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

Teorias implícitas dsos estudantes de Pedagogia sobre a docência nos anos iniciais do ensino fundamental

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

O ensino de portugês para crianças estrangeiras: reflexões sobre um fazer docente.

La presencia de personas extranjeras radicadas en la província de Rio Grande del Norte trae a la escuela el desafio de recibir alumnos hablantes de otros idiomas. En esa perspectiva, el estudio tiene como objetivo investigar la practica pedagógica desarrollada por una profesora de Pipa - RN, con destaque en la enseñanza de Portugués para niños inmigrantes en la Enseñanza Fundamental. Esa temática se hace relevante al proponer posibles alternativas para el desarrollo de una acción docente reflexiva y mediatizadora de la enseñanza de una língua segunda. Para la concretización de este trabajo disertativo, se há realizado un estudio de caso de tipo etnográfico y de naturaleza qualitativa en una institución privada de la playa de Pipa - RN, en el período de noviembre de 2007 a agosto de 2008. Se há utilizado como procedimientos, la observación participante, la entrevista semiestruturada gravadaen áudio, la análise documental, el registro en diário de campo y el registro fotográfico. Se há elegido como referencial teórico las discusiones de Almeida Filho (1992, 1997, 2002, 2005), Cunha (1999, 2002), Freire (1996, 2004), Moita Lopes (1996), Vygotsky (1998), Wachowicz (1995) y Zabala (1998). La análise revela que, aunque la profesora observada no tenga conocimientos específicos sobre la enseñanza de PL2 en la escuela regular, su acción educativa há demonstrado avanzos, especialmente, al considerar los aprendizes como sujetos del processo de enseñanza aprendizaje, entre ellos los niños extranjeros; contemplar la identidad y las diferencias culturales y linguísticas de estos educandos; incluyese el aspecto lúdico en la preparación de las actividades; articular vínculos sociales, afectivos y cognitivos, entre otros aspectos destacados. Sin embargo, evidenciase la necesidad de una formación pedagógica específica para el trabajo con niños inmigrantes, a través de la interlocución entre los currículuns de los cursos de Filología y Pedagogia de las Universidades brasileñas, a partir del cual estudios y debates podran ser fomentados en la busqueda por uma enseñanza de PL2 verdaderamente comunicativo y democrático.

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

As relações entre o público e o privado no processo de expansão do ensino superior no Brasil: democratização ou mercantilização?

The present study analyzes the expansion of Brazilian superior education, investigating how the public and the private sectors are inserted in this process, taking as analysis dimensions the philanthropic actions, the democratization and the mercantilism. The study had for general objective to analyze the dynamics of the expansion of superior education in Brazil, investigating how it configures the overlap between the public and the private in this process. More specifically was tried: a) to understand the process of participation of the non-state public, state and private sectors with lucrative goals in the expansion of superior education; b) to analyze the limits between the democratization and mercantilism in the process of expansion of superior education; c) to analyze the mechanisms that express the privatization in the process of expansion of superior education; d) to investigate, in a program of the government, how is materialized the overlap between the public and the private, in the expansion of superior education. In the development of the study, was adopted as theoretician and methodological way a historical and critical perspective, because is considered it allows to understand the mediations between the inquiry subject and the historical context in which it is developed, allowing, this way, the true explanation of the studied object. About the technician procedures, it was adopted documentary and bibliographical research. Also, secondary data were searched on the main governmental web sites (INEP, SISPROUNI, INEP, PNUD; IBGE) which produce statistics on superior education and sponsors of private institutions of superior education, as example ABMES and the Court of Accounts of the Union, amongst others. The study results had delineated a picture that allows to evidence that has been occurring, in the country, a process of expansion of superior education, marked for the articulated participation of the public state, private with lucrative ends and private without lucrative ends sectors, but it is distinguished in recent years the prevalence of the private sector with lucrative ends. In result, it is concluded that this process of expansion cannot be considered as dimension of the democratization because it occurs by means that move it away from the education as a right to be placed in the scope of the market, changing the right into a service that is appropriated by mercantile relations

