Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-06-14T11:55:40Z No. of bitstreams: 1 joseliolopesvalentimjunior.pdf: 8137715 bytes, checksum: 11a38a8a1ee15030396015030edcca40 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-07-13T14:03:45Z (GMT) No. of bitstreams: 1 joseliolopesvalentimjunior.pdf: 8137715 bytes, checksum: 11a38a8a1ee15030396015030edcca40 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-07-13T14:03:56Z (GMT) No. of bitstreams: 1 joseliolopesvalentimjunior.pdf: 8137715 bytes, checksum: 11a38a8a1ee15030396015030edcca40 (MD5) / Made available in DSpace on 2016-07-13T14:03:56Z (GMT). No. of bitstreams: 1 joseliolopesvalentimjunior.pdf: 8137715 bytes, checksum: 11a38a8a1ee15030396015030edcca40 (MD5) Previous issue date: 2013-03 / O presente trabalho teve como objetivo produzir um estudo histórico sobre a trajetória da geometria analítica como conteúdo da matemática escolar no ensino secundário, no período compreendido entre 1940 e 1970. Nessa pesquisa, o recorte temporal ficou restrito ao período no qual estiveram em vigência a Reforma Gustavo Capanema, a Portaria Ministerial de 1951 e um movimento de dimensão internacional denominado Movimento da Matemática Moderna (MMM). A pesquisa, inserida no campo da história da educação matemática, tomou os livros didáticos dessa disciplina para o colégio como fonte de pesquisa. Visando analisar historicamente as mudanças ocorridas nos livros didáticos relativamente ao conteúdo de geometria analítica, o presente trabalho histórico se apoiou nos pressupostos teóricos de historiadores e historiadores da educação que discutem a história cultural, a cultura escolar, as disciplinas escolares e os livros didáticos como objetos históricos, as noções de apropriação, de estratégias e de táticas. A análise dos livros revelou obras semelhantes e convergentes com os programas tanto nas décadas de 1940 quanto 1950. Especificamente em relação à geometria analítica na década de 1940, essa se constituiu num dos blocos que compunham a matemática do colégio, ainda como herança da matemática fragmentada em ramos das décadas anteriores. Na década de 1950, a geometria analítica deixou de aparecer explicitamente e ficou diluída entre o estudo de limites e derivadas, e restrita ao estudo da reta e da circunferência. A geometria analítica ganhou força novamente com o advento do MMM. Porém, não se verificou a padronização observada nas décadas anteriores, ao que tudo indica pela ausência de uma orientação oficial. / This study aimed to produce a historical study of the trajectory of analytic geometry and content of mathematics in secondary education, in the period between 1940 and 1970. In this research, the time frame was restricted to the period in which the Reformation were in effect Capanema, the Ministerial Decree of 1951, and a movement of international dimension named Modern Mathematics Movement (MMM). The research, part of the field of the history of mathematics education, took the textbooks of this discipline to the college as a research resource. To analyze the changes that have occurred historically in textbooks regarding, the content of analytical geometry, this historical work was supported in theoretical assumptions of historians and historians of education to discuss the cultural history, the school culture, school subjects and textbooks as objects historical, notions of ownership, strategies and tactics. The analysis revealed similar works and books converged with both programs in the 1940s as in 1950. Specifically in relation to analytic geometry in 1940, this constituted one of the blocks that made up the mathematical school, even as a legacy of mathematics fragmented into branches of the previous decades. In the 1950s, analytic geometry stopped appearing explicitly and was diluted by the study of limits and derivatives, and restricted to the study of the line and the circle. Analytic geometry has gained momentum again with the advent of the MMM. However, there was no standardization observed in previous decades, it seems the lack of official guidance.

