O ensino de matemática no Rio Grande do Norte: trajetória de uma Modernização (1950-1980)

This work aims to describe and analyze the process of the mathematics teacher modernizing in Rio Grande do Norte, in the period from 1950 to 1980. For that, we use as theoretical foundation assumptions of Cultural History and memories of the researchers Maurice Halbwach, Ecléa Bosi and Paul Thompson. As methodological tools, we used bibliographical resources and semi-structured interviews, in order to do a historical reconstruct of the mathematics educational scene of institutions and people who taught mathematics in Rio Grande do Norte, or those who participated in the modernization of the teaching of this subject, recovering their training and its practices in teaching. For the analysis of the bibliographical resources, initially we organized in a systematic way the transcripts of the interviews and documents, which were accumulated during the research, so long our thoughts, returning to the theoretical basis of this research, through questioning of knowledge acquired and that guided the problem of our study. The analysis showed that, important moments to modernize the teaching of mathematics in Rio Grande do Norte happened such: (1) Training Course of Lay Teachers in Rio Grande do Norte, in 1965, (2) Course for Teachers in Normal Schools, in 1971 (3) Satelite Project on Interdisciplinary Advanced Communications (SPIAC) in 1973; (4) Lectures of the teacher Malba Tahan, at Natal, from the end of the 50 s, that could be analyzed through the lessons notes of the teacher Maria Nalva Xavier de Albuquerque and the narrative of teacher Evaldo Rodrigues de Carvalho and (5) Courses of the Campaign for Improvement of Secondary Education and Broadcasting (CISEB). Thereby, the modernization of the school s mathematics teaching in Rio Grande do Norte, in the period from 1950 to 1980, was given mainly by disclosure of the Discovery Method and by the Set Theory contents in Teacher Training Courses

Investigação etnomatemática em contextos indígenas: caminhos para a reorientação da prática pedagógica

From the investigation, analysis, discussion and pondering about the activities developed by the lndians from the Porteira hamlet, members of the Xerente community, in the Tocantins state, we developed an investigative and descriptive study about the reality of this people with the aim of helping in the conceptual formation and in the reorientation of the pedagogical practice of the local teachers. In this sense, the undertaken research involved the teachers, the main representatives and experts in that cultural tradition, in order to investigate how the everyday activities (agriculture, food handling, assets distribution among the community members, etc.) and the cultural tradition (log race, body painting, clan division, Xerente numeration, Indian myths and histories, etc.), may enable the contextualization of the mathematics teaching in the lndian School Srêmtôwê of this hamlet, under a more transversal and globalizing perspective of the local and school knowledge. We based this research in the sociocultural conceptions of knowledge generation proposed by D Ambrosio (1990; 2002); Vergani (2007); Oliveras (1996); Gerdes (1991; 2002); Bishop (1999) e Sebastiani Ferreira (1997; 2004). ln the process of this study we propose some viable ways so that the Indian teachers may reorganize their classroom knowledge and actions, based in the strengthening of their history and culture. The observation of some social practices and knowledge as well as of the Xerente traditions helped us to point some possibilities of projection of a didacticalpedagogical dimension of these activities and practices, in the development of the school mathematical knowledge in this community

Ensino de matemática, história da matemática e artefatos: Possibilidade de interligar saberes em cursos de formação de professores da Educação Infantil e anos iniciais do Ensino Fundamental.

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.

Obstáculos superados pelos matemáticos no passado e vivenciados pelos alunos na atualidade : a polêmica multiplicação de números inteiros

