Investigação histórica na formação de professores de matemática: um estudo centrado no conceito de função

In this study we analyzed the development of a teaching experience, involving students with a bachelor s degree in mathematics from UFRN, based on the history of mathematics and mathematical investigations with the aim of contributing to the improvement of the teaching-learning of mathematics. The historical investigation tasks were planned and applied in the classroom, focusing on functional thought. The results obtained during the experience were described and evaluated based on authors who support the assumption of investigation and history as an alternative to the learning of mathematics. We emphasize that the material of analysis consisted of a work diary, audio recordings, questionnaires with testimony of the students involved, and, in addition, the assessment of the teacher of that subject. With regard to the mathematical content, the study was restricted to the concept of function, forms of representation and notation. It was evident that students showed great improvement with regard to the necessary formalization of the mathematical contents which were focused on, and to the active involvement of the students at different stages of the study. We can affirm that the completed study certainly represents significant contributions to an approach in the teaching-learning of functional thought

Historiando a política de formação de professores em serviço da UFRN

Les préoccupations gérées par les changements de l éducation nationale poussés par les réformes mises en places par le gouvernement de Fernando Henrique Cardoso, notamment la politique nationale de formation de professeurs, et le besoin de connaître comment ces réformes ont été incorporées par l Université Fédérale de Rio Grande do Norte - UFRN, constituent les questions centrales développées par cette thèse. Cette étude propose à montrer, à partir d une approche socio-historique, la façon comment la législation éducationnelle brésilienne sur la formation de professeurs pour l éducation basique expresse la politique de l État brésilien et, en même temps, comment le PROBÁSICA signifie une réponse de l UFRN à cette politique. En ce sens, cette recherche, selon sa perspective exploratoire, descriptive et analytique a privilégié plusieurs techniques et procédés de collectes des données conforme au modèle de la recherche participative, à savoir : enquête semi- structurée, observations directes, contacts formels et informels; enregistrement des opinions de professeurs, coordinateurs pédagogiques et étudiants; repérage, systématisation et analyses de plusieurs documents. L analyse des données, qui a été faite d une façon fondamentalement qualitative, a révélé que le PROBÁSICA a sa genèse à l intérieur de l UFRN et représente, en même temps, une réponse de cette université à la demande de la catégorie et la politique de formation de professeurs. Nous espérons que cette étude suscite d autres recherches qui développent des discussions sur les relations entre l État brésilien, ses politiques éducationnelles et les pratiques pédagogiques de formation de professeurs

O aluno surdo em classe regular: concepções e práticas dos professores

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

Pedagogia Freinet :mediação para o social, o político e a formação de professores

Ce projet présente dans son premier chapitre une étude historique-bibliographique basée sur la Pédagogie Freinet en France, ainsi que sa formation républicaine, ses courants politiques et idéologiques qui ont moulés l organisation sociale et éducationnelle de ce pays. Ce travail montre le rôle des courants de gauche dans ce processus, cela se reflète aussi sur le jeune Freinet. Les changements opérés dans la décennie de 1950 dans le système scolaire, dans le propre Mouvement Freinet et les ruptures qui ont eues à l intérieur de ce mouvement. Cela se termine avec les directions prises dans les dernières décennies, son arrivée au Brésil et les perspectives actuelles. Le deuxième chapitre aborde la reconstitution historique du Brésil dont sa phase coloniale et impériale. Les événements historiques de la IIIe, IVe et Ve République sont mis en relief avec ceux du Mouvement Freinet. La phase militaire imposée au Brésil et les luttes pour la reconquête de la démocratie. Il se termine avec les considérations sur la LDBEN 9394/96 et l implantation du Curso Normal Superior; un bref historique de la Pédagogie Freinet au Brésil, des thèmes importants travaillés dans le troisième chapitre. Dans ce chapitre une recherche qualitative est décrite basée dans l Etnographie Critique et Multiréférentiellel et aussi dans la Recherche-Action. Elle est développée auprès d un groupe de cinq professeurs des premières classes de l école primaire au collège, inscrites dans le Curso Normal Superior. Les données ont été obtenues à partir de rencontres régulières avec le groupe la médiation didactique , des entretiens, des questionnaires, des observations dans les salles de classe, du travail final du cours, nommé Mémorial de Formation. À travers l ensemble des données, on recherche les apports et l actualité d une proposition pédagogique historiquement firmée pour le développement de la praxis éducative

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

Escola para os filhos dos outros: trajetória histórica da escola industrial de Natal (1942-1968)