Submitted by isabela.moljf@hotmail.com (isabela.moljf@hotmail.com) on 2016-08-17T14:44:02Z No. of bitstreams: 1 susanaribeirosoares.pdf: 11842089 bytes, checksum: 0c5ec7b70ed143dc180b7c2868bb3c0b (MD5) / Rejected by Adriana Oliveira (adriana.oliveira@ufjf.edu.br), reason: Consertar o nome do mestrado: Mestrado Profissional em Educação Matemática (veja folha de rosto da dissertação) on 2016-08-18T12:35:46Z (GMT) / Submitted by isabela.moljf@hotmail.com (isabela.moljf@hotmail.com) on 2016-08-18T12:43:34Z No. of bitstreams: 1 susanaribeirosoares.pdf: 11842089 bytes, checksum: 0c5ec7b70ed143dc180b7c2868bb3c0b (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-08-19T12:06:35Z (GMT) No. of bitstreams: 1 susanaribeirosoares.pdf: 11842089 bytes, checksum: 0c5ec7b70ed143dc180b7c2868bb3c0b (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-08-19T12:10:34Z (GMT) No. of bitstreams: 1 susanaribeirosoares.pdf: 11842089 bytes, checksum: 0c5ec7b70ed143dc180b7c2868bb3c0b (MD5) / Made available in DSpace on 2016-08-19T12:10:34Z (GMT). No. of bitstreams: 1 susanaribeirosoares.pdf: 11842089 bytes, checksum: 0c5ec7b70ed143dc180b7c2868bb3c0b (MD5) Previous issue date: 2013-03-22 / Este trabalho apresenta um estudo histórico da disciplina geometria analítica como componente curricular do curso de licenciatura em matemática da Universidade Federal de Juiz de Fora, nas décadas de 1960 e 1970. O estudo histórico sobre a disciplina baseou-se na análise de apostilas adotadas e indicadas como referência bibliográfica por várias décadas, em entrevistas com professores e ex-alunos do autor deste material e em levantamento bibliográfico de obras de geometria analítica. Entre as questões que procuramos responder neste trabalho destacamos: Como se estruturou a disciplina geometria analítica na UFJF? No percurso da pesquisa verificou-se que as apostilas produzidas pelo ex-professor da UFJF, Hélio Siqueira Silveira, tiveram um papel importante na estabilização da disciplina de geometria analítica. Tal conclusão foi evidenciada graças a indícios de uso do referido material tanto por estar presente em indicações bibliográficas de outros professores de geometria analítica, quanto pela retirada do material da biblioteca até os dias atuais. Além disso, constatou-se a escassez de obras de geometria analítica em português neste período. Com o intuito de compreender esta disciplina em outro contexto, externo ao da UFJF, efetuamos levantamento de acervo bibliográfico do Instituto de Matemática e Estatística da USP, bem como realizamos entrevistas com professoras e ex-alunas de geometria analítica nesta instituição. A similaridade desses contextos se deu em torno da estabilização da disciplina a partir de um texto de referência. Entre as várias observações decorrentes das investigações, pudemos notar que as apostilas trazem conteúdos que vão se estabilizar no ensino superior, como o estudo de vetores, especialmente a partir da representação em coordenadas e outros que não se estabilizam, como é o caso da geometria vetorial no plano. / This research presents a historical study of analytical geometry on a curricular component of teaching degree in Mathematics at Federal University of Juiz de Fora, in the 1960s and 1970s decades. The historical study on the subject was based on the analysis of supplementary material used and indicated as bibliographic reference during decades, in interviews with the author’s professors and ex-students as well as in a research of analytical geometry work. Among the questions we tried to answer in this research we highlight: How was the analytical geometry course structured in UFJF? As the research developed, it was observed that the supplementary material produced by the ex-teacher of UFJF, Helio Siqueira Silveira, had an important role in the stabilization of analytical geometry subject. The conclusion was evidenced thanks to the fact that this material has been mentioned by other geometry professors in bibliographical references and also because the material is borrowed from the library even today. Besides this, we could see that there is not enough analytical geometry work published in Portuguese at the present moment. In order to understand this subject in another context outside UFJF, we compiled the bibliographic collection of Institute Mathematics and Statistics , USP, as well as interviews with professors and ex-students of analytical geometry in that institution. The similarity between these two contexts happened around the stabilization of the subject from a reference text. Among the various observations resulting from the researches, we could notice that the supplementary material presents contents that will be stabilized in the University teaching, as the study of vector, specially from the representation in coordinates and others that do not stabilize themselves such as vectorial and plane geometry.