88 resultados para Games of strategy (Mathematics)


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In this paper we introduce a type of Hypercomplex Fourier Series based on Quaternions, and discuss on a Hypercomplex version of the Square of the Error Theorem. Since their discovery by Hamilton (Sinegre [1]), quaternions have provided beautifully insights either on the structure of different areas of Mathematics or in the connections of Mathematics with other fields. For instance: I) Pauli spin matrices used in Physics can be easily explained through quaternions analysis (Lan [2]); II) Fundamental theorem of Algebra (Eilenberg [3]), which asserts that the polynomial analysis in quaternions maps into itself the four dimensional sphere of all real quaternions, with the point infinity added, and the degree of this map is n. Motivated on earlier works by two of us on Power Series (Pendeza et al. [4]), and in a recent paper on Liouville’s Theorem (Borges and Mar˜o [5]), we obtain an Hypercomplex version of the Fourier Series, which hopefully can be used for the treatment of hypergeometric partial differential equations such as the dumped harmonic oscillation.

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We discuss the geometry of the pair of foliations on a solid torus given by the Reeb foliation together with discs transverse to the boundary of the torus.

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The main goal of this work is to build a sketch on how language is used in mathematics classrooms. We specifically try to understand how teachers use language in order to share meanings with their students. We initially present our main intentions, summarizing some studies that are close to our purposes. The two theoretical frameworks which support our study – the Model of Semantic Fields and the Wittgensteinian “games of language” – are then presented and discussed about their similarities and distinctions. Our empirical data are some classroom activities recorded and turned into “clips”. Such clips were transcribed and our analysis was based on these transcriptions. Data analysis – developed according to our theoretical framework – allowed us to build the so-called “events” and, then, comment on some understandings on how language can be used in mathematics classrooms.

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The so called Campaign for the Improvement and Diffusion of High School (in Portuguese, CADES) took place between 1953 and 1971, in Brazil. During this period, the Campaign published or helped publish dozens of books, in different teaching areas, and several of them were located by the authors of this article. These books guided high school teachers with respect to curriculum planning, legal aspects and methods of teaching. In this article, we contextualize historically this Campaign and also mention its objectives. We briefly describe some of the books found - especially those related to the teaching of mathematics - in order to open perspectives for future approaches and research that can be done based on this written material. Our main aim is to discuss its orientations and to provide ingredients that enable the construction of considerations related to this perspective of training mathematics teachers during a period when there were few colleges and universities to prepare teachers in Brazil.

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The aim of this paper is to discuss the teachers' need, as autonomous professionals, to evaluate their own pratice. Considering that Descriptive Functional Analysis (DFA) may be a pedagogical method for analysis, implementation, and change of teachers' mathematics teaching practices, the objective of the present research was to teach repertoires compatible with DFA to two mathematics teachers in elementary schools of São Paulo state. When teachers are responsible for evaluation and self evaluation, they recognize themselves as fundamental agents of transformation in education.

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

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Não é difícil observar a importância das corridas de velocidade para o cenário esportivo mundial. Entretanto, do stádion, disputado pelos gregos nos Jogos Olímpicos da Grécia Antiga, aos atuais 100 metros rasos, foram várias as modificações. Não por outro motivo, o objetivo dessa pesquisa foi registrar as modificações que ocorreram no sistema de partida das corridas de velocidade ao longo dos tempos. Essa pesquisa teórica, caracterizada como uma pesquisa bibliográfica, concentrou-se na coleta de dados provenientes de livros, artigos, imagens e websites relacionados aos 100 metros rasos. Dentre as modificações identificadas merecem destaque as que ocorreram no sistema de partida e que incluem o bloco de partida utilizado pelos atletas na atualidade, sem o qual, talvez, não se tivesse chegado ao incrível recorde mundial dos 100 metros rasos de 9s58.

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Com o movimento da Matemática Moderna, a partir de 1950, o ensino da matemática passou a enfatizar o simbolismo e a exigir dos alunos grandes abstrações, distanciando a matemática da vida real. O que se percebe é que o aluno formado por este currículo aprendeu muito pouco de geometria e não consegue perceber a relação deste conteúdo com sua realidade. Por outro lado, o professor que não conhece geometria não consegue perceber a beleza e a importância que a mesma possui para a formação do cidadão. A geometria estimula a criança a observar, perceber semelhanças, diferenças e a identificar regularidades. O objetivo deste trabalho é identificar o nível de conhecimento dos alunos do Centro Específico de Formação e Aperfeiçoamento ao Magistério (CEFAM), futuros professores da 1ª a 4ª séries do Ensino Fundamental do Estado de São Paulo, quanto aos conceitos de ponto, reta, plano, ângulos, polígonos e circunferências e também verificar as contribuições do computador para a construção de conceitos geométricos. Para atingir esses objetivos, foi desenvolvida uma pesquisa com 30 alunos do CEFAM de Presidente Prudente-SP, na qual, com base no diagnóstico das dificuldades de aprendizagem, organizaram e desenvolveram-se os momentos de formação, que utilizaram o computador como ferramenta de aprendizagem e projetos de trabalho tendo como aporte teórico a abordagem construcionista. O futuro professor que não dominar a geometria e não perceber sua relação com a natureza não conseguirá contribuir para o desenvolvimento do pensamento geométrico da criança. Esse pensamento é que permite a criança observar, compreender, descrever e representar, de forma organizada, o mundo em que vive.

