Geometrias não-eucludianas como anomalias: implicações para o ensino de geometria e medidas

This present research the aim to show to the reader the Geometry non-Euclidean while anomaly indicating the pedagogical implications and then propose a sequence of activities, divided into three blocks which show the relationship of Euclidean geometry with non-Euclidean, taking the Euclidean with respect to analysis of the anomaly in non-Euclidean. PPGECNM is tied to the line of research of History, Philosophy and Sociology of Science in the Teaching of Natural Sciences and Mathematics. Treat so on Euclid of Alexandria, his most famous work The Elements and moreover, emphasize the Fifth Postulate of Euclid, particularly the difficulties (which lasted several centuries) that mathematicians have to understand him. Until the eighteenth century, three mathematicians: Lobachevsky (1793 - 1856), Bolyai (1775 - 1856) and Gauss (1777-1855) was convinced that this axiom was correct and that there was another geometry (anomalous) as consistent as the Euclid, but that did not adapt into their parameters. It is attributed to the emergence of these three non-Euclidean geometry. For the course methodology we started with some bibliographical definitions about anomalies, after we ve featured so that our definition are better understood by the readers and then only deal geometries non-Euclidean (Hyperbolic Geometry, Spherical Geometry and Taxicab Geometry) confronting them with the Euclidean to analyze the anomalies existing in non-Euclidean geometries and observe its importance to the teaching. After this characterization follows the empirical part of the proposal which consisted the application of three blocks of activities in search of pedagogical implications of anomaly. The first on parallel lines, the second on study of triangles and the third on the shortest distance between two points. These blocks offer a work with basic elements of geometry from a historical and investigative study of geometries non-Euclidean while anomaly so the concept is understood along with it s properties without necessarily be linked to the image of the geometric elements and thus expanding or adapting to other references. For example, the block applied on the second day of activities that provides extend the result of the sum of the internal angles of any triangle, to realize that is not always 180° (only when Euclid is a reference that this conclusion can be drawn)

A etnomatemática dos trabalhadores das cerâmicas de Russas-Ce e o contexto escolar: delineando recomendações pedagógicas a partir de uma experiência educacional

It is still common among contemporary educational proposals an overemphasis abstraction, to the formalism and symbolism of mathematical knowledge at the expense of the sociocultural aspects of Mathematics. Coming up by questioning some academic mathematical tenets and valuing knowledge developed in different sociocultural contexts within Mathematical Education, the Ethnomatematics is consolidating itself as a research field. Despite its contributions to the educational context, because its philosophical character and the paucity of debates about the subject, the implementation of educational proposals for basic education are scarce. Given this situation, this dissertation comes up with a view to develop an educational intervention in the light of Ethnomathematics in a class of 6th grade of an elementary school from a red ceramic industries workers community, located in a countryside from Russas-CE and from this intervention, to develop a set of pedagogical recommendations aiming basic education teachers. Adopting a perspective of qualitative research, particularly guided by action research, this study used observation, field diary, interviews and activities with students as tools for data collection. It was found that the use of field research as part of teaching and learning favored the placement of students as critical subjects of their own reality . Furthermore, the educational experience culminated in the development of a method of teaching based on a relationship between protocooperational Ethnomatematics and the Resolution of Problems. It is necessary to broaden the debate about the ways in which the Ethnomatematics can contribute to the school context, bringing proposals closer to the reality of basic education teachers in order to help the promotion of an education which values cultural diversity without taking away the students from the access of the academic knowledge

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

Proposta para uma abordagem do conceito de oxirredução no Programa Nacional de Integração da Educação Profissional com a Educação Básica na modalidade de Educação de Jovens e Adultos Educação Profissional Técnica de Nível Médio (PROEJA)

The National Program of Professional Education Integration with Basic Education for Youngsters and Adults (PROEJA) Technical Professional Education Ensino Médio has opened a new chapter in the history of education in Brazil, making possible the integration of basic education and professional education. This new form of education, which is still in its early implementation, presents a series of challenges to be overcome. Specifically about the teaching of Chemistry, didactic material to match PROEJA s specific needs is practically inexistent. Thus, this work has the purpose of developing didactic material for the teaching of Chemistry for Professional and Technological Education of Youngsters and Adults in the courses of Electronics, Technical Electronics and Maintenance and Support for Computing at Instituto Federal de Educação,Ciência e Tecnologia do Rio Grande do Norte. This material aims at working chemical concepts of oxi-reduction reactions through a theme approach following Freire s conceptions for the teaching of Youngsters and Adults

