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Until recently, Taiwan elementary mathematics curriculum has been changing for several times. The aim of this study is to refer to various curriculum reforms, and focus on the way ¡§Number and Calculation Standards¡¨ changed in the history of reforms. The specific objectives of this study: to refer to one curriculum standards and its subsequent standards and do pair wise comparison. To achieve the above objectives, the investigator referred to 7 target versions of mathematics curriculum standards: 41, 51, 57, 64, 82, 89, 92 (R.O.C year). The comparison was done qualitatively, using historical research methodology. The main research findings are the differences in the above 6 pair wise comparisons. 1. The change from Year 41 to Year 51: In the Year 51, the part on Writing numbers in Chinese characters was de-emphasized. Emphasis was on Ordinal numbers, division thinking, mental arithmetic and written algorithm. The size of numbers reduced to 4-digits (due to a change in currency, 4 dollars to 1 New Taiwan dollar). 2. The change from Year 51 to 57: more focus on symbols, did not require the revision on what was learned in previous year. 3. The change from Year 57 to 64: de-emphasized on mental arithmetic and written calculation; emphasized on Inverses, multiplication/division on ¡§0¡¦ and ¡§1¡¨, ratio, approximation, negative numbers and use of electronic calculators. 4. The change from Year 64 to 82: no need to include negative numbers and abacus. Emphasized on two-step problems, number line, and reading multiplication tables. 5. The change from Year 82 to 89: de-emphasis on odd and even numbers; emphasis on realistic contexts, understanding vertical algorithm. 6. The change from Year 89 to 91: no need to use calculators to check working; emphasis on vertical algorithm, whole number calculations, and the connections of multiples/factors, rate/speed, and, fractions/decimals.

Made available in DSpace on 2014-06-11T19:31:42Z (GMT). No. of bitstreams: 0 Previous issue date: 2005-05-04Bitstream added on 2014-06-13T20:02:45Z : No. of bitstreams: 1 martins_jcg_dr_rcla.pdf: 1204232 bytes, checksum: 1076800f1b73a083b5f84979e3080de1 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Tem sido unanimidade entre os filósofos da Matemática a compreensão de que as revoluções científicas, na forma como são apresentadas em A Estrutura das Revoluções Científicas, de Thomas S. Kuhn, não ocorrem na Matemática. Este trabalho pretende o contrário: fundado no Modelo Teórico dos Campos Semânticos e tendo a história da Matemática como cenário mais especificamente, a história da Álgebra esta tese foi elaborada para mostrar que a obra Kitab al mukhtasar fi hisab al-jabr wa l-muqabalah, de al- Khwarizmi, inaugura o primeiro período de pesquisa normal no desenvolvimento da Álgebra na Europa, um período altamente cumulativo e extraordinariamente bem sucedido em seus objetivos paradigmáticos e que se estendeu até as décadas iniciais do século XIX. Mostramos, ainda, que a demonstração do, hoje denominado, Teorema Fundamental da Álgebra, por Gauss, e a publicação do trabalho Sobre a resolução algébrica de equações, de Abel, trouxe à luz, na forma de um fato, uma anomalia irresolúvel do primeiro paradigma da Álgebra no Velho Continente. A partir daí, abriu-se um período de pesquisa extraordinária no âmbito dessa disciplina um período revolucionário de onde viria emergir um novo período de pesquisa normal, um novo paradigma para a Álgebra os sistemas algébricos abstratos fundado nas realizações matemáticas de Galois, Peacock e Hamilton. / Thus far, all the Mathematical Philosophers have unanimously agreed that the scientific revolutions, as it is presented in The Structures of the Scientific Revolutions, by Thomas S. Kuhn, do not take place in Mathematics. This paper intends to prove just the opposite: founded on The Theoretical Models of the Semantic Fields and considering the History of Mathematics as the scenery in question more precisely, the History of Algebra this thesis was prepared to show that the work Kitab al mukhtasar fi hisab al-jabr wa l muqabalah, by al-Khwarizmi, gives birth to the first period of normal research in the European development of Algebra, a highly cumulative and extraordinarily well succeeded period in its paradigmatic objectives, which extended until the first decades of the Nineteenth Century. We further show that the proof of the so called The Fundamental Theorem of Algebra, by Gauss, and the publication of Abel's work on The Algebraic Solutions of Equations, brought to light, as a fact, an unsolvable anomaly of the first paradigm of Algebra in the Old Continent which, from there on, caused the beginning of an extraordinary research period in this particular field in fact, a revolutionary period from which would surface a new time of normal research, a new algebraic paradigm the abstract algebraic systems based on the mathematical achievements of Galois, Peacock and Hamilton.