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We propose a method for accelerating iterative algorithms for solving symmetric linear complementarity problems. The method consists in performing a one-dimensional optimization in the direction generated by a splitting method even for non-descent directions. We give strong convergence proofs and present numerical experiments that justify using this acceleration.

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We prove a Theoretical result which relates phase-lag to the error constant of a numerical method for periodic problem y'' = f(x, y).

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Common sense tells us that the future is an essential element in any strategy. In addition, there is a good deal of literature on scenario planning, which is an important tool in considering the future in terms of strategy. However, in many organizations there is serious resistance to the development of scenarios, and they are not broadly implemented by companies. But even organizations that do not rely heavily on the development of scenarios do, in fact, construct visions to guide their strategies. But it might be asked, what happens when this vision is not consistent with the future? To address this problem, the present article proposes a method for checking the content and consistency of an organization's vision of the future, no matter how it was conceived. The proposed method is grounded on theoretical concepts from the field of future studies, which are described in this article. This study was motivated by the search for developing new ways of improving and using scenario techniques as a method for making strategic decisions. The method was then tested on a company in the field of information technology in order to check its operational feasibility. The test showed that the proposed method is, in fact, operationally feasible and was capable of analyzing the vision of the company being studied, indicating both its shortcomings and points of inconsistency. (C) 2007 Elsevier Ltd. All rights reserved.

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Dietary modification ought to be the first line of strategy in prevention of the development of cardiac disease. The purpose of this study was to investigate whether dietary restriction, dietary-fibre-enriched diet, and their interactions might affect antioxidant capacity and oxidative stress in cardiac tissue. Male Wistar rats (180-200 g; n = 10) were divided into four groups: control ad libitum diet (C), 50% restricted diet (DR), fed with fibre-enriched diet (F), and 50% restricted fibre-enriched diet (DR-F). After 35 days of the treatments, F, DR, and DR-F rats showed low cholesterol, LDL-cholesterol, and triacylglycerol, and high HDL-cholesterol in serum. The DR, DR-F, and F groups had decreased myocardial lipoperoxide and lipid hydroperoxide. The DR-F and F treatments increased superoxide dismutase and glutatione peroxidase (GSH-Px). The DR treatment increased GSH-Px and catalase activities. Dietary fibre beneficial effects were related to metabolic alterations. The F and DR-F groups showed high cardiac glycogen and low lactate dehydrogenase/citrate synthase ratios, indicating diminished anaerobic and elevated aerobic myocardial metabolism in these animals. There was no synergistic effect between dietary restriction and dietary fibre addition, since no differences were observed in markers of oxidative stress in the F and DR-F groups. Dietary fibre supplementation, rather than energy intake and dietary restriction, appears to be the main process retarding oxidative stress in cardiac tissue.

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The aim of this paper is initially to consider some issues related to the relationship between humanization and alienation in the process of historical social development of human gender. These considerations are fundamental for understanding the concept of classical in Dermeval Saviani and the consequences for research about the historical development of Mathematics currently found in school curriculums. The intention is to value the appropriation of school mathematics as a humanizing element that becomes accessible through the activity of teaching.

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The present text has the objective of presenting theoretical considerations regarding two types of strategy of research: phenomenology and ethnography. Based on a hermeneutic approach, the two conceptual propositions are presented, the first being dealt with in the sociological context, and the second presented as an anthropological basis. Their similar uses in an organizational context - as well as their differences - are highligthed according to the theoretical contributions of authors belonging to the qualitative universe of organizational research. The text reveals, by the presentations of reported theoretical assumptions, the relevance of the interpretative perspective for the conduction of research that has the organization as object of study, in the pursuit of the identification of ways of constructing the social reality that is the result of the analysis of meanings and experiences lived by the participants, highlighting the importance of the bond between researcher and the research object The theoretical discussion regarding the two perspectives allows to observe the competence of the phenomenological and ethnographic research practice within the field of organizational studies, showing their methodological possibilities to identify dynamics that relate to the experience of life, favoring the analysis of the human being as a phenomenon of interpretation. © FECAP.