Os problemas da matemática: o seu papel na matemática e nas aulas de matemática

A integração da História da Matemática no ensino da Matemática é defendida há muito tempo e em vários países. Embora a discussão sobre os “prós” e “contras” dessa integração seja de longa data, a tendência nos últimos anos tem sido a procura de uma base teórica e de uma metodologia que alicercem essa integração. Uma das formas apontadas na literatura para a integrar na sala de aula é através de problemas históricos, tendo sido esta também a forma adoptada neste estudo. Esta investigação tem como objectivo caracterizar a aprendizagem da Matemática quando mediada por problemas históricos. Para tal, foram formuladas as seguintes questões: (1) Que aspectos do ambiente de aprendizagem ajudam na aprendizagem da Matemática quando são usados problemas históricos? (2) De que forma os problemas históricos actuam como artefactos mediadores da aprendizagem da Matemática? (3) Como é que o uso dos problemas históricos na sala de aula contribui para promover a aprendizagem da Matemática? (4) Quais as contradições ocorridas quando são utilizados problemas históricos nas aulas de Matemática? Nesta investigação, de natureza qualitativa, foi adoptado o paradigma interpretativo e os dados foram recolhidos através de uma observação participante completa. Atendendo aos objectivos do estudo, e tomando o sistema de actividade da sala de aula como a unidade de análise, foram recolhidos dados, em algumas aulas de Matemática e de Estudo Acompanhado de Matemática de uma turma do 8º ano, entre Setembro de 2006 e Maio de 2007. Os dados foram analisados à luz da Teoria da Actividade, na perspectiva de Engeström (1987), tendo sido seguido o esquema metodológico proposto por Mwanza (2002). Os resultados deste estudo mostram que os problemas históricos, quando usados como um artefacto mediador, num ambiente de aprendizagem devidamente apoiado pela orientação e questionamento da professora, ajudam os alunos a compreender os conteúdos leccionados, além de desempenharem um importante papel de motivação.

Fragmentos da história das concepções de mundo na construção das ciências da natureza: das certezas medievais às dúvidas pré-modernas

A concepção filosófica do mundo se inicia com os gregos sintetizados por Platão e Aristóteles. Para o primeiro o mundo físico é aparente e para se chegar à verdade é preciso se lembrar das idéias originais que determinam seu significado. Para o segundo as coisas físicas são dirigidas pelas idéias e para entendê-las é preciso a lógica. Durante o helenismo a escola de Alexandria elabora o neoplatonismo, a base da Patrística. Após a queda de Roma, os filósofos bizantinos guardam a herança clássica. A Igreja constrói uma visão neoplatônica da cristandade, a Escolástica. No oriente os persas também sofreram a influência grega. Entre os árabes do Oriente o pensamento neoplatônico orienta filósofos e religiosos de forma que para eles a razão e a fé não se separam. Aí a ciências se desenvolvem na física, na alquimia, na botânica, na medicina, na matemática e na lógica, até serem subjugadas pela doutrina conservadora dos otomanos. Na Espanha mulçumana sem as restrições da teologia, a filosofia de Aristóteles é mais bem compreendida do que no resto do Islã. Também aí todas as ciências se desenvolvem rápido. Mas a Espanha sucumbe aos cristãos. Os árabes e judeus apresentam Aristóteles à Europa Ocidental que elabora um Aristóteles cristão. A matemática, a física experimental, a alquimia e a medicina dos árabes influenciam intensamente o Ocidente. Os artesãos constroem instrumentos cada vez mais precisos, os navegadores constroem navios e mapas mais eficientes e minuciosos, os armeiros calculam melhor a forma de lançamento e pontaria de suas armas e os agrimensores melhor elaboram a medida de sua área de mapeamento. Os artistas principalmente italianos, a partir dos clássicos gregos e árabes, criam a perspectiva no desenho, possibilitando a matematização do espaço. Os portugueses, junto com cientistas árabes, judeus e italianos, concluem um projeto de expansão naval e ampliam os horizontes do mundo. Os pensadores italianos, como uma reação à Escolástica, constroem um pensamento humanista influenciado pelo pensamento grego clássico original e pelos últimos filósofos bizantinos. Por todas essas mudanças se inicia a construção de um novo universo e de um novo método, que viria décadas mais tarde.

