Aprender a ser crítico com a matemática num curso de educação e formação

Em Portugal, de acordo com os princípios gerais da Lei de Bases do Sistema Educativo, um dos objetivos da educação é responder às necessidades resultantes da realidade social, fomentando a evolução plena e harmoniosa de cada indivíduo, no sentido de este se tornar um cidadão livre, responsável, solidário e autónomo, capaz de julgar com espírito crítico e criativo o meio social em que está inserido e de se empenhar na sua progressiva mudança. Para educar matematicamente os alunos é necessário contribuir para o desenvolvimento das suas competências e saberes, ajudando-os a se tornarem cidadãos críticos e conscientes, para que participem criticamente na comunidade e percebam como a matemática é utilizada. O presente estudo visou compreender como é que a Educação Matemática Crítica contribui para o desenvolvimento de competências matemáticas e na formação de cidadãos críticos e conscientes. Para a realização desta investigação foi selecionada uma turma de um Curso de Educação e Formação (CEF), na qual quase todos os alunos, que tinham idades compreendidas entre os 15 e os 17 anos, revelavam um percurso de insucesso em Matemática. O estudo foi do tipo qualitativo e tomou como método a observação participante. Recorreu-se a um conjunto de informações sobre vários temas, retirada da internet, para que os alunos as analisassem criticamente. Este estudo defende a ideia de que a Educação Matemática Crítica contribui para a realização de aprendizagens mais significativas e na formação de cidadãos mais críticos e conscientes, permitindo-lhes participar criticamente na sociedade onde estão inseridos.

Aprendizagem cooperativa e colaborativa em matemática no espaço facebook

O programa de matemática do ensino básico revela que a escola exige uma formação sólida em Matemática para que os alunos, ao longo do seu percurso escolar, possam compreendê-la e utilizá-la, mas o façam igualmente depois da escolaridade, na sua vida pessoal, profissional e social. A investigação feita visa compreender como é que a Educação Matemática Crítica e a rede social Facebook potenciam a aprendizagem crítica da Matemática. A utilização mais frequente desta rede social, possibilita chegar a um maior fluxo de informação/publicidade. Sob a égide da Educação Matemática Crítica, com o objetivo de observar que alterações ocorriam na forma como os alunos aprendiam determinados conceitos matemáticos em situações rotineiras da nossa sociedade. Esta aprendizagem pode ocorrer cooperativamente e/ou colaborativamente conforme as atividades e os alunos que realizam o estudo. O estudo realizado foi de natureza qualitativa de caráter interpretativo. Os alunos realizaram três atividades. A primeira denominada “Atmosfera Terrestre” para introduzir o capítulo de intervalos de números reais e para os discentes se familiarizarem com as ferramentas do Facebook. As outras duas foram uma publicidade de uma empresa e uma notícia sobre as tabelas de IRS para o ano de 2013. Depois de concluído esse estudo, verificou-se que os alunos não tiveram qualquer problema ao nível do manuseamento das ferramentas proporcionadas pelo Facebook. Na atividade introdutória para o capítulo de intervalo de números reais, os alunos conseguiram transpor o que tinha sido discutido em espaço Facebook para a sala de aula, apresentando exemplos da referida atividade. Conseguiram retirar, através da matemática, conclusões e resultados muito pertinentes para uma melhor perceção do que estava implicitamente presente em cada uma das atividades. As conclusões evidenciadas pelos alunos aludem que após várias discussões, argumentos e mesmo algum cálculo matemático conseguiram observar e justificar criticamente que algumas informações estavam camufladas nas distintas atividades. Os alunos constaram que após estas atividades estão mais alertas para situações similares, o que constitui uma conquista do papel da Matemática na sua vida.

