outras coisas, reduzem os postos gerenciais; (ii) práxis social-sistema: pela concepção pragmática-instrumental, as experiências dos Administradores são concebidas a partir do confinamento funcionalista em uma organização-sistema; (iii) emancipação-alienação: tanto a forma naturalizada com que especificam as organizações e sua Administração quanto a práxis interrompida velada em uma experiência reificada mostram-se como fenômenos intrinsecamente e subjetivamente alienantes e contraemancipatórios. Por outro lado, através do movimento de fuga da profissão, os entrevistados parecem (re)significar o silêncio fundador da alienação associada à condição de Administrador: a de pensar como capital, e não se pensar como trabalho. Finalmente, o texto propõe que as possibilidades de emancipação deste profissional residem na tomada de consciência de sua condição como integrante da classe trabalhadora, mesmo em tempos de riscos e incertezas. Assumindo-se como trabalhador, o Administrador poderá lutar pelo seu trabalho, repensando-o em novos termos, em que as dimensões pragmáticas-instrumentais que envolvem sua profissão possam ser dosadas e sempre mediadas por conteúdos substantivos e emancipatórios
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Discrepancies between classical model predictions and experimental data for deep bed filtration have been reported by various authors. In order to understand these discrepancies, an analytic continuum model for deep bed filtration is proposed. In this model, a filter coefficient is attributed to each distinct retention mechanism (straining, diffusion, gravity interception, etc.). It was shown that these coefficients generally cannot be merged into an effective filter coefficient, as considered in the classical model. Furthermore, the derived analytic solutions for the proposed model were applied for fitting experimental data, and a very good agreement between experimental data and proposed model predictions were obtained. Comparison of the obtained results with empirical correlations allowed identifying the dominant retention mechanisms. In addition, it was shown that the larger the ratio of particle to pore sizes, the more intensive the straining mechanism and the larger the discrepancies between experimental data and classical model predictions. The classical model and proposed model were compared via statistical analysis. The obtained p values allow concluding that the proposed model should be preferred especially when straining plays an important role. In addition, deep bed filtration with finite retention capacity was studied. This work also involves the study of filtration of particles through porous media with a finite capacity of filtration. It was observed, in this case, that is necessary to consider changes in the boundary conditions through time evolution. It was obtained a solution for such a model using different functions of filtration coefficients. Besides that, it was shown how to build a solution for any filtration coefficient. It was seen that, even considering the same filtration coefficient, the classic model and the one here propposed, show different predictions for the concentration of particles retained in the porous media and for the suspended particles at the exit of the media
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This article is about a study about the training needs for teachers of elementary school in the field of Geography. It is our objective to grasp their conceptions of training needs and reflect about their formative needs to teach geography. We consider the training as reflective process that involves the movement of changes and improvement beyond of formal learning, considering its numerous dimensions. We reflected about formative needs in light of the readings of Rodrigues Esteves (1993), Silva (2000), Roberts (2006), Vieira (2010). The discussions about conceptions were based on Ferreira (2007). The empirical reference constitutes to a private school in the city of Ceará-Mirim/RN, SECAT Centro de Ensino. The social subjects of our research are five teachers who work in the initial years of elementary school. We resorted a survey (auto) biographical, based on the studies of Passeggi (2011), Delory (2008), Bertaux (2010) e Josso (2010), since it is our intention to turn to the historicity of the subject and the learning, recognizing the links between him and the world and the experiences based on for learning and adult training. As technical and methodological procedure we will use the Training Narratives, whose application allows the understanding of memories and stories of schooling teachers, since are reported events occurred during the development of the individual through seminars Biographical. We observed on the narratives constructed by the teachers the absence assignments of meanings to a reworking of the theoretical formative needs and questions of its organizing principles. However, we notice the teachers were able to develop senses and means to conceive the phenomenon in study, in a descriptive way, through articulated enunciations, including aspects and opportunities linked to their teaching practices and future formative prospects. Regarding School Geography, we based our studies in the reflections of Smith Junior (1994, 2000), Tonini (2003), Vesentini (2004) and Vlach (1991), among others. We verified that the needs evidenced by the teachers to teach geography were constructed from the contexts of their teaching practices present in their school and professional trajectories. Therefore, we noticed the need for formal pedagogical qualification so that we can conceive the phenomenon in study beyond its descriptive character, understanding that it is necessary to point out reflections and questions about the dynamics of production of global capital, which conveys its interests in the contexts that often emerge formative needs of the educational system