In Mathematics literature some records highlight the difficulties encountered in the teaching-learning process of integers. In the past, and for a long time, many mathematicians have experienced and overcome such difficulties, which become epistemological obstacles imposed on the students and teachers nowadays. The present work comprises the results of a research conducted in the city of Natal, Brazil, in the first half of 2010, at a state school and at a federal university. It involved a total of 45 students: 20 middle high, 9 high school and 16 university students. The central aim of this study was to identify, on the one hand, which approach used for the justification of the multiplication between integers is better understood by the students and, on the other hand, the elements present in the justifications which contribute to surmount the epistemological obstacles in the processes of teaching and learning of integers. To that end, we tried to detect to which extent the epistemological obstacles faced by the students in the learning of integers get closer to the difficulties experienced by mathematicians throughout human history. Given the nature of our object of study, we have based the theoretical foundation of our research on works related to the daily life of Mathematics teaching, as well as on theorists who analyze the process of knowledge building. We conceived two research tools with the purpose of apprehending the following information about our subjects: school life; the diagnosis on the knowledge of integers and their operations, particularly the multiplication of two negative integers; the understanding of four different justifications, as elaborated by mathematicians, for the rule of signs in multiplication. Regarding the types of approach used to explain the rule of signs arithmetic, geometric, algebraic and axiomatic , we have identified in the fieldwork that, when multiplying two negative numbers, the students could better understand the arithmetic approach. Our findings indicate that the approach of the rule of signs which is considered by the majority of students to be the easiest one can be used to help understand the notion of unification of the number line, an obstacle widely known nowadays in the process of teaching-learning

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 Ensino de medidas e grandezas através de uma abordagem investigatória

This work relates our experience in an investigative practice in the classroom, carried out in State School Jorge Fernandes , located in Natal - RN, having as objective to validate the applying of a education module about Measures and Largenesses in Primary Teaching. We used the constructivist approach; using to Richard s Skemp (1980) theory in order to explicit the students learning according to their comprehension levels. Initially, we carry out an exploratory research to check the participant s previous knowledge. Then, we developed an intervention to validate an education module, structured from needs pointed out from results of the initial research, analyzing the students advances through the final evaluation, displaying growth stages of group front to the knowledge about the matter approached. Finally, we presented our reflections about our experience; putting forward suggestions of the teachers activities, aiming at contributing to the improvement of their practices in classroom during the approach of subject for us investigated

Um estudo sobre o ensino-aprendizagem das demonstrações matemáticas

Demonstrations are fundamental instruments for Mathematics and, as such, are frequently used by mathematicians, math teachers and students. In fact, demonstrations are part of every Mathematics teaching environment, because Mathematics considers something true when it can be demonstrated. This is in contrast to other fields of knowledge that employ observation and experimentation to validate truth. This dissertation presents a study of the teaching and learning of demonstrations in Mathematics, describing a Teaching Module applied in a course on the Theory of Numbers offered by the Mathematics Department of the Universidade Federal do Rio Grande do Norte for mathematics majors. The objective of the dissertation was to propose and test a Teaching Module that can serve as a model for teaching demonstrations. The Teaching Module consisted of the following five steps: the application of a survey to determine the students‟ profiles and their previous knowledge of mathematical language and techniques of demonstration; the analysis of a series of dialogues containing arguments in everyday language; the investigation and analysis of the structure of some important techniques of demonstration; a written assessment; and, finally, an interview to further verify the principal results of the Teaching Module. The analysis of the data obtained though the classroom activities, written assessments and interviews led to the conclusion that there was a significant amount of assimilation of the issue at the level of relational understanding, (SKEMP, 1980). These instruments verified that the students attained considerable improvement in their use of mathematical language and of the techniques of demonstration presented. Thus, the evidence supports the conclusion that the proposed Teaching Module is an effective means for the teaching/learning of mathematical demonstration and, as such, provides a methodological guide which may lay the foundations for a new approach to this important subject

História da matemática na formação do professor: dificuldades e sugestões

This work is the result of a study that aimed to start scoring difficulties that the math teacher is trying to get a historical formation. Considering that the textbook is the material with which the teacher has more contact, start with reading historical texts present in these books. Choose a theme and choose from that we observed limitations ranging from the search for sources of research in relation to the actual historical content. There are many studies that show the importance of the history of mathematics in teacher education and also in the teaching and learning of mathematics. These works , in particular the work of Feliciano (2008 ) entitled : " The use of history of mathematics in the classroom " , along with the information , experiences and opinions given by Professor Anderson Luís de Azevedo Paulo , in some meetings , point to need for materials for teaching , since they show that recognizes the importance of this knowledge and the ability to use it in the classroom , but several factors have pushed aside , even the texts present in textbooks. From the analysis of some of the work and contributions of Professor Anderson Paulo we pointed out some of the factors that make historical texts being ignored by teachers and among them are characteristics in appearance and content in the text. To assist in the preparation of materials that meet the expectations of the teacher, we present a manual with suggestions and / or features to choose or produce a good text. These suggestions can make the history books more enjoyable and thus approach the teacher of historical knowledge and later encouraged to seek, in fact, a historical formation