A díade saberes e práticas docentes : um estudo de suas inter-relações

This study The Dyad of knowledge and teaching practices: an inter-relational study deals with the relationship between conceptual knowledge on behalf of the teachers and their teaching practices. The research aims to investigate the relations amongst conceptual meanings related to the professor and the practices of three (03) Fundamental Cycle public schools teachers in Natal-Brazil. Thus, a collaborative research of qualitative nature was performed by us. It was based on collaboration and critical reflection, as well as the socialhistorical theoretical methodological principles of Ferreira (2009). This was acknowledged as an analytical support for the reflections that were realized on concepts related to teachers and teaching considering the archeology on these concepts. The methodological procedures and tools we used consisted of Formative Autobiographies, Reflexive Study, Collaborative Observation, as well as some Reflexive Sessions. The analysis framework was based on information obtained by these methodological procedures as well as the critical collaborative and reflexive procedures. The studies permitted us to widen our knowledge related to the conceptual meaning of teaching and teachers. But it was not always possible for us to (re)elaborate these meanings in the conceptual phase. This was only possible to understand once our Formative Autobiographies were analyzed. They reveal that the concept elaboration process is not a part of our own formative path. The time that was dedicated to that proved to not be enough. The concept elaboration process demands time, effort as well as life-long learning skills. This is not always possible to achieve in this part of the study, on the other hand, this was possible to acknowledge that in the different stages of our conceptual elaboration. The teaching practices that we analyzed were predominantly heterogeneous and were fundamented on meanings of concepts related to teachers and teaching, that were internalized beforehand, (re)elaborated according to the conflicted and contradictory situations. The reflexive and collaborative process that we experimented during the Reflexive Sessions pointed out the predominance of technical and practical reflection process. In some moments it was possible for us to critically reflect on teaching practices due to the collaborative mode that we experienced. The importance of collaboration for teaching formation and professional development of behalf of teachers in general is pointed out by this research. Also regarding this research it was possible to see that there was personal and professional growth, experiencing learning together to collaborative reflect, as well as to counter-argument, reformulate concepts and conceptions aiming to transform our teaching practice

Estágio Supervisionado na formação de professores em serviço dos anos iniciais do ensino fundamental

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

O memorial autobiográfico: uma tradição acadêmica do ensino superior no Brasil

The thesis has as object of study the autobiographical memmorials. The general objective is to describe the history of the memmorial as an academic tradition of higher education in Brazil. Considered a hybrid genre, memmorials are known for focusing on life stories from a scientific perspective. The investigation revolves around three intertwined branches: History of Education, educational practices and language usages, which allow us to conduct a dialogue with multiple theoretical-methodological references with a view to supporting our analyses. The corpus used for the analysis was made up of 40 autobiographical memmorials, distributed as follows: 16 academic memmorials, dated from 1935 to 1970; 07 academic memmorials, dated from 1980 to 2007; and 17 formation memmorials, dated from 1995 to 2000. In this corpus, we also included official documents, which relate to legislation contained in edicts, resolutions, ordinances, regulations, which we used with a view to: 1) getting to know and understanding the big picture of higher education regulation in Brazil and the aspects related to the higher education teaching career; 2) investigating the text of memmorials in the light of the injunctive discourse characteristic of the edicts and resolutions in which they were based. The analysis of the memmorial supported by the legislation which regulates it allowed us to reconstitute the image of the professor throughout 80 years in the Brazilian public university. For this purpose, the study was conducted in the theoretical-methodological perspective of the (auto)biographical research in Education and of the sociolinguistic studies on discourse genres and discursive traditions. The investigations reveal the memmorial as an academic genre in which the professor's academic-professional history and the history of the higher education teaching career in Brazil intertwine. Anchored in the Bakhtinian perspective on discourse genres, according to which the memmorials evolve and become more complex as their contexts of usage also evolve and become more complex themselves, the results of our analyses allowed us to correlate genre changes to the sociohistorical context and to its usage as an educational practice in the university, in the decades under study. Therefore, the analyses showed that these self-writings: go from latent subjectivity to pure objectivity from the 1930s to 1960s; they show total annulment of the subject from the 1960s to the 1970s; they reappear in the 1980s, having Professor Magda Soares' memmorial as perspective; they expand and diversify from the 1990s onwards, taking on a formative role and a perspective of future as well. So far as language usages are concerned, we investigated the relationship of the subject with the language, especifically the manifestation of alterity on the discursive tissue of the memmorials. In this branch, the analyses pointed to the influence of the authoritative discourse on the formation of the professor and of the injunction and reinventing discourses on the authorship process. Therefore, the autobiographical memmorial reveals itself as a specific expression of the Brazilian academy's cultural sphere and allows us to confirm the hypothesis that each memorial tackles a singular-plural situation, by presenting a dialectical articulation between private and public, according to the institutional structures, in which and with which the professor has already formed him/herself and with which he/she dialogues

É preciso estar atento: um estudo da relação entre desenvolvimento da atenção e aprendizagem

