Artigos - Matemática - IGCE

URI Permanente para esta coleçãohttps://hdl.handle.net/11449/25104

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Landscapes of Investigation, Dialogue, and Inclusion: about the Encounter Among Deaf and Hearing Students in Mathematics Classes
(2023-01-01) Moura, Amanda Queiroz ; Penteado, Miriam Godoy ; Universidade Estadual Paulista (UNESP) ; Visitante do Instituto Federal do Rio Grande do Sul
In this article, we present reflections on the meeting between deaf students and listeners in mathematics classes. In order to contribute to a better understanding of practices based on the concept of inclusion and equity, we bring a discussion about interactions in mathematics classes based on an approach in which the dialogic communication was privileged. Our reference for such discussions is the result of a research that is focused on interaction in which students speak different languages - Portuguese and Brazilian Sign Language. First, we present the context in which the research was carried out. Then, some relevant aspects of the dialogic perspective are elucidated. To illustrate how the interactions took place, we present an episode in which appears interactions among the participants. Finally, we present our reflections on the proposed landscapes of investigation and dialogue in a teaching environment that focuses on inclusion and equity. The results indicate the viability of dialogic interaction between two culturally different groups - deaf and hearing - and their participation in conditions of equity and cooperation during the mathematical learning process. We understand that the reflections and conclusions presented in this paper support mathematics education practices with a focus on diversity.
Landscapes of Investigation, Dialogue, and Inclusion: About the Encounter among Deaf and Hearing Students in Mathematics Classes
(2023-01-01) Moura, Amanda Queiroz ; Penteado, Miriam Godoy ; Universidade Estadual Paulista (UNESP)
In this article, we present reflections on the meeting between deaf students and listeners in mathematics classes. In order to contribute to a better understanding of practices based on the concept of inclusion and equity, we bring a discussion about interactions in mathematics classes based on an approach in which the dialogic communication was privileged. Our reference for such discussions is the result of a research that is focused on interaction in which students speak different languages — Portuguese and Brazilian Sign Language. First, we present the context in which the research was carried out. Then, some relevant aspects of the dialogic perspective are elucidated. To illustrate how the interactions took place, we present an episode in which appears interactions among the participants. Finally, we present our reflections on the proposed landscapes of investigation and dialogue in a teaching environment that focuses on inclusion and equity. The results indicate the viability of dialogic interaction between two culturally different groups — deaf and hearing — and their participation in conditions of equity and cooperation during the mathematical learning process. We understand that the reflections and conclusions presented in this paper support mathematics education practices with a focus on diversity.
Mathematics Education and Democracy: An Open Landscape of Tensions, Uncertainties, and Challenges
(2015-01-01) Skovsmose, Ole ; Penteado, Miriam Godoy ; Aalborg University ; Universidade Estadual Paulista (UNESP)
In their classic study assuming the perspective of analytical philosophy, Benn and Peters (1959) relate democracy to notions such as justice, equality, freedom, and responsibility. A further investigation of justice is provided by Rawls (1971/1999), who begins his inquiry in analytic philosophy but expands his investigations beyond this tradition. Ideas about deliberative democracy, as for instance presented by Bohman and Rehg (1997), relate the notion of democracy to participation, negotiation, and dialogue. Democracy can also be related to citizenship, autonomy, human rights, and inclusion. Together all such notions belong to an extended family of open concepts.
Contextualisation of Geometry Tasks in High School Mathematics Textbooks
(2022-01-01) Litoldo, Beatriz Fernanda ; Amaral, Rúbia Barcelos ; Mazzi, Lucas Carato ; Matemática e Tecnologias ; Universidade Estadual Paulista (UNESP)
Background: Geometry is often seen as an area of mathematics that is present in everyone’s daily life. Looking around, we see it in the shapes of objects, in nature, etc. Therefore, it would be natural to expect that its approach in textbooks, for example, would bring different contexts in which it would be present. Objective: To discuss how contexts are introduced in geometry tasks in a collection of mathematics textbooks. Design: We use a qualitative approach of the documentary type as a methodology. Environment and participants: A collection of high school mathematics textbooks approved by the National Textbook and Didactic Material Program – 2018 was selected. Data collection and analysis: Data were produced, organised, and analysed using horizontal and vertical analysis methods in each collection volume, according to the different references of contexts. Results: They concern the different references of contexts involved in the tasks. From the 1,335 tasks analysed, 1,108 were contextualised in purely mathematical situations, while the rest, 227, were in contexts of reality. In this, there are 215 referring to reasonable semi-realities, and, on the other hand, the real context contemplates only three. Finally, nine concern tasks in unreasonable semi-real contexts. Conclusions: The restriction of the different context references that students can experience from this collection is discussed. The contexts presented do not include a broad spectrum based on a diversity of experiences among the different references of contexts.
