Um estudo sobre a concepção de paradoxo segundo o pensamento de Augustus de Morgan

This work aims to analyze the concept of "paradox" posed in the work of The Budget Paradox (1872) of mathematical and logical English Augustus De Morgan (1806-1871). Here it is important to note that a large part of this book consists of re-prints of a series of writings by the author in journal Athenaeum, where its performance as auditor of literature. The tests refer to some scientific work produced between the years 1489 and 1866 and the rules of selection for the composition of the work is, basically, the methodological aspects used in the completion or disclosed by such scholars. The concept of paradox is presented in two distinct moments. At first, we found a study of definitions for the term in a philosophical approach, characterizing it as something that requires further investigation; which was complemented with the classic examples of a scientific context. In the second, we present a concept advocated by De Morgan and, under this perspective, that he conceptualized the "paradox" is directly related to the non-usual methods employed in the formulation of new scientific theories. In this study some of these scientific concepts are detailed, where, through the redemption history, engaging in issues of our study Mathematics, Physics, of Logic, among others. Possession of the preliminary analysis and comparison with the design of De Morgan, it became possible to diagnose some limitations in the conceptualization suggested by the author. Further, evidenced, in front of the cases, the nonlinearity of the process of production of knowledge and hence the progress of science

Itinerários e marcas na formação do sujeito formador: reflexões acerca de um caminho na educação matemática

This Study inserts in Mathematical Education & Education that search to investigate the (self) formation of formers that gets graduation e pass to graduate others that get graduation and are formers in Mathematical Education. This Is a qualitative search in a perspective from search-formation.The work is formed of four topics. First topic talks about : The self-formation of formers. Second topic: at way of suppositions theorical-methodological from search. Third topic tells over: The life of a former life. Fouth topic A Station called Ubiratan D´Ambrosio created in his reverence and for build all the Knowledge´s Corpus developed by his studies and searches. It´s in sense of come and go from knowledge created at action by mankind to get finality of Transcendency and Survive. Look for to investigate aspects of academical, professional and personal life where are translated in language, thinking and practices oriented for one know-how holistical and transdiciplined in a reflexion, search and the critical it constitute to be a Professor, Teacher, Searcher and Etnomathematic that confered him the merit in 2005 the Prize Félix Klein, that declared Valente (2007), maximum distinction that can receive someone from Mathematical Education. The results point that the narratives of life´s stories are prominences to one re-direction of teach practical in formation´s courses of Mathematical teachers, opening spaces for what the teachers and particularly of Mathematical thinking and take position about your process of formation to be Formers. The Study also given possibilities to propose fourteen stoppages in Station that are beginnings with direction that emerge from studies and searches about the trajectory of life of Professor Ubiratan D´Ambrosio in perspective of re-signify the formative process in education and Mathematical Education

Utilizando processos geométricos da história da matemática para o ensino de equações do 2º grau

The present work had as principal objective to analyze the, 9th grade students understanding about the solutions of an equation of the 2° degree, using geometric processes of the History of the Mathematics. To do so, the research had as base the elaboration and application of a group of teaching activities, based on Jean Piaget's construtivism. The research consisted of a methodological intervention, that has as subjects the students of a group of 9th grade of the State School José Martins de Vasconcelos, located in the municipal district of Mossoró, Rio Grande do Norte. The intervention was divided in three stages: application of an initial evaluation; development of activities‟ module with emphasis in constructive teaching; and the application of the final evaluation. The data presented in the initial evaluation revealed a low level of the students' understanding with relationship to the calculation of areas of rectangles, resolution of equations of the 1st and 2nd degrees, and they were to subsidize the elaboration of the teaching module. The data collected in the initial evaluation were commented and presented under descriptive statistics form. The results of the final evaluation were analyzed under the qualitative point of view, based on Richard Skemp's theory on the understanding of mathematical concepts. The general results showed a qualitative increase with relationship to the students' understanding on the mathematical concepts approached in the intervention. Such results indicate that a methodology using the previous student‟s knowledge and the development of teaching activities, learning in the construtivist theory, make possible an understanding on the part of the students concerning the thematic proposal

Os saberes dos professores da escola fundamental: concepções sobre as abordagens geográficas / Márcia Maria Dias