Formação docente e conhecimento profissional: desafios para o ensino da matemática na EJA

As for the Education for Youth and Adult (EYA), the challenge of training these teachers is to provide tools to understand and act on the teaching of mathematics. It is realized just how special education in this modality and as such teaching is lacking in an adequate and solid training in the area of knowledge. One of the major problems affecting this type of education is the high dropout and failure rates, and lack of motivation among students. Thus the need to provide differentiated profile with a professional to teach youth and adults students, so that they are able to mobilize didactic-pedagogic knowledge, methodologies and theoretical frameworks that serve as a basis for school-developed teaching practice. This thesis aims to investigate how the math teacher, who acts in adult education from elementary school, has developed its didactic and pedagogical action, and that professional knowledge has been mobilized to teach? It has highlighted the importance of initial and continuing training and professionalization of teachers dedicated to this specific type of education, when teachers should be the protagonists of their professional development. The methodological approach was begun with a literature review, then the research was anchored mainly on the ideas by Gauthier, Nuñez and Ramalho (2004); Imbernon (2011), Garcia (2006); Perrenoud (2000); Tardif (2007 ); Haddad, Di Pierro (2000), D'Ambrosio (2002), Mendes (2006, 2009), Freire (1996, 2011), and other theorists and official documents of field of adult education here and abroad. That work leads us to the understanding of the present moment from a foray into historical and conceptual aspects, as well as educational policies of EYA, as well as training, professionalism, knowledge and skills necessary for professional practice. Then, the subjects and the locus of research and the instrument for data collection were set up and led by the object of study. To consolidate the study was selected a sample of 27 mathematics teachers, working in municipal EYA Network Teaching of Natal. This research is in an investigative nature, within the quantitative and qualitative approaches focused on the responses of study subjects from the content analysis by Bardin (1977). Results from the analyzes have revealed that the initial training of mathematics teachers of adult education needs to be reconfigured in order to formalize the knowledge base of professionals (the mathematical content, didactics and professional knowledge). Thus the study suggests that this base knowledge is embedded in the pedagogical practice of these teachers, so that there is a completion of the teaching and learning process for young people and adults. The study also has pointed out that there is a need for teachers to participate in a continuing education plan that prioritizes learning situations of mathematical content considering the previous knowledge of the students. The final analyses thus indicate that knowledge of mathematics and the didactic and pedagogical strategies to be mobilized by teachers must be able to motivate the students in such a way that they feel need to incorporate in their knowledge, mathematical knowledge capable of making them more likely to have access to social, economic and labor market

Autoconhecimento e práticas corporais: para uma educação transpessoal integradora do saber ao ser no processo de formação inicial dos alunos de educação física

This thesis deals with the self-knowledge importance and corporal practices and the contribution of the Transpersonal Education for the initial formation process of students of Physical Education. In this context, students are stimulated to come in contact with the bases of learning to know, to make, to live together and to be for the promotion of integral education. We give priority to holistic conception of educating based in Emergent Paradigm. In this conception, student in initial formation is led to get back the view of integral being, life and love as education basis. We had as starting point, the essential dimensions to the learning geared toward the embodiment integration, autopoiesis and trans-disciplinarity. This work presents tracks for the teacher formation of Physical Education. It deals with the unfolding of teaching experiences in 2006, in Graduation Course in Physical Education of Universidade Federal do Rio Grande do Norte, in subject of Corporal Conscience, offered to undergraduate students which can be characterized as an action-research. This process was chosen as knowledge and intervention method because it allowed knowing and acting at the same time, studying the conditions and results of accomplished experience. In shared meetings with reflected experiences, we appeal to the experiences of situations that had mobilized the corporal, emotional, mental and spiritual dimensions of participants. The data collected through observations, accounts, questionnaires and interviews of learning processes had been starting points for the beginning of dialogue along with students of Graduation Course in Physical Education. The findings had been interpreted through of hermeneutics and discourse analysis. In this research, participants are considered as protagonist and boosters of educative process. The theoretical basis was supported by Transpersonal Education which contributed for a peace culture and respectful relationship. In its initial formation process, this research protagonists had evidenced of the importance of transpersonal education, geared toward action and changing, new ways of being and living together, facing the daily conflicts from a human and rational perspective. The research emphasized the importance of a new look on the teacher formation of Physical Education to face the limits of fragmented formation. Thus, we recognize that through the teacher education process, the transpersonal education provided wide significant changes reported during research, extending and re-meaning different learning levels such as: cognitive, emotional, attitudinal, and behavioral geared toward the personal and transpersonal development, reiterating the relevance of self-knowledge for development and establishment of pedagogical practice which prioritizes the life direction. The necessity of integrating knowledge to being in the initial process of teaching formation was emphasized in all the transpersonal meetings