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The right to artistic expression, freedom granted in the western democratic constitutionalism, is a fundamental right that cyclically, compared to other cohesive rights of expression, has been forgotten and put in an irrelevant juridical-dogmatic position. The first reason for this behaviour that disesteems artistic freedom is the valorisation of rationalism and scientificism in the modern society, subordinating academic researches to utilitarianism, relegating the purpose of feelings and spirituality on men s elocution, therefore, we investigate, guided by philosophy, the attribution of art on human formation, due to its capacity in harmonising reason and emotion. After that, we affirm the fundamental right to artistic expression s autonomy in the 1988 valid constitutional order, after a comparative explanation of freedom in the Fundamental Laws of United States, Portugal, Spain and Germany; and the construction historic-constitutional of the same right in the Brazilian Constitutions. In this desiderate, the theoric mark chosen is the Liberal Theory of the fundamental rights, guiding the exam through jusfundamental dimensions: juridical-subjective and juridical-objective. Whilst the first, classical function of resistance, delimitates the protection area of the artistic expression right from its specific content, titularity and its constitutional and subconstitutional limits, the other one establishes it as cultural good of the Social Order, defining to the State its rendering duties of protection, formation and cultural promotion. We do not admit artistic communication, granted without legal reserve, to be transposed of restrictions that belong to other fundamental rights and, when its exercise collides with another fundamental right or juridical-constitutional good, the justification to a possible state intervention that tangentiates its protection area goes, necessarily, through the perquisition of the artist s animus, the used method, the many viable interpretations and, at last, the correct application of the proportionality criteria. The cultural public politics analysis, nevertheless, observes the pluralism principle of democratic substratum, developer of the cultural dialogue and opposed to patterns determined by the mass cultural industry. All powers are attached, on the scope of its typical attributions, to materialise public politics that have the cultural artistic good as its aim, due to the constant rule contained in §1, art. 5º of the Federal Constitution. However, the access and the incentive laws to culture must be constantly supervised by the constitutional parameter of fundamental right to equality
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The main focus of this thesis is the formation of a mathematical teacher at a college institution. The general aim is to describe and to analyze the formation process of a mathematical teacher which is an undergraduate student in Mathematics at the Instituto de Educação Superior Presidente Kennedy IFESP, in Natal-RN. It is based on a qualitative ethnographic approach, and has its theoretical anchorage in the (auto)biographical narratives, the social representative theories, and the mathematical education. The number of participants in this investigation was 12 undergraduate students, which corresponds to 25% of the total number of students. The corpus utilized in our analysis included 48 (auto)biographical essays, 12 (auto)biographies (formation's memories), and 12 contextualization files, besides the research's diary. The sources were obtained from the whole program of studies, i.e. from November 2003 to December 2006. The analysis revealed that the reminiscences of the 12 students' academic trajectory influenced their professional formation, since their images of a mathematical teacher were intrinsically related to the one they had before. These representations were being either demolished or constructed in a network along the assertive image of their profession, changing afterwards the mathematical representation and the teaching way of this discipline. Our study also shows that the beginning of their teacher career was marked by mechanical practices influenced by their old teachers. The (trans)formation of themselves and their teaching practices happened in a smooth way as soon as they increased their knowledgements in Mathematics, and it reflected upon the way they learned mathematics. The writing of their (auto)biographies helped the set up of new knowledgements, leaving to a self-consciousness as well as a self-formation, and contributed for the construction of a new way to see and to live the profession. Therefore, a mathematical teacher, for the undergraduate students of the IFESP involved in this work, is made at the interface of the familiar, academic, and professional context, besides the reflexive writings about the formation path, the way of life and the relationships among them
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This work aims to describe and analyze the process of the mathematics teacher modernizing in Rio Grande do Norte, in the period from 1950 to 1980. For that, we use as theoretical foundation assumptions of Cultural History and memories of the researchers Maurice Halbwach, Ecléa Bosi and Paul Thompson. As methodological tools, we used bibliographical resources and semi-structured interviews, in order to do a historical reconstruct of the mathematics educational scene of institutions and people who taught mathematics in Rio Grande do Norte, or those who participated in the modernization of the teaching of this subject, recovering their training and its practices in teaching. For the analysis of the bibliographical resources, initially we organized in a systematic way the transcripts of the interviews and documents, which were accumulated during the research, so long our thoughts, returning to the theoretical basis of this research, through questioning of knowledge acquired and that guided the problem of our study. The analysis showed that, important moments to modernize the teaching of mathematics in Rio Grande do Norte happened such: (1) Training Course of Lay Teachers in Rio Grande do Norte, in 1965, (2) Course for Teachers in Normal Schools, in 1971 (3) Satelite Project on Interdisciplinary Advanced Communications (SPIAC) in 1973; (4) Lectures of the teacher Malba Tahan, at Natal, from the end of the 50 s, that could be analyzed through the lessons notes of the teacher Maria Nalva Xavier de Albuquerque and the narrative of teacher Evaldo Rodrigues de Carvalho and (5) Courses of the Campaign for Improvement of Secondary Education and Broadcasting (CISEB). Thereby, the modernization of the school s mathematics teaching in Rio Grande do Norte, in the period from 1950 to 1980, was given mainly by disclosure of the Discovery Method and by the Set Theory contents in Teacher Training Courses
