Submitted by Filipe dos Santos (fsantos@pucsp.br) on 2016-09-01T14:34:37Z No. of bitstreams: 1 Ana Rebeca Miranda Castillo.pdf: 4300226 bytes, checksum: 2a6d4a8336390def71101c782b5a7247 (MD5) / Made available in DSpace on 2016-09-01T14:34:37Z (GMT). No. of bitstreams: 1 Ana Rebeca Miranda Castillo.pdf: 4300226 bytes, checksum: 2a6d4a8336390def71101c782b5a7247 (MD5) Previous issue date: 2016-03-16 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This work discourses about mathematical knowledge incorporated and mobilized in the construction and use of the staff (cross-staff), measuring instrument discussed in the treatise A Boke Named Tectonicon, written and published by Leonard Digges (1520-1559). Its objectives are: identifying the context in which the work and its author were inserted; checking from that context, what mathematical knowledge were mobilized and addressed in the treaty and its relation between mathematical practices and erudite knowledge from that time and analyze these mathematical knowledge added in staff, considering the practice of measurement and the procedures written by the author. Three analytical dimensions have been articulated, the historiography, the contextual and the epistemological and the study focused specifically on the construction and use of the staff (cross-staff). The social and political context of the 16th century has shown that the appreciation of mathematical knowledge it was a gradual result of social historical process occurred in England and promoted a rich dialogue among scholars of universities and craftsmen connected to different sectors of society. By reading and analyzing the treated, it was found how was made calculation of measure of a land area with several shapes and also calculation of measure of height of objects. Regarding the staff, it was observed that it was more than a simple measuring device, because in the process of its manufacture it was necessary a segment division of knowledge in equal parts, perpendicularity and demarcation scales. In its handling to achieve the desired measure it was necessary to mobilize the similarity of triangles property and to know that a line is determined by two points. And on its use the relative positions between the lines and orthogonal projections were skills that were implicit in making the measures. The results of this work concluded that both the staff and the other instruments addressed in Tectonicon, are more than simple tools, they are instruments that incorporate knowledge, they show the relation between to know and to do of an era and raises issues of epistemological to reflection on the construction of scientific and mathematical process / Este trabalho discorre sobre os conhecimentos matemáticos incorporados e mobilizados na construção e no uso do báculo (cross-staff), instrumento de medida abordado no tratado A Boke Named Tectonicon, escrito e publicado por Leonard Digges (1520-1559). Tem como objetivos: identificar o contexto no qual a obra e seu autor estavam inseridos; verificar, a partir desse contexto, quais conhecimentos matemáticos foram mobilizados e abordados no tratado e sua relação com as práticas matemáticas e o saber erudito da época além de analisar esses conhecimentos matemáticos incorporados no báculo, considerando a prática de mensuração e os procedimentos descritos pelo autor. Foram articuladas três dimensões de análise, a historiográfica, a contextual e a epistemológica e o estudo centrou-se especificamente na construção e uso do báculo (cross-staff). O contexto social e político do século XVI mostrou que a valorização do conhecimento matemático foi uma consequência gradual do processo histórico social ocorrido na Inglaterra e promoveu um rico diálogo entre os eruditos das universidades e artesãos ligados a diferentes setores da sociedade. Com a leitura e análise do tratado, verificou-se como era feito o cálculo de medida de área de terrenos com diversos formatos e também o cálculo da medida de altura de objetos. Em relação ao báculo, foi observado que era mais que um simples dispositivo de medição, pois já no processo de sua fabricação eram necessários conhecimentos de divisão de um segmento em partes iguais, perpendicularismo e demarcação de escalas. No seu manuseio, para obter a medida desejada, era necessário mobilizar a propriedade de semelhança de triângulos e saber que uma reta é determinada por dois pontos. E no seu uso posições relativas entre retas e projeções ortogonais eram conhecimentos que estavam implícitos ao fazer as medições. Com os resultados deste trabalho conclui-se que tanto o báculo como os outros instrumentos abordados em Tectonicon, são mais que simples ferramentas, são instrumentos que incorporam conhecimentos, mostram a relação entre o saber e o fazer de uma época e apontam questões de ordem epistemológica para reflexão a respeito do processo de construção do conhecimento científico e matemático

