L'activité d'Eudoxe de Cnide, savant grec du IVe siècle av. n. è., s'est déployée dans de nombreux domaines incluant la philosophie, les mathématiques, l'astronomie, la géographie, la médecine, la législation et l'astrologie. La présente thèse de doctorat consiste en une édition traduite et commentée des fragments et témoignages relatifs à Eudoxe. Elle réunit quelque 800 passages de textes antiques et byzantins faisant référence à Eudoxe. Elle inclut notamment des textes inédits et des conjectures nouvelles. L'édition est accompagnée de la première traduction en langue moderne de tous les fragments et témoignages antiques relatifs à Eudoxe. Le commentaire donné en notes de bas de page éclaire les difficultés d'interprétation et s'attache à déterminer la valeur des différentes sources pour la reconstruction de l'œuvre d'Eudoxe. La notice qui précède l'édition traduite et commentée contient un exposé synthétique de l'activité intellectuelle d'Eudoxe, qui restitue sa profondeur et sa cohérence dans l'ensemble des domaines où elle s'est déployée, tout en la replaçant dans son contexte historique et culturel. / Eudoxus of Cnidus, a Greek scholar from the 4th century BCE, was active in a wide range of fields including philosophy, mathematics, astronomy, geography, medicine, legislation and astrology. This doctoral thesis consists of an edition, translation and commentary of the fragments and testimonia concerning Eudoxus. It brings together some 800 passages from ancient and Byzantine texts dealing with Eudoxus. In particular, it includes unpublished texts and new conjectures. The edition is comes with the first modern-language translation of all ancient fragments ant testimonia concerning Eudoxus. The commentary provided in the footnotes sheds light on problems of interpretation and endeavours to determine the value of the various sources for reconstructing Eudoxus' work. The introduction preceding the edition, translation and commentary contains a synthetic account of Eudoxus' intellectual activity which reconstitutes its depth and consistency in all of the fields in which it took place, and puts it back in its historical and cultural context.

A dissertação apresenta uma pesquisa que se situa no campo da História da Educação Matemática e que tomou por objeto de estudo a formação dos professores primários no Instituto de Educação General Flores da Cunha (IE), em Porto Alegre. Dialogando com autores da Histórica Cultural e da Histórica Oral busca-se compreender os modos de apropriação, aprender para ensinar os saberes matemáticos na instituição nas décadas de 1950 a 1970, período caracterizado pelo Movimento da Matemática Moderna (MMM). Inferiu-se, a partir das evidências verificadas em documentos localizados no acevo do Laboratório de Matemática da instituição e das entrevistas realizadas com as ex-alunas e ex-professoras, que o MMM norteou a formação das normalistas. Tal movimento materializou-se nas ações das professoras e estudantes que aprendiam e ensinavam a Moderna Matemática, nos materiais didáticos estudados e produzidos pelas normalistas no Laboratório de Matemática da instituição, bem como nos discursos das ex-alunas e da imprensa da época. Evidenciou-se que o envolvimento das normalistas com a renovação da Matemática, no interior do IE, partiu, inicialmente, das inquietações e ações da professora Odila Barros Xavier que almejava mudanças no ensino da Matemática desde o final da década de 1940. Na época, a professora já estudava mudanças no currículo da Matemática do Curso Normal, na incansável busca pela renovação na formação das professoras primárias Através da fundação e organização do Laboratório de Matemática, a partir dos anos 1950, a professora Odila amplia os espaços de formação de professores para além das portas do IE e contribui para a divulgação do pensamento modernizador, coordenando grupos de estudos, ministrando cursos sobre fundamentação teórica e metodológica da Matemática Moderna e incentivando práticas em aulas experimentais com materiais manipuláveis. O ápice deste percurso ocorre no final dos anos 1960 e início dos anos 1970 que, por conseguinte, é fundado o Grupo de Estudos sobre o Ensino da Matemática de Porto Alegre (GEEMPA), sob a liderança da professora Esther Grossi. Através do GEEMPA foram oportunizados cursos de formação de professores com a presença de vários estudiosos, entre eles, Zoltan Dienes, um dos principais autores estudados no Instituto de Educação General Flores da Cunha. Ao longo dos anos 1950 e 1970, a instituição tornou-se referência não só na formação inicial das normalistas, mas também na formação continuada dos professores de Matemática no Rio Grande do Sul, com reconhecimento nacional e internacional, no período marcado pelo MMM. / The dissertation presents a research that is located in the field of History of the Mathematics Education and that took as object of study, the formation of primary teachers at the Flores da Cunha (IE) General Education Institute in the city of Porto Alegre. In dialogue with authors from Cultural, Historical and Oral History, we sought to understand the ways of appropriation to learn how to teach the mathematical knowledge in the institution from 1950 to 1970, a period characterized by the Modern Mathematical Movement (MMM). We infer from the evidence verified in documents located in the acquis from the Laboratory of Mathematics from the institution and the interviews with the former students and the former teachers, that the MMM guided the formation of the normalists. This movement materialized in the actions of the teachers and students who learned and taught Modern Mathematics, in the didactic materials studied and produced by the normalists in the Mathematics Laboratory of the institution, as well as in the speeches of the former students and the press of the time. It was evidenced that the involvement of the normalists with the renewal of Mathematics, within IE, started, initially, from the concerns and the actions of the teacher Odila Barros Xavier, who aspired for changes in the teaching of Mathematics since the end of the 1940s At the time, the teacher was already studying changes in the curriculum of Normal Mathematics Course, in the relentless search for renewal in the training of primary teachers. Through the founding and organization of the Mathematics Laboratory, from the 1950s on wards, teacher Odila expanded the spaces for teacher training beyond IE's doors and contributed to the dissemination of modernizing thinking, coordinating study groups, giving courses on fundamentals theoretical and methodological approach of Modern Mathematics and encouraging practices in experimental classes with manipulative materials. The culmination of this course takes place in the late 1960s and early 1970s, which is why the Mathematics Teaching Group of Porto Alegre (GEEMPA) was founded under the leadership of teacher Esther Grossi. Through the GEEMPA, teacher training courses were offered in the presence of several scholars, among them Zoltan Dienes, one of the main authors studied at the Flores da Cunha General Education Institute. Throughout the 1950s and 1970s, the institution became a reference not only in the initial formation of the normalists, but also in the continuing formation of Mathematics teachers in Rio Grande do Sul, with national and international recognition, during the period marked by the MMM.