Mathematics Education and Democracy an Open Landscape of Tensions, Uncertainties, and Challenges
(Routledge, 2016-01-01) Skovsmose, Ole ; Penteado, Miriam Godoy ; English, L. D. ; Kirshner, D. ; Aalborg Univ ; Universidade Estadual Paulista (UNESP)
CONCERNS OF a CRITICAL MATHEMATICS EDUCATION Challenges for Teacher Education
(Information Age Publishing-iap, 2012-01-01) Skovsmose, Ole ; Penteado, Miriam Godoy ; Jacobson, L. J. ; Mistele, J. ; Sriraman, B. ; Aalborg Univ ; Universidade Estadual Paulista (UNESP)
ON INTERSECTION AND TRANSVERSALITY OF MAPS
(Amer Mathematical Soc, 2023-03-31) Libardi, Alice K. M. ; Mattos, Denise de ; Santos, Edivaldo L. dos ; Universidade Estadual Paulista (UNESP) ; Universidade de São Paulo (USP) ; Universidade Federal de São Carlos (UFSCar)
Given a smooth map fV: V-+ K with f*V(nu K) = nu V, a gen-eral question arises: under which conditions there exists a smooth extension f : M-+ N of fV such that f is transverse to K and f-1(K) = V, where M, N are smooth closed manifolds of dimension m and n, V, K are closed submanifolds of M and N, respectively, of same codimension and nu K, nu V are the normal bundles of K in N and V in M, respectively. In this paper, we give conditions to the existence of extensions, by using bordism intersection pro d-uct. Moreover, we present an interesting and non-trivial example illustrating the systematic construction of such extensions, skeletonwise.
ECOLOGY IN TEXTBOOKS: AN ANALYSIS OF ACADEMIC PRODUCTION IN BIOLOGY TEACHING AREA
(Centro Univ Nove Julho, 2022-10-01) Morais, Wanderson Rodrigues ; Almeida, Maria Jose Pereira Monteiro de ; Rink, Juliana ; Universidade Estadual Paulista (UNESP) ; Universidade Estadual de Campinas (UNICAMP)
This paper aims to reflect on the research scenario in the field of biology teaching and textbooks, in order to understand what contributions and challenges are announced by academic productions in the area, regarding to ecology. We start from the consideration that ecology is still considered a recent science, with its concepts in constant construction and reformulation, and that basic elements of its field are influenced by society and, similarly, with regard to its teaching and presence in textbooks. Thus, we believe that the present work can contribute with a general framework that allows recognizing trends, identifying and systematizing the written production on the subject, collaborating with possible ramifications and the development of the area. Thus, we carried out a bibliographic survey in seven brazilian and two international journals, from 2001 to 2021. As a result, we identified twelve papers dealing with ecology and textbooks, from which it was possible to observe a variety of topics studied, such as: biodiversity, environment, food chain, nitrogen cycle, population flows, population ecology and ecosystem ecology. Furthermore, a third of the works point to the importance of considering historiographical aspects and the contexts of knowledge production in ecological contents, denouncing their absence and/or scarcity.
