Guilherme de La Penha: uma história do seu itinerário intelectual em três dimensões

This study focuses on the central Brazilian historiography of science, focusing specifically on the life and work of a contemporaneous mathematician-physicist, and becomes part of the set of research results that investigate, organize and describe personal, intellectual and professional itineraries of Brazilian scientists and educators. The theme chosen for the study ran from seminars on Mathematics in Pará and is up to organize and describe the life history, education, professional experience and scientific production of William Mauricio Souza Marcos de La Penha (Guilherme de La Penha), considering their academic, professional and intellectual life history, so that their academic and intellectual production be spread over the Brazilian scientific and academic community. We adopted the historical research as theoretical and methodological base for the development of this study, rising arguments about the profile of Guilherme de La Penha to characterize him as a multiskill intellectual and to reveal that his thoughts about science, technology, training scientists and educators were in accordance with their writings and their professional practice in order to build a first story about the life and work of William de La Penha. In this sense, we took the theoretical aspects related to historical research, biographies, intellectual itineraries, files and inventories as sources and historical construction vehicles in order to point out the essential elements to form a profile of the transdisciplinary intellectual historians, ie a profile scientist who carries out the research, management and administration, as well as a committed educator to the on-going training and forming process. The results pointed in different directions, among which we highlight the creation of Seção Guilherme de La Penha at Universidade da Amazonia, producing several articles about the life and work of William de La Penha presented at national and international conferences and the proposal for documentary displays which could contribute to understanding the implementation of a scientific area in Pará State, an area that would not only be restricted to the production of knowledge, but more than that, it would include the spreading, which provides various means, primarily through education. Thus it was possible to ensure that La Penha has an intellectual profile that can be considered a multi-and transdisciplinary intellectual who defends the possibility of forming a scientist one and multiple, non-linear attitudes and dialogues with all other areas in order to be understood under a model scientist for the twenty-first century based on the model clearly inspired by the scientist authors with which he identified throughout their training and professional activities, like the three that stood out in their relationship science: Archimedes, Leonhard Euler and Cliford Ambrose Truesdell

Práticas etnomatemáticas no Liceu do Paracuri :a propósito dos ornamentos geométricos da cerâmica

The present study analyzes the ethnomatematics practices presents in the creation of the geometric ornaments of the icoaraciense ceramic, originated and still practiced in the neighborhood of Paracuri, District of Icoaraci, belonging to Belém, capital of the State of Pará/Brasil. The object of our study was centered at the workshops supplied by the artisans master of the School of Arts and Occupations, Master Raimundo Cardoso. Referred school provides to its students, formation at fundamental level as well professional formation, through vocational workshops that help to maintain alive the practice of the icoaraciense ceramic. Our interest of researching that cultural and vocational practice appeared when we got in touch with that School, during the development of activities of a discipline of the degree course of mathematics. In order to reach our objective, we accomplished, initially, a research about the icoaraciense ceramic historic, since the first works with the clay until to the main characteristics of that ceramic. Soon afterwards, we discussed on ethnomatematics, culture, knowledge, cognition and mathematical education. At the end, we analyzed the creation of the geometric ornaments of the icoaraciense ceramic, considering the proportion concepts, symmetry and some geometry notions, that are used by the artisans when they are ornamenting the pieces of that ceramic. We verified that, in spite of the artisans, usually, do not demonstrate to possess a bit of domain on the mathematical concepts that they are working with, for instance, the ones of translaction symmetry, rotation and reflection, they demonstrate full safety in the use of those concepts, as well as the capacity to recognize them, even if in a singular specific and very peculiar way, what opens the possibility of a partnership among mathematics teachers and master-artisans of the archeological ceramic and icoaraciense workshops