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-07-28T14:19:58Z No. of bitstreams: 1 carlosrenatosoares.pdf: 1185338 bytes, checksum: c957d4c9167a840ad3db636f64c45f67 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-08-09T14:46:02Z (GMT) No. of bitstreams: 1 carlosrenatosoares.pdf: 1185338 bytes, checksum: c957d4c9167a840ad3db636f64c45f67 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-08-09T14:47:29Z (GMT) No. of bitstreams: 1 carlosrenatosoares.pdf: 1185338 bytes, checksum: c957d4c9167a840ad3db636f64c45f67 (MD5) / Made available in DSpace on 2017-08-09T14:47:29Z (GMT). No. of bitstreams: 1 carlosrenatosoares.pdf: 1185338 bytes, checksum: c957d4c9167a840ad3db636f64c45f67 (MD5) Previous issue date: 2011-04-05 / O presente trabalho está inserido no campo de pesquisa da história da educação matemática e refere-se às avaliações externas, em particular, à avaliação realizada no Estado de Minas Gerais pelo SIMAVE, Sistema Mineiro de Avaliação da Educação Pública, mais especificamente o Programa de Avaliação da Educação Básica, o Proeb, aplicado em turmas da terceira série do Ensino Médio, na cidade de Lavras. Nosso objetivo é investigar as transformações que vêm ocorrendo na disciplina Matemática, da terceira série do Ensino Médio, a partir da constituição do SIMAVE/Proeb no ano de 2000. Tratamos a questão numa perspectiva da história cultural, utilizando conceitos da história das disciplinas escolares. Analisamos documentos oficiais, oriundos da Secretaria de Estado da Educação de Minas Gerais (SEE-MG) e do Centro de Políticas Públicas e Avaliação da Educação da Universidade Federal de Juiz de Fora – Caed e depoimentos colhidos em conversas informais e entrevistas de professores. As conclusões apontam para uma interferência no currículo da disciplina, no momento em que os resultados da avaliação do SIMAVE são parâmetros para o recebimento de uma premiação instituída pelo governo de Minas para que as escolas alcançassem metas que variam ano após ano. Que os professores acabam sendo pressionados pelos colegas da escola em função deste prêmio ser balizado a partir dos resultados das avaliações dos conteúdos Matemática e Língua Portuguesa, que são as provas aplicada pelo SIMAVE/Proeb. / The present work follows in the search field of the History of Mathematics Education and refers to external evaluations, in particular, the assessment conducted in the State of Minas Gerais by SIMAVE, Sistema Mineiro de Avaliação da Educação Pública, specifically the Programa de Avaliação da Educação Básica, (PROEB) applied to classes of third grade high school in the city of Lavras. Our goal is to investigate the transformations that have been taking place in the Mathematics subject for the third grade of high school, since the constitution of SIMAVE / PROEB in 2000. We have treated the issue in the cultural history perspective, using concepts from the subject of history of school. We analyzed Official documents from the Secretaria de Estado da Educação de Minas Gerais (SEE-MG) and from the Centro de Políticas Públicas e Avaliação da Educação da Universidade Federal de Juiz de Fora – Caed. In addition, we analyzed testimonies gathered in informal conversations and interviews with teachers. The findings pointed to an interference in the subject’s curriculum since the evaluation results became SIMAVE’s parameters for receiving an award instituted by the government of Minas Gerais for the schools which achieve goals that vary every year. The teachers end up being pressured by classmates because the award competition is based on the results of mathematics and Portuguese’s evaluations, which are applied by SIMAVE / PROEB.

