The aim of this study was to investigate the roles of year in teacher education program and gender on prospective elementary mathematics teachers&rsquo / knowledge of history of mathematics and their attitudes and beliefs towards the use of history of mathematics in the teaching and learning of mathematics. Moreover, the relationship between prospective teachers&rsquo / knowledge of history of mathematics and their attitudes and beliefs about the history of mathematics usage was examined. The data of the study were obtained from 1593 prospective teachers who were enrolled in first, second, third, and fourth years of Elementary Mathematics Education undergraduate program of nine universities located in seven geographical regions of Turkey through clustered random sampling. The scales used in the data collection were Knowledge of History of Mathematics (KHM) Test and Attitudes and Beliefs towards the Use of History of Mathematics in Mathematics Education (ABHME) Questionnaire. The two-way ANOVA results clarified that prospective teachers&rsquo / knowledge of history of mathematics improved as the years enrolled in the program increased. Results also revealed that males had significantly higher mean scores on KHM Test than females in the first two years of the program. In the third and fourth years, this situation reversed such that females had higher KHM mean scores, but this difference was not statistically significant. Results also showed that prospective teachers&rsquo / ABHME mean scores increased as years of enrollment in the program increased. More clearly, senior prospective teachers&rsquo / relevant mean scores were significantly higher than that of freshmen and sophomores, and juniors&rsquo / attitudes and beliefs were significantly higher than that of freshmen. In addition, females&rsquo / ABHME mean scores were significantly higher than that of males for all years. Lastly, a positive correlation between prospective elementary mathematics teachers&rsquo / KHM mean scores and ABHME mean scores was found through Pearson product-moment correlation analysis.

This thesis addresses an issue in the philosophy of Mathematics which is little discussed, and indeed little recognised. This issue is the phenomenon of a ‘change of setting’. Changes of setting are events which involve a change in a scientific framework which is fruitful for answering questions which were, under an old framework, intractable. The formulation of the new setting usually involves a conceptual re-orientation to the subject matter. In the natural sciences, such re-orientations are arguably unremarkable, inasmuch as it is possible that within the former setting for one’s thinking one was merely in error, and under the new orientation one is merely getting closer to the truth of the matter. However, when the subject matter is pure mathematics, a problem arises in that mathematical truth is (in appearance) timelessly immutable. The conceptions that had been settled upon previously seem not the sort of thing that could be vitiated. Yet within a change of setting that is just what seems to happen. Changes of setting, in particular in their effects on the truth of individual propositions, pose a problem for how to understand mathematical truth. Thus this thesis aims to give a philosophical analysis of the phenomenon of changes of setting, in the spirit of the investigations performed in Wilson (1992) and Manders (1987) and (1989). It does so in three stages, each of which occupies a chapter of the thesis: 1. An analysis of the relationship between mathematical truth and settingchanges, in terms of how the former must be viewed to allow for the latter. This results in a conception of truth in the mathematical sciences which gives a large role to the notion that a mathematical setting must ‘explain itself’ in terms of the problems it is intended to address. 2. In light of (1), I begin an analysis of the change of setting engendered in mathematical logic by Gottlob Frege. In particular, this chapter will address the question of whether Frege’s innovation constitutes a change of setting, by asking the question of whether he is seeking to answer questions which were present in the frameworks which preceded his innovations. I argue that the answer is yes, in that he is addressing the Kantian question of whether alternative systems of arithmetic are possible. This question arises because it had been shown earlier in the 19th century that Kant’s conclusion, that Euclid’s is the only possible description of space, was incorrect. 3. I conclude with an in-depth look at a specific aspect of the logical system constructed in Frege’s Grundgesetze der Arithmetik. The purpose of this chapter is to find evidence for the conclusions of chapter two in Frege’s technical work (as opposed to the philosophical). This is necessitated by chapter one’s conclusions regarding the epistemic interdependence of formal systems and informal views of those frameworks. The overall goal is to give a contemporary account of the possibility of setting-changes; it will turn out that an epistemic grasp of a mathematical system requires that one understand it within a broader, somewhat historical context.