Um estudo sobre a aprendizagem de alguns conceitos algébricos e geométricos

The objective of the present work was develop a study about the writing and the algebraic manipulation of symbolical expressions for perimeter and area of some convex polygons, approaching the properties of the operations and equality, extending to the obtaining of the formulas of length and area of the circle, this one starting on the formula of the perimeter and area of the regular hexagon. To do so, a module with teaching activities was elaborated based on constructive teaching. The study consisted of a methodological intervention, done by the researcher, and had as subjects students of the 8th grade of the State School Desembargador Floriano Cavalcanti, located on the city of Natal, Rio Grande do Norte. The methodological intervention was done in three stages: applying of a initial diagnostic evaluation, developing of the teaching module, and applying of the final evaluation based on the Mathematics teaching using Constructivist references. The data collected in the evaluations was presented as descriptive statistics. The results of the final diagnostic evaluation were analyzed in the qualitative point of view, using the criteria established by Richard Skemp s second theory about the comprehension of mathematical concepts. The general results about the data from the evaluations and the applying of the teaching module showed a qualitative difference in the learning of the students who participated of the intervention

A Compreensão da idéia do número racional e suas operações na EJA: uma forma de inclusão em sala de aula

The awareness of the difficulty which pupils, in general have in understanding the concept and operations with Rational numbers, it made to develop this study which searches to collaborate for such understanding. Our intuition was to do with that the pupils of the Education of Young and Adults, with difficulty in understanding the Rational numbers, feel included in the learning-teaching process of mathematics. It deals with a classroom research in a qualitative approach with analysis of the activities resolved for a group of pupils in classroom of a municipal school of Natal. For us elaborate such activities we accomplished the survey difficulties and obstacles that the pupils experience, when inserted in the learning-teaching process of the Rational numbers. The results indicate that the sequence of activities applied in classroom collaborated so that the pupils to overcome some impediments in the learning of this numbers

Os artigos de Euler sobre os números amigáveis

Among the many methodological resources that the mathematics teacher can use in the classroom, we can cite the History of Mathematics which has contributed to the development of activities that promotes students curiosity about mathematics and its history. In this regard, the present dissertation aims to translate and analyze, mathematically and historically, the three works of Euler about amicable numbers that were writed during the Eighteenth century with the same title: De numeris amicabilibus. These works, despite being written in 1747 when Euler lived in Berlin, were published in different times and places. The first, published in 1747 in Nova Acta Eruditorum and which received the number E100 in the Eneström index, summarizes the historical context of amicable numbers, mentions the formula 2nxy & 2nz used by his precursors and presents a table containing thirty pairs of amicable numbers. The second work, E152, was published in 1750 in Opuscula varii argument. It is the result of a comprehensive review of Euler s research on amicable numbers which resulted in a catalog containing 61 pairs, a quantity which had never been achieved by any mathematician before Euler. Finally, the third work, E798, which was published in 1849 at the Opera postuma, was probably the first among the three works, to be written by Euler

Geometria e arirmética numa visão multicultural: uma experiência pedagógica

This paper aims to build a notebook of activities that can help the teacher of elementary school mathematics. Topics covered are arithmetic and geometry and the activities proposed here were developed aiming print them a multicultural character. We take as a base line developed by Claudia Zaslavsky multiculturalism and reflected in his books "Games and activities worldwide" and "More games and activities worldwide." We structure our work around four themes: the symbol of the Olympic Games, the pyramids of Egypt, the Russian abacus abacus and Chinese. The first two themes allow you to explore basic concepts of geometry while the latter two themes allow us to explore numerical notation and arithmetic operations

A leitura de fontes antigas como possibilidade didatica: um exemplo a partir do Almagesto de Ptolomeu

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

A etnomatemática dos trabalhadores das cerâmicas de Russas-Ce e o contexto escolar: delineando recomendações pedagógicas a partir de uma experiência educacional

