Recorte dos produtos educacionais em história no ensino da matemática e em didática da matemática a partir das dissertações e teses defendidas no brasil entre 1990-2010

This work has the main purpose of conducting a survey of educational products present in dissertations and doctoral theses focused on the use of history in mathematics teaching and Didactics of mathematics with a French foundation produced in graduate programs in the strict sense of the Brazil between 1990 and 2010, the areas of Education, Mathematics Education, school of Natural Sciences and Mathematics and related areas, according to the research proposal of Mendes (2010). Our interest was to select the products that present concrete proposals for educational activities that can be used in the classroom of Basic Education and Training of Teachers of Mathematics. The research was implemented through a bibliographic study documents the Bank of dissertations and theses from CAPES, libraries and archives of some Postgraduate programs in the country who focus their studies on the subject object of this research, besides the Brazilian Digital Library Theses and Dissertations (BDBTD). From this survey we selected works that present educational products materialized in blocks of activities based on the use of teaching history of mathematics to the classroom as well as the sequence of activities based on the Teaching of Mathematics. In possession of material, produce a CD-ROM containing the selected activities, in order to help support the work of teachers regarding the use of these activities, as a supplementary material to textbooks in their math classes

Linguagem matemática: uma proposta de ensino e avaliação da compreensão leitora dos objetos da matemática

This paper discusses aspects related to the mathematical language and its understanding, in particular, by students of final years of elementary school. Accordingly, we aimed to develop a proposal for teaching, substantiated by mathematical modeling activities and reading, which takes advantage of the student of elementary school a better understanding of mathematical language for the content of proportion. We also aim to build / propose parameters for the assessment of reading proficiency of the language of the student in analyzing and modeling process, its ability to develop/improve/enhance this proficiency. For this purpose, we develop a qualitative research, with procedures for an action research whose analysis of the data is configured as Content Analysis. We refer to epistemological and didactic, in the studies: Piaget (1975, 1990), Vygotsky (1991, 2001), Bakhtin (2006), Freire (1974, 1994), Bicudo and Garnica (2006), Smole and Diniz (2001), Barbosa (2001), Burak (1992), Biembengut (2004), Bassanezi (2002), Carrasco (2006), Becker (2010), Zuin and Reyes (2010), among others. We understand that to acquire new knowledge one must learn to read and reading to learn it, this process is essential for the development of reading proficiency of a person. Modeling, in turn, is a process which enables contact with different forms of reading providing elements favorable to the development here mentioned. The evaluation parameters we use to analyze the level of reading proficiency of mathematical language proved to be effective and therefore a valuable tool that allows the teacher an efficient evaluation and whose results can guide you better in the planning and execution of their practice

Matemática Védica no ensino das quatro operações

This paper describes a study on the possibilities of teaching Vedic Mathematics for teaching the four operations. For this various literature sources were consulted considering three main aspects. The first of a historical-cultural, in order to gather information about the Mathematics originated from Vedic civilization, which highlight (Plofker, 2009), (Joseph, 1996), (Bishop, 1999), (Katz, 1998), (Almeida , 2009). This sought to emphasize relationships of the development of this culture with the math involved in the book Vedic Mathematics written by Tirthaji and published in 1965. In this respect the work brings notes on the history of mathematics on the development of mathematics in ancient India. The second aspect was related to teaching mathematics through research activities in the classroom, in this sense, I sought a bibliography to assist in the construction of a proposed activity to teach the four operations, based on the sutras of Vedic Mathematics, but within an investigative approach, assisting in the development of mental calculation strongly stimulated by the Vedic Mathematics Sutras. The authors were adopted (Mendes, 2006, 2009a, 2009b), Bridge (2003). The third aspect considered to search for books on teaching Vedic Mathematics, written by other authors, based on the book by Tirthaji. This revealed Vedic Mathematics textbooks adopted in schools and free courses in the UK, USA and India, all based on the book Vedic Mathematics of Tirthaji. From the bibliographical studies were prepared didactic guidelines and suggested activities for the teacher, to assist in teaching the four operations. The educational product, consisting of Chapters 4 and 5, is the body of the dissertation and consists of didactic guidelines and suggestions for activities that aim to contribute to the teachers who teach initial years of elementary school

Física do meio ambiente: desafios de uma disciplina focada na formação de habilidades gerais