This paper presents a reconstruction of the historical trajectory of the Escola Industrial de Natal (Industrial School of Natal), in the period 1942 to 1968, based on the analysis of its cultural, social and pedagogical characteristics in a process in which its educational practices and the individuals who constructed them were getting involved in their actions. In this sense, the concepts of memory and school culture occupied a central place to understand the elements that characterized its administrative and pedagogical organization such as, for example, its curriculum, aims, disciplinary rules, clientele, teachers, leaders and the configuration of the institutional power. Designed to meet the demands of an industrial process that has strengthened in the country, throughout its history, the Escola Industrial de Natal was becoming a space predominantly occupied by individuals, from economically disadvantaged social groups in society, in search of a professional training that would guarantee them the exercise of a profession. The time frame from 1942 to 1968 allowed us to verify the changes caused by the Organic Law of Industrial Education of 1942, and the Law number 3.552, from 1959, in the organizational structure of this school. In this context, a characteristic that was evident was the purpose of making it flow between the students the love for the country, the respect for civic values and the belief that industrial education would be able to boost the country's development, an aspect that reached a bigger dimension from the 1950 s. Marked the disciplinary character of this institution the control over the actions of individuals, developed through its multiple educational practices in specific areas and in the predetermined time, under the constant gaze of those who participated, in some from, in driving this process. On the other hand, the vocational and human training, provided to students, allowed new opportunities for social integration, not only in the state of Rio Grande do Norte, but also in other regions of Brazil. Conversely, during his career, the Escola Industrial de Natal has remained being seen as an organized institution, with good teachers, but intended for the children of others

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

Investigação histórica nas aulas de matemática: avaliação de duas experiências

This study reflects on some procedural aspects about the development of mathematics learning from the experience with investigative activities concerning the resolution of second degree equation, which was tested a proposal for education, supported the use of texts in history of mathematics. The survey was conducted in two stages, taking the first-served basis for the second, which was carried out with a study group remainder of the first experiment. The intention was to investigate how the group participant, known as the study group, involved in the implementation of activities of research in mathematics, supported the use of the history of mathematics. Based on the results achieved during the study, it was possible to understand that the activities of research enable the development of students, range of learning mathematics and the development of skills and expertise for research as a vehicle for construction of their mathematical knowledge. This approach proposed research into the classroom is important, both for prospective teachers of mathematics and for students from elementary school, bringing a new phase for mathematical education that will come to schools

A utilização de espaços de educação não formal por professores de biologia de Natal-RN

La práctica educativa en espacios no formales es un recurso didáctico catalizador de motivación e interese, tanto para alumnos como para los profesores. El crecimiento de los espacios no formales coincide con los cambios recientes en el mundo en los campos sociales, políticos, económicos y culturales. Como una de las consecuencias de esos cambios, tenemos el crecimiento de otras instancias difusoras de conocimientos rompiendo, así, la hegemonía de la escuela. De esa forma, en este trabajo busqué investigar la frecuencia y las formas de utilización de los espacios de educación no formal por profesores de biología, de la enseñanza media, de la Ciudad de Natal (RN). Procuré también, identificar cuales son los espacios de educación no-formal que son utilizados; describir los recursos y las acciones desarrolladas en eses espacios; identificar la existencia o no de interese y la importancia que atribuyen a los espacios para la enseñanza de biología, además de divulgar los espacios utilizados como recursos didácticos. Para alcanzar estos objetivos fueron hechas observaciones de los espacios, aplicados cuestionarios y realizadas entrevistas con los profesores que realizan actividades junto a tales instituciones. Para el análisis de los datos se utilizó tanto el abordaje cuantitativo como cualitativa. Nos basamos en referenciales teóricos de autores que buscan establecer las relaciones entre diferentes modalidades de educación para mejor comprender lo que es la educación no-formal y su trayectoria histórica. Constaté que los profesores utilizan los espacios de educación no-formales, aun la cantidad de visitas al año sea reducida, en virtud de varias dificultades por ellos apuntadas, tales como el transporte, la falta de recursos financieros y de apoyo para viabilizar la visita, entre otros. Verifiqué también que los profesores demostraron un alto interese por los espacios no-formales y apuntaron como principales justificativas para considerarlos importantes para la enseñanza de la biología la posibilidad de establecer conexiones entre la teoría y la practica, además de la complementariedad

Uma investigação histórica sobre os logaritmos com sugestões didáticas para a sala de aula

This study was conducted from a preliminary research to identify the conceptual and didactic approach to the logarithms given in the main textbooks adopted by the Mathematics teachers in state schools in the School of Natal, in Rio Grande do Norte. I carried out an historical investigation of the logarithms in order to reorient the math teacher to improve its educational approach this subject in the classroom. Based on the research approach I adopted a model of the log based on three concepts: the arithmetic, the geometric and algebraic-functional. The main objective of this work is to redirect the teacher for a broad and significant understanding of the content in order to overcome their difficulties in the classroom and thus realize an education that can reach the students learning. The investigative study indicated the possibility of addressing the logarithms in the classroom so transversalizante and interdisciplinary. In this regard, I point to some practical applications of this matter are fundamental in the study of natural phenomena as earthquakes, population growth, among others. These practical applications are connected, approximately, Basic Problematization Units (BPUs) to be used in the classroom. In closing, I offer some activities that helped teachers to understand and clarify the meaningful study of this topic in their teaching practice

