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

Obras complementares: um elo entre a leitura e os conteúdos matemáticos

The Federal Government through its Plans and Programs invests in various policies intended to achieve the main goal of the millennium, provide basic education for all. Among them, we highlight in this paper The National Textbook Program, with emphasis on Complementary Works. These works are presented through different genres, such as poems, poetry, short stories, parables, novels, literature, educational materials etc.. providing a range of possible teaching work. However, little is known about the levels of education of teachers as intended. Based on the discussions and studies in this direction, sparked concerns us in the process of teaching and learning in math classes. This made us pay attention to a possibility of study where reading could be included in this process. In this sense, the present study aims at investigating the potential of conceptual and didactic use of Complementary Works on developing the skills of reading and writing mathematics of the first three years of elementary school, and from there, propose a courseware with guidelines for use of these works by teachers of 1st to 3rd year of elementary school. For this, we outline the issues of reading and understanding of mathematical interests as those of our study. In this sense, the proposal was built from the bibliographic works that address the contributions of reading for learning mathematical content, like Machado (2001), Nacarato (2009); Dantas (2011), Smole and Diniz ( 2001). As a result, we created the Guidance for the use of Complementary Works for Teachers to Teach Mathematics with a view to support the practice of teachers and future teachers who teach mathematics. Supported the use of Complementary Works, especially those distributed in public schools by the National Textbook - PNLD and have mathematical content, this guide is intended to present some of the possible use of this feature in math classes. (Education Observatory - Capes / INEP. Ed. 038-2010. TELL Research Group - UFRN - PPGED / PPGEL / PPGECNM - PROPESQ)

Fission track and U-Pb in situ dating applied to detrital zircon from the Vale do Rio do Peixe Formation, Bauru Group, Brazil

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Os jogos com regras na educação matemática inclusiva

This present study aimed to examine the use of games with rules in working with math education in regular classes included in Elementary School, in the municipal education schools of Natal/RN, observing the learning process and development of all students, especially those with disabilities. The theoretical references used are based on Vygotsky's works and other authors from the historical-cultural perspective, as well as researchers in the field of Inclusive Education and Mathematics Education. The investigation was based on the qualitative research guidelines, with the application of semi-structured interviews with educational coordinators and teachers from the schools involved as well as classroom observations, looking for, in the speeches of those involved and in their teaching practices, elements to reflect on the Mathematics Inclusive Education, the use of games with rules -starting from its goals, the participation of disabled students, the pedagogical mediations, up to its accessibility - and from the learning of disabled students. The analysis results showed that the concepts underlying the development of inclusive teaching practices still refer to the clinical-medical paradigm, understanding the student with disabilities from their deficiencies; which teachers use, in their majority, the mathematical games with rules in their classes, but which the teaching mediation, during these activities, still needs to be qualified so that they can, effectively, contribute to the learning and development of all students; students with disabilities do not always participate in games with others colleagues; games with rules are rarely accessible; and that the Universal Design principles are not adopted in the selected classrooms for this study. Thus, it is clear that much remains to be done so that Mathematics Education can contribute to the learning and development of all students, and among those actions the teacher continuing education is recommended

From Amazonia to the Atlantic forest: Molecular phylogeny of Phyzelaphryninae frogs reveals unexpected diversity and a striking biogeographic pattern emphasizing conservation challenges

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A logical approach to the management of object identifiers in non-conventional database management systems

Non-conventional database management systems are used to achieve a better performance when dealing with complex data. One fundamental concept of these systems is object identity (OID), because each object in the database has a unique identifier that is used to access and reference it in relationships to other objects. Two approaches can be used for the implementation of OIDs: physical or logical OIDs. In order to manage complex data, was proposed the Multimedia Data Manager Kernel (NuGeM) that uses a logical technique, named Indirect Mapping. This paper proposes an improvement to the technique used by NuGeM, whose original contribution is management of OIDs with a fewer number of disc accesses and less processing, thus reducing management time from the pages and eliminating the problem with exhaustion of OIDs. Also, the technique presented here can be applied to others OODBMSs. © 2011 IEEE.

Primeiro Colóquio Brasileiro de Matemática: identificação de um registro e pequenas biografias de seus participantes

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Narrativas sobre a prática de ensino de matemática de professores dos anos iniciais do ensino fundamental

Pós-graduação em Educação Matemática - IGCE

A prática do professor de matemática em classes de recuperação de ciclo II no regime de progressão continuada do estado de São Paulo

Pós-graduação em Educação Matemática - IGCE

Conhecimentos e práticas de professores que ensinam Matemática na infância e suas relações com ampliação do Ensino fundamental

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

O cálculo e a invenção na poética de Stockhausen

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Tempo e saberes: a constituição do professor experiente em matemática

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Theodoro Augusto Ramos: um estudo comentado de sua tese de doutoramento

Pós-graduação em Educação Matemática - IGCE

Uma proposta para ensinar os conceitos da análise combinatória e de probabilidade: uma aplicação do uso da história da matemática, como organizador prévio, e dos mapas conceituais

Discutimos, neste trabalho, uma proposta de utilização da história da matemática, como organizador prévio, para o ensino da análise combinatória e da probabilidade. Esse uso da história da matemática tem como objetivo desenvolver os conhecimentos subsunçores, presentes na estrutura cognitiva dos alunos, para que possa ocorrer, de forma significativa, a aprendizagem dos conceitos desses tópicos da matemática, e que serão ensinados, de modo mais detalhado, posteriormente, através dos mapas conceituais. Vale ressaltar que, a utilização dos organizadores prévios do conteúdo, assim como a teoria dos mapas conceituais, têm fundamentação teórica nos trabalhos sobre aprendizagem significativa, do psicólogo educacional David P. Ausubel.

Notas de testemunho e recalque: uma experiência musical dos traumas sociais brasileiros em Chico Buarque e Paulinho da Viola (de meados da década de 1960 a meados da década de 1970)

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)