947 resultados para Teorema fundamental do cálculo


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This work is located at the shield of research that defends the use of Mathematics History, based on the utilization of historical artifacts at teaching activities, at Mathematics classrooms, and at graduation courses for teachers of Elementary School and of the first grades of High School. The general objective is to examine the possibility of the use of historical artifacts, at teaching activities, at graduation courses for teachers of Elementary School and of the first grades of High School. Artifact, at this work, is comprehended as objects, documents, monuments, images and other kinds of materials that make sense to the Human actions at the past and that represent what have been said and done at the Human history. At the construction of the theoretical-methodological way of the research we have based ourselves upon the ideas of the authors that are engaged at the teachers formation; at researchers adherents to the use of Mathematics History (MH) as a methodological resource, and at studies accomplished that elucidate the role of the artifacts at the history and as a mediatory element of learning. We defend the thesis that the utilization of historical artifacts at teaching activities enables the increasing of the knowledge, the development of competencies and essential abilities to the teacher acting, as well as interact at different areas of the knowledge, that provides a conception of formation where the teacher improves his learning, learning-doing and learning-being. We have adopted a qualitative research approach with a theoretical and pratic study disposition about the elements that contribute to the teachers works at the classroom, emphasizing the role of the Mathematics history at the teacher s formation and as a pedagogical resource at the mathematics classroom; the knowledge, the competencies and abilities of the historical artifacts as an integrative link between the different areas of the knowledge. As result, we emphasize that the proposition of using the MH, through learning activities, at the course of teacher graduation is relevant, because it allows the investigation of ideas that originate the knowledge generated at every social context, considering the contribution of the social and cultural, political and economical aspects at this construction, making easy the dialog among the areas and inside of each one The historical artifact represents a research source that can be deciphered, comprehended, questioned, extracting from it information about knowledge of the past, trace and vestiges of the culture when it was created, consisting of a testimony of a period. These aspects grant to it consideration to be explored as a mediatory element of the learning. The artifacts incorporated at teaching activities of the graduation courses for teachers promote changes on the view about the Mathematics teaching, in view of to privilege the active participation of the student at the construction of his knowledge, at the reflection about the action that has been accomplished, promoting stimulus so the teachers can create their own artifacts, and offer, either, traces linking the Mathematics with others knowledge areas.

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The 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

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Cette étude appartient à l un des principaux défis de l éducation dans l actualité qui est la production de connaissances concernant la mort comme objet d investigation théorique et empirique dans le domaine éducationnel. Des recherches récentes signalent le besoin d une éducation contemplant des études sur la mort et montrent l école tel qu un lieu de débats et reflexions à propos de ce thème. Cette reflexion est relevante et fondamentale, étant donné que la mort fait partie du cycle de la vie et se trouve présente dans les contenus scolaires des différents domaines de la connaissance. Ce travail a, donc, l objectif d analyser les signification attribués à ce concept mort et la relation qui s établit entre eux et la pratique des professeurs de l enseignement fondamental. Il adopte en tant que référentiel les principes de la recherche qualitative du type étnographique (André, Chizzotti et Meksenas), dans une approche socio-historique et en ce qui concerne la formation et le développement des concepts (Vygotsky, Kopnin, Guetamanova et Ferreira). La participation des professeurs a été faite par l observation participante, registres en cahier de bord et application d un instrument de construction de données pour l appréhension des significations attribués aux concepts qui sont à la base de la pratique de cinq enseignantes des premières séries de l Enseignement Fondamental d une école publique du réseau d enseignement de l État du Rio Grande do Norte située dans la Zone Sud de Natal. De ce fait, les analyses et les interprétations des observations de la pratique dans la salle de classe et des réponses aux quinze questions liées au thème ont permis de construire les significations des concepts qui appuient les pratiques enseignantes de ces professeurs, tout en mettant en relief la fragmentation et la désarticulation entre les expressions décrites dans les questionnaires et les pratiques développées en salle de clase. Ces reflexions mettent en évidence la nécessité de re-penser l articulation entre l énnoncé et la pratique des professeurs à propos de cette thématique au cours d une formation initiale et continue