A disciplina Física do Meio Ambiente (FMA) foi criada em 1976 no Departamento de Física Teórica e Experimental da UFRN e, atualmente, faz parte da estrutura curricular do curso de Licenciatura em Física da UFRN e é de caráter obrigatório. Tal caráter se justifica, dentre outros motivos, pelo fato de que esta disciplina representa uma boa oportunidade dos licenciandos estudarem de que forma a Física pode contribuir para a compreensão de fenômenos relativos ao nosso Meio Ambiente, sejam eles relacionados às atividades humanas ou aos fenômenos naturais propriamente ditos e que, de uma forma ou de outra, afeta a sociedade. O nosso trabalho de pesquisa teve como objetivo principal elaborar um novo programa de ensino para a disciplina de Física do Meio Ambiente adequado às necessidades da educação científica para o século XXI. A pesquisa foi conduzida inicialmente com um levantamento histórico da disciplina desde sua origem no Departamento de Física ate os dias atuais, analise dos Projetos Pedagógicos do curso de Licenciatura em Física da UFRN, revisão bibliográfica sobre as definições de competências e habilidades em um contexto de ensino e segundo o pensamento de vanguarda nesse campo de pesquisa, acompanhamento do curso durante um semestre através de aulas observacionais, aplicação de questionário para a coleta de dados e análise de alguns livros didáticos de Física do Ensino Médio. A partir do perfil ou modelo profissional para o licenciado em Física da UFRN definimos os objetivos gerais para a disciplina de FMA em termos de habilidades gerais relacionadas com as atividades que um futuro professor de Física irá desempenhar no seu dia a dia. O nosso programa de ensino foi pensado no sentido de introduzir conteúdos de didática específica ao longo da disciplina, isto é, familiarizar os professores em formação com investigação e inovação didáticas voltadas para o ensino de temas que envolvam a conexão entre Física e Meio Ambiente. Como resultado de nossa pesquisa foi proposto um novo Programa de Ensino para FMA que pode ser útil aos futuros professores desta disciplina e foi elaborado segundo uma metodologia de organização científica do processo ensino

Um estudo de práticas matemáticas históricas e sugestões de uso na matemática escolar

This dissertation aims to contribute on teaching of mathematics for enabling learning connected to the relationship among science, society, culture and cognition. To this end, we propose the involvement of our students with social practices found in history, since. Our intention is to create opportunities for school practices that these mathematical arising from professional practice historical, provide strategies for mathematical thinking and reasoning in the search for solutions to problematizations found today. We believe that the propose of producing Basic Problematization Units, or simply UBPs, in math teacher formation, points to an alternative that allows better utilization of the teaching and learning process of mathematics. The proposal has the aim of primary education to be, really forming the citizen, making it critical and society transformative agent. In this sense, we present some recommendations for exploration and use of these units for teachers to use the material investigated by us, in order to complement their teaching work in mathematics lessons. Our teaching recommendations materialized as a product of exploration on the book, Instrumentos nuevos de geometria muy necessários para medir distancia y alturas sem que interuengan numeros como se demuestra em la practica , written by Andrés de Cespedes, published in Madrid, Spain, in 1606. From these problematizations and the mathematics involved in their solutions, some guidelines for didactic use of the book are presented, so that the teacher can rework such problematizations supported on current issues, and thus use them in the classroom

História da matemática na formação do professor: dificuldades e sugestões

This work is the result of a study that aimed to start scoring difficulties that the math teacher is trying to get a historical formation. Considering that the textbook is the material with which the teacher has more contact, start with reading historical texts present in these books. Choose a theme and choose from that we observed limitations ranging from the search for sources of research in relation to the actual historical content. There are many studies that show the importance of the history of mathematics in teacher education and also in the teaching and learning of mathematics. These works , in particular the work of Feliciano (2008 ) entitled : " The use of history of mathematics in the classroom " , along with the information , experiences and opinions given by Professor Anderson Luís de Azevedo Paulo , in some meetings , point to need for materials for teaching , since they show that recognizes the importance of this knowledge and the ability to use it in the classroom , but several factors have pushed aside , even the texts present in textbooks. From the analysis of some of the work and contributions of Professor Anderson Paulo we pointed out some of the factors that make historical texts being ignored by teachers and among them are characteristics in appearance and content in the text. To assist in the preparation of materials that meet the expectations of the teacher, we present a manual with suggestions and / or features to choose or produce a good text. These suggestions can make the history books more enjoyable and thus approach the teacher of historical knowledge and later encouraged to seek, in fact, a historical formation

Elaboração de atividades didáticas para o ensino de matemática a partir de livros antigos: o exemplo do leçons élémentaires de Lagrange