Atividades de natureza investigada no estudo de funções: uma experiência com estudantes de matemática aplicada às ciências sociais

ades de natureza investigativa contribuem para a aprendizagem matemática de alunos do ensino secundário. O estudo incidiu sobre uma turma do décimo primeiro ano de escolaridade do curso de línguas e humanidades. Foram trabalhadas três atividades no âmbito do capítulo Modelos Populacionais. Estas foram desenvolvidas com o auxílio de tecnologia, nomeadamente, calculadora gráfica e computador através da exploração do software Graph 4.4.2, no sentido de motivar os alunos e facilitar a compreensão dos conteúdos abordados. Tendo em conta que um dos objetivos deste estudo é analisar as atitudes reveladas pelos alunos aquando da realização das propostas, os dados obtidos são constituídos essencialmente por pormenores descritivos de tal forma que foi aplicada uma metodologia de natureza qualitativa através da observação participante. A utilização da tecnologia motivou os alunos, que se mostraram desde logo entusiasmados com a realização das atividades. Foi também visível, ao longo da realização das propostas, o desenvolv

A motivação dos alunos face à utilização de materiais manipuláveis na aula de matemática: um estudo realizado no 8º ano

O presente trabalho foi elaborado no âmbito do Mestrado em Ensino da Matemática no 3º Ciclo do Ensino Básico e Secundário, da Universidade da Madeira, no ano letivo de 2012/2013. Tem como objetivo analisar e refletir sobre o trabalho implementado nas duas turmas do 8º ano que me foram atribuídas, incidindo sobre a motivação dos alunos face à presença de outros materiais além do típico caderno de exercícios e do manual na aula de matemática. Deste modo, relatarei algumas aulas onde foram propostas atividades com recurso a materiais manipuláveis, jogos e computadores. Esta pesquisa foi realizada com base numa avaliação qualitativa que incidiu sobre a observação direta do trabalho desenvolvido pelos alunos, através dos registos escritos e de gravações de vídeo e áudio de algumas aulas, de forma a poder transmitir com maior exatidão a postura e o empenho dos alunos no decurso destas atividades.

A união entre técnica e musicalidade na metodologia de ensino do piano da professora Isabelle Vengerova

GOMES FILHO, Tarcísio. A união entre técnica e musicalidade na metodologia de ensino do piano da professora Isabelle Vengerova. In: Encontro Regional da ABEM Nordeste, 7., João Pessoa, PB, 2008. Anais ... João Pessoa, PB, 2008.

Democratização do acesso ao ensino superior: os cursos de graduação à distância na UFRN

This thesis pursuits to contextualize the theoretical debate between the implementation of public education policy of the Federal Government focused in a distance learning and legal foundations for its enforcement, in order to raise questions and comments on the topic in question. Its importance is back to provide scientific input and can offer to the academy, particularly in the UFRN, and elements of society to question and rethink the complex relationship between the socio-economic and geographic access to higher education. It consists of a descriptive study on the institutionalization of distance education in UFRN as a mechanism for expanding access to higher education, for both, the research seeks to understand if the distance undergraduate courses offered by the UAB system and implemented at UFRN, promote expanding access to higher education, as it is during implementation that the rules, routines and social processes are converted from intentions to action. The discussion of this study lasted between two opposing views of Implementation models: Top-down and Bottom-up. It is worth noting that the documents PNE, PDE and programs and UAB MEETING reflect positively in improving the educational level of the population of the country It is a qualitative study, using the means Bibliographic, Document and Field Study, where they were performed 04 (four) in 2010 interviews with the management framework SEDIS / UAB in UFRN. The data were analyzed and addressed through techniques: Document Analysis and Content Analysis. The results show that the process of implementation of distance education at UFRN is in progress. According to our results, the research objective is achieved, but there was a need to rethink the conditions of the infrastructure of poles, the structure of the academic calendar, the management of the SEDIS UFRN, regarding the expansion of existing vacancies and the supply of new courses by the need for a redesign as the Secretariat's ability to hold the offerings of undergraduate courses offered by the Federal Government to be implemented in the institution. It was also found that levels of evasion still presents a challenge to the teaching model. Given the context, we concluded that the greatest contribution of UAB and consequently UFRN by distance learning for undergraduate courses (Bachelor in Mathematics, Physics, Chemistry, Geography and Biological Sciences, beyond the bachelor's degrees in Business and Public Administration ) is related to increasing the number of vacancies and accessibility of a population that was previously deprived of access to university