El presente trabajo, intitulado, Los saberes de los profesores de la Escuela Fundamental: concepciones sobre los abordajes geográficos objetiva investigar los saberes del profesor de los años iniciales de la Escuela Fundamental en relación a la naturaleza especifica de los abordajes geográficos y reflexionar como en el proceso de investigación colaborativa los profesores aprendieron los saberes específicos de los abordajes geográficos vinculando sus asimilaciones teóricas a un determinado nivel de concepción . Buscamos con base en la investigación cualitativa del tipo colaborativa y en la aplicación de diferentes procedimientos técnicos-metodológico, responder a nuestras cuestiones de estudio: ¿Cuales los saberes geográficos que los profesores construyeron en la trayectoria de sus formaciones? ¿Cómo, en el proceso de investigación colaborativa, los profesores aprendieran los saberes específicos de los abordajes geográficos? Conforme principios de la perspectiva socio-histórica. Así, utilizamos específicamente las narrativas tópicas (orales y escritas) con base en los ejes norteadores Como aprendí y lo que aprendí referentes a los saberes geográficos constituidos en la trayectoria de formación, para realizar el diagnostico de los conocimientos previos de los profesores. El proceso reflexivo y la profundización del estudio ocurrieron, respectivamente, por medio de los Seminarios de Estudios Reflexivos y de los Ciclos de Estudios Reflexivos indicando la concepción de aprehensión de los saberes propuestos en esa construcción científica. Los postulados teóricos de Ferreira (2007), Charlot (2000, 2005), Tardif (2002), Tonine (2003), Soares (2000), Moraes (2005), Pimenta (2007), entre otros, proporcionaron comprensión sobre la temática en estudio. La pesquisa ocurrió en una acción colaborativa en la escuela pública de la ciudad de Natal/RN, en el Barrio de Nova Descoberta, en el turno matutino, con tres colaboradores, que participaron voluntariamente de ese proceso: Angico, Jacarandá y Carvalho desarrollaron sus prácticas pedagógicas, en los 1ºs y 4ºs años de la Enseñaza Fundamental. Los resultados obtenidos de los análisis, apuntaron un alcance descriptivo de las concepciones de los colaboradores sobre los saberes de los abordajes geográficos, que se refieren a enumeración de los aspectos característicos del fenómeno concebido, aunque nos haya empeñado para los alcances transformadores de nuestras concepciones

Educação matemática, ciência e tradição: tudo no mesmo barco

Les connaissances de la tradition et position de la Science dehors pour un non-hiérarchique dialoguez qui frappe pour les distinguer mais ils sont undésavouer inséparable étant donné les compléments ils composent. Cet essai assume la possibilité de ce roi de dialogue dans un place spéciale: la classe. Sur ce qui vient au connaissance de la tradition, le centre remarquable est pour la construction de bateaux du travail manuel, una pratique culturellement déployé dans la ville d'Abaetetuba, dans le État de Pará, Brésil. En revanche, la Science est concentrée par le le contenu d'école a adopté dans l'Ensino Fundamental (École primaire). La construction du dialogue est faite en utilisant des activités de l'enseignement qui accentuez des aspects géométriques (solide, géométrique, angles et symétries) aussi bien que par information qui implique le tableau, poésie, histoire, géographie et physique - les deux inspiré dans le chiffre de bateau résumé dans un CD-ROM interactif. Les activités ont eu lieu dans D'Escola Ensino Pedro Teixeira Fondamental (Abaetetuba-Pa), avec étudiants du 6e niveau (plus spécifiquement avec un groupe de 13 étudiants) d'août à octobre2004. Ethnomathématiques et transdisciplinarité sont le support théorique sous-jacent du projet. Dans résumé, c'est possible pour dire que l'interaction entre Science et Tradition, à travers activités au-delà lesquelles vont le le contenu a restreint à mathématiques d'école, contribuées à,: identifiez le contenu a appris pas sur dans série antérieure; renouveler le rôle joué par école dans ses fonctions didactique pédagogiques; réduire le isolement entre information passée historique et les étudiants présent culturel; indiquer des obstacles à l'érudition des mathématiques intéresser aux aspects cognitifs et behavioristes; et provoquer un participation affective qui rôle principal à la qualité d'apprendre l'école contenu aussi bien que les connaissances de la tradition

