A transversalidade no currículo do ensino fundamental: as questões ambientais em foco

This thesis is the result of an investigation about the transversality of the environmental issues into the daily curriculum of High Schools (from first to eighth grade). The research field was the county of Santo Antonio de Jesus in the state of Bahia, Brazil. The investigation is related with the challenge that the present model of social development and organization has put to the school institution: to bring the regular discussion about Environmental Education (EE) to the school s daily life. Facing the complexity of the socio-environmental issues and the basic functions of Education, the object of study was restricted to the identification of the challenges and paradoxes of the EE inside the curriculum organization of Politic-Pedagogic Project of the schools and the teachers daily practices. About the methodology, we adopted different references for the qualitative research: sociology, history, economy, and education. As for the investigative procedures about the teacher s practices, we related the school s daily practices to the context of the community. We also adopted several investigative procedures, such as questionnaires, interviews, observations and formative intervention. The theoretical basis was organized based on references to curriculum organization, environmental culture, teacher education and also considering the pillars of a capitalistic system that is based on consumerism and that generates social exclusion. At the initial considerations, we contextualized the contemporary environmental issues in an attempt to interpret the conditions of the EE transversality into the school s daily practices, which are still oriented to the traditional Cartesian Education. Based on the collected data, we found the reasons for the teachers dilemma and reluctances to the insertion of the environmental issues into the organization of the work plan and into the management of a school. Nevertheless, the results also signed promising possibilities to the EE tranversality, in case the curriculum of the school could be more sensible towards the cultural and social-economical issues of a community. We especially questioned The National Curriculum Parameter s (PCN), which is considered highly insufficient to inform the teachers about the environmental issues, facing the actual local conditions of social and pedagogic work. The final considerations showed the role and the importance of this research as one strategy to organize the curriculum education into the perspective of the transversality of environmental issues inside the education of both teacher and student

A inclusão do aluno com deficiência mental no ensino médio: um estudo de caso

La défense d une école inclusive dans les forums internationaux du monde entier a stimulé l adoption de politiques éducationnelles d inclusion et la pratique d inclusion dans les écoles, de sorte à ce que la scolarisation des élèves aux besoins éducatifs spéciaux dans les classes comunes est devenue une réalité dans la majorité des systèmes d éducation. Et pourtant, l inclusion scolaire, au Brésil, avance à pas lents et pose d innombrables questions, notamment quand il s agit de l inclusion des personnes qui présentent une déficience mentale dans les niveaux d enseignement plus avancés. Basé sur ce fait, et tout en considérant que les études et recherches sur ce thème, au Brésil, sont centrées majoritairement sur l éducation enfantine et les séries initiales de l enseignement fondamental, cette étude se propose d analyser l inclusion d une élève ayant une déficience mentale, inscrite dans l Enseignement Moyen, dans une école appartenant au réseau d enseignement de l Etat, dans la ville de Natal RN. Pour répondre aux questions proposées dans cette étude nous avons fait appel aux méthodologies qualitatives, du genre Etude de Cas, et au cours de sa réalisation avons utilisé l interview demi-structurée et l observation libre dans l ambiance naturelle de l école. Ont participé de l étude, en plus de l élève qui présentait une déficience mentale, sa mère et deux segments de l école, desquels ont fait partie trois professionnels de l équipe administrative pédagogique et quatre enseignants. L analyse des données a mis en relief la résistence de l école à répondre au projet pédagogique d éducation inclusive, aspect qui a un rapport très étroit avec les spécificités de l Enseignement Moyen, la structure traditionnelle d un enseignement basé sur l idée d une classe homogène, et le bas niveau d attentes des éducateurs concernant les possibilités d apprentissage et de développement de l élève handicapée mentale. De surcroît, le manque de directives pour conduire les adaptations pédagogiques et du curriculum à l école ont rendu fragile l action des enseignants, dont le résultat est une pratique d intégration rudement malmenée. Au travers des points de refléxions suscités par cette étude, nous considérons que l inclusion des élèves qui présentent une déficience mentale doit être centrée sur une pratique pédagogique qui repousse l idée de soumettre tous les élèves à des procédures universelles cristalisées sur des pratiques imposées par les contraintes d homogénéisation, et qui, contrairement, puisse trouver à l école des conditions favorables au développement de chacun, au travers des processus d apprentissages formés par des instances de médiation et d interaction sociales