Um modelo analítico da qualidade da dieta de adolescentes estudantes da rede publica de ensino de Natal, Brasil

Conselho Nacional de Desenvolvimento Científico e Tecnológico

Olhares sobre a formação do professor de matemática. Imagem da profissão e escrita de si

The main focus of this thesis is the formation of a mathematical teacher at a college institution. The general aim is to describe and to analyze the formation process of a mathematical teacher which is an undergraduate student in Mathematics at the Instituto de Educação Superior Presidente Kennedy IFESP, in Natal-RN. It is based on a qualitative ethnographic approach, and has its theoretical anchorage in the (auto)biographical narratives, the social representative theories, and the mathematical education. The number of participants in this investigation was 12 undergraduate students, which corresponds to 25% of the total number of students. The corpus utilized in our analysis included 48 (auto)biographical essays, 12 (auto)biographies (formation's memories), and 12 contextualization files, besides the research's diary. The sources were obtained from the whole program of studies, i.e. from November 2003 to December 2006. The analysis revealed that the reminiscences of the 12 students' academic trajectory influenced their professional formation, since their images of a mathematical teacher were intrinsically related to the one they had before. These representations were being either demolished or constructed in a network along the assertive image of their profession, changing afterwards the mathematical representation and the teaching way of this discipline. Our study also shows that the beginning of their teacher career was marked by mechanical practices influenced by their old teachers. The (trans)formation of themselves and their teaching practices happened in a smooth way as soon as they increased their knowledgements in Mathematics, and it reflected upon the way they learned mathematics. The writing of their (auto)biographies helped the set up of new knowledgements, leaving to a self-consciousness as well as a self-formation, and contributed for the construction of a new way to see and to live the profession. Therefore, a mathematical teacher, for the undergraduate students of the IFESP involved in this work, is made at the interface of the familiar, academic, and professional context, besides the reflexive writings about the formation path, the way of life and the relationships among them

Geometrizando no segundo ciclo :relato de uma intervenção pedagógica voltada à construção de conceitos geométricos no ensino fundamental

This work has proposed to relate the experience product of a pedagogical intervention, performed in a public institution of teaching situated in this capital. It had as objective to validade the applying of a teaching module of geometry, more specifically about the conceptions of perimeter and área in the second cycle of fundamental teaching. This dissertation has presented the problematic which involves the teaching of geometry in different contexts. It has adopted the broach of the radical constructivism while methodological theoretical referencial through which it has tried to explain the phenomena that involves the teaching and the apprenticeship. It appropriates Jean s Piaget contributions related to the development stages, while referencial that will dialogue in the search by sense and comprehension of the geometric apprenticeship process and it runs over Richard s Skemp (1980) theory in order to explicit the student s apprenticeship according to the levels of instrumental comprehesion and relacional comprehension . The research has presented datum related to initial diagnosis evaluantion, the pedagogical intervention and analysis of the activities and students perfomance displaying still the results of the final evaluation. According to the results got, we could check the students group growth front to the acquisition of the concepts of perimeter and área in comparison with the previous knowledges presented in the initial diagnosis evoluation of the students participants of the research. We have concluded evaluating the objectives of the research, connecting the strategies and reasoning employed by the students in order to resolve the questions and then to reach the objectives proposed by the teaching module. We have presented still the main obstacles to the apprenticeship of such concepts

A transversalidade no currículo do ensino fundamental: as questões ambientais em foco