Objetiva(ação) da medida e contagem do tempo em práticas socioculturais e educativas

This thesis describes and analyzes various processes established and practiced by both groups about the socio-cultural objective (action) the measurement and timing, mobilized some socio-historical practices as the use of the gnômon of the sundial and reading and interpretation of movements celestial constellations in cultural contexts such as indigenous communities and fishermen in the state of Pará, Brazil. The Purpose of the study was to describe and analyze the mobilization of such practices in the socio-historical development of matrices for teaching concepts and skills related to geometric angles, similar triangles, symmetry and proportionality in the training of mathematics teachers. The record of the entire history of investigation into the socio-historical practice, the formative action was based on epistemological assumptions of education ethnomathematics proposed by Vergani (2000, 2007) and Ubiratan D'Ambrosio (1986, 1993, 1996, 2001, 2004) and Alain Bishop conceptions about mathematics enculturation. At the end of the study I present my views on the practices of contributions called socio-cultural and historical for school mathematics, to give meaning to the concept formation and teaching of students, especially the implications of Education Ethnomatematics proposed by Vergani (2000) for training of future teachers of mathematics

Pelos caminhos das idéias e da existência: a propósito das cartografias de J. T. de Moura Filho

The present study aimed to investigate the intellectual, personal and professional tracjetory of José Tavares de Moura Filho. Civil engineer who devoted him self to cartographic cience, though not a cartographer, and to literature. At 65 years old, already with retirement, he devoted his attention to writing his books and see the world, as he said. There were nine books, five of poetry, prose and short stories, and four of cartographic nature. The published his books independently. He wrote and his wife Elza typed. Once ready, he would seek the graphics, later a publisher, to reproduce his writing. He liked to say he would rather to pay for your books than bay a new car, and did so. Died at age of 82 years, leaving a rich material for the young students, those who read, as he always did by dedicating his books. In order to achieve the objectives of this study, we used as a theoretical some authors dealing with historiography, oral history, intellectual intineraries and history of ideas, as Garnica, Nóvoa, Barros, Bosi, Le Goff among others. From this perspective, we constructed an archeology of ideas and the existence of Moura Filho, to point contributions of the teaching of mathematics from his work

Educação inclusiva e formação continuada: contribuições dos casos de ensino para os processos de aprendizagem e desenvolvimento profissional de professores

This study focuses on processes of learning and professional development experienced by elementary school teachers who have students with special educational needs in their classrooms. Cases and case methods can be used as methodological resource to articulate the continued training of teachers in an inclusive perspective. This research-intervention adopted a constructive-collaborative model for continued teachers formation. The main objective was to investigate the possible contributions of teaching cases, while investigative and formative strategies, for the processes of learning and professional development of teachers who work in the regular school. The data were collected by means of analytical activities, drafting collective discussion and teaching cases, having eight teachers as participants in a regular public school, located in the municipality of Natal/RN, Brasil. The theoretical reference covers the inclusive education, teaching learning, teachers professional development, the knowledge base for teaching and teaching cases as a resource for continued teachers formation in an inclusive perspective. The results indicated that teaching cases allowed description and analysis of educational practices developed by regular education teachers and adoption of reflective processes about situations reported and on their own pedagogical actuation, achieving indications of changes. It also indicates the contribution of cases for the clarification, systematization and extension of professional knowledge about inclusive education process as well as for involvement by the teachers of the study in a pedagogical thinking process. The lessons learned are related mainly to own role as teachers of regular education, to the role of professional support and specialized institutions faced to school inclusion. The analyses showed the methodological option was suitable to develop a schoolcentric training process, allowing teachers to seek in their actual environment alternatives for construction of a new logic of teaching that encloses diversity. The conclusion is that the cases, while bringing educational situations closer to the reality experienced by teachers in their daily professional role, causes relevant improvement on teachers education, because it offers training in conjunction with the experience and knowledge that teachers already have