Uma visita ao universo matemático de Lewis Carrol e o (re)encontro com sua lógica do nonsense

Notable mathematics teacher, Lewis Carroll, pseudonym of Charles Lutwidge Dodgson (1832-1898), made the mixture of mathematics with literature a ludic environment for learning that discipline. Author of Alice s Adventures In Wonderland and its sequel Alice Through The Looking Glass, he eventually created a real and complex universe which uses what we call the logic of the nonsense as an element to motivate the development of mathematical thinking of the reader, taking it as well, learn by establishing a link between the concrete (mathematics) and the imaginary (their universe). In order to investigate and discuss the educational potential of their works and state some elements that can contribute to a decentralized math education from the traditional method of following the models and decorate formulas, we visited his works based on the studies of archeology of knowledge (FOUCAULT, 2007), the rational thought and symbolic thinking (VERGANI, 2003) and about the importance of stories and narratives to the development of human cognition (FARIAS, 2006). Through a descriptive, analytical study, we used the literary construction and presented part of our study in form of a mathematical novel, to give the mathematical school a particular charm, without depriving it of its basics properties as discipline and content. Our study showed how the works of Carroll have a strong didactic element that can deploy in various activities of study and teaching for mathematics classes

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

Uma reavaliação do pensamento lógico de George Boole à luz da história da matemática

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

A (re)significação conceptual nas práticas colaborativas com professores do Ensino Fundamental

The work objectified to apprehend the degree of the teachers' concept concerning the territory concept and to intervene with situations of critical reflections to accompany and to analyze the process of conceptual elaboration. It contemplates on the (new)meaning of knowledge and (new)elaboration of the concept in study done inside a pedagogic intervention. The Municipal School Dr. Julio Senna - Ceará-Mirim/RN and six (6) teacher-collaborators that taught in the 3rd and 4th grades of the fundamental teaching, constitutes the empiric field of the research. Its theoretical-methodological contributions are built in the studies of Vigotski (2000a, 2000b and 2001) on the formation process and development of concepts; in the methodology colaborate (Ibiapina (2004), Bartomé (1986), Kemmis and Mctaggart (1988), Arnal, Del Ricon and Latorre (1992), Pepper and Ghedin (2002), among others) and in the critical-reflexive conception of the Geography (Soares Júnior (2000 and 1994), Silva (1998), Raffestin (1993), Santos (1994), Felipe (1998), among others). The accomplishment of the work presupposed starting from the reflections on the following subjects: which the teachers' understanding in the school space concerning the territory concept? How does happen the process of conceptual construction territory for the teachers? The analysis of the teachers' previous knowledge on the concept in study, evidenced that its apprehensions on the attributes of the referred concept went mentioned the to light of the perceptible dimension of the real-concrete relationships of the reality linked to the degree of the spontaneous concepts and followed by the ideas of the traditional, humanistic and cultural geographical conceptions (positivism and phenomenology), restricting the territory meaning the notion of State-Nation and place of the men's dwelling. In the intervention process, it was verified to real possibility of the acquisition of indispensable scientific concepts to the process of (new)meaning conceptual of geographical knowledge through the continuous practice of the educational formation, when it was evidenced that the teacher-collaborators acquired high degrees of attributions of the significance of the territory concept to the they elaborate generalizations by means of analyses and syntheses of the concept-attribute (essential and multiples) of the reference conceptual in study

Prototexto, narrativa poética da ciência: uma estratégia de construção do conhecimento e religação de saberes no ensino de física