Students today need to be taught not only the real life context of their mathematics lessons but also the historical context of the theory behind their mathematics lessons. Using history to teach mathematics, makes your lessons not only interesting but more meaningful to a large percentage of your students as they are interested in knowing the who, how and why about certain rules, theorems, formulas that they use everyday in class. Students are captivated by learning the history behind mathematicians, rules, etc. and therefore can link the lesson to something in history and a concept. Even learning the mathematics behind historical events motivates and interests them. They cannot get enough!

Orientador: Miriam Godoy Penteado / Banca: Claudia Coelho de Segadas Vianna / Banca: Marcos Teixeira Vieira / Resumo: Esta dissertação apresenta uma pesquisa de mestrado em Educação Matemática cujo objetivo foi analisar o processo de construção e adaptação de uma História em Quadrinhos sobre Matemática para alunos cegos e videntes. No texto a revista é denominada História em Quadrinhos Adaptada - HQ-A. Para a realização da pesquisa buscou-se suporte teórico em trabalhos sobre Educação Inclusiva com ênfase na educação de cegos e sobre o uso educacional de histórias em quadrinhos. A abordagem metodológica é a de design social, considerando-se que o processo de construção contou com a participação de possíveis usuários. A HQ-A possui 76 páginas impressas em um papel A4 (140g) adequado para escrita e leitura manual do sistema braille e adaptada em relevo. Para as adaptações foram utilizadas uma máquina de escrever braille e uma carretilha de costura, e, para garantir uma leitura pelo tato, houve a ajuda de um jovem cego. Espera-se que este material seja utilizado como recurso de ensino em sala de aula por todos os alunos / Abstract: This thesis presents a research in the field of mathematics education whose aim was to analyze the process of construction and adaptation of a comic book about mathematics to blind students and seers. In the paper, the material is called Comic Book Adaptation - HQ-A. To carry out the research we aimed to support theoretical work about Inclusive Education with an emphasis on education for the blind people and the use of educational comics. The methodological approach is to social design, considering that the construction process only happens with the participation of potential users. HQ-A has 76 pages printed on A4 paper (140g) suitable for reading and writing manual Braille and adapted in relief. For the adjustments were used a Braille typewriter and a reel of sewing, and to ensure a reading by touch, there was the help of a young blind. Adaptations in HQ-A were in favor of building a reading material accessible by feel, because tactile representation is very important for blind readers. In addition to HQ-A can also be read by sighted people. It is hoped that this material is used as a teaching resource in the classroom for all students / Mestre

My thesis deals with various methods of solving the correlation of~the~diametres of four mutually tangent circles. It also deals with the history of~the~derivation of mathematical property. The didactic part contains a book of solved tasks. It involves the topic of Apollony fractals, gothic vaults, examples of~mutually tangent circles and set of exercises for practising different solutions of the various cases.