In this paper the project for 15-year-old students with the title Ancient Greece and Rome and the sub-title Is the Legacy of Ancient Greece and Rome really the Cradle of European Civilization? is introduced. It shows how to connect mathematics with art, history, physics, geography and philosophy by studying ancient Greek scientists and their achievements. Collaborative teaching is introduced. The major aim of the project was to show mathematics as a part of human civilization and to follow its development through history. Some topics from theory of numbers and geometry were studied. One part of the project was also a theatre performance, which should make the students aware of the difficulties of many dedicated mathematicians to find the answers to some problems from the ancient times.

The purpose of this paper is to compare curriculum documents for K-12 education from the state of North Carolina from two time periods, 1920s and 2003. The historical development of the mathematics curriculum in North Carolina provides a snapshot of the shifts in mathematics teaching and learning. North Carolina, a state in the southeast of the United States, has had a statewide standard course over a period spanning more than eighty years. A document analysis of printed curriculum standards from allows a description of the mathematics concepts and tasks that were expected of students in those years. The analysis revealed stark contrasts in the focus of mathematics from a very computational emphasis to one of problem solving. The analysis also highlighted the understanding of algebraic concepts and ideas as an essential outcome of current mathematics programs.

No description available.

The goal of this diploma thesis is to gather and describe ways the optimisation problems had been solved before the calculus was invented. Some of the methods identified through history are generalised and these which could be utilised at secondary or primary school education are described more in depth. Thesis descri- bes the method, where educator follows historical development of the problem in classroom and what benefits it might bring, as well. There is a section dedicated to evaluation of experiment which goal was to investigate understanding of pupils to certain concepts in the field of optimisation, mainly concerning isoperimetric problem. It was also focused on the pupils fe- edback to different approaches of optimisation problem solving. 1

[pt] O objetivo deste trabalho é propor atividades experimentais, fundamentadas na História da Matemática, que problematizem o conteúdo ensinado no 9º ano do ensino fundamental da escola básica, com base nos seus processos históricos de produção provocando o diálogo entre duas abordagens que fundamentam o presente estudo: a história da matemática e o ensino por atividades experimentais. Acreditamos que esse diálogo possibilita o alcance de objetivos específicos importantes: humanização da matemática possibilitando que alunos deste ano de escolaridade compreendam a matemática como produto da necessidade humana e significação da matemática promovendo o aprendizado através do desenvolvimento de atividades práticas que tragam sentido e motivação à aprendizagem de novos saberes. Três conteúdos tradicionais que constam no currículo deste segmento são apesentados com base na conjugação simultânea destas abordagens: o teorema de Tales, o teorema de Pitágoras e a equação do segundo grau. Para cada um deles, apresentamos uma abordagem histórica, levantamos reflexões importantes sobre construções e autorias e sugerimos atividades fundamentadas no diálogo entre história e prática como propostas a serem desenvolvidas juntos aos alunos. / [en] The objective of this work is to propose experimental activities, based on the History of Mathematics, that problematize the content taught in the 9th grade of elementary school, based on their historical production processes, provoking a dialogue between two approaches that underlie the present study: the history of mathematics and teaching by experimental activities. We believe that this dialogue enables the achievement of important specific objectives: humanization of mathematics enabling students of this school year to understand mathematics as a product of human need and meaning of mathematics promoting learning through the development of practical activities that bring meaning and motivation to learn new knowledge. Three traditional contents that appear in the curriculum of this segment are presented based on the simultaneous combination of these approaches: the Tales theorem, the Pythagorean theorem and the 2nd degree equation. For each of them, we present a historical approach, raise important reflections on constructions and authorship and suggest activities based on the dialogue between history and practice as proposals to be developed together with the students.