Se discute en este estudio la relación entre o desarrollo de la atención y el aprendizaje de la lengua escrita realizada con los alumnos del 5º grado de la Enseñanza Primaria, compuesta de 25 alumnos, con la edad entre 9 e 13 años, de la Escola Municipal Professor Arnaldo Monteiro Natal/RN. Para el desarrollo de este proceso investigativo, utilizamos como aporte teórico el materialismo histórico-dialéctico, pues ese método posibilita el análisis de los fenómenos y, a través de esa lógica, se revelan los elementos que dieron sustentación a la mediación pedagógica y comprensión de los fenómenos con mayor eficacia. También fueron usados los estudios de Vigotski (1991), Rubinstein (1973), Ferreira (2003), Ibiapina (2007), y otros que convergen con ese posicionamiento. Se adoptó la pesquisa colaborativa que supone la construcción de un objeto del conocimiento entre investigador y profesor y también asocia al mismo tiempo actividades de producción del conocimiento y de desenvolvimiento profesional, proponiéndose una mediación entre comunidad de investigadores y comunidad de profesores. Utilizamos como elementos metodológicos el diagnóstico de la atención, el diagnóstico de la producción escrita del texto narrativo, siguiendo las etapas elaboradas por Infante (1998), los diarios reflexivos, el planeamiento y las sesiones reflexivas (con alumnos y con los pares). Para análisis del desarrollo de la atención, utilizamos las categorías definidas por Luria (1991): volumen de la atención, estabilidad de la atención, oscilación de la atención. El análisis de la producción textual tuve como parámetros las categorías de cohesión y coherencia (COSTA VAL, 1999). Para esto, se reflexionó con ellos sobre la importancia del desenvolvimiento de la atención para aprendizajes más efectivas. Propusimos situaciones de aprendizajes que posibiliten el desarrollo de la atención de esos alumnos y el dominio de la producción textual; y se analizaron las interrelaciones entre desenvolvimiento de la atención y la producción de textos narrativos. Los resultados presentados en los textos permiten afirmar que es notoria la relación entre la atención y el aprendizaje de la escritura. Vale resaltar que la reflexión no puede tener un fin en si mismo o entonces ser usada apenas para justificar una acción, mas debe tener como objetivo mejorar la enseñaza y tornar los profesores más conscientes y, por lo tanto, más capacitados para ejercer su profesión

O ensino de artes nos anos iniciais do ensino fundamental: (re)pensando a prática docente

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

A teoria de Dienes no ensino de transformação de medidas de comprimento, área e volume no curso de pedagogia

The study was aimed to test a teaching module on the Zoltan Paul Dienes theory, focusing on the content: The transformation of measurements: length, areas and volumes. The study based on constructivist theory consisted in a methodological intervention with students of the 7th period of the Course of Pedagogy, in Central Campus, Federal University of Rio Grande do Norte (UFRN). A preliminary study with 40 students called diagnostic evaluation found that students did not understand the concept of measurements transformation and its processing steps. The latter was performed only with the help of the table of measurements transformation with no understanding of the content. He applied a pretest, a set of activities and a post-test. The latter was used as a tool for evaluation of the student learning process. The answers of these ones were evaluated according to the concept of reflective abstraction of Jean Piaget, one of the authors who influenced the Dienes theory

O processo ensino-aprendizagem de história no ensino fundamental: seus limites, suas possibilidades

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

Trabalho e formação docente na rede municipal de ensino de natal

The study Teacher work and education in the municipal schools of Natal objectifies the analysis of the education and work conditions of the teachers in the municipal schools of Natal, placing them within the scenario of the public policies outlined for Basic Education (2005-2010). The thesis is based on the perspective that the educational reforms implemented by the Brazilian government in an attempt to answer to the new contextual demands originated from the world of work and globalization, demanding increasingly higher levels of qualification and constant extension of the teaching functions in school from the teachers, have been configured withal as a strategy for intensifying the teacher s work. The empirical field of study was constituded by thirteen municipal schools that offer basic education. Four hundred and seventeen teacher subjects that work in the municipal school system of Natal, two representatives of the Secretaria Municipal de Educação de Natal (SME)1 that work in the pedagogical team and one representative of the Sindicato dos Trabalhadores em Educação do Rio Grande do Norte2 took part in the study. The procedures/instruments used in the research were: bibliographic review, document research, questionnaires and recording of information in a field journal. The study confirmed that the majority of the teachers that work in the municipal school system were admitted by means of public entry exams, therefore meeting the requirements set by Law 9.394/96. Most of the teachers have the initial education demanded to work in basic education, although with some limitations due to the fact that they do not correspond to the needs of the educational system. The SME has a plan for continued training of the teachers in accordance to the current ideas defended by researchers of this field. There is, although, a disconnection between the purpose of the plan and the training strategies, because, in truth, predominate repetitive and specific actions that do not contemplate the training needs of the teachers, nor the demands of the system. Although the work conditions are evaluated, by the teachers, as relatively good, limits in relation to the physical structure of the schools are observed (dirty walls with holes in them, broken ceiling fans, old chairs and desks, old and stained black boards, inadequate restroom installations, poor maintenance of the computers, amongst other items). It was also verified the an increase in the functions of the teachers and an intensification of their work, materialized through an overburden of activities undertaken daily at school (and outside of it) and through the demand in taking part in activities that go beyond those inherent to the teaching process, such as the elaboration of political-pedagogical projects, participation in collegiate, registration of student information solicited by the SME and the participation in commissions, has been happening