In this thesis I present the prototexto notion and to I base as a complex system while strategy of knowledge construction and reconexion of you know in physics teaching. Prototexto is a poetic narrative of the science, proposal and used initially as "instrument of creative" learning for students apprentice of science of the medium and technical teaching of the Vitória da Conquista's CEFET-BA, in the period of 1997-2004. Later become pregnant as a strategy of knowledge construction, in the Universidade Estadual da Bahia - UESB, the prototexto notion configures a complement to the mathematical formulation. The proposal of a poetic narrative of the science is that the apprentice of science starts to organize in an aesthetic-literary way your knowledge, dispersed in disciplines, starting from a theme of the physics. The prototexto emerges of my reflections concerning the classic science, identified for Edgar Morin as tends a thought excessively numeric, and that it has been reproduced in physics teaching, in most of the schools, limiting him/it to an order pattern with the mistake absence. They are operations of the prototexto: the poetic language, the pedagogic stamp, the unfinished of the argument, the system character and the apprentice's of science inclusion as subject implicated in the construction of the knowledge. the theoretical foundations are based Morin's proposition of the method as strategy, the beginning of the complementarity of Niels Bohr in conceiving excluding categories as face of a same phenomenon and the conception of creative time of Ilya Prigogine that enunciates the alliance among the nature and the man that it describes her

Professoras e projetos: concepções e práticas no ensino fundamental

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.

A cultura da produção de farinha: um estudo da matemática nos saberes dessa tradição

This research argues about the mathematical knowledge built in the tradition of the cassava flour production, seeking to analyse these mathematical knowledge in the perspective of the categories of time and measure, built and practiced in the flour production, located in Serra do Navio and Calçoene, in Amapá - Brazil. The following work discuss the identification and the description of the mathematics during the production activities of the flour, where is presented elements related to generation and transmission of the traditional knowledge, which is the basis for maintenance of the tradition of the flour, characterizing the research as an Ethnomathematic study. The methodological procedures highlight ethnographical techniques and elements that characterize the participating observation. The results obtained showed us that the flour workers articulate some length, area and volume measure due to own and traditionally acquired systems, which is apprehended and countersigned by other kind of culturally established system; thus they relativism the measures systems and the official calendars. And it lifts as one of the main proposal that the academic mathematics and the tradition establish knowledge make conjunction of the both knowledge, that is important for a possible reflection and application in the construction of a pedagogical practice in mathematical education, trying to establish points of socio-economic and cultural mark

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

O ensino da história e o pensamento reflexivo-crítico da professora no 3º ano do Ensino Fundamental

This collaborative research is a qualitative approach, from historical and cultural perspective, made about a teacher of third grade of basic education in the area of history, in the municipality of Caicó / RN. It has as objective to investigate, in a collaborative action, if the design process of teaching and learning the discipline of history based on the relationship before / after allows the development of critical reflective thinking of the teacher in school practices. The theoretical and methodological approaches are supported in the postulates of Vygotsky (1998), Rubinstein (1973) and Linblinskaia (1979), among others, whose understanding has led us to reflect if the teacher develops the reflective critical-thinking in history discipline classes. The complexity of the study led us to an analysis exercise, using different methodological procedures, such as: bibliographic review of the literature, considering also the literature of the history area, interviews, observation in the classroom, video recordings and reflective sessions, enabling clarify the construction and reconstruction of thought that the teacher had been developing during the process of teaching and learning. The test results point to a dichotomy between theory and practice, and also to a certain fragility in the position of professor in teaching and learning the discipline of history, at the third grade of basic education. The teacher recognizes that she requires a theoretical deepening with more intensity, as a process of continuous training to improve the practice of teaching in history school, though, stating in her speech that her teaching practice is based on critical reflection. However, she presents serious limitations in classroom practices. We conclude that, although she has shown willing to work on a critical perspective of reality, showed also poor change at school practices, starting to reflect about her own actions, pointing her limits and the changes needed that didn t become reality yet. It s necessary a formative process for her. The study therefore showed that even with the sessions and reflective of deepening theoretical studies, the teacher does not change its profile, while maintaining its traditional vision in any pedagogical action. This research recommends the formation of school groups for further studies and discussion on the practices of education in history area from a reflective-critical thought perspective as a mean of personal and professional development

