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

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

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.

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.

Formação de professores de matemática: um estudo sobre a influência da formação pedagógica prévia em um curso de licenciatura

O presente texto tem como objetivo discutir a influência da formação pedagógica prévia em um curso específico de Licenciatura em Matemática. Como instância prévia de formação este artigo considera o CEFAM, e o curso de Licenciatura em foco é o da Faculdade de Ciências da UNESP de Bauru. O enfoque metodológico é nitidamente qualitativo, tendo sido os procedimentos analíticos pautados no estudo de convergências e divergências detectadas nos discursos dos estudantes-depoentes.

Um ensaio sobre as concepções de professores de Matemática: possibilidades metodológicas e um exercício de pesquisa

Este artigo tem como tema principal as concepções dos professores de Matemática. Considerando o termo concepção a partir do pragmatismo de Peirce, elabora-se um conjunto de parâmetros metodológicos - chamado de método indireto - a ser aplicado no estudo das concepções de professores de Matemática. Trata-se, em síntese, de investigar as concepções dos professores interpelando-os não sobre suas crenças, mas sobre suas práticas. Fundamentando essa abordagem indireta e explicitando-a em sua natureza qualitativa, o artigo segue apresentando, como exemplo, um exercício desse método indireto: um estudo sobre os critérios que os professores utilizam quando escolhem livros-texto para sua sala de aula, abordando, conseqüentemente, quais concepções de Matemática e de seu ensino e aprendizagem tais critérios desvendam. Partindo de depoimentos de professores de Matemática, o estudo indica que os professores agem com certa independência quando escolhem os materiais utilizados em suas atividades docentes. Buscam, ao mesmo tempo, apoio em uma vasta gama de livros didáticos, desconsiderando as particularidades de cada obra e as abordagens e perspectivas defendidas por seus autores. Embora submetam-se ao livro didático - considerado uma referência legítima e segura -, os professores o subvertem, buscando adequá-lo ao que consideram correto. Dessa constatação, algumas das concepções dos professores podem ser realçadas: o aluno, via de regra, é avaliado e classificado pelas lacunas que apresenta em relação aos conteúdos. Dessa postura, segue a valorização da precedência lógica dos conteúdos, de sua apresentação linear, e a defesa de pré-requisitos que viabilizariam o ensino e, conseqüentemente, implicam a legitimidade de aulas predominantemente expositivas.

Um Ensaio Sobre História Oral e Educação Matemática: pontuando princípios e procedimentos

Recently, we can perceive an intensification of assignments developed into Mathematical Education with the use of oral history as a research methodology. In this article, facing the living experiences during the preparation of our Phd tasks and later, when we had the role of advisors of scientific papers and of Postgraduate students in their researches also using the same methodology, we discussed the implication of ethics, mathematical education and oral history. Furthermore, we enunciated possibilities of the posture of the researcher before interviews, texts and iconography - photos and several images-provided by collaborators of our projects on Oral history and Mathematical Education.

Contribuições da CADES para a Educação (Matemática) Secundária no Brasil: uma Descrição da Produção Bibliográfica (1953-1971)

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.

Avaliação de Interações entre Professor e Alunos na Educação Matemática: ensino e aprendizagem de recursos pedagógicos

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.

Princípio da Indução Matemática no Ensino Médio

We developed this dissertation aiming its in the process of teaching and learning of the Principle of Mathematical Induction and we set our efforts so that the students of the first year of the high school can assimilate the content having the knowledge seen in the basic education as foreknowledge. With this, we seek to awake in the student the interest on proofs, showing how much it s needed in examples that involve contents that he is already seen