Propriedades dos sistemas de numeração: uma sequência didática em uma abordagem histórica

This paper aims to describe the construction and validation of a notebook of activities whose content is a didactic sequence that makes use of the study of ancient numbering systems as compared to the object of our decimal positional numbering system Arabic. This is on the assumption that the comparison with a system different from our own might provide a better understanding of our own numbering system, but also help in the process of arithmetic operations of addition, subtraction and multiplication, since it will force us to think in ways that are not routinely object of our attention. The systems covered in the study were the Egyptian hieroglyphic system of numbering, the numbering system Greek alphabet and Roman numbering system, always compared to our numbering system. The following teachung is presented structured in the form of our activities, so-called exercise set and common tasks around a former same numbering system. In its final stage of preparation, the sequence with the participation of 26 primary school teachers of basic education

Um lugar (in)existente: o "país" de Mossoró" nas tramas da consciência histórica

This work aims to analyze, on the one hand, how the academy has created the spatial term the country of Mossoró and, on the other hand, is to discover, by the teachers testimony, how the History teaching works with this spatiality. The academic production in Mossoró-RN, particularly during the last two decades of the century XX, focuses on the practices that built a historic memory based on political interests of the Rosado family. Therefore, this work is divided in three chapters. In the first one, we identify how the academic production has created a group of meanings related to the country of Mossoró , because it is a way to realize how this place is seeing and understand. In the second one, there is an explanation about the ideology concepts, that structure meanings created by the academic production, as well as the historic conscience that is used to think about the dynamic of teaching History. In the third, we analyze how teachers, expressing their historic conscience, figure meaning to this country of Mossoró

Lembranças de alunos, imagens de professores: narrativas e diálogos sobre a formação médica

Se trata de una incursión histórica por el pensamiento y por la enseñanza médica, discutiéndose la formación médica de manera contextualizada, con el objetivo de comprenderla para interpretarla a través del recuerdo que haya sido fijado por los alumnos. Se dará un enfoque a la mediación pedagógica de esa formación, intentando proporcionar el diálogo entre la historia social de la Medicina y los recuerdos de alumnos, ubicándolas en un contexto histórico-social y cultural, al mismo tiempo en que se ha buscado sujetar las imágenes de los profesores que hayan dejado huellas significativas en la vida de los alumnos, en cuestiones profesionales, sociales y culturales. Se configura, asimismo, una memoria de la formación médica de la Faculdade de Medicina da Universidade Federal do Rio Grande do Norte (UFRN), desde su creación en el 1955, como Faculdade de Medicina de Natal, hasta el 1963, como Faculdade de Medicina da UFRN. Los recuerdos han sido recolectados por medio de entrevistas temáticas con alumnos ya formados de las tres primeras turmas concluyentes, de los años del 1961, 1962 y 1963, de la referida Facultad y fueron interpretadas utilizándose la cartografía como técnica que envuelve la construcción de cuadros interpretativos, teniendo como unidad de análisis las palabras representativas de los elementos constituyentes de la mediación pedagógica, sacadas de las narrativas de los sujetos, que cargan también las imágenes de los profesores que han compuesto dicho diálogo por sus contribuciones para la existencia del saber y hacer de la educación médica en Natal/RN. Aún se comprende que esa Facultad fue creada en un momento histórico-social y cultural en que Brasil y el mundo todavía intentaban encontrar nuevos caminos, después de turbulencias causadas por la Segunda Guerra Mundial, y la intelectualidad natalense visualizaba el encaje de la ciudad en los parámetros de la modernidad. El currículum implantado era técnico/racional, pero al ser interpretado por la acción, a través de la reconstrucción de los recuerdos de los alumnos, en los vestigios de la mediación pedagógica de la formación médica y en las imágenes de los profesores todavía vivas en sus memorias, se vuelve posible entender que a esos alumnos ha sido enseñado: un saber relacional que permitía el diálogo, la transmisión de experiencia y el compromiso médico con vista a un atendimiento a la populación en primer lugar, siguiéndole el sentimiento que fomentaba deseos de ayuda al próximo, siendo los propios profesores el ejemplo, conformándose, así, con un saber contextual, agregado a una participación política y de responsabilidad ética para con la sociedad

Concepções sobre os livros didáticos de geografia: narrativas autobiográficas de professores do ensino fundamental