Notre travail de recherche porte sur l'analyse de l'action du professeur et ses interactions avec les élèves dans le domaine spécifique de l'étude du numérique en Cours Préparatoires. L'objectif de notre thèse est d'analyser l'action du professeur et ses pratiques didactiques en classes, et formatives dans une Cellule d'Animation Pédagogique. La première partie comporte une présentation du contexte socio économique et éducatif du Niger. Nous nous interrogeons ensuite sur les pratiques professorales permettant ou non aux élèves de prendre de réelles responsabilités par rapport aux savoirs, et sur la pertinence du travail de conception collective de séances. Dans la deuxième partie, nous exposons nos outils théoriques, les travaux antérieurs en lien avec nos objets de recherche, et la problématique générale de notre travail. La troisième partie est consacrée à la démarche méthodologique qui fonde notre étude sur l'analyse des manuels, des vidéos de classe et les observations in situ. La quatrième partie examine les ressources mathématiques utilisées à l'écoleprimaire au Niger, en interrogeant l'influence de ces ressources sur les pratiques habituelles des professeurs enquêtés. Les cinquième et sixième parties analysent les séances empiriques en termes de topogénèse, et de recours aux systèmes sémiotiques pour étudier le savoir en jeu dans les situations didactiques. Dans la septième partie, nous proposons un dispositif innovant de formation continue sur la conception collective de leçons dans une CAPED. En conclusion, dans une huitième partie nous présentons d'abord une synthèse de nos résultats, et nous exposons ensuite les perspectives que ce travail de recherche offre en termes de propositions en vue de l'élaboration d'ingénieries didactiques qui pourraient permettre la mise en place d'un travail coopératif entre professeurs et chercheurs

Solving cubic equations by a formula that involves only the elementary operations of sum, product, and exponentiation of the coefficients is one of the greatest results in 16th century mathematics. This was achieved by Girolamo Cardano's Ars Magna in 1545. Still, a deep, substantial difference between the quadratic and the cubic formula exists: while the quadratic formula only involves imaginary numbers when all the solutions are imaginary too, it may happen that the cubic formula contains imaginary numbers, even when the three solutions are anyway all real (and different). This means that a scholar of the time could stumble upon numerical cubic equations of which he already knew three (real) solutions and the cubic formula of which actually contains square roots of negative numbers. This will be lately called the 'casus irreducibilis '. Cardano's De Regula Aliza (Basel, 1570) is (at least, partially) meant to try to overcome the problem entailed by it.

Made available in DSpace on 2014-06-11T19:31:42Z (GMT). No. of bitstreams: 0 Previous issue date: 2011-12-13Bitstream added on 2014-06-13T19:25:50Z : No. of bitstreams: 1 trivizoli_lm_dr_rcla.pdf: 2133545 bytes, checksum: a9e357b75fe07dc5c3fd1a7eeccde5cb (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Esta pesquisa de doutorado propôs-se a identificar os matemáticos brasileiros que fizeram parte da fase inicial do intercâmbio acadêmico entre Brasil e Estados Unidos por meio de bolsas de estudos concedidas por fundações privadas, iniciando, assim, as reflexões acerca das influências estadunidenses na Matemática no Brasil, situando-se dentro de uma área de investigação que trata da história do desenvolvimento da Matemática no Brasil. A identificação desses matemáticos se deu por meio de consulta e análise de documentação e listagens de bolsistas fornecidas pelas instituições abordadas: a Fundação Rockefeller, Fundação Guggenheim e Comissão Fulbright. Parte da documentação foi obtida por meio da consulta aos arquivos no Rockefeller Archive Center, em New York, pela listagem fornecida pelo Escritório da Comissão Fulbright no Brasil, pela listagem encontrada no site oficial da Comissão Fulbright e no site oficial da Fundação Guggenheim. Com esse objetivo, empreenderam-se estudos sobre a história do desenvolvimento da Ciência no Brasil, em uma visão geral e em particular da Matemática, focalizando ocasiões nas quais a participação