This thesis is the result of an investigation about the transversality of the environmental issues into the daily curriculum of High Schools (from first to eighth grade). The research field was the county of Santo Antonio de Jesus in the state of Bahia, Brazil. The investigation is related with the challenge that the present model of social development and organization has put to the school institution: to bring the regular discussion about Environmental Education (EE) to the school s daily life. Facing the complexity of the socio-environmental issues and the basic functions of Education, the object of study was restricted to the identification of the challenges and paradoxes of the EE inside the curriculum organization of Politic-Pedagogic Project of the schools and the teachers daily practices. About the methodology, we adopted different references for the qualitative research: sociology, history, economy, and education. As for the investigative procedures about the teacher s practices, we related the school s daily practices to the context of the community. We also adopted several investigative procedures, such as questionnaires, interviews, observations and formative intervention. The theoretical basis was organized based on references to curriculum organization, environmental culture, teacher education and also considering the pillars of a capitalistic system that is based on consumerism and that generates social exclusion. At the initial considerations, we contextualized the contemporary environmental issues in an attempt to interpret the conditions of the EE transversality into the school s daily practices, which are still oriented to the traditional Cartesian Education. Based on the collected data, we found the reasons for the teachers dilemma and reluctances to the insertion of the environmental issues into the organization of the work plan and into the management of a school. Nevertheless, the results also signed promising possibilities to the EE tranversality, in case the curriculum of the school could be more sensible towards the cultural and social-economical issues of a community. We especially questioned The National Curriculum Parameter s (PCN), which is considered highly insufficient to inform the teachers about the environmental issues, facing the actual local conditions of social and pedagogic work. The final considerations showed the role and the importance of this research as one strategy to organize the curriculum education into the perspective of the transversality of environmental issues inside the education of both teacher and student

A inclusão do aluno com deficiência mental no ensino médio: um estudo de caso

La défense d une école inclusive dans les forums internationaux du monde entier a stimulé l adoption de politiques éducationnelles d inclusion et la pratique d inclusion dans les écoles, de sorte à ce que la scolarisation des élèves aux besoins éducatifs spéciaux dans les classes comunes est devenue une réalité dans la majorité des systèmes d éducation. Et pourtant, l inclusion scolaire, au Brésil, avance à pas lents et pose d innombrables questions, notamment quand il s agit de l inclusion des personnes qui présentent une déficience mentale dans les niveaux d enseignement plus avancés. Basé sur ce fait, et tout en considérant que les études et recherches sur ce thème, au Brésil, sont centrées majoritairement sur l éducation enfantine et les séries initiales de l enseignement fondamental, cette étude se propose d analyser l inclusion d une élève ayant une déficience mentale, inscrite dans l Enseignement Moyen, dans une école appartenant au réseau d enseignement de l Etat, dans la ville de Natal RN. Pour répondre aux questions proposées dans cette étude nous avons fait appel aux méthodologies qualitatives, du genre Etude de Cas, et au cours de sa réalisation avons utilisé l interview demi-structurée et l observation libre dans l ambiance naturelle de l école. Ont participé de l étude, en plus de l élève qui présentait une déficience mentale, sa mère et deux segments de l école, desquels ont fait partie trois professionnels de l équipe administrative pédagogique et quatre enseignants. L analyse des données a mis en relief la résistence de l école à répondre au projet pédagogique d éducation inclusive, aspect qui a un rapport très étroit avec les spécificités de l Enseignement Moyen, la structure traditionnelle d un enseignement basé sur l idée d une classe homogène, et le bas niveau d attentes des éducateurs concernant les possibilités d apprentissage et de développement de l élève handicapée mentale. De surcroît, le manque de directives pour conduire les adaptations pédagogiques et du curriculum à l école ont rendu fragile l action des enseignants, dont le résultat est une pratique d intégration rudement malmenée. Au travers des points de refléxions suscités par cette étude, nous considérons que l inclusion des élèves qui présentent une déficience mentale doit être centrée sur une pratique pédagogique qui repousse l idée de soumettre tous les élèves à des procédures universelles cristalisées sur des pratiques imposées par les contraintes d homogénéisation, et qui, contrairement, puisse trouver à l école des conditions favorables au développement de chacun, au travers des processus d apprentissages formés par des instances de médiation et d interaction sociales