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

Um estudo sobre o estágio supervisionado na formação inicial de professores de matemática na Bahia

This work arose from our concerns with the issues of teacher training for early childhood education. From the difficulties encountered as a novice teacher in elementary, we deem important to research training needs of these professionals. Thus, we define the objective of this research to investigate the training needs of novice teachers teaching Early Childhood Education/Elementary school. Our work fits in Educational Research Qualitative Approach, and its construction procedures of the semistructured interview data and document analysis. Our empirical field was made up of schools in the metropolitan region of Natal / RN, offering kindergarten / elementary school. The subjects are five teachers who act as holder of the elementary school class and have 0-3 years of teaching practice, characterizing the second Huberman (2007) as novice teachers. Data analysis, based on principles of content analysis, three themes emerged: Beginner Teaching Professor in Early Childhood Education / Preschool; Reasons explaining the difficulties Faculty / Formative Needs Teaching and Training in Early Childhood Education / Elementary school, from the Training Needs Analysis, with their respective categories, subcategories, contributing to our understanding of the subject matter. The entry into the profession is marked by mixed feelings of euphoria and fear, where there seems to be a "clash" with reality. The difficulties are related to the planning / execution of activities, meet the individual needs of learning and assessment of children. As a strategy to overcome the difficulties the teachers exercise the action-reflection-action in their practices and seek continuous updates in the theoretical and methodological framework of early childhood education. The reasons that define these difficulties may be related to the teacher, school, family, and students of these institutions. In experiencing these difficulties has outlined the need for teacher training, among which stand out studies on ethics in teaching with children, the concept of children and their childhoods, peculiarities of teaching / learning in preschool, toys and legal determinations on early childhood education, multi-language and expressions in early childhood education, specific content areas of knowledge, among others. Furthermore, studies on the theoretical as Piaget, Vigotsky, Maria Carmen Barbosa and Emily Smith. For these professionals to be a professional early childhood education is: like children, be patient and careful, have specific theoretical and practical training for teachers in kindergarten, being able to improvise with seriousness and competence and get updates on continuing education. The surveys, together with the authors and teachers, to confirm our understanding that the training needs of beginners may be related to shortcomings in the initial and continuing 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

Concepões e práticas pedagógicas de professoras da educação infantil na inclusão de alunos com deficiência

This research focuses on inclusive in childhood education. Its purpose was to investigate and analyze the conceptions and expectations of teachers of childhood education, childhood education center form Natal/RN, on the inclusion students with disabilities, school and pedagogical practices developed and implications for students learning. Theoric base of the cultural historic perspective, the search took by qualitative analysis of numbers form the case study method. It was used methodological procedures: documentary analysis, participant observation, field journal and semi structures interview.Three teachers participated in the survey of that school had student with disabilities in their classrooms. These teachers were called: Rapunzel, Snow white e Pretty. The teacher s nouns involved the refered kind of education. The data obtained from the observation indicated the regular school of childhood education provides educational practices that promote the participation and participation and development of students with disabilities, live situation that may create barriers to learning and to the development of these children. The analysing data of interview from Bardin content analysis (1994) was based in Cunha s studies (2001) Brun (2006, 2008), Mantoam (2006, 2008), Palacios, Paniagua (2007), among others. The dada showed that correlation and divergence of perceptions and expectations about the issues surrounding inclusion in childhood education. The results shaved that teaching strategies, affective ties, sensitivity and own routine of childhood education are factors that can promote inclusive proposal, but also needs a greater fulfillment individual differences of each child in order to their potentiality. The study also shaved that the negative of pedagogic support to teacher, the ignorance of them as guidelines and strategies that include the student s diversity, the importance having positive conceptions about the learning and development of student with severe learning disabilities and the need for a pedagogic training and of a collective work at school which everybody collaborates : parents, direction, coordination getting inclusive school. Believe that this study pointed relevant issues to be focus new research, since the theme is still lacking in study, therefore emphasize, the importance of conducting research that continuous this job