de instituições estadunidenses foi decisiva para a formação da elite intelectual brasileira, no período de 1945 a 1980. Além disso, apresentamos uma síntese do referencial teórico que foi utilizado na pesquisa, discutindo o conceito de globalização da Ciência e da Matemática, para estabelecer um entendimento da ideia dos intercâmbios científicos a partir da dinâmica dos encontros culturais e sob uma perspectiva da história social, considerando que a atividade científica é uma das vias para a compreensão das relações sociais e culturais. A partir desse panorama de estudo, destacamos indícios que nos ajudam a responder uma série de perguntas históricas acerca do... / This PhD research is aimed at identifying Brazilian mathematicians who were part of early academic exchanges between Brazil and the United States by means of scholarships awarded by private foundations and reflecting on the on the American influences in mathematics in Brazil, within an area of research that deals with the history of the development of mathematics in Brazil. The identification of these mathematicians was done through consultation and analysis of documents and lists of scholarships provided by the addressed institutions: the Rockefeller Foundation, the Guggenheim Foundation and Fulbright Commission. Some of the documentation was obtained by consulting the files found in the Rockefeller Archive Center in New York, the list supplied by the Office of the Fulbright Commission in Brazil, and the lists found on the official websites of the Fulbright Commission and Guggenheim Foundation. With this objective, studies were undertaken on the history of the development of science in Brazil, and an overview of mathematics in particular, focusing on occasions in which the participation of American institutions was decisive for the formation of the Brazilian intellectual elite in the period 1945 to 1980. In addition, we present the theoretical synthesis that was used in the research, which describes the concept of globalization of science and mathematics to establish an understanding of the idea of scientific exchange from the dynamics of cultural encounters and from a perspective of social history, considering that the scientific activity is one of the ways to understand the social and cultural relations. From this overview study, we highlight clues that help us to answer a series of questions about the historical development of mathematics in Brazil and point to a close relationship between science... (Complete abstract click electronic access below)

Made available in DSpace on 2014-06-11T19:24:51Z (GMT). No. of bitstreams: 0 Previous issue date: 2012-09-19Bitstream added on 2014-06-13T19:31:57Z : No. of bitstreams: 1 caire_e_me_rcla.pdf: 1389119 bytes, checksum: ea2e9b574c106bff7f9cf806fe23534b (MD5) / Esta investigação tem como objetivo a história da origem da curva normal identificando a contribuição de Abraham de Moivre na dedução da fórmula para a função densidade de distribuição normal. Serão analisados trechos de obras originais de Abraham de Moivre, Jacob Bernoulli, James Stirling / This research aims at the history of the origin of the normal curve identifying the contribution of Abraham de Moivre in deducing the formula for the density function of normal distribution. Parts of original works of Abraham de Moivre, Jacob Bernoulli, James Stirling will be analysed

Orientador: Arlete de Jesus Brito / Banca: Antonio Miguel / Banca: Andreia Dalcin / Banca: César Donizetti Pereira Leite / Banca: Ivete Maria Baraldi / Resumo: Esta pesquisa objetiva investigar como práticas de ensino de aritmética se manifestam explicitamente na obra ficcional A Aritmética da Emília, do escritor brasileiro Monteiro Lobato (1882 - 1948), e a que rastros de outras práticas culturais o referido livro pode arremeter, com base no contexto de ensino de matemática compreendido entre 1920 e 1940. Para tanto, nossa opção de análise segue a intertextualidade entre alguns documentos da época, tais como A Aritmética da Emília (1935, 1° edição, 1939; 2° edição; 1942, 3° edição; 1944, 4° edição), Emília no país da Gramática e Aritmética da Emília (1947); outras obras de Lobato; livros didáticos de aritmética da época; Legislação sobre ensino; cartas entre Lobato e Anísio Teixeira; carta entre Lobato e Julio Cesar de Mello e Souza; revistas sobre ensino; textos sobre educação daquela época; livros de literatura infantil. Temos por referenciais Guinzburg, Chartier e Burke. Concluimos que A Aritmética da Emília reúne em si todas as contradições filosóficas e pedagógicas daquela época, confrontando