Um estudo sobre a apreciação do raciocínio matemático na formação inicial de professores

The present work focused on developing teaching activities that would provide to the student in initial teacher training, improving the ability of mathematical reasoning and hence a greater appreciation of the concepts related to the golden section, the irrational numbers, and the incommensurability the demonstration from the reduction to the nonsensical. This survey is classified itself as a field one which data collection were inserted within a quantitative and qualitative approach. Acted in this research, two classes in initial teacher training. These were teachers and employees of public schools and local governments, living in the capital, in Natal Metropolitan Region - and within the country. The empirical part of the research took place in Pedagogy and Mathematics courses, IFESP in Natal - RN. The theoretical and methodological way construction aimed to present a teaching situation, based on history, involving mathematics and architecture, derived from a concrete context - Andrea Palladio s Villa Emo. Focused discussions on current studies of Rachel Fletcher stating that the architect used the golden section in this village construction. As a result, it was observed that the proposal to conduct a study on the mathematical reasoning assessment provided, in teaching and activity sequences, several theoretical and practical reflections. These applications, together with four sessions of study in the classroom, turned on to a mathematical thinking organization capable to develop in academic students, the investigative and logical reasoning and mathematical proof. By bringing ancient Greece and Andrea Palladio s aspects of the mathematics, in teaching activities for teachers and future teachers of basic education, it was promoted on them, an improvement in mathematical reasoning ability. Therefore, this work came from concerns as opportunity to the surveyed students, thinking mathematically. In fact, one of the most famous irrational, the golden section, was defined by a certain geometric construction, which is reflected by the Greek phrase (the name "golden section" becomes quite later) used to describe the same: division of a segment - on average and extreme right. Later, the golden section was once considered a standard of beauty in the arts. This is reflected in how to treat the statement questioning by current Palladio s scholars, regarding the use of the golden section in their architectural designs, in our case, in Villa Emo

Custo social de oportunidade na trajetória de acesso ao ensino superior: o caso dos ingressantes na UFRN nos vestibulares de 2006 a 2010

Access is a problem of higher education in Brazil that has existed since the formalization of this has occurred since the installation of the Portuguese court in Brazil in 1808. Only 10% of young people between 18 and 24 years of age attending this level of education in 2000, arriving in 2010 just 15%, far from that determined the National Education Plan in 2001, triple that percentage by the year 2010. In addition, a majority of seats of public HEIs is populated by students from the private network, especially in high-demand courses. In this context, this study aims to identify the costs related to the trajectories of students who were successful in the vestibular UFRN editions from 2006 to 2010. Presents an overview of higher education in Brazil, a brief history of vestibular, as well as new forms of access, and some of the policies to expand such access, highlighting the argument Inclusion UFRN. Focusing on the theme of the paper presents the concepts of opportunity costs and social. After collecting data through a questionnaire and consultation of databases COMPERVE was developed to search for a descriptive and analytical, with the participation of 3,995 students, of whom 1642 (41.1%) had completed secondary education in schools public, and 2,078 (52%) in private schools. The profile indicates that 90% are single, about 50% are 21 years of age, are white and female. In the course of preparation for college entrance exams, 80% chose the course during or after completion of the last year of high school, and almost 70% said they had started preparing at that time. Findings related to the costs involved with this preparation indicate that, in most cases there were school fees and disbursements and workshops, and the purchase of books and other materials, with parents primarily responsible for this cost, the amount disbursed each month was up $ 300 for 64% of respondents and only 7% of them exceeded $ 1,000, the major non-financial costs were characterized by the following resignations: job opportunities (24%) or temporary work (20%) courses of languages (26%), leisure activities (48%), leisure travel (43%), and parties and / or shows (54%). Of social investments by the government, stand out in the tax waiver scholarships for study in private institutions, grant exemption from the registration fee of vestibular, the preparatory courses UFRN, and seminars by COMPERVE / UFRN with networks of high school. From the junction of the opportunity costs (private costs) and social costs (public costs), a new concept: the social opportunity cost, which measures the combined efforts of families and government to finance the opportunity to access higher education of an individual. This concept can and should be incorporated as a strategic vector for the sake of democratic university, which reflects the social model that is sought