Este trabalho apresenta uma pesquisa sobre a utilização da História da Matemática no ensino básico do Colégio Militar do Rio de Janeiro CMRJ através de manifestações artísticas, fazendo uso, principalmente, do teatro,para que alunos percebam a matemática como uma ciência temporal, humana e sujeita a interferências políticas e sociais e, dessa forma, desenvolver a criticidade, aumentar a sensibilidade e o senso de solidariedade. A partir de um tema da história envolvendo fatos matemáticos os alunos pesquisam, escrevem uma peça teatral e encenam para um público formado por pessoas da comunidade escolar. Como a intenção é tornar essa prática efetiva, a pesquisa culmina na fundação do Clube de História da Matemática, espaço onde, espera-se, atividades recorrentes sejamdesenvolvidas, atraindo alunos afetos tanto às ciências humanas e sociais como às ciências exatas. Realiza-se um estudo de caso com observação participante, por ser o autor também professor do CMRJ. Este estudo busca referência teórica principalmente em autores relacionados à História da Matemática, Arte na Educação, gestão democrática, relações de poder e na legislação vigente. A pesquisa aponta a importância do trabalho com a história e com a arte e nos leva a concluir que, para formar cidadãos participativos e críticos, o primeiro passo é a sociedade tornar-se participativa e crítica, sendo a escola o principal locuspara tal formação. / This paper presents a survey on the use of history of mathematics in basic education at the Military College of Rio de Janeiro - CMRJ through artistic expressions, making use mainly of the theater, so that students understand mathematics as a temporal science, human science and subject to political interference and social interference and thus develop criticality, increasing the sensitivity and the sense of solidarity. From a theme of the story involving math facts students research, write and act out a play for an audience of people from the school community. As the intention is to make this effective practice, research culminates in the founding of the Club History of Mathematics, space where, hopefully, recurring activities is developed, attracting students affects both the humanities science and socia sciencel and the sciences. Carried out a case study with participant observation, as the author also professor CMRJ. This study seeks theoretical reference authors mainly related to the History of Mathematics, Art Education, democratic management, power relations and current legislation. The research points to the importance of working with the history and the art and leads us to conclude that, to form critical citizens and participatory citizens, the first step is the society become critical and participatory, with the school being the main locus for such training.

Made available in DSpace on 2014-06-11T19:24:52Z (GMT). No. of bitstreams: 0 Previous issue date: 2009-12-22Bitstream added on 2014-06-13T19:52:44Z : No. of bitstreams: 1 martines_mcs_me_rcla.pdf: 781716 bytes, checksum: 8987931f68f38e58e234c3d74a591306 (MD5) / Esta dissertação tem por objetivo trabalhar Topologia no Ensino Médio, usando como recurso pedagógico, a História da Matemática. Iniciaremos com o trabalho de Euler sobre as pontes de Königsberg, pois é com ele que se dá início as pesquisas neste ramo científico da Matemática. Em seguida resgataremos a descoberta de Euler acerca da “propriedade geral dos sólidos limitados por faces planas”, conhecida hoje como relação de Euler. Seu trabalho, intitulado “Demonstratio nonnullarum insignium proprieatatum, quibus solida hedris planis inclusa sunt praedita”, surgiu do incômodo de demonstrar que existia uma propriedade geral para os sólidos limitados por faces planas, uma vez que a propriedade geral para os polígonos já era conhecida. Também iremos trabalhar com as obras de Cauchy e Lhuilier que contribuíram enormemente com a evolução da propriedade citada por Euler. Para encerrar, destacaremos algumas observações sobre a Característica de Euler, assunto que se desenvolveu a partir da preocupação deste e que hoje faz parte da Topologia Algébrica. / This dissertation aims to work topology in high school using as a teaching resource the History of Mathematics. We will start with Euler’s work about the bridges of Königsberg, is with them that begins the research in this scientific branch of Mathematics. After that, we will redeem Euler’s discovery about the “ general property of the solids bounded by flat faces”, known today as Euler’s relation. His work, entitled “ Demonstratio nonnullarum Insignium proprieatatum, quibus solida sunt hedras planis included praedita” arose from the inconvenience of demonstrate that there was a general property for solid bounded by flat faces since the general property for the polygons was already known. We will also work with Cauchy and Lhuilier’s works, which contributed a lot of the evolution of property mentioned by Euler. As closing, we will detach some observations about Euler’s Characteristic, a subject that was develop from Euler’s concerns and now is part of Algebraic Topology.