Quando as professoras se encontram para estudar matemática: saberes em movimento

This text results of a research in an Education Doctorate about teachers, professional background, formation, teaching knowledge and abilities. In this text, it s described the history of a study group in mathematics education composed by teachers who teach mathematics in the 2nd cycle of Ensino Fundamental (5th year of schooling), all belonging to the same school of the municipal public schools network. It presents the trajectory of the collaborative group, in all particularities, singularities, and the constant search to become collaborative. This trajectory was marked by the stories of it s participants in the ceaseless path to constitute teachers, by the sharing of knowledge, by the process of collaboration, by the thinking about the teaching practice, and by the personal and professional improvement of the teachers that form the group. The interpretative and qualitative research had as its investigation field the study group. The data supplied by the collect instruments indicate us that the collaboration between the teachers, the access to specific knowledge of mathematics area, the reflections about the teaching practice in a given context, are paths that lead to and make possible the re-elaboration of the teaching skills by teachers that teach mathematics to the first years

O Programa Pró-Letramento e a formação de alfabetizadores: repercussões nas concepções e práticas de professores cursistas

This paper intents to investigate the repercussions of the Pró-Letramento - Alphabetization and Language Course Program in the practices and conceptions of alphabetization of learning teachers, according to their own perspectives. The program, part of the National Formation Network of the Education Ministry, in partnership with public universities since 2006, is destined to aid the formation of teachers acting in the first three years of public basic education, with the goal of qualifying them to work with alphabetization and improve quality of learning processes and results. This investigation adopted the qualitative research paradigm as well as the Case Study methodology, being our empirical field a Belém do Brejo do Cruz/PB public school. The subjects are five Program graduation female teachers, including the tutor-trainer and four graduated teachers that already teach in the first three years of basic education. The data, gathered with documental analysis, individual and collective semi-structured interview, and non-participant observation, were analyzed according with Speech Analysis principals. Based on those principals, we intersected teachers enunciations, observation sessions registries and the Program s propositions and built interpretations based on theorization taken as fundaments of the investigation, among which we highlight: studies on a criticalreflexive perspective of a teacher s formation; continued formation as a permanent development process; the principals of historical-cultural approach on alphabetization processes and development with the centrality of language; alphabetization in a interactionist approach. The analysis focused on the Program s repercussions: 1) in the teachers conceptions about: 1.1) learning; 1.2) Alphabetization and literacy; and in the practices and conceptions related to: 1.3) alphabetization in a literacy perspective and 1.4) appropriation of the writing system. The corpus analysis evidenced relations of continuity and discontinuity, approach and distancing between the teachers conceptions and the Program s propositions, as well as conceptions/significance of their speeches and related or observed practices. Observing teachers elaborations evidences the repercussion of the Program s formation, whilst also showing gaps and mismatches in their appropriation process in concepts/assumptions as well as teaching propositions. These mismatches involve interaction relationships between teachers and students, with their possibilities and limitations surrounding the Program s knowledge objects complexity, also linking to the social, economical, political, and cultural conditions that involve both the implementation of the Program in each context and the conditions in which alphabetization in public schools are developed, demanding permanent and accompanied formation processes, investments to improve work conditions and valuing teaching

O currículo e as práticas pedagógicas na EJA: concepções e crenças dos professores da escola municipal Francisca Leonísia Cruz

The present investigation deals with the Curriculum and Pedagogical Practices of Young and Adults, EJA, and articulates with the conceptions and beliefs of teachers sitting. The empirical scope of this investigation consisted in the Municipal School Francisca Leonísia, located in the Agrarian Reform Settlement Serra Nova, city of Florânia/RN. Seeks to analyze the relationship between the Curriculum and Educational Practices of Young and Adult EJA - conceptions beliefs of these teachers. This work is based on qualitative research, interpretative character reflective and makes use of documentary analysis, structured interviews and reflective sessions as methodological procedures which ensure the achievement of our goals in research. These procedures allowed us to enter the practice setting and curriculum for teachers to understand how they think, prepare and practice of adult education in school curriculum research field. The documentary analysis provided the rethinking of the curriculum selected references, Political Pedagogical Project and Proposed Course of EJA, from a critical reading of concepts and conceptions given in these references, with a view to construction and reconstruction of concepts that reclaim the identity of young people and adult field, inserted in the Rural Workers Movement landless/MST. As reflective sessions were constituted in spaces of collective training and allowed the group to selfreflection e collective reflection about the ideas and beliefs that permeate the curriculum and guide their practices education in adult education. In these areas of training are also discussed current problems of adult education, the construction of an educational project of the adult education field to, warranties of learning and cultural identity of the adult education field and placed in the context of the MST. Under this view, it is concluded that the conceptions and beliefs of teachers seated directly relate to the curriculum designed, developed and practiced in adult education, as well as the educational practices that permeate the curriculum. This relation is in the midst of adversities of Rural Education, inserted in the Movement of Landless Rural Workers-MST, and requires the commitment of teachers to the necessary changes to an education are critical and emancipatory