O parto dos caminhos: Formação dos Sindicatos Rurais no Rio Grande do Norte (1960 - 1964)

The present work treats the movements dedicated to reinvidication per land and social rights for the field works, among 1960 and 1964. Trying to understand this question in the Rio Grande do Norte it is necessary to consider the connection between the catholic church and the rural syndicates besides the influence of the Brazilian communist party, and still other social movements and the state. The structures politics local, national and international, had considerable importance to the organization rural potiguares workers. The rural potiguares syndicate appear in 1961 - after a hard organization work starting of the Service of Rural Assistance - and expand itself through state until the middle of 1962. Soon the first big conflicts an important manifestation are perceive, indirectly referring to a increasing movement's performance. The Favoring Progresses chains co quested a biggest influence in the politics destiny of the Rio Grande do Norte, in front of integration among syndicates, educational projects, and favoring progress's politics. But the military coup hired that the hope overflow the field

A prática docente de Myriam Coeli na década de 1960

The present work has as objective to reconstitute the biographical profile and pedagogical practices of the teacher Myriam Coeli de Araújo Dantas da Silveira, in the Professionalizing scholl of the Federal Net of the Rio Grande do Norte, in the 60 s years. The choice of the period is justified by being this the time of important changes in the Education, as an example we have the implementation of the Law of Lines of direction and Bases of the National Education, the 4.024/1961. This teacher contributed for the formation of the potiguar s society scholar, acting in the press, the journalism and the teaching, activity that I analyzed in this study. How the pedagogical practices of her had happened in the 60 s years? This question guided the research and, in the search to answer it I used as source the Public Archive of the Rio grande do Norte, the Historical and Geographic Institute of the Rio grande do Norte, the periodicals of the time, photographs, sketch books of Myriam Coeli and interviews with familiar, former-pupils and contemporaries of this master. I verified that her performance always was based in the educational changes lived deeply for her, carrying through a series of activities in the school as: elaboration of the annual program of Portuguese Language, organization of literary competitions and an practice based on the effective norms without leaving to unite respect and the understanding for the pupils. Of this form, the analysis is not summarized only to the practices of a teacher, but the configuration, in part, of the Rio Grande do Norte educational history in a determined period, the 60 s years

Um estudo sobre a relação entre matemática e religião na obra de Blaise Pascal

The aim of the present study is to investigate the way through which the relations between Mathematics and Religion emerge in the work of Blaise Pascal. This research is justified by the need to deepen these relations, so far little explored if compared to intersection points between Mathematics and other fields of knowledge. The choice for Pascal is given by the fact that he was one of the mathematicians who elaborated best one reflection in the religious field thus provoking contradictory reactions. As a methodology, it is a bibliographical and documental research with analytical-comparative reading of referential texts, among them the Oeuvres complètes de Pascal (1954), Le fonds pascalien à Clermont-Ferrand (2001), Mathematics in a postmodern age: a cristian perspective by Howell & Bradley (2001), Mathematics and the divine: a historical study by Koetsier & Bergmans (2005), the Anais dos Seminários Nacionais de História da Matemática and the Revista Brasileira de História da Matemática. The research involving Pascal's life as a mathematician and his religious experience was made. A wider background in which the subject matter emerges was also researched. Seven categories connected to the relation between mathematics and religion were identified from the reading of texts written by mathematicians and historians of mathematics. As a conclusion, the presence of four of these seven categories was verified in Pascal's work

Anayde Beiriz e a escrita de si: (Educação, história e relações de gênero)