Os ateliês (auto)formativos na constituição do sujeito docente da educação matemática

The object of study of this thesis is the use of (self)training workshops as a fundamental process for the constitution of the teaching subject in mathematics education. The central purposes of the study were to describe and analyze a learning process of mathematics teachers supported by the training-research methodology, which procedures have been affected with the practice of (self)training workshops as a way of collaborating to the constitution of the teaching subject in Mathematics Education. The survey was conducted with a group of teachers in the city of Nova Cruz, Rio Grande do Norte through a process of continued education realized in the training workshops having as main goal the realization of the group s (self)training sessions in order to lead participants to the extent of their autonomy in their personal and professional transformations. The results obtained in the formative processes have shown the need to develop activities of mathematics teaching as a contribution to overcome the conceptual difficulties of the teachers, apart from their (self)reflections about themselves and the educational processes in which they belong. The results raised some propositions about (self)training workshops that may be incurred in practices to be included in the curriculum frameworks or materialize as a strategy of pedagogical work in training courses for teachers of mathematics. Also, they can constitute an administrative and educational activity to be instituted in the public schools of Basic Education

Ateliês de história e pedagogia da matemática: contribuições para a formação de professores que ensinam matemática nos anos iniciais

This paper presents a discussion about the use of the History of Mathematics as an educational resource and conceptual mediator in the formation of teachers who teach mathematics in the years of elementary school. It was a qualitative action method, in order to show the importance of holding workshops of History and Pedagogy of Mathematics as contribution to overcome the conceptual difficulties of teaching and teachers regarding the content covered in the course of education and afterwards they have to teach in the early of elementary school. We assume that understanding the historical, social and cultural comprehension as a conceptual and didactic focus effectively nurture the pursuit of a teaching and learning of mathematics students safe and justified in order to contribute to overcoming the difficulties of teaching and learning usually occurred in the classroom of the early years. In this sense, we organized a study group formed by students of Bachelors in Education and Mathematics at the University of Piauí. We developed five training workshops in History and Pedagogy of Mathematics, with a workload of 20 hours each and four follow-up sessions and advicement, totalizing 180 hours. The purpose of workshops was to develop studies on the History of Mathematics that could support the formation of a conceptual and didactic group with a view to prepare teaching materials and activities based on information drawn from undertaken historical studies .The products designed were used in formation of the group itself and will later be used in training teachers of public school in Teresina, in the form of workshop of History and Pedagogy of Mathematics in order to overcome problems arising from teaching and conceptual this education degree in Education Based on the obtained informations it was possible to suggest new referrals procedural level of education and university extension that may contribute to the reorientation of initial and continuing training of teachers in the early years elementary school

Geometria e simetria nas rendas de bilro: contribuições para matemática escolar

A tese tem como objetivo descrever e analisar características e princípios dos padrões das rendas de bilro de modo a estabelecer relações com a Matemática escolar, principalmente, no que se refere aos tópicos como Geometria, simetria, isometria, área, perímetro, entre outros. Desse modo, elaboramos atividades didáticas, com base na Matemática explorada nos padrões da criação da renda de bilro, visando concretizar um exercício investigatório nas aulas de Matemática, de modo que, sejam estabelecidas relações conceituais entre a prática investigada e os conteúdos da Matemática escolar. Para satisfazer esses objetivos, buscamos apoio metodológico na pesquisa bibliográfica, do tipo documental em catálogos como o da Professora Valdelice Girão (1984) e também o de Dawson (1984). Realizamos também a pesquisa empírica durante as visitas ao Museu do Ceará e ao Centro das Rendeiras na Prainha, em Aquiraz, no Ceará. Para realizar as atividades didáticas, apoiamo-nos em Mendes (2009). Consideramos relevante essa abordagem de ensino porque pressupõe a experiência direta do aprendiz com situações reais vivenciadas, nas quais a abordagem instrucional é centrada no aluno. Desse modo, concluímos que para o ensino de conteúdos como Geometria, simetria, isometria, relação entre perímetro e área, entre outros que são abordados na Educação Básica, os modelos decorrentes da criação renda de bilro e outros modelos já descritos na tradição cearense podem ser usados como artefato cultural na criação de atividades didáticas