The thesis focuses on the reception history of Bernard Bolzano (1781- 1848) in the Czech intellectual culture of the 1945-1989 period. The aim of the thesis is not only to summarize existing studies of Bolzano's life and work or to study some of the partial themes related to Bolzano - but to discover basic features of Bolzano reception that can be found accross the different fields of Bolzano research and that are also connected to intellectual and political history background. The expected merit of the thesis can be considered from two different perspectives: In the context of intellectual history the reception of Bolzano is just a very partial theme, however it can expose some of more general features concerning Czech intellectual history of investigated period. From this point of view Bolzano is just a criterion of historical sources selection that enables to study very complex issue of the Czech intellectual history. In the context of Bolzano research this thesis is also a contribution to the better understanding of Bolzano's life and work. The thesis is pointing out themes which should be researched more thoroughly and, it is more important, it discovers the basic contexts of the potential further studies. Keywords: Bernard Bolzano (1781-1848), Czech history 1945-1989, Czech culture 1945-1989,...

Cryptography fascinates people of all generations and is increasingly presented as an example for the relevance and application of the mathematical sciences. Indeed, many principles of modern cryptography can be described at a secondary school level. In this context, the mathematical background is often only sparingly shown. In the worst case, giving mathematics this character of a tool reduces the application of mathematical insights to the message ”cryptography contains math”. This paper examines the question as to what else cryptography can offer to mathematics education. Using the RSA cryptosystem and related content, specific mathematical competencies are highlighted that complement standard teaching, can be taught with cryptography as an example, and extend and deepen key mathematical concepts.

Made available in DSpace on 2016-04-27T16:58:08Z (GMT). No. of bitstreams: 1 dissertacao_gustavo_miranda.pdf: 594697 bytes, checksum: 12a44cd827b057543633c4cda536191f (MD5) Previous issue date: 2004-12-03 / With the purpose of studying the calculus teaching history and, particularly, the consequences of Calculus Made Easy (1910) in the mathematics education context, this work intends to make an historical analysis to clarify the connections between Silvanus Phillips Thompson (its author) and the education in the early twentieth century, mainly mathematics education. Thompson was concerned about Physics and Radiology, however, at the dawn of the new century, his interests in technical education had also burgeoned. One of his goals was to demystify Calculus, tackling the subject intuitively Calculus Made Easy. The book did not draw much respect from mathematicians and was acridly criticized / Com o intuito de estudar a história do ensino de Cálculo e, mais especificamente, os desdobramentos do livro Calculus Made Easy (1910) no contexto da educação matemática, este trabalho procura fazer uma análise histórica que elucide as relações entre Silvanus Phillips Thompson (autor do livro) e a educação do início do século XX, particularmente a educação matemática. Thompson legou muito às áreas da física e da radiologia, porém, com a chegada do novo século, passou a se dedicar intensamente à educação técnica de seus compatriotas ingleses. Tal dedicação, aliada a preocupações políticas e sociais da época, foi crucial para a publicação do seu texto didático mais polêmico: o Calculus Made Easy (1910). A polêmica estava atrelada às discussões sobre o rigor e a intuição no ensino de matemática, visto que o didático tratava dos conceitos fundamentais do Cálculo de maneira intuitiva e com aplicações. Apesar das críticas e do repúdio dos matemáticos da época, Thompson granjeou a admiração e o respeito de muitos alunos de Cálculo durante o século XX. Tornou-se, assim, parte da história do ensino de Cálculo