O livro didático é um complexo objeto cultural, haja vista ser ao mesmo tempo elemento de intermediação nos processos de ensino e aprendizagem, produto comercializado que contém o conhecimento para a formação do aluno e objeto de compra, pelo Governo Federal, para ser distribuído para escolas em todo o Brasil. Configura-se, assim, como um produto cultural composto, híbrido, que se encontra no “cruzamento da cultura, da pedagogia, da produção editorial e da sociedade”. (STRAY,1993, p.77-78). Outrossim, o livro didático, tradicionalmente, é “um dos lugares formais do conhecimento escolar, pelo menos daquele saber julgado necessário à formação da sociedade e dos seus indivíduos” (MEDEIROS, 2006, p.34) e a materialização do seu uso pelo professor encontra-se interconectada pelas representações e conceitos construídos nas múltiplas transições na história de vida docente, tendo em vista que a práxis humana constrói-se numa perspectiva retroativa (do presente para o passado), numa hermenêutica social dos atos individuais. É nesse contexto que se situou a pesquisa, entendida como uma possibilidade de contribuição significativa ao debate da educação geográfica, ao propor a compreensão das concepções construídas nas múltiplas transições na narrativa de vida do docente com o livro didático de Geografia. A pesquisa se definiu como um estudo qualitativo, ancorado nas entrevistas narrativas, o qual abrangeu um levantamento de dados sobre as Histórias de vida de professores/professoras dos anos iniciais do Ensino Fundamental de uma escola da rede pública, no intuito de recorrermos às suas memórias escolares, acadêmica (formação inicial) e profissional para situarmos no espaço-tempo as suas concepções sobre o livro didático de Geografia. O livro didático de Geografia foi a área de interesse escolhida, sendo problematizada a partir do seguinte questionamento: quais as concepções atribuídas pelos professores do Ensino Fundamental aos livros didáticos de Geografia? As ideias dos professores expressas nas entrevistas narrativas da nossa pesquisa confirmam a conjuntura de indefinição e superficialidade teóricometodológica sobre o livro didático de Geografia, cujas concepções ficaram restritas aos seus aspectos descritivos, evidenciando a ausência de atribuições de significados pertinentes a uma reelaboração teórica do narrar produzido, como também, de questionamentos dos princípios organizadores das concepções sistematizadas. Desse modo, as ideias apontadas pelos professores em foco, restringiram-se à enumeração dos aspectos característicos do fenômeno em questão – o livro didático de Geografia – na sua superficialidade, isto é, não expressaram elementos que possibilitassem ver as concepções numa perspectiva macro, destacando-se mais as explicações das partes e das percepções isoladas, do que níveis mais abrangentes de generalidade do referido objeto de estudo. Enfatizamos, por fim, a necessária continuidade da pesquisa, e consequentemente, desse processo permanente de reflexão sobre as concepções do livro didático de Geografia, sendo mister explicitar, portanto, a razão histórica que as norteiam para que se possa buscar uma prática docente mais crítica e propositiva.

A formação da habilidade de explicar no contexto do ensino médio: o que dizem os livros? o que pensam os professores?

The discussion about explanation in knowledge has been made for decades. Through this course, we present different ways of understanding about what is to explain the history: the primitive ethnographic description, the chronicler, the positivist construction of a historical science and historiography of the second half of twentieth century. Nowadays this discussion needs to be continued both in the general framework of scientific practice as within educational institutions as cognitive - linguistic ability. The focus of our research is by the second approach, which is the explanation as cognitive - linguistic ability. The formation of skills, among them, the explaining one, has been studied by the authors as: (NÚÑEZ 2012; JORBA et al, 2000; SANMARTÍ and IZQUIERDO 2000). This research had as general purpose: to study the processes of formation of the ability to explain social revolution in history classes in high school, by teachers opinion and by content as this theme among history books, in order to support the continuing education of history teachers for high school. Th e qualitative based research used instruments of data collection and analysis protocol for the books prepared for this study, and interviews with teachers. For this, the techniques of content analysis and discourse referenced in Bardin and Orlandi , respec tively were used. At first, the instruments for data collection were developed and validated, while in the second, the data were collected, organized and analyzed. From the answers to the questions of the study results shows that: a) in the analyzed books - do not express the work with the definition of Social Revolution, considering the processes for the formation of this definition, the predominant type of explanation has characteristics of multicausality; proposals for teaching are characterized as eclec tic; b) while teachers speech - it is important the students know the definition of Social Revolution, the ability to explain is more linked to didactic explanation in the classroom than the explanation through epistemological sense. These results indicate that the formation of the ability to explain Social Revolution based in Cultural History approach, are not expressed in the analyzed books, but they can serve as an important resource for this purpose. The discourse of teachers has a potential pointing to the possibility of teaching organization and learning process, based on training or upgrading the explanation skill from the theory of stepwise formation of mental actions and concepts by P.Ya. Galperin. For this purpose, the research constitutes a contri bution to support the continued education of history teachers in high school.