Philosophy of Mathematics Education
(Springer, 2016-01-01) Ernest, Paul ; Skovsmose, Ole ; van Bendegem, Jean Paul ; Bicudo, Maria ; Miarka, Roger ; Kvasz, Ladislav ; Moeller, Regina ; Exeter Univ ; Aalborg Univ ; Vrije Univ Brussel ; Universidade Estadual Paulista (UNESP) ; Charles Univ Prague ; Univ Erfurt
Preface
(2019-01-01) Kollosche, David ; Marcone, Renato ; Knigge, Michel ; Penteado, Miriam Godoy ; Skovsmose, Ole ; Pädagogische Hochschule Vorarlberg ; Universidade Federal de São Paulo (UNIFESP) ; Universität Potsdam ; Universidade Estadual Paulista (UNESP) ; Aalborg Universitet
The Role of the Interpreter of Brazilian Sign Language in the Dialogue Among Deaf and Hearing Students in Mathematics Classes
(2019-01-01) Moura, Amanda Queiroz ; Penteado, Miriam Godoy ; Universidade Estadual Paulista (UNESP)
This chapter is based on a research project whose focus is the teaching and learning of mathematics in environments where deaf students and hearing students are together. In this context, the complexity of teaching and learning processes becomes more evident due to the use of two languages for communication and the presence of a new person in the classroom, the interpreter, whose function is to interpret/translate the Portuguese to Libras and vice versa. However, using a teaching methodology based on an inquiry approach, in which the dialogue is the main pattern of communication, the role of the interpreter can have other characteristics. In order to contribute to a better understanding of the practices of the interpreter, this chapter discusses some episodes from mathematics classes, highlighting the interpreter’s participation. We first present the working context of the interpreter, including the policies, challenges, and perspectives of this profession. After this, some relevant aspects of the dialogue perspective adopted in the research are elucidated. Finally, we present two episodes in which the interactions in the mathematics classes were mediated by an interpreter. The results indicate that in the context of landscapes of investigation, the role of the interpreter gains characteristics that go beyond the interpretation/translation. We recognize the role of the interpreter as fundamental in promoting equality in classrooms where deaf and hearing are together. And we understand this equality as a crucial point for creating new ways of understanding, especially with respect to mathematics.
Inclusive Mathematics Education: An Introduction
(2019-01-01) Kollosche, David ; Marcone, Renato ; Knigge, Michel ; Penteado, Miriam Godoy ; Skovsmose, Ole ; Pädagogische Hochschule Vorarlberg ; Universidade Federal de São Paulo (UNIFESP) ; Universität Potsdam ; Universidade Estadual Paulista (UNESP) ; Aalborg Universitet
Inclusion has become a global topic in education and educational studies. This introduction briefly recapitulates the idea of inclusion and the essential steps in this development.
Inclusive Mathematics Education: State-of-the-Art Research from Brazil and Germany
(2019-01-01) Kollosche, David ; Marcone, Renato ; Knigge, Michel ; Penteado, Miriam Godoy ; Skovsmose, Ole ; Pädagogische Hochschule Vorarlberg ; Universidade Federal de São Paulo (UNIFESP) ; Universität Potsdam ; Universidade Estadual Paulista (UNESP) ; Aalborg Universitet
The book provides an overview of state-of-the-art research from Brazil and Germany in the field of inclusive mathematics education. Originated from a research cooperation between two countries where inclusive education in mathematics has been a major challenge, this volume seeks to make recent research findings available to the international community of mathematics teachers and researchers. In the book, the authors cover a wide variety of special needs that learners of mathematics may have in inclusive settings. They present theoretical frameworks and methodological approaches for research and practice.
Inclusive Mathematics Education in Brazil
(2019-01-01) Penteado, Miriam Godoy ; Marcone, Renato ; Universidade Estadual Paulista (UNESP) ; Universidade Federal de São Paulo (UNIFESP)
The inclusive education movement in Brazil has accompanied an international movement since the last years of the twentieth century, starting with the Jomtien declaration in 1990. As far as legislation is concerned, students with disability are well represented regarding access to education from the early years to higher education, but the enforcement of this legislation still has a long way to go. However, creating the legislation is only one step towards inclusion. The very notion of what a disability means must be addressed in order to create proper and coherent laws. The research about inclusion in Brazil has grown since the first decade of the twenty-first century, going beyond research on early school years, addressing inclusion in higher education as well - in part thanks to the legislation that opened the way for those students - and showing the impact of public policies on inclusion.
OSCILLATION AND NONOSCILLATION CRITERIA FOR IMPULSIVE DELAY DIFFERENTIAL EQUATIONS WITH PERRON INTEGRABLE COEFFICIENTS
(2022-01-01) Silva, M. A. ; Federson, M. ; Gadotti, M. C. ; Universidade de São Paulo (USP) ; Universidade Estadual Paulista (UNESP)
We present new criteria for the existence of oscillatory and nonoscillatory solutions of measure delay differential equations with impulses. We deal with the integral forms of the differential equations using the Perron and the Perron-Stieltjes integrals. Thus the functions involved can have many discontinuities and be of unbounded variation and yet we obtain good results which encompass those in the literature. Examples are given to illustrate the main results.