Made available in DSpace on 2014-06-11T19:24:53Z (GMT). No. of bitstreams: 0 Previous issue date: 2007-03-01Bitstream added on 2014-06-13T18:52:56Z : No. of bitstreams: 1 bonfim_sh_me_rcla.pdf: 808338 bytes, checksum: 460ea850d7abfe2858f1146e6f6d5902 (MD5) / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / O escopo dessa pesquisa trata de identificar elementos matemáticos presentes na narrativa da descrição do primeiro templo do povo judeu, ou seja, do Templo de Jerusalém, em quatro versões bíblicas distintas. Deste modo, durante seu desenvolvimento, fizeram-se presentes determinadas ticas de matema relacionadas a essa descrição que corroboram o quadro da análise efetuada. Para tanto, a condução do trabalho teve como aportes os olhares da Etnomatemática, além de recorrências a estudos de História da Arquitetura, bem como de Geometria Sagrada e Simbolismo Religioso. Um conciso relato sobre a história do povo judeu, compreendendo desde a sua formação até a destruição da última reconstrução do Templo, com a conseqüente invasão da cidade de Jerusalém pelos romanos, compõe o texto com vistas a uma contextualização histórica. Ao final, verificaram-se características de uma descrição de natureza simples, embora a obra tenha possuído um caráter suntuoso. Além disso, depreende-se também a existência de uma matemática voltada à aplicabilidade construtiva, à presença de formas geométricas, unidades de peso, comprimento, capacidade, etc., possivelmente relacionadas à edificação do Templo e às atividades realizadas. Essas características se constituem como parte do quadro dos elementos matemáticos procurados. / This research aims to identify mathematical elements in the narrative of the description concerned with the first temple of the Jewish people, the Temple of Jerusalem, in four different biblical versions. In that way, during the development of this research, it has turned out determined ticas of matema related to those descriptions that corroborate an outline of the analysis. For that, the drive of this work had contributions of Ethnomathematics, studies of History of Architecture, Sacred Geometry and Religious Symbolism. A concise report on history of the Jewish people, seeking an understanding of their formation and the destruction of the last reconstruction of the Temple with the consequent invasion of the city of Jerusalem by Romans compose a text, which aims to present a historical context. In the end, characteristics of a description of simple nature were verified, although the work has got a magnificent character. Besides that, it has also been inferred the existence of mathematics turned to a constructional applicability, the presence of geometric shapes, units of weight, length, capacity, etc., possibly related to the construction of the temple and to the carried out activities. Those characteristics constitute part of an outline of the sought mathematical elements.

Made available in DSpace on 2014-06-11T19:24:53Z (GMT). No. of bitstreams: 0 Previous issue date: 2009-04-30Bitstream added on 2014-06-13T18:52:56Z : No. of bitstreams: 1 mariotto_r_me_rcla.pdf: 3109190 bytes, checksum: 20e6c44e3a7e7ff868db70b04527f232 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Esta pesquisa situa-se na área de História da Matemática, e pertence às publicações do Grupo de Pesquisa em História da Matemática e/ou suas relações com a Educação Matemática (GPHM) da UNESP de Rio Claro. Com o olhar voltado à História da Educação Matemática, este trabalho analisa a obra literário-educacional do professor Mario Tourasse Teixeira. Este professor foi uma personalidade importante, tanto para o desenvolvimento da Matemática na UNESP de Rio Claro quanto para a criação do curso de pós-graduação em Educação Matemática nesta universidade. A obra analisada (estórias narrativas e ilustradas, poemas, contos e peças teatrais) é constituída pelos textos inéditos encontrados nos manuscritos do autor, e também por suas publicações no SAPEANDO, o boletim informativo do S.A.P.O. (Serviço Ativador em Pedagogia e Orientação). Esse foi um movimento de grande repercussão nas questões de ensino e aprendizagem em Matemática na década de 1970, tendo sido liderado pelo professor Mario, entre outros. Em especial, são destacadas aqui as estórias da série “As Desventuras do Figurinha Difícil”, visto que nelas é evidenciado muito de seu pensamento acerca do mundo, da matemática e da educação. Também são explicitadas as teorias sobre Educação presentes nos textos educacionais do autor. Tais idéias revelam este professor como um dos pioneiros na busca pelas questões da Educação Matemática e pela busca de alternativas para a sala de aula, mesmo em caráter universitário. Tendo como base esses argumentos, o presente trabalho conclui que entender suas aspirações em Educação, de modo geral, contribui para a construção da História da Matemática no Brasil, e em particular no estado de São Paulo. / This research pertains to the history of mathematics and is a publication of the Research Group in History of Mathematics and/or its associates with Mathematics Education (GPHM) UNESP, Rio Claro. This work examines the literary and educational accomplishments of Professor Mario Tourasse Teixeira. This professor played an instrumental role in the development of mathematics at UNESP, Rio Claro and in the creation of the Graduate Program of mathematics education in this university. The works examined consist of unpublished texts (illustrated stories and narratives, poems, stories and plays) found in manuscripts of the author and also of its publications in SAPEANDO, the newsletter of S.A.P.O. (Active Service in Education and Guidance). The movement fomented by these works a significant effect on the teaching of mathematics in the 1970s, and was, among others, led by Professor Tourasse. In particular, there is the story in the series The Misfortunes of the Figurinha Dificil, in which are evident many of his thoughts about the world, the mathematics and the education. The author's theories on education expounded in his educational texts are also discussed in this work.These ideas show this professor as one of the pioneers in the search for the field of Mathematics Education and for the search for alternatives to the classroom, even in the university. Understanding Professor Tourasse educational aspirations contributes to the construction of the History of Mathematics in Brazil and in particular in the state of São Paulo.