De nombreuses études sur l`utilisation pédagogique de l`histoire des mathématiques viennent a identifier les arguments qui sous-tiennent ces actions éducatives comme une façon d`aborder les mathématiques scolaires afin de mener les élèves à un apprentissage réflexif et significatif des mathématiques. Cherchant a vérifier, de manière pratique, comment ces relations entre histoire des mathématiques et l`enseignement des mathématiques peuvent se matérialiser sous la forme d`activités didactiques, nous avons effectué un sondage sur les oeuvres du mathématicien Joseph Louis Lagrange (1736-1813) et identifié le potentiel d`exploration éducatif, de l`oeuvre Leçons élémentaires sur les mathématiques données a l`École Normale en 1795, de cet mathématicien. L`objectif principal de notre étude était de faire des recherches sur le potentiel d`une oeuvre antique dédié à l`enseignement des mathématiques et de la considérer comme support conceptuel et didactique pour la création d`un modèle d`activités didactiques pour l`enseignement des mathématiques, dans la formation des enseignants de mathématiques et aussi en ce qui concerne l`apprentissage des mathématiques des élèves de l`école primaire. Nous avons fait une lecture, la traduction et l`ajout de notes et commentaires sur le travail et une recherche bibliographique sur la relation entre l`histoire des mathématiques et l`enseignement des mathématiques, de façon a comprendre les aspects conceptuels et didactiques pour l`élaboration d`um module activités didactiques pour l`enseignement des mathématiques basée sur certains chapitres du livre de Lagrange. À cette fin, l`oeuvre a été utilisé comme source primaire et a été étudié sous un fondement théorique appuyer sur les travaux des Institut de recherche sur l`enseignement des mathématiques IREM. Dans le module élaboré, les activités apportent les contenus dans une suite integrée à une logique de classe, à partir de la lecture directe des découpages du texte original, disposés entre les questions et les situations-problémes , historiquement mis en contexte avec la période et associés à des contenus spécifiques. Comme il s`agit d`une recherche basée sur l`exploitation de livres anciens, nous croyons que des modules d`activités basées sur des source primaires peuvent être utilisées comme un matériel pédagogique pour la formation des enseignants de mathématiques ainsi que pour les dernières années de l`école élémentaire, reformulées ou accrues d`autres questions telles l`intérêt de chaque enseignant qui l`utilise

Fontes primárias da história do vácuo e da pressão atmosférica na sala de aula: cartas e jornais históricos em articulação com o livro-texto do ensino médio

The use of the History and the Philosophy of Science (HPS) for the teaching of science and scientific subjects has been advocated in recent decades. It has been pointed out that the History of Science could make for a deeper learning of scientific concepts, since it would promote a contact with the problems which that knowledge has set out to solve. Furthermore, historical episodes would serve to put the discussions about the nature of scientific knowledge into context. With a view to explore those potentialities, the literature in the field has sought to identify the challenges and obstacles for the didactic transposition of subjects from the History of Science. Amongst many aspects, the deficiencies in the training of teachers, so that they can work with the insertion of HPS in the classroom have been highlighted. Another aspect that has been mentioned to be a challenge has to do with the didactic transposition of the Primary Sources, that is, of the original texts on the History of Science. The Primary Sources have significant potentialities: making a connection possible between scientists and concepts, showing the difficulties faced during scientific endeavors, perceiving the role of mistakes as obstacles to be surpassed, not as defeat, etc. On the other hand, there has been little exploration of these concepts in an educational context, due to their own peculiarities. The original texts are often hard to understand and their interpretation demands knowledge of the historical and scientific context in which they were written, as well as skills pertaining to the conduction of research in the field of the History of Science. With this scenario in mind, the research towards this Professional MSc degree starts from the challenge of elaborating and discussing proposals which could enable the didactical transposition of the Primary Sources. We have worked specifically with Primary Sources on the History of the Vacuum and of the Atmospheric Pressure, because of the insertion of these subjects in the Brazilian High School curriculum, in connection with the didactical textbooks. "Historic Journals" were made up from clippings of the original historical texts, as was a Didactical Unit, which takes the usual textbooks as a basis and contemplates using the Journals and the entire Primary Sources in High School. At last, we have elaborated and implemented a course designed for the preparation of teachers and for being an opportunity for the discussion of the feasibility of putting these kinds of proposal into practice

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

Refletindo dificuldades de aprendizagem de alunos do ensino médio no estudo do equilíbrio químico

This research intends to identify the main conceptual mistakes committed by High School students when studying Chemical Equilibrium and also how the didactic books can influence in their formation. For the data - collecting we applied 150 questionnaires with 11 open questions e 4 restricted ones. Students from three different private schools in Natal-RN were used in this survey. The questionary about the book analysis tried to understand how the subject has been boarded, making it easier or not for the knowledge building. The books were chosen by being usually the most used ones at the chemistry classes in the schools in town. On the didactic book analysis we evaluated 12 items that tried to identify the clarity with which the books would bring up the subjects, the contextualization of the exercises, the analogies used, the amount and the quality of exercises, the connections between the subjects, and the retaken of important concepts. The questionary given to the students tried to get their knowledge about the concepts related to Chemical Equilibrium. The main mistakes found were: the definition of the state of equilibrium in a chemical reaction, the constant, the double headed arrow, confusions between mass and concentration, the representation of a microscopic reaction in equilibrium, partial pressure and total pressure, and the function of the catalyser. The results demonstrated a lot of insecurity or lack of knowledge about the subject when it was realized that there was a big number of blank questions and a considerable percentage of questions with conceptual errors. We concluded that those errors could be eased or even avoided if the didactic books and the teachers boarded the contents in a more conceptual form with the application of a largest number of good quality exercices, watching the building of definitions by the students, avoiding this way the formation of wrong concepts