Le thème de cette dissertation est l Histoire de l éducation de la femme. Une analyse des pratiques culturelles de la professeur Anayde da Costa Beiriz (1905-1930), dans le contexte paraibanais du début du XXe siècle, est proposée. Le référentiel théoricométhodologique de l Histoire Culturelle est utilisé, pour aller contre l histoire passée sous silence dans le canon traditionnel. Basée sur le concept de représentation (Chartier, 1990), rompant avec les anciennes idées de sens intrinsèque, absolu, unique, liée aux pratiques complexes, multiples et différenciées, qui construisent le monde comme représentation. Basée aussi sur le concept de configuration (Elias, 1980), en comprenant que apparemment individu et société sont deux objets qui existent indépendamment, mais en vérité, se rapportent à deux niveaux inséparables du monde social, sont unis par des liens d interdépendance. Un dialogue est recherché entre le passé et le présent et les différentes dimensions: historique, sociale, politique et culturelle vécues par la professeur Anayde Beiriz. Pour obtenir des informations sur ses pratiques culturelles, une recherche des marques de cette histoire dans de multiples sources est effectuée: dans la bibliographie disponible parmi les domaines de la littérature, de l histoire, dês sciences sociales et de l éducation; dans des archives de l Institut Historique et Géographique de la Paraiba et de Natal; dans les Bibliothèques de l Université Fédérale de la Paraiba et du Rio Grande do Norte et chez des bouquinistes. L inventaire comprend: des périodiques, la législation en vigueur, des écrits de contemporains, dês témoignages oraux de parents, des lettres et des photos. On comprend de cette façon, que l idée d éplucher au travers de cette étude, des aspects qui n ont pas encore été vus et rappelés, peut non seulement répondre à nos doutes, mais, peut à partir de la réflexion qui se fait, se traduire par une nouvelle compréhension de cette histoire. En conclusion, des significations multiples sont contenues dans le processus d insertion de la femme dans l éducation à partir des Écoles Normales, qui englobent les relations de genre, l histoire du pouvoir, de la morale, de surpassement, des luttes et insatisfactions. On perçoit l héritage de résistances et de conquêtes. Cela a été sous l inspiration des airs de la modernité avec la Belle Époque, en répercutant dans le monde et aussi dans la Parahyba du Nord, que s est concrétisée la formation sociale de la professeur Anayde Beiriz et des femmes de son temps. L analyse de l écriture de soi confirme le discours normatif du contrôle moral social, le joug et les préjugés soufferts par Anayde Beiriz et l éducation différencié de genre qui ont déterminé ses habitudes et coutumes. C est-àdire, pour la femme, la permanence dans l espace privé, la retenue, l anoblissement des tâches ménagères et de la maternité comme sa plus haute aspiration, le support moral de la famille, la préservation de la tradition et la perpétuation des règles religieuses

Educação matemática, ciência e tradição: tudo no mesmo barco

Les connaissances de la tradition et position de la Science dehors pour un non-hiérarchique dialoguez qui frappe pour les distinguer mais ils sont undésavouer inséparable étant donné les compléments ils composent. Cet essai assume la possibilité de ce roi de dialogue dans un place spéciale: la classe. Sur ce qui vient au connaissance de la tradition, le centre remarquable est pour la construction de bateaux du travail manuel, una pratique culturellement déployé dans la ville d'Abaetetuba, dans le État de Pará, Brésil. En revanche, la Science est concentrée par le le contenu d'école a adopté dans l'Ensino Fundamental (École primaire). La construction du dialogue est faite en utilisant des activités de l'enseignement qui accentuez des aspects géométriques (solide, géométrique, angles et symétries) aussi bien que par information qui implique le tableau, poésie, histoire, géographie et physique - les deux inspiré dans le chiffre de bateau résumé dans un CD-ROM interactif. Les activités ont eu lieu dans D'Escola Ensino Pedro Teixeira Fondamental (Abaetetuba-Pa), avec étudiants du 6e niveau (plus spécifiquement avec un groupe de 13 étudiants) d'août à octobre2004. Ethnomathématiques et transdisciplinarité sont le support théorique sous-jacent du projet. Dans résumé, c'est possible pour dire que l'interaction entre Science et Tradition, à travers activités au-delà lesquelles vont le le contenu a restreint à mathématiques d'école, contribuées à,: identifiez le contenu a appris pas sur dans série antérieure; renouveler le rôle joué par école dans ses fonctions didactique pédagogiques; réduire le isolement entre information passée historique et les étudiants présent culturel; indiquer des obstacles à l'érudition des mathématiques intéresser aux aspects cognitifs et behavioristes; et provoquer un participation affective qui rôle principal à la qualité d'apprendre l'école contenu aussi bien que les connaissances de la tradition