Orientador: Ubiratan D'Ambrosio / Banca: Marcos Vieira Teixeira / Banca: Edilson Roberto Pacheco / Banca: Sergio Roberto Nobre / Resumo: O escopo dessa pesquisa trata de identificar elementos matemáticos presentes na narrativa da descrição do primeiro templo do povo judeu, ou seja, do Templo de Jerusalém, em quatro versões bíblicas distintas. Deste modo, durante seu desenvolvimento, fizeram-se presentes determinadas ticas de matema relacionadas a essa descrição que corroboram o quadro da análise efetuada. Para tanto, a condução do trabalho teve como aportes os olhares da Etnomatemática, além de recorrências a estudos de História da Arquitetura, bem como de Geometria Sagrada e Simbolismo Religioso. Um conciso relato sobre a história do povo judeu, compreendendo desde a sua formação até a destruição da última reconstrução do Templo, com a conseqüente invasão da cidade de Jerusalém pelos romanos, compõe o texto com vistas a uma contextualização histórica. Ao final, verificaram-se características de uma descrição de natureza simples, embora a obra tenha possuído um caráter suntuoso. Além disso, depreende-se também a existência de uma matemática voltada à aplicabilidade construtiva, à presença de formas geométricas, unidades de peso, comprimento, capacidade, etc., possivelmente relacionadas à edificação do Templo e às atividades realizadas. Essas características se constituem como parte do quadro dos elementos matemáticos procurados. / Abstract: This research aims to identify mathematical elements in the narrative of the description concerned with the first temple of the Jewish people, the Temple of Jerusalem, in four different biblical versions. In that way, during the development of this research, it has turned out determined ticas of matema related to those descriptions that corroborate an outline of the analysis. For that, the drive of this work had contributions of Ethnomathematics, studies of History of Architecture, Sacred Geometry and Religious Symbolism. A concise report on history of the Jewish people, seeking an understanding of their formation and the destruction of the last reconstruction of the Temple with the consequent invasion of the city of Jerusalem by Romans compose a text, which aims to present a historical context. In the end, characteristics of a description of simple nature were verified, although the work has got a magnificent character. Besides that, it has also been inferred the existence of mathematics turned to a constructional applicability, the presence of geometric shapes, units of weight, length, capacity, etc., possibly related to the construction of the temple and to the carried out activities. Those characteristics constitute part of an outline of the sought mathematical elements. / Mestre