Deficient and multiple points of maps into a manifold
(Univ Houston, 2020-01-01) Goncalves, D. A. C. I. B. E. R. G. L. ; Monis, T. H. A. I. S. F. M. ; Spiez, S. T. A. N. I. S. L. A. W. ; Universidade de São Paulo (USP) ; Universidade Estadual Paulista (UNESP) ; Polish Acad Sci
The notion of Hopf's absolute degree is classically defined for mappings between manifolds of the same dimension, even when they are not necessarily orientable. In this paper, we extend such notion for mappings from more general spaces into manifolds. Once we have stablished a version of Hopf's absolute degree for certain maps f : X -> M, where M is a manifold but X need not be, we study the sets of deficient and multiple points of f. In case of the set of deficient points, we estimate its dimension. For multiple points, we study its density in X, and we also provide examples where its complement is dense.
Aspects of computational thinking in unplugged activities with origami and mathematics
(Univ Nove Julho, 2022-01-01) Graciolli, Carolina Yumi Lemos Ferreira ; Rocha Junior, Romario Costa da ; Silva, Ricardo Scucuglia Rodrigues da ; Universidade Estadual Paulista (UNESP)
The article aims to present some of the existing relationships between origami and computational thinking and how they can complement each other and serve as mutual support. A contextualization about the art of paper folding is presented, as well as some understandings about computational thinking, specifically its four pillars: decomposition, algorithm, pattern recognition and abstraction. As a possibility, we resort to unplugged activities involving instructions for folding animals and geometric solids that can be developed both in Elementary School and in High School or Undergraduate Degree. Finally, it is shown that the proposals can enable the development of the four pillars of computational thinking. Thus, it can be noted that the activities described open possibilities for computational thinking when worked in consonance with origami.
Semi-automatic CNN Architectural Pruning using the Bayesian Case Model and Dimensionality Reduction Visualization
(Scitepress, 2022-01-01) Marcilio-Jr, Wilson E. ; Eler, Danilo ; Guilherme, Ivan ; Hurter, C. ; Purchase, H. ; Bouatouch, K. ; Universidade Estadual Paulista (UNESP)
Visualization techniques have been applied to reasoning about complex machine learning models. These visual approaches aim to enhance the understanding of black-box models' decisions or guide in hyperparameters configuration, such as the number of layers and neurons/filters in deep neural networks. While several works address the architectural tuning of convolutional neural networks (CNNs), only a few works face the problem from a semi-automatic perspective. This work presents a novel application of the Bayesian Case Model that uses visualization strategies to convey the most important filters of convolutional layers for image classification. A heatmap coordinated with a scatterplot visualization emphasizes the filters with the most contribution to the CNN prediction. Our methodology is evaluated on a case study using the MNIST dataset.
On the hardy space H1 on products of half-spaces
(1989-01-01) Bertolo, Nativi Viana Pereira ; Universidade Estadual Paulista (UNESP)
We show that the Hardy space Hanal1(R+2 × R+2) can be identified with the class of functions f such that f and all its double and partial Hubert transforms Hkf belong to L1(R2). A basic tool used in the proof is the bisubharmonicity of |F|q, where F is a vector field that satisfies a generalized conjugate system of Cauchy-Riemann type. © 1989 by Pacific Journal of Mathematics.
Derivation of the half-side tangent formulas via lagrange’s theorem (For polar spherical triangles)
(2022-01-01) Caritá, Lucas Antonio ; Dos Santos, Carla Patrícia Ferreira ; Gadotti, Marta Cilene ; Ciência e Tecnologia de São Paulo-IFSP ; Universidade Estadual Paulista (UNESP)
Spherical Geometry is a non-Euclidean geometry that provides good tools for terrestrial location and has great applicability in Astronomy. For this reason, trigonometry in spherical triangles is an interesting subject to study. Because it is a well-developed field, there are many widely known theorems and formulas with classical demonstrations. This article aims to present an alternative proof for the Half-Side Tangent Formulas, using the Langrange’s Theorem concerning polar triangles.

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