a tradição didática do ensino conservador com o movimento renovador da Escola Nova, oscilando o caráter inovador de sua proposta pedagógica e recaindo nas práticas professorais de sua contemporaneidade / Abstract: This research claims to investigate how practices of arithmetic teaching manifest explicitly in the fictional work Aritmética da Emília, by the brazilian writer Monteiro Lobato (1882 - 1948). Besides, it dialogues to tracks of others cultural practices the mentioned book can point to, based on the historical context of mathematical teaching between 1920 and 1940. Our analysis follows to intertextuality methods between a several documents from this period, such as A Aritmética da Emília (1935, 1° edition, 1939; 2° edition; 1942, 3° edition; 1944, 4° edition), Aritmética da Emília (1947); others works made by Lobato; arithmetics books written at that time; laws about teaching; letters between Lobato and Anísio Teixeira; letter between Lobato and Julio Cesar de Mello e Souza; magazines on teaching; texts on decades 1920 and 1940 education; youth literature books. We have as a reference Chartier, Burke and Ginzburg. We concluded that Aritmética da Emília shows all philosophical and pedagogical contradiction of those years, confronting the didactic tradition of conservative education with the renewal movement of the New School, swinging the innovative nature of its pedagogical proposal and falling in pratices professorial of those times / Doutor

Orientador: Ubiratan D'Ambrósio / Banca: Línlya Sachs / Banca: Roger Miarka / Banca: Rosana Giaretta Sguerra Miskulin / Banca: Ana Maria Haddad Baptista / Resumo: Este trabalho se constitui da leitura de algumas cartas, que tratam de Filosofia, Lógica e Física, presentes no polêmico livro O Verdadeiro Método de Estudar. O autor, o controverso Luís António Verney, ao publicar essa obra, acreditou na possibilidade de mudança da Educação em Portugal. Apoiado nas ideias do movimento europeu que ficou conhecido como Iluminismo, Verney elaborou um riquíssimo texto no qual faz duras críticas ao ensino ministrado pelos padres da Companhia de Jesus, naquela época em Portugal. Ao sugerir o rompimento com esse sistema de ensino, o autor procura introduzir um ensino pautado no experimentalismo, colocando a Matemática como conhecimento fundamental para o estudo da Física e simultaneamente como ferramenta social necessária para o bem da nação / Abstract: This work consist at reading of some letters dealing with Philosophy, Logic and Physics presented at polemic book, The True Method of Study, authored by the controversial Luís António Verney that by publishing his work believed in the possibility of changes in education of Portugal. Supported on the ideas of European movement known as the Enlightenment Verney produced a rich text in which he harshly criticized the teaching realized by priests of Society of Jesus at that moment in Portugal. To suggest a rupture with that education system, the author tried to introduce teaching based on the experimentalism, introducing mathematics as fundamental knowledge for the physics study and simultaneously as a social tool necessary for the good of the nation / Doutor

Orientador: Circe Mary Silva da Silva Dynnikov / Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-15T01:53:37Z (GMT). No. of bitstreams: 1 Soares_WaleriadeJesusBarbosa_M.pdf: 5077444 bytes, checksum: 6209ae12c97ad644f16db661f3fd992c (MD5) Previous issue date: 2009 / Resumo: O presente trabalho investiga os livros didáticos de matemática, produzidos no Maranhão ou publicados por maranhenses, durante o século XIX. Para tal pesquisa, considera as produções que tratavam de juros, visto ser este conteúdo parte integrante do ensino da matemática que preparava os alunos já no ensino primário, para o ofício de comerciante. Toma por base então, a obra ?Primeiras Noções de Arithmética para o uso dos alunos das escolas de ensino primário", de Ayres de Vasconcellos Cardoso Homem, considerada a mais antiga, tendo como norte a pergunta: como era tratado o estudo de juros no livro e em outras produções maranhenses? A metodologia qualitativa analisa a partir de aportes teóricos de Marc Bloch, Gert Schubring, André Chervel, Roger Chartier e Allan Chopin, documentos de fontes primárias do século XIX, da província do Maranhão (pesquisa in loco) e de Portugal (via e-mail). Considera o contexto histórico na qual a obra foi escrita; dados biográficos de Ayres de Vasconcellos Cardoso Homem e a aritmética por ele apresentada no livro; além de um esboço histórico sobre os juros com enfoque em Nicolo Fontana de