Morfologia matemática aplicada à detecção de sombras e nuvens em imagens de alta resolução

The spatial resolution improvement of orbital sensors has broadened considerably the applicability of their images in solving urban areas problems. But as the spatial resolution improves, the shadows become even a more serious problem especially when detailed information (under the shadows) is required. Besides those shadows caused by buildings and houses, clouds projected shadows are likely to occur. In this case there is information occlusion by the cloud in association with low illumination and contrast areas caused by the cloud shadow on the ground. Thus, it's important to use efficient methods to detect shadows and clouds areas in digital images taking in count that these areas care for especial processing. This paper proposes the application of Mathematical Morphology (MM) in shadow and clouds detection. Two parts of a panchromatic QuickBird image of Cuiab-MT urban area were used. The proposed method takes advantage of the fact that shadows (low intensity - dark areas) and clouds (high intensity - bright areas) represent the bottom and top, respectively, of the image as it is thought to be a topographic surface. This characteristic allowed MM area opening and closing operations to be applied to reduce or eliminate the bottom and top of the topographic surface.

Conexão entre as redes complexas e estatística de Kaniadakis e busca eficiente das propriedades críticas do processo epidêmico difusivo 1D

In this work we study a connection between a non-Gaussian statistics, the Kaniadakis statistics, and Complex Networks. We show that the degree distribution P(k)of a scale free-network, can be calculated using a maximization of information entropy in the context of non-gaussian statistics. As an example, a numerical analysis based on the preferential attachment growth model is discussed, as well as a numerical behavior of the Kaniadakis and Tsallis degree distribution is compared. We also analyze the diffusive epidemic process (DEP) on a regular lattice one-dimensional. The model is composed of A (healthy) and B (sick) species that independently diffusive on lattice with diffusion rates DA and DB for which the probabilistic dynamical rule A + B → 2B and B → A. This model belongs to the category of non-equilibrium systems with an absorbing state and a phase transition between active an inactive states. We investigate the critical behavior of the DEP using an auto-adaptive algorithm to find critical points: the method of automatic searching for critical points (MASCP). We compare our results with the literature and we find that the MASCP successfully finds the critical exponents 1/ѵ and 1/zѵ in all the cases DA =DB, DA DB. The simulations show that the DEP has the same critical exponents as are expected from field-theoretical arguments. Moreover, we find that, contrary to a renormalization group prediction, the system does not show a discontinuous phase transition in the regime o DA >DB.

PROFESSOR E PROFESSOR DE MATEMÁTICA: DAS INFORMAÇÕES QUE SE TEM ACERCA da FORMAÇÃO QUE SE ESPERA

O presente artigo faz um levantamento da bibliografia disponível acerca da formação de professores em cursos de licenciatura, iniciando com um tratamento hermenêutico ao termo formação, passando pela atual situação dos docentes no estado de São Paulo. Caracteriza a constituição das instituições formadoras e levanta aspectos convergentes em relação ao tratamento do tema na literatura. Finalmente são feitas considerações específicas sobre a formação dos professores em cursos de Licenciatura em Matemática.

As Memórias de Lacroix: a instrução pública na França revolucionária, em geral, e o ensino de Matemática, em particular

O artigo - um exame hermenêutico do livro Essais sur l'enseignement en général, et sur celui des mathématiques en particulier, de 1805, de Sylvestre-François Lacroix, enfatizando sua segunda parte, na qual o autor discute seu Curso de Matemática Elementar, uma série de manuais escolares elaborados para a Escola Central das Quatro Nações - tem sua fundamentação ligada à Hermenêutica de Profundidade de Thompson conjugada a procedimentos de investigação textual sugeridos por Genette quanto aos paratextos editoriais. Defende que o livro de Lacroix é uma obra auto-referencial, de cunho claramente autobiográfico, que responde mais aos ideais iluministas da França do Setecentos que às perspectivas do século XIX, quando a obra circulou, tendo sido reeditada por quatro vezes, sob Napoleão, na primeira metade do Oitocentos. Raramente focalizado em trabalhos de pesquisa, o livro - cujas edições estão disponíveis eletronicamente - tem uma única tradução, ainda inédita, para o português.