Made available in DSpace on 2016-04-28T14:16:43Z (GMT). No. of bitstreams: 1 Alexandre Marcos de Mattos Pires Ferreira.pdf: 6236788 bytes, checksum: 4d3ad3ea20314c747f667d8c94a66e04 (MD5) Previous issue date: 2009-10-09 / The present work refers to a study about creation of Faculty of Philosophy, Sciences and Letters / USP, specifically about the early formation of researchers and teachers of mathematic and physic in Sao Paulo. The objective of the work was to know how was occurred the formation of these professionals in the period from 1934 to 1936. The employed method was constituted in using authorities depositions that are preserved in books, in magazines and in the registered interviews. The most important fountains were: Anuário da Faculdade de Filosofia, Ciências e Letras da USP, years: 1934, 1935, 1936, 1937 and 1938; Anuário do Centro Brasileiro de Pesquisas Físicas and of Sociedade Brasileira de Matemática / O presente trabalho refere-se a um estudo sobre a criação da Faculdade de Filosofia, Ciências e Letras da USP, especificamente sobre a formação inicial de pesquisadores e professores de Matemática e de Física em São Paulo. Seu objetivo consiste em explicitar como ocorreu a formação de pesquisadores e professores de matemática e física no período de 1934 a 1936. O método empregado constituiu em utilizar os depoimentos de autoridades da época que se encontram preservados em livros, em revistas e nas entrevistas documentadas. As fontes mais importantes foram: Anuário da Faculdade de Filosofia, Ciências e Letras da USP, anos: 1934, 1935, 1936, 1937 e 1938; Anais do Centro Brasileiro de Pesquisas Físicas e da Sociedade Brasileira de Matemática

Sonderausgabe des "Dresdner Universitätsjournal" von 2001

Bien que ma dissertation de thèse consiste essentiellement en trois pièces de nature assez distincte (il s'agitde la traduction en tchèque de l'Analyse des infiniment petits, son commentaire et l'étude d'introduction),cependant, je subsume le tout sous une idée unificatrice de la loi de continuité leibnizienne qui régit le systèmede symboles au fondement du calcul différentiel. Quant à la première partie, elle décrit premièrement l'histoire dela vie du marquis de l'Hospital dite « officielle» ou bien « académique » due à l'Éloge de Bernard de Fontenellequi sert de l'arrière-plan de la seconde partie, de l'étude introductrice, du portrait « caché», consistant en l'analysedes succès géométriques du marquis, des solutions de problèmes physico-géométrique célèbres en comparaisonde celles de Jean Bernoulli, son jeune précepteur – fondée bien évidemment sur la correspondance mutuelle. Enraison de la nature du calcul leibnizienne tant physique que géométrique je démontre que c'était précisément lapureté géométrique de son esprit qui faisait obstacle à l’invention géométrique du marquis. En deuxième lieu jeprésente la description des controverses qui ont éclaté entre Leibniz et Nieuwentiijt sur la questions de fondementdu calcul, tout en précisant sur les écrits leibniziennes la nature symbolique ambiguë de différentielles. L'autrecontroverse, entre Rolle et Varignon, sert à décrire les contrainte institutionnelles du développement du calculaussi que les explication fondatrices de la part de Varignon qui indique la futur transformation newtonienne ducalcul infinitésimal. Enfin le commentaire, d'après ladite idée unificatrice, marque sur des exemplesmathématiques la transformation algébrique de la géométrie grecque pendant le XVIIe siècle tout en illustrant lesarticles de l'Analyse et comparant ses sources bernoulliennes. / The basis of my dissertation consists in three rather distinct parts, that is Czech translation, a commentaryand introduction to the famous Analyse des infiniment petitis by marquis the l'Hospital. Nevertheless I unify thewhole in virtue of the leibnizien metaphysical idea of the law of continuity governing the symbolic systemfundamental to the differential calculus of Leibniz. Concerning the first part of the introduction I represent the socalled academical or official picture of marquis de l'Hospital based on the Éloge by Bernard de Fontenelle. I usethis picture as a background to the so called hidden picture of the marquis, which consists in the analysis of thephysico-geometrical problems solved by the marquis de l'Hospital in comparison to those of Johann Bernoulli,based naturally on the correspondence of the two of them. I demonstrate, regarding the nature of the calculusboth physical and