Mestrado Profissional em Matemática em Rede Nacional (PROFMAT-SJC)
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- ItemAcesso aberto (Open Access)Olimpíadas do Conhecimento: uma proposta inovadora para um momento novo(Universidade Federal de São Paulo (UNIFESP), 2021) Silva, Jose Lucivaldo Leite Da [UNIFESP]; Mesquita, Claudia Aline Azevedo Dos Santos [UNIFESP]; Universidade Federal de São PauloThe changes that society has been going through and the speed with which the world has been changing suggest that we need to be frequently rebuilding ourselves. For this moment, we need a new set of skills, with which we can adapt and evolve in such a dynamic world scenario. In this dissertation, we highlight the work with the knowledge Olympiad, which, due to their scope, dynamism and playful ability, show a path to be explored in the search for the development of these new skills. We will present a brief history on the origin of the Mathematics Olympiad, the emergence of the Knowledge Olympiad in Brazil and the great offer of scientific Olympiads that we have witnessed these days, in addition to highlighting the benefit and the transformation that these have already exercised in the lives of some of our young students who have met with this universe. We will also point out how this initiative is intrinsically linked to working with highly skilled young people - and for that reason we will provide an overview of the topic and present some of the characteristics of the work with this group of students - and we will also provide details on the process of creation, organization and elaboration of the International Mathematics and Knowledge Olympiads – OIMC (IMKO), idealized by us and carried out by the Alpha Lumen Institute (Instituto Alpha Lumen) of São José dos Campos, in which we figure as one of the founders.
- ItemAcesso aberto (Open Access)Pesquisa Estatística para desenvolvimento de senso crítico: uma proposta envolvendo Educação Financeira(Universidade Federal de São Paulo, 2022-07-22) Ferreira, Jéssica Mara [UNIFESP]; Cespedes, Juliana [UNIFESP]; http://lattes.cnpq.br/1034384160736943; http://lattes.cnpq.br/5311679988084807O intuito desse projeto é fornecer uma sequência didática para o professor que o possibilite dar a oportunidade aos estudantes de compreender e participar de todas as etapas de uma pesquisa estatística, realizar questionamentos e discussões em cada processo visando desenvolver o senso crítico em relação a análise de dados e interpretação de forma consistente de informações de gráficos e tabelas, para que percebam a possibilidade de manipulação de dados, pois, mesmo com informações verdadeiras é possível induzir o leitor despreparado a determinado pensamento. Esse percurso é realizado juntamente com o tema transversal educação financeira, orientando o estudante em pesquisas sobre alguns tipos de investimentos, o que torna esse projeto mais atraente, pois é um grande aliado ao professor de Matemática do ensino básico, que precisa estudar e ensinar conceitos relacionados a esses dois tópicos, pesquisa estatística e educação financeira, que são relativamente novos frente às abordagens da BNCC (Base Nacional Comum Curricular).
- ItemAcesso aberto (Open Access)Trigonometria Esférica: origens e aplicações(Universidade Federal de São Paulo (UNIFESP), 2020-02-28) Faria, Jorge Maurilio De [UNIFESP]; Moraes, Rodolpho Vilhena De [UNIFESP]; Universidade Federal de São PauloThe present work aims to carry out a historical study of Spherical Trigonometry, covering since its origins and purposes, as well as applications in daily life and its relationship with Astronomy. Also take a trip on the national curriculum to observe how the theme is inserted in the school grid. I highlight here the works of (USUI, 2014) , which inspired me with some contribution in the development of my research, in which I was able to deepen the questions about the coordinate transformations. The elements of Spherical Trigonometry are presented through definitions and theorems. We present the fundamental relation, known as the relation of the four elements (Law of the Cosines) and the Law of the Sines, the Celestial Sphere, its elements and its coordinates in the equatorial system, horizontal system and hourly system. Also present the triangle of position as being a spherical triangle, relating the coordinates of different systems of a star. From the studies carried out, we present a didactic sequence, allowing the calculation of distances between two distinct stars in the Celestial Sphere, involving Spherical Geometry, Spherical Trigonometry and the Celestial Sphere, especially the distance between cities on our planet. This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Financial Code 001.
- ItemAcesso aberto (Open Access)Proposta didática para o ensino interdisciplinar: Óptica Geométrica e Matrizes(Universidade Federal de São Paulo (UNIFESP), 2020-07-31) Oliveira, Arthur Alves De [UNIFESP]; Sakamoto, Kelly Cristina Jorge [UNIFESP]; Universidade Federal de São PauloLight and its behavior have always been the subject of several studies and much discussion, until it has been concluded that light can have a wavy and corpuscular behavior (particles), which characterizes the theory of wave-particle duality. Various optical phenomena can occur from the interaction of light with matter, such as refraction, reflection, diffraction, absorption, among others. What scientists have observed is that depending on the phenomenon and the ease of better understanding, one can choose whether to explain it, using light as a wave or as a particle. For example, by the wave theory, it is possible to understand the diffraction effect that light suffers when passing through a crack (an obstruction) using the Huygens Principle, and well demonstrated by Young's double-slit experiment. Another example is when light strikes the surface of a mirror, which, in this case, can be treated as a particle and as a wave. In the situation where the size of the opening through which the light beam is propagated, it is much larger compared to the wavelength of the light used, the diffraction effect can be neglected and thus, geometric optics can be applied. In this case, ray tracing and geometry tools are used to determine the parameters that make up the optical image system, such as the distances of the object and image planes in relation to the lens position and the sizes of the object in these planes. The didactic proposal of this work explores the formation of image by an optical system, composed of one or more lenses using four different forms, utilizing the algebraic form by using the lens equation; the geometric shape through the ray tracing; in a matrix form by the application of transfer matrices and the last form with practical classes, experimentally setting up the optical system. In this way, this proposal relates geometric optics (image formation) and matrices to be an interdisciplinary teaching of Physics and Mathematics. Several authors defend the interdisciplinarity in the teaching of Mathematics and Physics, for connecting these contents and showing a real application of Mathematics. In addition, the use of practical activities interferes in the teaching of Physics, as the student can visualize and understand a content that appears, in most cases, abstract. Therefore, it is expected that teaching together both concepts can offer contextualization in class, improvements in student learning and teacher satisfaction, reaping the positive results of their work.
- ItemAcesso aberto (Open Access)Ladrilhamentos no plano e pentaminós: uma proposta para o ensino da Geometria no Ensino Médio(Universidade Federal de São Paulo (UNIFESP), 2020-02-17) Campos, Paulo Roberto Pola [UNIFESP]; Jorge, Grasiele Cristiane [UNIFESP]; Universidade Federal de São PauloIn this work we study tiling in the plane, complementing with a study of the area of some plane figures. We present and discuss the different tiling patterns, demonstranting the different types of tiling in the plane by regular polygons. We also present the concept of pentaminoes and how we can use them for a playful activity of paving different areas. As a didactic proposal, we present a sequence that targets high school students. This sequence proposes activities that aim to broaden students' viem of Mathematics, presenting application of results common to basic education in Geometry.