Brescia, o Tartaglia; Alexis Clairaut; e, Leonhard Paul Euler. Compara a obra de Homem com outros didáticos publicados no Maranhão ou escritos por maranhenses, no século XIX, além da obra de Cristiano Benedicto Ottoni por sua referência nacional; apresenta uma análise dos documentos oficiais que norteiam o ensino da matemática no Brasil e no Maranhão, nos dias atuais. Constata que a matemática escolar maranhense do século XIX, presente nos didáticos pesquisados, dava ênfase aos juros devido ao caráter comercial, pelo qual permeava a sociedade, reforçando a interferência da política e economia sobre a educação. / Abstract: We seek to investigate the mathematics textbooks produced in Maranhão or published by persons from Maranhão, during the nineteenth century. For this research, we consider the productions that dealt with interest, since it is part of the content of mathematics teaching that prepared students already in the primary for the occupation of the merchant. We take for base then, the most ancient work for us found and, on which, it produced the question that orientates our work: how it was treated the study of interest in the book "First Principles of Arithmética for the use of the students in primary schools" and others productions from persons from Maranhão? Qualitative methodology was performed with primary sources documents of the nineteenth century, from the Maranhão's province (research in loco) and Portugal (by email) and analyzed based on theoretical contributions from Marc Bloch, Gert Schubring, André Chervel, Roger Chartier and Allan Chopin. To answer this question we present the historical context in which the work was written, biographical data of Ayres de Vasconcellos Cardoso Man and arithmetic which he presented in the book, include historical sketch about interest focusing on Nicolo Fontana of Brescia, the Tartaglia; Alexis Clairaut; and, Leonhard Paul Euler. We compared the work of the Man with other textbooks published in Maranhão or written by persons from Maranhão, in the nineteenth century, and the work of Cristiano Ottoni by its National reference, we present an analysis of official documents that orientate the teaching of mathematics in Brazil and in Maranhão, in the current days. We found that in schools mathematics present in this textbooks emphasis at the interest due the commercial character, which permeated Maranhão's society, reinforcing the interference of politics and economics about education. / Mestrado / Historia da Matematica / Mestre em Matemática

When the effects of wind and air pressure combine with a high tide to give unusually high water levels this can lead to severe coastal flooding. This happened in England in early 1953 when 307 people died in the East Coast Flood. In Britain today such events, now called storm surges, are forecast daily using computer models from the National Oceanographic Centre in Liverpool, formerly the Liverpool Tidal Institute (TI). In 1919, when TI was established, such events were considered unpredictable. TI's researchers, Joseph Proudman (1888-1975), Arthur Doodson (1890-1968), Robert Henry Corkan (1906-1952) and Jack Rossiter (1919-1972), did much mathematical work to attempt to change this. In 1959 Rossiter published a set of statistical formulae to forecast storm surges on the East Coast and a national warning system was predicting such events using these formulae. At this point TI believed they had made surges at least as predictable as they could with their existing methods. This thesis provides a narrative of how this perceived rise in the predictability of surges happened, analysing how TI worked to achieve it between 1919 and 1959 by following two interwoven, contingent and contested threads: practices of calculation and patronage. A key aspect of this thesis is the attention I pay to material practices of calculation: the methods, technologies and management practices TI's researchers used in their mathematical work on storm surge forecasting. This is the first study by historians of oceanography or meteorology that pays this detailed level of attention to such practices in the construction of forecasting formulae. As well as using published accounts, I analyse statistical research in the making, through notes, calculations, graphs and tables produced by TI's researchers. They used particular practices of calculation to construct storm surges as calculable and predictable scientific objects of a specific kind. First they defined storm surges as the residuals derived from subtracting tidal predictions from observations. They then decided to use multiple