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

Reconceitualização das categorias de skemp de compreensão relacional e compreensão instrumental como critérios globais

The thesis presents a systematic description about the meaning, as Skemp, relational understanding and understanding instrumental, in the context of mathematics learning, being that we had as a guide his understanding of the schema. Especially, we analyze some academic productions, in the area of Mathematics Education, who used the categories of understanding relational and instrumental understanding how evaluative instrument and we see that in most cases the analysis is punctual. Being so, whereas the inherent understanding relational schema has a network of connected ideas and non-insulated, we investigated if the global analysis, where it is the understanding of the diversity of contributory concepts for formation of the concept to be learned, is more appropriate than the punctual, where does the understanding of concepts so isolated. For this, we apply a teaching module, having as main content the Quaternos Pythagoreans using History of Mathematics and the work of Bahier (1916). With the data we obtained the teaching module to use the global analysis and the punctual analysis, using research methodology the Case Study, and consequently we conduct our inferences about the levels of understanding of the subject which has made it possible for us to investigate the ownership of global analysis at the expense of punctual analysis. On the opportunity, we prove the thesis that we espouse in the course of the study and, in addition, we highlight as a contribution of our research evidence of need for a teaching of mathematics that entices the relational understanding and that evaluation should be global, being necessary to consider the notion of schema and therefore know the schematic diagram of the concept that will be evaluated

Guilherme de La Penha: uma história do seu itinerário intelectual em três dimensões

This study focuses on the central Brazilian historiography of science, focusing specifically on the life and work of a contemporaneous mathematician-physicist, and becomes part of the set of research results that investigate, organize and describe personal, intellectual and professional itineraries of Brazilian scientists and educators. The theme chosen for the study ran from seminars on Mathematics in Pará and is up to organize and describe the life history, education, professional experience and scientific production of William Mauricio Souza Marcos de La Penha (Guilherme de La Penha), considering their academic, professional and intellectual life history, so that their academic and intellectual production be spread over the Brazilian scientific and academic community. We adopted the historical research as theoretical and methodological base for the development of this study, rising arguments about the profile of Guilherme de La Penha to characterize him as a multiskill intellectual and to reveal that his thoughts about science, technology, training scientists and educators were in accordance with their writings and their professional practice in order to build a first story about the life and work of William de La Penha. In this sense, we took the theoretical aspects related to historical research, biographies, intellectual itineraries, files and inventories as sources and historical construction vehicles in order to point out the essential elements to form a profile of the transdisciplinary intellectual historians, ie a profile scientist who carries out the research, management and administration, as well as a committed educator to the on-going training and forming process. The results pointed in different directions, among which we highlight the creation of Seção Guilherme de La Penha at Universidade da Amazonia, producing several articles about the life and work of William de La Penha presented at national and international conferences and the proposal for documentary displays which could contribute to understanding the implementation of a scientific area in Pará State, an area that would not only be restricted to the production of knowledge, but more than that, it would include the spreading, which provides various means, primarily through education. Thus it was possible to ensure that La Penha has an intellectual profile that can be considered a multi-and transdisciplinary intellectual who defends the possibility of forming a scientist one and multiple, non-linear attitudes and dialogues with all other areas in order to be understood under a model scientist for the twenty-first century based on the model clearly inspired by the scientist authors with which he identified throughout their training and professional activities, like the three that stood out in their relationship science: Archimedes, Leonhard Euler and Cliford Ambrose Truesdell

Investigação histórica nas aulas de matemática: avaliação de duas experiências

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