Title: Life and Work of Josef Úlehla Author: Lukáš Vízek Department: Department of Mathematics Education Supervisor: prof. RNDr. Martina Bečvářová, Ph.D. Abstract: Josef Úlehla (1852-1933) was an important Czech teacher, he taught mathematics and natural sciences at primary and secondary schools in Moravia. He wrote a number of monographs, textbooks, articles and translations of foreign language publications. This thesis describes Úlehla's life, brings the detail analysis and evaluation of his mathematical works and mentions his other publications. The text contains a lot of illustrations and the thesis is supplemented by factual attachments. Keywords: Josef Úlehla, mathematics, education, history

Du premier congrès des scientifiques italiens de 1839 à la veille de la Grande Guerre, de nombreux mathématiciens italiens ont pris part à la vie politique de leur pays. Cette thèse examine les différentes modalités de cet engagement : le mouvement national, qui se décline dans le domaine scientifique par une forme spécifique de patriotisme dans un contexte d’unification de l’Italie, en est un aspect. Mais il s’agit d’analyser plus généralement la façon dont le statut de mathématicien peut être réinvesti dans le champ politique pour fonder un discours de légitimation, une forme d’expertise, revendiquer un regard spécifique sur le politique. Cela suppose de penser la circulation entre champ mathématique et politique avec les outils de l’histoire des intellectuels : comparer les stratégies d’ascension dans ces deux champs, analyser comment les conflits s’y transposent, comment les acteurs répartissent leur temps entre les différentes activités. Il s’agit donc de comprendre comment les transformations de la vie politique italienne autour de l’unification ont permis l’émergence de nouveaux hommes politiques, de mesurer leur réception par le milieu politique mais aussi dans le champ académique, ainsi que la façon dont leur double appartenance a pu affecter leur façon d’être mathématiciens. / From the first congress of Italian scientists in 1839 to the eve of World War I, many Italian mathematicians took part to the political life of their country. This PhD deals with the different modalities of this involvement: Italian national movement, which results in the scientific field in a specific shape of patriotism in a context of Italian unification, is one aspect. But I intend to draw a more general analysis of the way the position of a mathematician can be used in the political field to found a legitimating discourse, some kind of expertise, or to claim a specific way to consider political questions. In order to do so, I will need to consider circulations between mathematical and political fields with tools the history of intellectuals: I will thus compare the strategies of advancement in those two fields, analyze how the conflicts are transposed and how the actors divide their time between their different activities. So I intend to understand how the transformations of the Italian political life around national unification made possible the emergence of new politicians, to assess their reception in political and academic worlds and the way their double belonging influenced their practice as mathematicians.

Submitted by CLÁUDIO MÁRCIO RIBEIRO MAGALHÃES null (claudiormagalhaes@uninove.br) on 2016-06-08T19:54:34Z No. of bitstreams: 1 Luis Antonio Verney O Verdadeiro Método de Estudar - Uma Contribuição para o Ensino em Portugal e no Brasil.pdf: 47738896 bytes, checksum: 33705b028f640da23cadbe4d5f53a20c (MD5) / Approved for entry into archive by Ana Paula Grisoto (grisotoana@reitoria.unesp.br) on 2016-06-09T16:57:00Z (GMT) No. of bitstreams: 1 magalhaes_cmr_dr_rcla.pdf: 47738896 bytes, checksum: 33705b028f640da23cadbe4d5f53a20c (MD5) / Made available in DSpace on 2016-06-09T16:57:00Z (GMT). No. of bitstreams: 1 magalhaes_cmr_dr_rcla.pdf: 47738896 bytes, checksum: 33705b028f640da23cadbe4d5f53a20c (MD5) Previous issue date: 2016-04-25 / 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. / 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.