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The discussion we have established in this study is about how the practice is developing educational projects based on work with because the methodological choice of the teacher. The study of an ethnographic qualitative approach was conducted with a group of six teachers in two public schools in School Administrative Zone north of the city of Natal / RN. Data were constructed from semi-structured, reinforced by the direct observation of the practice of teaching of teachers. The goals outlined were to identify the reasons why the option for the project, listing the benchmarks that subsidized their construction, the observation of everyday experience in educational planning and development of projects developed. In the light of information we can notice a complex and even contradictory, which is confusing the concepts and practices are weakened. The analysis revealed inconsistencies between theory and practice in working with projects, the fruit of little theoretical development of teachers. The adoption of the project as a methodological option has meant a change in direction of the effective action didactic. Reflects on this situation, it was concluded that there is a need to broaden the understanding of the significance of this type of work, covering the different dimensions that involve the practice of research, research and training of teachers. Even preventing the intentions and initiatives of the teachers, it must be emphasized is the process of learning within an approach that focuses the process of learning in multiple dimensions, inter-relational, both the capabilities of students in the areas of knowledge.

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Metaphorically, research is presented as a journey by sea, having as object of study the social representations of Continuing Education for teachers of elementary school and as aim, to analyze them in comparison of participants from state and municipal systems, located in Natal-RN, Brazil .They have contributed to the achievement of this objective the voices of 158 teachers, the vast literature on training in professional development and the theoretical formulations proposed by Moscovici and colleagues, with relevance to the Central Nucleus Theory advocated by Abric. The corpus resulting from evocations about continuing education, as well as teachers' justifications were submitted to different computer methods/techniques, through the EVOC ALCESTE Programs, respectively, providing the opportunity to highlight a network of interconnections between the likely core and the production of discourse. Although the educational ideologies that underlie social perception of the state teachers are anchored in New School and technicist concepts and the teachers in the city tend to an ideology of social interaction, the choice of working with the symbolic field identified the political-social commitment of groups with the impacts of training on learning of their students

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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

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Ce travail s'inscrit dans le cadre du débat autour de l'organisation du corps enseignant dans l'Enseignement Fondamental. Son objectif est de couvrir les limites et possibilités de la mise en application de la pratique interdisciplinaire dans les cycles I et II de l'enseignement fondamental à partir des sens attribués, par les enseignantes, à la pratique interdisciplinaire développée par elles mêmes, à leur école. L'étude défend la pratique interdisciplinaire non pas comme étant descriptive mais construite dans le vrai contexte de l'école. La méthodologie utilisée est basée sur les principes théorico-méthodologique de l'entretien compréhensif et de l'analyse de contenu. Parmi les principaux résultats de l'enquête, ressortent les limites pour la pratique de l'interdisciplinarité, situées dans le champ théorique en ce qui concerne l‟incertitude théorique sur le terme et sur le non-accès à des théoriciens qui puissent discuter la question et sur le champ de l'organisation du travail pédagogique, qui ne prévoit pas d'espace de travail collectif entre professeurs des différents terrains de la connaissance. Les possibilités proportionnées par la pratique interdisciplinaire se trouvent dans sons importance pour élargir la vision de monde du professeur et de l'élève, dans son potentiel de formation continue, pour motiver la quête à des nouvelles connaissances, des nouvelles formations pour l'élève et professeurs pour qu'ils agissent auprès des difficultés de manière plus compétente et critique. Il signale la nécessité d'un besoin institutionnel en ce qui concerne la formation continue des enseignants et l'organisation de l'espace/temps de l'école de façon à motiver les professionnels à la recherche et à la consolidation de connaissances autour de l'interdisciplinarité et des multiples champs de la connaissance ainsi que le travail collectif

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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