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From the investigation, analysis, discussion and pondering about the activities developed by the lndians from the Porteira hamlet, members of the Xerente community, in the Tocantins state, we developed an investigative and descriptive study about the reality of this people with the aim of helping in the conceptual formation and in the reorientation of the pedagogical practice of the local teachers. In this sense, the undertaken research involved the teachers, the main representatives and experts in that cultural tradition, in order to investigate how the everyday activities (agriculture, food handling, assets distribution among the community members, etc.) and the cultural tradition (log race, body painting, clan division, Xerente numeration, Indian myths and histories, etc.), may enable the contextualization of the mathematics teaching in the lndian School Srêmtôwê of this hamlet, under a more transversal and globalizing perspective of the local and school knowledge. We based this research in the sociocultural conceptions of knowledge generation proposed by D Ambrosio (1990; 2002); Vergani (2007); Oliveras (1996); Gerdes (1991; 2002); Bishop (1999) e Sebastiani Ferreira (1997; 2004). ln the process of this study we propose some viable ways so that the Indian teachers may reorganize their classroom knowledge and actions, based in the strengthening of their history and culture. The observation of some social practices and knowledge as well as of the Xerente traditions helped us to point some possibilities of projection of a didacticalpedagogical dimension of these activities and practices, in the development of the school mathematical knowledge in this community
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The aim of the present study is to investigate the way through which the relations between Mathematics and Religion emerge in the work of Blaise Pascal. This research is justified by the need to deepen these relations, so far little explored if compared to intersection points between Mathematics and other fields of knowledge. The choice for Pascal is given by the fact that he was one of the mathematicians who elaborated best one reflection in the religious field thus provoking contradictory reactions. As a methodology, it is a bibliographical and documental research with analytical-comparative reading of referential texts, among them the Oeuvres complètes de Pascal (1954), Le fonds pascalien à Clermont-Ferrand (2001), Mathematics in a postmodern age: a cristian perspective by Howell & Bradley (2001), Mathematics and the divine: a historical study by Koetsier & Bergmans (2005), the Anais dos Seminários Nacionais de História da Matemática and the Revista Brasileira de História da Matemática. The research involving Pascal's life as a mathematician and his religious experience was made. A wider background in which the subject matter emerges was also researched. Seven categories connected to the relation between mathematics and religion were identified from the reading of texts written by mathematicians and historians of mathematics. As a conclusion, the presence of four of these seven categories was verified in Pascal's work
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Le texte se rapporte à une recherche sur les conceptions d enseignants concernant l inclusion scolaire d élèves sourds , et leurs ralations avec les pratiques qu ils développent dans les classe régulières. Elle a été conduite dans une école publique régulière appartenant à la commune de Assu RN, et dont le choix méthodologique a été une approche qualitative, du genre ethnographyque. La construction des données devient d un processus d observation, de l application d entretiens demi-structurés et de l analyse de documents, ayant pour sujets quatre enseignants des années initiales de l enseignement fondamental. L apport théorique de base a été la théorie socio-culturelle proposée par Vygotsky (2003 ; 2005), censée traduire la compréhension de l homme dans sa dimension historique et culturelle, et mettre en évidence l interaction sociale en tant que condition pour le développement des individus. Les données font connaître que les enseignants sujets de la recherche sont favorables à l inclusion scolaire des élèves sourds dans les classes régulières, néanmoins soulignent le besoin d un changement à l école pour que l inclusion devienne une réalité. Les enseignants sont d avis que l apprentissage des élèves sourds se fait d une façon qui met trop de temps, moyennant l utilisation de recours spécifiques, tels que l usage du langage des signes (Libras). Ils signalent les difficultés qu ils doivent faire face quand il s agit de travailler pédagogiquement avec ces élèves dans le quotidien, telles que : manque d un travail collectif à l école ; besoin d une formation spécialisée ; démonstration de sentiments de peur, ou préjugés de la part de quelques uns du personnel de l école , tout celà interférant directement dans leurs attitudes et leurs actions faces aux élèves ; manque d appui des instances administratives de l école ; absence de politiques consistentes pour guider l éducation sous un regard inclusif. Quant aux pratiques pédagogiques développées à l école, la recherche laisse voir que, par rapport à la présence des élèves sourds, très peu d adaptations y ont été introduites, d où se dégage que la planification des actions éducatives à l école se tourne, prioritairement, vers les élèves qui écoutent, c est-à-dire, vers un groupe apparemment homogène. On a constaté, en plus, qu il n existe pas à l école aucun professionnel habilité pour l établissement d un processus de communication avec les élèves sourds. Malgré ces difficultés, les enseignants avouent, quand même, que travailler avec ces élèves rapporte toujours des bénéfices, tels que la collaboration et le respect mutuels chez les élèves, l acquisition de nouveaux savoirs et l amélioration de la pratique pédagogique des enseignants