Educação inclusiva e formação continuada: contribuições dos casos de ensino para os processos de aprendizagem e desenvolvimento profissional de professores

This study focuses on processes of learning and professional development experienced by elementary school teachers who have students with special educational needs in their classrooms. Cases and case methods can be used as methodological resource to articulate the continued training of teachers in an inclusive perspective. This research-intervention adopted a constructive-collaborative model for continued teachers formation. The main objective was to investigate the possible contributions of teaching cases, while investigative and formative strategies, for the processes of learning and professional development of teachers who work in the regular school. The data were collected by means of analytical activities, drafting collective discussion and teaching cases, having eight teachers as participants in a regular public school, located in the municipality of Natal/RN, Brasil. The theoretical reference covers the inclusive education, teaching learning, teachers professional development, the knowledge base for teaching and teaching cases as a resource for continued teachers formation in an inclusive perspective. The results indicated that teaching cases allowed description and analysis of educational practices developed by regular education teachers and adoption of reflective processes about situations reported and on their own pedagogical actuation, achieving indications of changes. It also indicates the contribution of cases for the clarification, systematization and extension of professional knowledge about inclusive education process as well as for involvement by the teachers of the study in a pedagogical thinking process. The lessons learned are related mainly to own role as teachers of regular education, to the role of professional support and specialized institutions faced to school inclusion. The analyses showed the methodological option was suitable to develop a schoolcentric training process, allowing teachers to seek in their actual environment alternatives for construction of a new logic of teaching that encloses diversity. The conclusion is that the cases, while bringing educational situations closer to the reality experienced by teachers in their daily professional role, causes relevant improvement on teachers education, because it offers training in conjunction with the experience and knowledge that teachers already have

Saberes pedagógicos/comunicacionais, pesquisa/formação: reflexões sobre as experiências formativas das professoras online

The thesis, entitled, Pedagogical/comunication knowledge, research/formation: Reflections on the formative experiences of teachers online , developed dialogues on the pedagogical/communication knowledge, research-formation and the formative experiences of teachers online, for the purpose of understanding how pedagogical/communication knowledge is establishing/established from the formative experience of teachers online. For this reason we began with the following question: how does pedagogical/communication knowledge become estabilishing/established beginning with the formative experience of teachers online? The methodological approach for the selected research was research/formation, based on Ethnoresearch of critical formation. This became a rich route for reflections on pedagogical/communication knowledge and formative experiences, making a contribution for formation and autoformation of the teacher/researcher and the teachers online. This provided moments of formation, of reflection-in-action and on the action, potentialized/structured the process of comprehending, analyzing, interpreting, reflecting on the formative experiences and contributing for reflections on pedagogical/communication knowledge of the teacher online. The theoretical referential dialogue was based on concepts such as: education online, interactivity Silva (2002), Santos (2005), Moran (2003), teaching, Veiga (2005), Pimenta (2002), Freire (2005), Tardif (2002), teaching online Sacramento (2006), teaching knowledge Tardif (2002), Charlot (2000), Porlán (1997), García (1992), Freire (2005), Ethnoresearch-formation Macedo (2000), formation Macedo (2010), Josso (2010). The discoveries revealed that the pedagogical/communication knowledged becomes establishing/established beginning with formative experience of the teachers online, from the emergency of a collective communicative dialogue, structuring and potentialized by the experiences of the context online, from the didactic pedagogical/communicational organization online, of the research, of the relation created by the expertise and the presents itself along the itinerary of the family , the school, academic and professional. From this we can conclude that of knowledge and plural experiences, which became broken down because they are parts that relate themselves with other parts, which become united in one whole, the singular/plural, the local/global, the text and the context, agregating principles a pedagogical- communication perspective that orients :the dialogue, the interactivity, the hypertextuality, themultivocallity, formative dispositions, formative experiences all of wich makes for the possibilities for researdh and the training of professors and teachers who accept their point of departure and enddind points as pedagogy and experience