Contribuições de uma unidade de ensino potencialmente significativa UEPS para o ensino de ecologia em escola pública da educação básica

The research aims to evaluate the contributions of a teaching unit to enhance the learning contents ecological green areas in elementary school. The work was conducted with elementary students in a public school in Natal-RN. We sought to identify the students´ previous knowledge about the contents of ecology, develop and implement a Potentially Meaningful Teaching Units PMTU; assess learning of ecological concepts in Teaching Unit Potentially Significant; assess the contribution of interpretative trail as strategy teaching to learning content ecology. The survey of students´ previous knowledge through the pre-test was essential to identify the appropriate subsumers and partially correct, since they served as "anchor" for further expansion of scientific concepts contained in this research. The green areas of the school as an educational, contributed the motivational aspect, as students were protagonists throughout the entire process of teaching and learning. The method of stimulated memory was effective to evidence learning ecological concepts in interpretive trails. The use of diverse activities organized on a PMTU promoted intellectual autonomy of the students and facilitated the acquisition of new meanings through progressive differentiation, and integrative reconciliation consolidation of ecological content and concepts related to biotic and abiotic factors on the basis of the central ideas thematic Life and Environment. The development of procedural skills to capture and share meanings, observe, collect and record data, hypotheses, ability to explain, to apply knowledge to solve problem situations, argue, identify, compare, differentiate and relate concepts, negotiate meanings, reflecting Critically, systematize data was evidenced. Collaborative activities promoted the incorporation of attitudinal contents as developing respect for differences, learn to work in teams to plan, develop and implement actions together for citizenship and environmental responsibility. The application of the Potentially Meaningful Teaching Units PMTU showed evidence of Critical meaningful learning ecological concepts covered in elementary school.

Dificuldades de aprendizagem sobre conceitos de genética no ensino fundamental

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

Saberes ambientais e estações do ano

La enseñanza de las estaciones es fundamental para la comprensión de muchos ciclos naturales de la Tierra y, por consiguiente, debe integrar una educación en astronomía comprometidos con una educación ambiental más amplio. Sin embargo, la literatura en la educación científica ha puesto de manifiesto durante mucho tiempo la existencia de asociaciones erróneas de las estaciones astronómicas con características contradictorias de los ambientes que experimentamos en nuestro país. Los estudios de los autores de la historia de la astronomía y la astronomía cultural sugieren que la corrección de este error requiere la sistematización de los conocimientos sobre el comportamiento anual del medio ambiente local y, al mismo tiempo, la comprensión de los diferentes puntos de vista en el que las estaciones estaban y se cree por diferentes culturas, en particular, pero sin limitarse, a la perspectiva que utiliza como referencia el movimiento anual del Sol como base para la división del año en cuatro estaciones. Agregado a la reflexión sobre el enfoque humanista a la enseñanza de la astronomía, estos estudios sirvieron de base para la realización de investigaciones con los pescadores de la playa de Ponta Negra, durante los meses de mayo, junio y julio de 2012 y mayo-agosto en 2013; con el fin de conocer sus percepciones sobre el ambiente de la playa e investigar las posibles referencias que tienen del cielo durante el año. Más allá de la contextualización y reflexiones desarrolladas en la tesis, se presentan como un producto de la investigación el material educativo que consiste en el video "Las estaciones del mar de Ponta Negra" para ser utilizado como apoyo en talleres o cursos para estudiantes universitarios y profesores, que implica el tema de las estaciones . El material se utiliza la percepción de los pescadores en la playa dirigidas a contribuir así al diálogo entre la ciencia y el conocimiento cotidiano, y para reducir la brecha del conocimiento sistematizado sobre las características y los cambios anuales en el entorno de Natal / RN, en particular en el contexto de la enseñanza de las Ciencias. Al mismo tiempo, se espera favorecer la mirada del los profesores y futuros profesores para el medio ambiente local y la variedad que las diferentes culturas perciben los ciclos anuales y sus entornos

Saberes de astronomia no 1º e 2º ano do ensino fundamental numa perspectiva de letramento e inclusão