Det här examensarbetet undersöker vilka effekter en undervisning med matematikhistorisk prägel har på eleverna, samt vilka faktorer i en sådan undervisning som kan påverka utfallet. När matematikhistoria betraktas som ett verktyg i matematikundervisningen förväntas elever påverkas affektivt och/eller kognitivt. Med synen på matematikhistoria som ett verktyg är två strategier för undervisning lämpliga – historisk upplysning och historiska paket. Med historisk upplysning inkluderas matematikhistoria i matematikundervisningen genom kortare anekdotiska inslag eller problem. Historiska paket är små moduler i undervisningen, som behandlar ett avgränsat ämne inom matematiken, och har en nära koppling tillläroplanen. Analysen genomfördes utifrån en litteraturstudie, och visar att båda strategiernakan påverka eleverna affektivt och kognitivt. Faktorer som kan påverka utfallet är elevernas ålder och förkunskaper, lärarens kompetens, graden av interaktivitet i undervisningen ochdet material som används. / This thesis investigates potential effects on students from including history of mathematics inmathematics education, and what circumstances within such education can influence the outcome. When the history of mathematics is considered a tool in teaching, pupils are expected to be influenced in a cognitive and/or affective way. From this perspective, two strategies are considered appropriate – the illumination approach or historical packages. The illumination approach includes short historical anecdotes or problems, whereas the historical packages are designed to teach an isolated subject within mathematics and are closely connected to the curriculum. The analysis was based on a literature study and shows that both strategies can influence pupils in a cognitive and affective way. Circumstances that influence the outcome are the age and previous knowledge of the pupils, teacher competence, the level of interactivity amongst the pupils and the material used in the teaching.

Orientador: Ivete Maria Baraldi / Resumo: O presente estudo, inscrito no campo da História da Educação Matemática, tem como tema central a Campanha de Aperfeiçoamento e Difusão do Ensino Secundário (Cades) em suas diferentes frentes de atuação, que visavam à criação de um novo modelo de professor Secundário no período de sua vigência, as décadas de 1950 e 1960. Considerando a criação de tal modelo como uma estratégia do Ministério da Educação e Cultura (MEC), o trabalho, como uma pesquisa qualitativa e bibliográfica, pretende investigar as táticas mobilizadas pela Cades tendo como objetivo essa intenção. Para isso, analisa, especialmente, os Cursos de Orientação aos Exames de Suficiência, a revista Escola Secundária, o Concurso Dia do Professor e os livros por ela publicados como táticas, e, por meio das táticas ali percebidas, defende-se a criação de um novo modelo de professor secundário, amparado principalmente nos ideais da Escola Nova. / Abstract: This thesis, developed according to an historiographical, qualitative and bibliographic approach, has as its main objective to study Cades-Campanha de Aperfeiçoamento e Difusão do Ensino Secundário (Campaign for the Improvement and Diffusion of Secondary Education), created by the Brazilian federal government, in 1953, to disseminate and improve higher education. Cades developed many different actions, all of them implemented aiming the creation of a new model of teacher for the secondary education. The intention of Cades, here, is taken as a strategy, while its actions developed along the Fifties and Sixteth are taken as tatics. With this, we analyze, in particular, the courses of Orientation to Examination of Sufficiency, the magazine Secondary School, the Teacher's Day Contest and the books published by the Campaign as tactics, and, through the tactics perceived there, defends the creation of a new model of secondary teacher, supported mainly in the ideals of the New School. / Doutor

Made available in DSpace on 2016-04-27T16:58:09Z (GMT). No. of bitstreams: 1 dissertacao_marilene_moussa_miranda.pdf: 291834 bytes, checksum: 692a23cfd34a77403a0f62a0d4ba4443 (MD5) Previous issue date: 2003-12-16 / This dissertation is a study on the North American experiment of merging subjects such as Arithmetic, Algebra and Geometry, and the influence of this experiment over the Mathematic education in Brazil. We have analyzed a few changes occurred in the secondary school in North America between 1890 and 1930, and also how Professor Euclides Roxo used that initiative as he presented his proposal for a change in the curriculum of the D. Pedro II Secondary School, creating the subject of Mathematics. We finally make a comparative analyzes of the proposals on the teaching of Mathematics both in Brazil and in the USA. In our conclusion, we justify the lack of success of both proposals, in two different contexts, whose purpose was to merge the different branches of Mathematic for teaching / O trabalho estuda a experiência norte-americana de fusão da Aritmética, Álgebra e Geometria e sua influência na Educação Matemática Brasileira. São analisadas algumas modificações ocorridas no ensino secundário norte-americano, durante o período compreendido entre 1890 a 1930, e o modo como o professor Euclides Roxo apropria-se dessas iniciativas ao apresentar sua proposta de alteração na seriação do curso secundário do Colégio Pedro II criando a disciplina Matemática. Ao final é feito um estudo comparativo das propostas para o ensino de Matemática nos EUA e no Brasil concluindo por justificar o fracasso dessas duas reformas, em contextos diferentes, que visavam fundir os ramos matemáticos para o ensino