Uma visita ao universo matemático de Lewis Carrol e o (re)encontro com sua lógica do nonsense

Notable mathematics teacher, Lewis Carroll, pseudonym of Charles Lutwidge Dodgson (1832-1898), made the mixture of mathematics with literature a ludic environment for learning that discipline. Author of Alice s Adventures In Wonderland and its sequel Alice Through The Looking Glass, he eventually created a real and complex universe which uses what we call the logic of the nonsense as an element to motivate the development of mathematical thinking of the reader, taking it as well, learn by establishing a link between the concrete (mathematics) and the imaginary (their universe). In order to investigate and discuss the educational potential of their works and state some elements that can contribute to a decentralized math education from the traditional method of following the models and decorate formulas, we visited his works based on the studies of archeology of knowledge (FOUCAULT, 2007), the rational thought and symbolic thinking (VERGANI, 2003) and about the importance of stories and narratives to the development of human cognition (FARIAS, 2006). Through a descriptive, analytical study, we used the literary construction and presented part of our study in form of a mathematical novel, to give the mathematical school a particular charm, without depriving it of its basics properties as discipline and content. Our study showed how the works of Carroll have a strong didactic element that can deploy in various activities of study and teaching for mathematics classes

Uma análise histórico-epistemológica do conceito de grupo

This work aims to analyze the historical and epistemological development of the Group concept related to the theory on advanced mathematical thinking proposed by Dreyfus (1991). Thus it presents pedagogical resources that enable learning and teaching of algebraic structures as well as propose greater meaning of this concept in mathematical graduation programs. This study also proposes an answer to the following question: in what way a teaching approach that is centered in the Theory of Numbers and Theory of Equations is a model for the teaching of the concept of Group? To answer this question a historical reconstruction of the development of this concept is done on relating Lagrange to Cayley. This is done considering Foucault s (2007) knowledge archeology proposal theoretically reinforced by Dreyfus (1991). An exploratory research was performed in Mathematic graduation courses in Universidade Federal do Pará (UFPA) and Universidade Federal do Rio Grande do Norte (UFRN). The research aimed to evaluate the formation of concept images of the students in two algebra courses based on a traditional teaching model. Another experience was realized in algebra at UFPA and it involved historical components (MENDES, 2001a; 2001b; 2006b), the development of multiple representations (DREYFUS, 1991) as well as the formation of concept images (VINNER, 1991). The efficiency of this approach related to the extent of learning was evaluated, aiming to acknowledge the conceptual image established in student s minds. At the end, a classification based on Dreyfus (1991) was done relating the historical periods of the historical and epistemological development of group concepts in the process of representation, generalization, synthesis, and abstraction, proposed here for the teaching of algebra in Mathematics graduation course

Uma reavaliação do pensamento lógico de George Boole à luz da história da matemática

The aim of the present study is to reevaluate the logical thought of the English mathematician George Boole (1815 - 1864). Thus, our research centers on the mathematical analysis of logic in the context of the history of mathematics. In order to do so, we present various biographical considerations about Boole in the light of events that happened in the 19th century and their consequences for mathematical production. We briefly describe Boole's innovations in the areas of differential equations and invariant theory and undertake an analysis of Boole's logic, especially as formulated in the book The Mathematical Analysis of Logic, comparing it not only with the traditional Aristotelian logic, but also with modern symbolic logic. We conclude that Boole, as he intended, expanded logic both in terms of its content and also in terms of its methods and formal elaboration. We further conclude that his purpose was the mathematical modeling of deductive reasoning, which led him to present an innovative formalism for logic and, because the different ways it can be interpreted, a new conception of mathematics

A (re)significação conceptual nas práticas colaborativas com professores do Ensino Fundamental

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