This work suggests a discussion about methodologies and didactic-pedagogical activities for the teaching of Astronomy in first and second cycles of the primary school, in a perspective of literacy and inclusion. The presented proposals have been developed in a group of the Public School Alceu Amoroso Lima, North of Natal city, with children since six years old, amongst which two considered as being with special needs . This research aims to demonstrate that it is possible to develop with those children the contents of Astronomy, while they participate of the process of literacy and inclusion. From this, we are searching a theoretical-practical contribution so that the Parâmetros Curriculares Nacionais (Brazilian Nacional Curricular Guideness) include the referred contents in first cycle of primary school. For the accomplishment of this research, Experiential Astronomy was initially proposed. Later on, many workshops had been carried through (clay, ripping , crepon paper, plasticine, cardboard and gastro-lunar ). All the proposed activities were based on the conjunction of contents, which characterized the interdisciplinarity. Through the approach we adopted and the practices we proposed, we could evidence that not only children considered as being normal , but also that ones who carries special needs could appropriate themselves of our writing code, develop and incorporate a daily relationship close to the stuffs of the sky, learn many information about all of this, besides constructing attitudinal, procedural and conceptual contents

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

Sensoriamento remoto hidroacústico no mapeamento de macrófitas aquáticas submersas

Macrófitas são importantes produtoras primárias do ecossistema aquático, e o desequilíbrio do ambiente pode ocasionar seu crescimento acelerado. Portanto, levantamentos de dados relacionados a macrófitas submersas são importantes para contribuir na gestão de corpos de água. Contudo, a amostragem dessa vegetação requer um enorme esforço físico. Nesse sentido, a técnica hidroacústica é apropriada para o estudo de macrófitas submersas. Assim, os objetivos deste trabalho foram avaliar os tipos de dados gerados pelo ecobatímetro e analisar como esses dados caracterizam a vegetação. Utilizou-se o ecobatímetro BioSonics DT-X acoplado a um GPS. A área de estudo é um trecho do Rio Uberaba, MG. A amostragem foi feita por meio de transectos, navegando de uma margem à outra. Depois de processar os dados, obteve-se informação a respeito de ocorrência de macrófitas submersas, profundidade, altura média das plantas, porcentagem da cobertura vegetal e posição. A partir desse conjunto de dados, foi possível extrair outras duas métricas: biovolume e altura efetiva do dossel. Os dados foram importados de um Sistema de Informação Geográfica e geraram-se mapas ilustrativos das variáveis estudadas. Além disso, quatro perfis foram selecionados para analisar a diferença entre as grandezas de representação de macrófitas. O ecobatímetro mostrou-se uma ferramenta eficaz no mapeamento de macrófitas submersas. Cada uma das medidas - altura do dossel, ECH ou biovolume - caracteriza de forma diferente a vegetação submersa. Dessa forma, a escolha do tipo de representação depende da aplicação desejada.

Gêneros, sexualidades e Educação Física escolar: um início de conversa

Physical Education establishes relations about sex-gender-sexuality by its programs. Thinking approaches among gender and sexuality questions from scholar Physical Education is a productive challenge. Inspired in post-structuralism studies, we problematized dialogues among body, gender, identity and body movement culture. Bodily our sports practices educate citizens beyond their performances, health and beauty. Their "truths" produce gender and sexuality brands in a culture process of branding differences. Cultural events are related in binary categories as good-bad, beautiful-ugly, thin-fat, similar-different, normal-unnatural, man-women, heterosexual-homosexual, that don't let to observe the multiplicity of people educate. We must to understand the pedagogical speeches about bodies as constituents of their own bloods.