It is still common among contemporary educational proposals an overemphasis abstraction, to the formalism and symbolism of mathematical knowledge at the expense of the sociocultural aspects of Mathematics. Coming up by questioning some academic mathematical tenets and valuing knowledge developed in different sociocultural contexts within Mathematical Education, the Ethnomatematics is consolidating itself as a research field. Despite its contributions to the educational context, because its philosophical character and the paucity of debates about the subject, the implementation of educational proposals for basic education are scarce. Given this situation, this dissertation comes up with a view to develop an educational intervention in the light of Ethnomathematics in a class of 6th grade of an elementary school from a red ceramic industries workers community, located in a countryside from Russas-CE and from this intervention, to develop a set of pedagogical recommendations aiming basic education teachers. Adopting a perspective of qualitative research, particularly guided by action research, this study used observation, field diary, interviews and activities with students as tools for data collection. It was found that the use of field research as part of teaching and learning favored the placement of students as critical subjects of their own reality . Furthermore, the educational experience culminated in the development of a method of teaching based on a relationship between protocooperational Ethnomatematics and the Resolution of Problems. It is necessary to broaden the debate about the ways in which the Ethnomatematics can contribute to the school context, bringing proposals closer to the reality of basic education teachers in order to help the promotion of an education which values cultural diversity without taking away the students from the access of the academic knowledge

Dificuldades na construção de gráficos de funções

This study describes about graduation s students difficulties of to draw functions graph. Specifically, we intend to observe their abilities evolution, as well as their difficulties during Calculus I subject in engineering course. For that, we show them publications about the elaboration of graphs and its difficulties in obstacle terms and some researches witch contain this subject and that it was done during postgraduate studies in mathematical education. It shows by research methodology aspects related to French didatic s mathematic and some theories of cognitive psychology considering the high value between theoretical-methodological relation that was evidenced in both theoretical conceptions about ways to understand and teach mathematic. This methodology is based on didactic engineering purpose, that consist in preliminaries analysis, conception and didactic sequence analysis prior, trials by application followed analysis up and conclusion. We had also used pedagogicals actions and analysis of results achieved, to classify types of errors made by the 2005 s students during second semester, from conceptions related to the episthemologic and didactics obstacles

Leitura e Interpretação de Dados Prontos em um Ambiente de Modelagem e Tecnologias Digitais: o mosaico em movimento

Neste artigo, analisamos a leitura e a interpretação de dados prontos coletados por alunos para desenvolverem projetos de modelagem. Consideramos dados prontos as informações coletadas na Internet, como um gráfico ou uma fórmula, sem maiores explicações de como foram geradas. Com isso, repensamos o mosaico de pesquisas do GPIMEM, grupo de pesquisa ao qual pertencemos e que desenvolve pesquisas sobre modelagem e informática há cerca de vinte anos. Na análise, privilegiamos a apresentação oral e o relatório escrito de um grupo de alunas do Curso de Ciências Biológicas da Universidade Estadual Paulista (UNESP). Os dados prontos sugerem uma nova faceta na relação entre tecnologias digitais e modelagem: eles parecem ser tratados de maneira idêntica a dados empíricos usualmente coletados em outros trabalhos de modelagem encontrados na literatura. Assim, o mosaico de pesquisas sobre o tema ganha novas dimensões na medida em que a Internet parece modificar a própria noção do que são dados.

Varenius e o conhecimento matemático do século XVII

Neste artigo, discutimos o contexto do desenvolvimento da Geografia que, no século XVII, liberou-se do seu papel nas diferentes fés cristãs, bem como a importância da cisão dos Protestantes, em Luteranos e Calvinistas, para o processo de secularização, e o conseguinte estabelecimento da Geografia como ciência moderna. Analisamos a contribuição fundamental do luterano Bernhard Varen, cuja obra Geografia Geral apresenta o paradigma dessa nova ciência. Naquela época, a Geografia era considerada um ramo da matemática, e esta obra nos dá indícios sobre notações e conceitos matemáticos utilizados naquele século. Analisamos, particularmente, o uso da notação decimal de números não inteiros e algumas aplicações de conceitos trigonométricos, comparando a edição original com as principais reedições desta obra.

Estudo da utilização de medidas não-oficiais em uma comunidade de vocação rural

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Um Estudo de pavimentação do plano utilizando caleidoscópios e o software Cabri Géomètre II

Pós-graduação em Educação Matemática - IGCE

Um estudo sobre as relações entre atitudes, gênero e desempenho de alunos do ensino médio em atividades envolvendo frações

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Um estudo sobre os conhecimentos geométricos adquiridos por alunos do ensino médio

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)