Orientador: Romulo Campos Lins / Banca: Antonio Vicente Marafioti Garnica / Banca: Francisco César Polcino Miles / Banca: Ligia Arantes Sad / Banca: Marcos Vieira Teixeira / Resumo: Tem sido unanimidade entre os filósofos da Matemática a compreensão de que as revoluções científicas, na forma como são apresentadas em A Estrutura das Revoluções Científicas, de Thomas S. Kuhn, não ocorrem na Matemática. Este trabalho pretende o contrário: fundado no Modelo Teórico dos Campos Semânticos e tendo a história da Matemática como cenário mais especificamente, a história da Álgebra esta tese foi elaborada para mostrar que a obra Kitab al mukhtasar fi hisab al-jabr wa’l-muqabalah, de al- Khwarizmi, inaugura o primeiro período de pesquisa normal no desenvolvimento da Álgebra na Europa, um período altamente cumulativo e extraordinariamente bem sucedido em seus objetivos paradigmáticos e que se estendeu até as décadas iniciais do século XIX. Mostramos, ainda, que a demonstração do, hoje denominado, Teorema Fundamental da Álgebra, por Gauss, e a publicação do trabalho Sobre a resolução algébrica de equações, de Abel, trouxe à luz, na forma de um fato, uma anomalia irresolúvel do primeiro paradigma da Álgebra no Velho Continente. A partir daí, abriu-se um período de pesquisa extraordinária no âmbito dessa disciplina um período revolucionário de onde viria emergir um novo período de pesquisa normal, um novo paradigma para a Álgebra os sistemas algébricos abstratos fundado nas realizações matemáticas de Galois, Peacock e Hamilton. / Abstract: Thus far, all the Mathematical Philosophers have unanimously agreed that the scientific revolutions, as it is presented in The Structures of the Scientific Revolutions, by Thomas S. Kuhn, do not take place in Mathematics. This paper intends to prove just the opposite: founded on The Theoretical Models of the Semantic Fields and considering the History of Mathematics as the scenery in question more precisely, the History of Algebra this thesis was prepared to show that the work Kitab al mukhtasar fi hisab al-jabr wa’l muqabalah, by al-Khwarizmi, gives birth to the first period of normal research in the European development of Algebra, a highly cumulative and extraordinarily well succeeded period in its paradigmatic objectives, which extended until the first decades of the Nineteenth Century. We further show that the proof of the so called The Fundamental Theorem of Algebra, by Gauss, and the publication of Abel's work on The Algebraic Solutions of Equations, brought to light, as a fact, an unsolvable anomaly of the first paradigm of Algebra in the Old Continent which, from there on, caused the beginning of an extraordinary research period in this particular field in fact, a revolutionary period from which would surface a new time of normal research, a new algebraic paradigm the abstract algebraic systems based on the mathematical achievements of Galois, Peacock and Hamilton. / Doutor

No description available.