As crenças docentes sobre a criatividade a as práticas pedagógicas criativa: o caso do programa do ensino médio inovador no RN

Estamos vivendo no século da criatividade em que os sujeitos precisam ser estimulados a criar e inovar nos processos de aprendizagem escolar. Nesse sentido, a criatividade precisa ser compreendida como um bem cultural, um direito de todos e uma condição histórica e cultural do sujeito, e não como uma capacidade inerente ao sujeito ou pertencente alguns poucos eleitos. Para que a criatividade do aluno seja estimulada, faz-se necessário, dentre outros elementos, que o conhecimento profissional do professor considere as crenças como componente de seu processo de profissionalização com o objetivo de reconhecer o seu papel e influências como formas de nortear as ações profissionais docentes. Para tanto, a presente tese tem o objetivo de estudar as crenças dos professores sobre a criatividade dos estudantes no Ensino Médio Inovador. O ensino, nessa perspectiva, mais especificamente, o ensino médio precisa inovar-se, e nesse processo, o Programa Ensino Médio Inovador PROEMI emerge como uma das iniciativas das políticas públicas educacionais vigentes. Para tanto, no intuito de fundamentar as nossas discussões dialogamos com autores que discutem a criatividade no contexto da educação, às crenças, o conhecimento profissional do professor e o ensino médio. Nessa pesquisa, 207 professores que atuam no ensino médio em escolas estaduais na cidade de Natal e sua Região Metropolitana dentro do PROEMI constituíram-se em nosso público-alvo. O instrumento de coleta de dados foi um questionário normativo de crenças contendo perguntas fechadas e abertas. Para a organização dos dados utilizamos os softwares estatísticos R. 2.15.1 e o Modalisa. O tratamento dos dados se deu mediante análises estatísticas como a análise descritiva dos enunciados, da média, do desvio padrão e a Análise de Componentes Principais ACP em relação aos resultados oriundos das perguntas fechadas e a análise de conteúdo em se tratando dos resultados referentes às perguntas abertas. Os resultados corroboraram com a tese de que os professores apresentam em suas crenças a predominância do enfoque tradicional ou clássico da criatividade, ou seja, creem-na como algo inato ao ser humano e que se desenvolve independentemente dos fatores sociais e culturais. No tocante às principais características do aluno criativo, a autonomia e o alto grau de originalidade em sua aprendizagem se destacaram, dentre outras características. Suas crenças, em relação aos elementos que inibem a criatividade do aluno apontaram que a escola, ao privilegiar os conteúdos escolares compromete a criatividade dos alunos e sobre os elementos que favorecem, destacaram-se as áreas da Arte, da Educação Física e da Literatura como disciplinas, que preferencialmente, desenvolvem a criatividade dos alunos no contexto escolar. Assim, constatamos que as crenças dos professores se configuram de forma reducionista e inatista e que precisam, urgentemente, ser repensadas para que não continue a comprometer o desenvolvimento da criatividade do aluno no contexto escolar, e nesse caso, as crenças se constituem em um dos elementos básicos da profissionalização docente que precisam constantemente ser repensadas e incluídas nas discussões sobre a formação e atuação docente, principalmente, dentro do PROEMI que tem como objetivo principal inovar e estimular a criatividade dos alunos no ensino médio