regression, correlating their residuals with pressure gradients, to make surges predictable. By considering TI's practices of calculation the thesis adds to the literature on mathematical research as embodied and material, showing how particular practices were used to make a specific phenomenon predictable. I combine this attention to mathematical practice with analysis of why TI's researchers did this work. US historians have emphasised naval patronage of physical oceanography in this period but there is very little secondary literature for the British case. The thesis provides a British case study of patronage of physical oceanography, emphasising the influence on TI's work not only of naval patronage but also of local government, civil state and industrial patronage. Before TI's establishment Proudman argued that it should research storm surges to improve the Laplacian theory of tides. However, when the new Institute received patronage from the local shipping industry this changed and the work on forecasting surges was initially done as part of a project to improve the accuracy of tidal predictions, earning TI further patronage from the local shipping industry. After a flooding event in 1928 the reasons for the work and the patronage again shifted. Between then and 1959 TI did this work on commission from various patrons, including local government, civil state and military actors, which connected their patronage to national debates about state involvement in flood defence. To understand why TI's researchers worked on forecasting surges I analyse this complex mix of patrons and motivations. I argue that such complex patronage patterns could be fruitfully explored by other historians to further existing debates on the patronage of oceanography.

Esta pesquisa insere-se na temática da formação de professores de matemática. Apresenta um estudo sobre a relação entre a ciência e a religião presente nos livros História da Matemática, de Carl B. Boyer, e a Introdução à história da matemática, de Howard Eves, os mais utilizados no curso de licenciatura. Tendo em vista que as atuais propostas de ensino enfatizam que os alunos devem ser formados para serem cidadãos, considera que a forma com que essa relação aparece no material disponível pouco contribui para que isso ocorra. A tese partiu da idéia de que a história das ciências, na formação de professores de matemática, pode dar sustentação a uma educação científica que mostre a complexidade existente entre o pensamento religioso e o pensamento científico. Para isso, foram apresentados episódios da revolução científica causada por pensadores como Kepler, Galileu, Newton e Leibniz. O estudo enfatiza que a educação científica deve incluir uma discussão acerca da natureza do conhecimento científico e sua relação com outros aspectos da cultura, mostrando a existência de descontinuidades e revoluções, como propõe a historiografia atual. Para o enriquecimento do horizonte das discussões o trabalho levanta argumentos envolvendo aspectos sociais e éticos e valores, visando à formação do cidadão. Destaca, também, a tensão entre uma formação do professor mais técnica e uma formação mais ampla. / This research is inserted in the thematic of the graduation of math teachers. It presents a study about the relation between science and religion present in the books History of math, by Carl B. Boyer, and Introduction to the history of math, by Howard Eves, the most used in the graduation course. Having in sight that the current teaching proposals emphasizes that the students must be formed to become civilians, it considers that the way this relation appears in the available material doesn\'t contribute much for it to occur. The thesis stared from the idea that the history of sciences, in the formation of math teachers, can give support to a scientific education that shows the existing complexity between the religious thought and the scientific thought. For this to be made, episodes of the scientific revolution caused by thinkers like Kepler, Galileu, Newton, and Leibniz were presented. The study emphasizes that the scientific education must include a discussion about the nature of the scientific thought and it\'s relation with other aspects of culture, showing the existence of discontinuations and revolutions, as the current historiography proposes. For the enrichment of the discussions\' horizon this work shows arguments involving social and ethical aspects and values, in spite of forming a civilian. Also shows the tension between the more technical formation of a teacher and the most wide formation.