Trilhas da inclusão escolar percorridas por uma aluna com paralisia cerebral na EJA: concepções e práticas

On this qualitative study, it has been discussed the school inclusion paths done by a student with cerebral palsy, who we call Liz, and who was also the reference and indirect subject for this study. For the representation of landscapes found, it follows throughout historical, political and pedagogical paths, getting through the case study method references on the current Brazilian educational context, analyzing, which concepts are attributed to the inclusion and which practices are developed by educational managers and teachers in a regular school of the City of Natal/RN. The theory which based this research is supported on Vygotsky's central ideas (1991, 1997, 2004) and his followers. Furthermore, it was essential to bring to this investigative journey a literature which could dialogue with the most relevant aspects of the cultural-historical approach, emphasizing the assumptions of a progressive education tendency, which promotes the subject involvement of his/her work in the world and for the world. This way, it was necessary to seek for theoretical support on assistive technology and on alternative communication, in order to show the importance of establishing other communications, which is, to break away from the conventional pattern established by the school. On this journey it was used procedures for the data construction, such as: observation, conducting semistructured interviews and questionnaires; and document analysis that supported and legitimized the inclusion, besides the permanent field diaries record. On the access paths to this landscape it entered in the Youth and Adults Education (Educação de Jovens e Adultos - EJA), seeking to establish a dialogue among Youth and Adult Education and Special Education. It was verified that, still, there are large gaps in these policies articulation. Among the results obtained it was raised discussions on new scenery, in which Youth and Adults Education (EJA) emerges as prominent mode of the established relationships throughout the school inclusion process. There were target reflections on: the planning and evaluation systematic, the pedagogical articulation among the Youth and Adults Education (EJA) teachers and the multifunctional resource room teacher's actions and the continuous training importance of the educators involved. It was considered, therefore, that the necessary mediations for school inclusion may be sustained if the walkers are involved in a permanent contact with the nature of a proposal from the Special Education inclusive perspective

Currículo e arquitetura escolar: concepções de professoras e equipe gestora do Colégio Nossa Senhora das Neves-Natal-RN

The present study aims to investigate the conceptions of teachers and management team of the Colégio Nossa Senhora das Neves - Natal / RN about curriculum, school architecture and possible relationships established between these components. To develop the study, we rely on the theoretical contributions of Viñao Frago (2001), Escolano (2001); Benconstta (2005), among others, about the architecture school, and with regard to curriculum, ancoramo us in theoretical reflections Silva (2000, 2006, 2008). We assume that the school place is a social construct and as such, reflects the interests of certain groups, to organize, establish ways to condition their unctions and uses. In this space, people's lives is planned, both those who work there, as those who study there. Thus, the architecture school promotes, through representations, signs, symbols and shapes, certain charges that impact the ways of being and acting subjects by establishing appropriation and expropriation of rights and legitimate forms of inclusion and exclusion. Thus, it is an expression of power. A power that is expressed in the form of lead the way people should behave in a certain space. Clarity on these aspects of the architecture school is important, since in the same way that the opinion of several experts is important to discuss the adequacy of school architecture (environmentalists, architects, engineers, planners), the / the teacher / and the / as managers / must also meet the educational nature of the architecture school, so as to present its share of contribution in order to make the post-school conducive to learning multiple. From this perspective, we analyze the concepts of four teachers and eight individuals who are part of the management team of the CNSN, whose views were seized through participant observation, semi-structured interviews and documentary analysis. The construction of the data indicated levels of conceptual curriculum varied, ranging from those rooted in traditional theories of curriculum as those regarding the curriculum tied to discursive and contextual aspects. The conceptions of architecture school, predominantly focused on the aspects of the architecture school materials and most established subject, differently, relations between curriculum and school architecture