geometrical, that it was precisely the geometrical purity of his mind had forbidden him to makeinventions in geometry, unlike Johann Bernoulli. In the third part I describe the controversies that made part ofthe development of the calculus; firstly the controversy between Nieuwentijt and Leibniz concerning thefundamental questions of calculus. I precise on this occasion my views on the nature of leibnizian calculus asstated above, that is ambiguous symbolism of differentials. The second controversy, between Rolle and Varignonputs forward institutional obstacles of the development of the calculus as well as the foundational attempts madeby Varignon that indicated the future transformation of the calculus according to the spirit of Newton. Finally thecommentary, by the symbolic idea above, indicates the algebraical shift of the 17th century geometry; illustratesarticles of the Analyse des infiniment petits and shows the dependence on Bernoulli's inventions. / Práce je věnována přelomové, epochální práci prvního období infinitesimálního počtu, Analyse desinfiniment petits Guillauma, markýze de l'Hospitala. Dělí se na tři podstatné části: překlad, komentář a úvodnístudii. Účelem je představit toto dílo v jeho jedinečných okolnostech jeho vzniku a zároveň určit jeho obecnémísto v dějinách matematických idejí. Úvodní studie je věnována především osobnosti markýze de l'Hospitala.Na pozadí rozvoje infinitesimálního počtu se vykresluje jeho po dlouhou dobu oficiální obraz v dějináchmatematiky. V druhé části se rozebírá blízký lidský i matematický vztah markýze de l'Hospitala s JohannemBernoullim; a na základě rozboru markýzových geometrických úspěchů se ve srovnání s řešeními JohannaBernoulliho, bratra Jakoba a Leibnize se podává obecná charakteristika prvního infinitesimálního počtu cobygeometrické i fyzikální teorie a možností jeho objevitelských cest prostřednictvím analogií založených nanejzazším požadavku harmonie přírody. Třetí část úvodní studie v historických souvislostech sporů a výměnstran základů diferenciálního počtu objasňuje z hlavní ideje Leibnizovy symbolické přírody, totiž zákonakontinuity, povahu diferenciálního znaku dx, jeho radikální novost a argumenty ospravedlnění přesnostiinfinitesimálního počtu. Druhá kontroverze, která je v práci představena, probíhá mezi Rollem a Varignonem;podstatnými rysy jsou institucionální podmínky rozvoje počtu a Varignonovy pokusy o důkazy nekonečněmalých v Newtonově duchu. Komentář Analýzy nekonečně malých slouží k historickému, filologickému afilosofickému objasnění nových metod a dokládá utváření Analýzy nekonečně malých z jejích zdrojů, tj.přednášek Johanna Bernoulliho markýzi de l'Hospitalovi a jejich dopisové výměny

Sonderausgabe des 'Dresdner Universitätsjournal' von 2001:Zum Geleit S. 3 Vorwort S. 4 Inhaltsverzeichnis S. 5 Vom Knopf an der Turmspitze der Annenkirche: Die Geometrie des Gotthelf Fischer (1763–1832) S. 6 Frühe Lehrerbildung in Dresden: Lehrer und Eisenbahner – anfänglich stärkste Absolventengruppen S. 8 Junge Wissenschaftler auf neuen Lehrstühlen: Antimathematische Tendenzen – chancenlos unter Gustav Zeuner (1828–1907) S. 10 Von der Feinmechanik zur Mathematik: Die Verbindung von Technik, Kunst und darstellender Geometrie S. 12 Zwischen Mathematik und Physik: Der 2. Mathematische Lehrstuhl unter Aurel Voss (1845–1931) S. 14 Mathematiker als Bibliothekare: Die Katalogisierung – weiterentwickelt von Mathematikern S. 15 Gebündelte Reformbestrebungen: Neuer Aufschwung nach einem schwierigen Jahrzehnt S. 16 Neues vom Kreuzgymnasium: Einführung der Differential- und Integralrechnung in Mathematiklehrpläne S. 18 Mathematiker in der Gesellschaft ISIS: Wachsendes Interesse an mechanischen Rechengeräten S. 20 Rententafeln und Nettotarife: Zur Geschichte des Versicherungstechnischen Seminars S. 22 Dresdner als Ordinarien in Heidelberg: Erfolgreich auf dem Gebiet der kombinatorischen Topologie S. 24 Ein mitreißender Hochschullehrer: Gerhard Kowalewski (1876–1950) – Lehrer von Generationen Studierender S. 26 Frauen leben für die Mathematik: Dresdner Mathematik-Promovendinnen S. 28 Wissenschaftler und Humanist: Erich Trefftz (1888–1937) – „Motor“ der Akademischen Fliegergruppe Dresden S. 30 Mathematik und Politik: Personelle Veränderungen in der Dresdner Mathematik um 1940 S. 32 Impressum / Bildnachweis S. 34