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The aim of the present study is to reevaluate the logical thought of the English mathematician George Boole (1815 - 1864). Thus, our research centers on the mathematical analysis of logic in the context of the history of mathematics. In order to do so, we present various biographical considerations about Boole in the light of events that happened in the 19th century and their consequences for mathematical production. We briefly describe Boole's innovations in the areas of differential equations and invariant theory and undertake an analysis of Boole's logic, especially as formulated in the book The Mathematical Analysis of Logic, comparing it not only with the traditional Aristotelian logic, but also with modern symbolic logic. We conclude that Boole, as he intended, expanded logic both in terms of its content and also in terms of its methods and formal elaboration. We further conclude that his purpose was the mathematical modeling of deductive reasoning, which led him to present an innovative formalism for logic and, because the different ways it can be interpreted, a new conception of mathematics
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This work is located at the shield of research that defends the use of Mathematics History, based on the utilization of historical artifacts at teaching activities, at Mathematics classrooms, and at graduation courses for teachers of Elementary School and of the first grades of High School. The general objective is to examine the possibility of the use of historical artifacts, at teaching activities, at graduation courses for teachers of Elementary School and of the first grades of High School. Artifact, at this work, is comprehended as objects, documents, monuments, images and other kinds of materials that make sense to the Human actions at the past and that represent what have been said and done at the Human history. At the construction of the theoretical-methodological way of the research we have based ourselves upon the ideas of the authors that are engaged at the teachers formation; at researchers adherents to the use of Mathematics History (MH) as a methodological resource, and at studies accomplished that elucidate the role of the artifacts at the history and as a mediatory element of learning. We defend the thesis that the utilization of historical artifacts at teaching activities enables the increasing of the knowledge, the development of competencies and essential abilities to the teacher acting, as well as interact at different areas of the knowledge, that provides a conception of formation where the teacher improves his learning, learning-doing and learning-being. We have adopted a qualitative research approach with a theoretical and pratic study disposition about the elements that contribute to the teachers works at the classroom, emphasizing the role of the Mathematics history at the teacher s formation and as a pedagogical resource at the mathematics classroom; the knowledge, the competencies and abilities of the historical artifacts as an integrative link between the different areas of the knowledge. As result, we emphasize that the proposition of using the MH, through learning activities, at the course of teacher graduation is relevant, because it allows the investigation of ideas that originate the knowledge generated at every social context, considering the contribution of the social and cultural, political and economical aspects at this construction, making easy the dialog among the areas and inside of each one The historical artifact represents a research source that can be deciphered, comprehended, questioned, extracting from it information about knowledge of the past, trace and vestiges of the culture when it was created, consisting of a testimony of a period. These aspects grant to it consideration to be explored as a mediatory element of the learning. The artifacts incorporated at teaching activities of the graduation courses for teachers promote changes on the view about the Mathematics teaching, in view of to privilege the active participation of the student at the construction of his knowledge, at the reflection about the action that has been accomplished, promoting stimulus so the teachers can create their own artifacts, and offer, either, traces linking the Mathematics with others knowledge areas.
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The discussion we have established in this study is about how the practice is developing educational projects based on work with because the methodological choice of the teacher. The study of an ethnographic qualitative approach was conducted with a group of six teachers in two public schools in School Administrative Zone north of the city of Natal / RN. Data were constructed from semi-structured, reinforced by the direct observation of the practice of teaching of teachers. The goals outlined were to identify the reasons why the option for the project, listing the benchmarks that subsidized their construction, the observation of everyday experience in educational planning and development of projects developed. In the light of information we can notice a complex and even contradictory, which is confusing the concepts and practices are weakened. The analysis revealed inconsistencies between theory and practice in working with projects, the fruit of little theoretical development of teachers. The adoption of the project as a methodological option has meant a change in direction of the effective action didactic. Reflects on this situation, it was concluded that there is a need to broaden the understanding of the significance of this type of work, covering the different dimensions that involve the practice of research, research and training of teachers. Even preventing the intentions and initiatives of the teachers, it must be emphasized is the process of learning within an approach that focuses the process of learning in multiple dimensions, inter-relational, both the capabilities of students in the areas of knowledge.