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This article refers to a research which tries to historically (re)construct the conceptual development of the Integral and Differential calculus, taking into account its constructing model feature, since the Greeks to Newton. These models were created by the problems that have been proposed by the history and were being modified by the time the new problems were put and the mathematics known advanced. In this perspective, I also show how a number of nature philosophers and mathematicians got involved by this process. Starting with the speculations over scientific and philosophical natures done by the ancient Greeks, it culminates with Newton s work in the 17th century. Moreover, I present and analyze the problems proposed (open questions), models generated (questions answered) as well as the religious, political, economic and social conditions involved. This work is divided into 6 chapters plus the final considerations. Chapter 1 shows how the research came about, given my motivation and experience. I outline the ways I have gone trough to refine the main question and present the subject of and the objectives of the research, ending the chapter showing the theoretical bases by which the research was carried out, naming such bases as Investigation Theoretical Fields (ITF). Chapter 2 presents each one of the theoretical bases, which was introduced in the chapter 1 s end. In this discuss, I try to connect the ITF to the research. The Chapter 3 discusses the methodological choices done considering the theoretical fields considered. So, the Chapters 4, 5 and 6 present the main corpus of the research, i.e., they reconstruct the calculus history under a perspective of model building (questions answered) from the problems given (open questions), analyzing since the ancient Greeks contribution (Chapter 4), pos- Greek, especially, the Romans contribution, Hindus, Arabian, and the contribution on the Medium Age (Chapter 5). I relate the European reborn and the contribution of the philosophers and scientists until culminate with the Newton s work (Chapter 6). In the final considerations, it finally gives an account on my impressions about the development of the research as well as the results reached here. By the end, I plan out a propose of curse of Differential and Integral Calculus, having by basis the last three chapters of the article

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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

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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

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Esta tesis (desarrollada en la Base de Pesquisa, Formação e Profissionalização Docente da UFRN) concentra su ámbito de interés en el problema de la formación, de la profesionalización del pensamiento del profesor, buscando investigar las Teorías Implícitas de los estudiantes del Curso de Pedagogía sobre la docencia en los años iniciales de la Enseñanza Fundamental. La emergente necesidad de términos acceso a las Teorías Implícitas de estudiantes de Pedagogía (futuros profesores) sobre la docencia en los años iniciales de la Enseñanza Fundamental, a través de un instrumento de pesquisa que posibilite su aplicación en varios contextos formativos para contribuir con su proceso de profesionalización docente, constituye el problema analizado. La pesquisa tiene como objetivo elaborar un instrumento investigativo para estudiar las Teorías Implícitas de los profesores sobre la docencia en los años iniciales de la Enseñaza Fundamental. La complejidad del estudio nos ha llevado a integrar diferentes procedimientos metodológicos, según orientación del paradigma sociocultural, tales como: estudios exploratorios, a través de la revisión bibliográfica de la literatura especializada y técnica de trabajo creativo en grupo; técnicas normativas y psicométricas. A través de los estudios exploratorios identificamos y configuramos tres teorías profesionales de la docencia en los años iniciales de la Enseñanza Fundamental, las cuales presentan una importante relación con el Estado: la docencia como actividad laica, la docencia como actividad técnica y la docencia como actividad profesional. Para la configuración de la teorías, definimos siete subdominios estructurales de la docencia: función docente, concepción de aluno, contenidos de enseñanza, gestión de aula de clase, proceso formativo, condiciones de trabajo y naturaleza del grupo profesional. El cuestionario normativo ha sido el instrumento orientado para investigar las representaciones de los estudiantes a nivel de conocimientos establecidos y reglamentados por la cultura, como condición básica para investigar sus Teorías Implícitas sobre a docencia. El estudio ha constatado que los subdominios determinados para la comprensión del objeto de estudio están presentes, de manera reincidente, en la literatura especializada como los son representativos en las identificaciones de los estudiantes investigados. Hemos concluido que las teorías configuradas para caracterizar la profesión docente en los años iniciales de la Enseñanza Fundamental hacen parte de la estructura de conocimientos de los estudiantes sobre la docencia, aunque los enunciados de las teorías, como actividad laica y como actividad técnica, no presente índice de tipicidad y de polaridad muy significativo cuanto aquellos relativos a la teoría de la docencia como actividad profesional. Las Teorías Implícitas de los estudiantes enseñan que ellos comparten elementos o rasgos de todas las teorías de la docencia, aunque se revelen más predispuestos a la docencia como actividad profesional. El estudio orienta la aplicación del cuestionario reglamentado a un grupo de profesores actuantes en el nivel de enseñanza en cuestión, para que averigüemos si los enunciados que hacen parte de la estructura de conocimientos de los profesores son los mismos que componen la estructura de conocimiento de los estudiantes, de modo a fortalecer la validación de nuestro instrumento de pesquisa