This article presents the results of a survey whose aim was to identify whether or how the Mathematics teachers of municipal schools in Aracaju make use of the History of Mathematics to deal with mathematical contents on the final years of Junior High School. In order to accomplish such a task, first it was identified the subjects through the intersection between the names of the students who attended the subject History of Education at Universidade Federal de Sergipe - UFS, and the names of the teachers who had taught at municipal schools in 2010. From a quantity of 37 students who met the above criteria, 19 semi structured interviews were made with the group. In addition, two professors of the subject History of Mathematics, offered for the graduates in Mathematics at UFS, were also interviewed. In this case, the aim was to identify the historical contents presented in the course plans in an attempt to establish the same theoretical bases in relation to the contents and the way how they were studied by the teachers of the municipal schools in Aracaju. As theoretical foundation, it was adopted the authors: Fauvel (1997) to differentiate between history of mathematics written with initial capitals and lower case with initial Feliciano (2008), Miguel (1997), Miguel e Miorim (2008) about the uses of history of mathematics in the classroom e Valente (2007) to the treatment of sources. Based on the data collected, it is possible to affirm that most teachers use the History of Mathematics in the classroom. In relation to how, the most frequent use is the History of Mathematics as teaching resources, tied to the use as motivation, as curiosity, as explanation of the why. In these cases, the main role performed by the teacher is to present the contents and the historical information. The confirmation of this is in the verbs used, such as: to count, to explain and to cite, considered as indicative that the teachers adopt the model of lecture and the historical information as a form of explaining some why, which contributed to the students to become not only listeners in face of the knowledge which are passed on them. The result of this survey is an indicative that as soon as possible, it should be made an investment on other surveys in order to experiment the use of the History of Mathematics as a teaching methodology in which the historical information is the starting point to teach mathematical contents. / Neste trabalho é apresentado o resultado de uma pesquisa cujo objetivo foi identificar o se e o como professores de Matemática da rede municipal de ensino de Aracaju-SE fazem uso da história da matemática para abordar conteúdos matemáticos nos anos finais do Ensino Fundamental. Para realizar tal empreitada um primeiro passo foi identificar os sujeitos a partir da intersecção entre os nomes dos alunos que cursaram a disciplina História da Matemática na Universidade Federal de Sergipe - UFS e os nomes de professores que em 2010 atuavam na rede municipal de ensino. De um quantitativo de trinta e sete que atendiam ao referido critério foram realizadas dezenove entrevistas semiestruturadas com esses sujeitos. Além disso, foram entrevistados também dois docentes da disciplina História da Matemática, ofertada para os licenciados em Matemática da UFS. Nesse caso, o objetivo era identificar os conteúdos históricos presentes em ementas e em programas do curso, na tentativa de estabelecer um mesmo lastro teórico em relação aos conteúdos e a forma como que foram estudados pelos professores da rede municipal de Aracaju. Como sustentação teórica, foram adotados autores como, Fauvel (1997) para a diferenciação entre história da matemática grafada com iniciais maiúsculas e com iniciais minúsculas, Feliciano (2008), Miguel (1997), Miguel e Miorim (2008) sobre os usos da história da matemática em sala de aula e Valente (2007) para o tratamento das fontes. Com base nos dados coletados é possível afirmar que a maioria dos professores utiliza a história da matemática em sala de aula. Já em relação ao como, o uso mais frequente é a história da matemática como um recurso didático, atrelado à utilização como motivação, como curiosidade, como explicação dos porquês. E nesses casos, o papel predominante exercido pelo professor é o de expositor do conteúdo e das informações históricas. A confirmação dessa constatação está nos verbos utilizados para descrever o uso, a exemplo da presença de verbos como contar, explanar, citar, considerados aqui como indicativos de que os professores adotam o modelo da aula expositiva e as informações históricas como recurso para motivar ou explicar alguns porquês. O que contribui para que os alunos se tornem apenas ouvintes diante do conhecimento que lhes é informado. O resultante desta pesquisa é um indicativo que o mais breve possível deve ser realizado um investimento de outras pesquisas com o intuito de experimentar o uso da história da matemática como uma metodologia de ensino em que as informações históricas sejam o ponto de partida para ensinar conteúdos matemáticos

<p>This dissertation deals with geometry instruction in Sweden in the period 1905-1962. The purpose is to investigate textbooks and other literature used by teachers in elementary schools (ES) and lower secondary schools (LSS) – Folkskolan and Realskolan – connection to geometry instruction. Special attention is given to debates about why a course should be taught and how the content should be communicated.</p><p>In the period 1905-1962, the Swedish school system changed greatly. Moreover, in this period mathematics instruction was reformed in several countries and geometry was a major issue; especially, classical geometry based on the axiomatic method. However, we do not really know how mathematics instruction changed in Sweden. Moreover, in the very few works where the history of mathematics instruction in Sweden is mentioned, the time before 1950 is often described in terms of “traditional”, “static” and “isolation”.</p><p>In this dissertation, I show that geometry instruction in Sweden did change in the period 1905-1962: geometry instruction in LSS was debated; the axiomatic method and spatial intuition were major issues. Textbooks for LSS not following Euclid were produced also, but the axiomatic method was kept. By 1930, these alternative textbooks were the most popular.</p><p>Also the textbooks in ES changed. In the debate about geometry instruction in ES, visualizability was a central concept. </p><p>Nonetheless, some features did not change. Throughout the period, the rationale for keeping axiomatic geometry in LSS was to provide training in reasoning. An important aspect of the debate on geometry instruction in LSS is that the axiomatic method was the dominating issue; other issues, e.g. heuristics, were not discussed. I argue that a discussion on heuristics would have been relevant considering the final exams in the LSS; in order to succeed, it was more important to be a skilled problem solver than a master of proof.</p>