Citação e modernidade em Álvares de Azevedo: do sublime ao dessublime

El estudio de la citación en Lira de los Veinte Años, de Álvares de Azevedo, desde la óptica de Antoine Compagnon e Gerárd Genette, se muestra relevante a los estudios de la Literatura Comparada, en la perspectiva conteporánea, pués el tema provoca la posibilidad de discutir la elaboración de si del(los) otro(s), sucitando imágenes estéticas y de los pensamientos que se aproximan de una noción de tesitura textual muy presente en la modernidad literaria. Este proceso instaura procedimientos de lectura, traducción, autoria y escritura, aún, por ser utilizados, confirman la potencialidad inegable en que se escribi el trabajo poético del escritor. En la primer parte de la obra, se sugieren experiencias com lo bello y lo sublime, advindos del europeu, pero vuelto para una pesquisa de posibilidad discursivas. En la según parte, esa instancia sublimada es puesta en crise, por el sujeto poético cribado por el deseo de tornarse singular. Se instauran en el campo valorativo de los signos románticos elementos desfavorables de sentido diferentes. Dase, así, la problematización puesta por las citaciones que ora, realizan cambios simbólicos, ora, actuan en las márgenes de los textos primeros, desorganizando el material de autoria, desublimandolo, en la irrupción de nuevos cuerpos discursivos y cuerpúsculos cituacionales. En la tecer parte, ligado a Tánatos, como la dimensión por venir, marcando el presentimiento del poeta de que morirá temprano, como también la despedida de él. En esta tesi, se pretende, así, circunscribir como se figura, elabora esa constituición estética azevediana y su escritura, situando cuestiones recortadas por el actor en su obra, las quales remeten a Hegel, Kant y la otras lecturas filosóficas, ali puestas. Tal procedimiento toma la citación como estrategia poética de inscrición del sujeto y de las alteridades que le atravesan, concebiendo eso proceso autoral en la forma de reconstrución de una ciudadela de libros en este aspecto, considerandose el enfoque de Félix Guatarí, la propósito de los nuevos paradigmas y las espacialidades emergentes de estos -, o la biblioteca subjetiva, que se abre en vias y pasagenes. A través de ellas el discurso captura no solamente los objetos poéticos, pero también trazos autobiográficos rasurados, traduciendo la lucha por la visibilidad del sujeto en la formación de su pensamiento poético y estético

Efeito da adição de lodo de estação de tratamento de água (ETA) nas propriedades de material cerâmico estrutural

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

Cartografias do desejo em asfalto selvagem - engraçadinha, seus amores e seus pecados: humor, erotismo e o pornógrafo no romance rodrigueano

Trata-se nesta dissertação de estabelecer, partindo do pensamento contemporâneo francês da linha deleuziana e guattariana, sobretudo, uma analítica do desejo capaz de reconfigurar o romance de Nelson Rodrigues, Asfalto selvagem: Engraçadinha, seus amores e seus pecados, desterritorializá-lo em relação à tradição crítica e estética, fundada no paradigma realista-naturalista enraizado no pensamento literário brasileiro, especificamente no século XX. Movemo-nos por discussões sobre o autor e sobre o romance, empreendidas por Rolnik, interlocutora de Guattari, o qual está ligado aos novos paradigmas estéticos, à questão da produção de subjetividades, à micropolítica, às multiplicidades e às minorias. Buscamos contribuir para esse redimensionamento, colocando-nos na perspectiva cartográfica e rizomática para surpreender, em Asfalto, seus processos de subjetivação, incidindo sobre as singularidades selvagens, considerando os conceitos de Foucault, aplicados à construção literária enquanto espaço heterotópico, configurando a experiência do fora, como princípios estéticos. Veremos que as personagens, com foco em Engraçadinha, funcionam, como pequenas máquinas desejantes, Corpos sem Órgãos, moléculas desestabilizando as formações molares. Destarte, Nelson Rodrigues, na perspectiva da produção autoral, torna-se o pornógrafo, o literato iterador, como agenciador de uma palavra perversa, para além dos dogmas, da cena romantizada, originando, em sua poética, a revelação da obs-cena, a obscenidade, como crítica às instituições falidas. Trazemos, nesse sentido, referências de Bataille, quanto ao que na atividade estética se relaciona com o excedente da visão, relacionados ao espaço tático-ótico, concepção deleuziana referentes ao corpo-linguagem, pornografia, pornógrafo, narrativas abomináveis. Acompanhamo-nos, pois, dos conceitos da problemática da diferença e da alteridade, repercutindo na larvaridade, nas afecções, que abrem vias comunicantes com fenômenos extremos, atuantes em torno do mesmo e do outro, trazendo a rizomaticidade do mal e da monstruosidade para a construção estética de Asfalto selvagem, vistos sob a ótica de Bataille, Deleuze, Baudrillard, em ensaios que rompem o olhar estrutural em torno da obra e oferecem subsídios para a construção de uma cartografia outra, o território do ficcional, habitado por um povo por vir, na perspectiva tratada por Deleuze e por Blanchot