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This report aims to present the results of research on the possibilities and limits of Supervised Traineeship in a the course of Training of Teachers in Service of the early years of primary education conducted through an agreement between the Federal University of Piauí and the Teresina city council (PI) UFPI/PMT, offers subsidies to teaching practices that address the reality of students who live, work and/or studying in school located in rural areas. The research is based on a theoretical and methodological approach that places the object of study in the critical perspective and using procedures such as: literature (bibliographical research), documentary analysis, semi-structured interview and photographic record. We researched 10 (ten) teachers of the course promoted by UFPI graduating in 2006 and who develop teaching activities in schools located in rural areas in the city of Teresina-PI, 02 (two) teachers who are trainee supervisor of UFPI and the coordinator of the course. The analysis evidenced that the object, historically, educational policies have changed, but did not break the traditional patterns of teacher education, enough, especially in the curricular proposals in light of the changes required by the information and global society. We also note that in the supervised training, the process of critical reflection on teaching practice was made possible, in part, and raised the reconstruction of specific knowledge to make teaching in order to conduct the teaching-learning process articulating different realities of primary teaching and facing situations due to conservative practices in relation to education in rural areas. It contributed, therefore, this curricular component to resize, in part, the pedagogical action of the teachers graduated. The study also drives the research toward to similar studies in the perspective of overcoming the current model of teacher training that does not correspond to the demands of society in change and to the crisis of capital, with immeasurable consequences in the workplace. The contemporary claims for a University to form professionals capable of directing the destiny of society, where teacher training is a social and political demands on which is co-responsible

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This paper aims to investigate the formative needs of Elementary School Arts teachers at municipal public schools in Natal, Rio Grande do Norte, working in the initial grades. The research was developed using the qualitative approach and the investigation can be classified as an action research-inspired collaborative, distinguished by mutual collaboration among all participants, as well as a reflection upon their practice. Conducted with four Arts teachers of Municipal Education de Natal/RN, this work triggered a (re)thinking of teaching practice in Arts, discussing the teachers' formation and encouraging a group reflection about their academic and professional path. Their motivation towards teaching was also discussed, as well as the way their progress as Arts teachers and the contributions and limits of college education, also including experiential knowledge as a possibility of formation. The main formative needs suggested by the research were knowledge on child development and child learning, and the need of an Arts curriculum proposal for the initial grades of Elementary School. From those data, a reflexive context was built with the participant teachers to give a new meaning to Arts teaching practice in the first years of Elementary School. Finally, it was shown that the Arts teacher formation must be broad and involve not only specific knowledge on Arts, but also knowledge about childhood. It was also clearly shown that a curriculum review in education undergraduate courses must be considered, besides the offering of a continual formation to teachers already giving classes. Concerning the Arts curriculum proposal, it should be done based on a work joining officials of Municipal Education, research and formation institutions and teachers working in the first years of Elementary School. Finally, the work highlights the Arts are essential in all levels of Elementary School, since its first years, and it must be taught and learnt since childhood

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Study about the teaching-learning process in History, which intents to point limits and possibilities to this process, starting from its characterization and analysis and understanding of the concepts of history, time, society and culture, used by teachers and students. The field research was performed in the Municipal School of Basic Education Zumbi dos Palmares, located in the city of João Pessoa, Paraíba State, in the period between 1996 and 2006. To achieve the objective of the study, a number of research instruments were used, amongst which, interviews, questionnaires and exercises emphasizing conceptual learning. The theoretical-methodological premises of the qualitative research justify the use of these various instruments, and serve as base for the interpretation and analysis of the data. This study demonstrated that some limits and possibilities that are found in the teaching-learning process in History are originated in the school context of the 1st phase of basic education and remain in the 2nd phase of this education level, partly, because of the understanding that teachers and students have regarding the concepts of history, time, society and culture