Atribuição de significado ao conceito de proporcionalidade: contribuições da história da matemática

This study is the result of a work which approaches the Mathematics History how source of the meaning s attribution in the proportionality concept. We adopt the methodology of the source qualitative and we work with a group of teachers from instruction s public system of the fundamental and medium level from Pocinhos City Paraíba. For the data collection, we use the field notes, the questionnaire, a sequence of activities and the interview semistructured like instruments. The study had how objective to know the significates attributeds to proportionality concept through of the activity mediate from Mathematics History, besides to investigate if a approach of the nature enables modification according to this sense. The results obtaineds though the data analysis indicate that the activities bring contributions which refer to achieve objectives. On the other hand they also showed that we have a long trajectory to be trailed in the meaning of to turn the Mathematics History a subsidy effective in the teachers practice, in view of the formation absence in the knowledge area, besides the necessity of the approach adequated of the Mathematics History in the didatics books of Mathematic

Vídeo-aula de história da matemática: uma possibilidade didática para o ensino de matemática

In this work we are disagreeing with the possibility of production and of the use of video-class for the disciplines of history of mathematics by the teachers of elementary e middle school as a way to contribute to the development of their classes. Our goal is to provide to the mathematics teachers the option of connecting social, scientific, cognitive, and didactic aspects of topics in math thoughts to their students. That shall be based in the presence of mathematics in the history of humanity. Thus, we consider possible that teachers and their students can link and relate mathematics to other sciences, education culture, and reflect about the many ways of represent them, as well as the patters of organization of nature and of culture. In this way, they shall be able to observe and interpret situations that involve mathematical questions associated to the various means of historic-epistemological studies already done by other researchers and scholars in the field of history of mathematics who works in creating video-classes. In addition to that, we can use all the available media in order to give edifying dynamics to the mathematical formulations established throughout history. In this sense, we are based and focused on the objectives, which are sustained by educational computer technology, techniques for video making, as well as mathematical teaching proposals and the historical inquiring made by Mendes (2001, 2009a, 2009b). The validating experimentation allowed us to conclude that the techniques we used in the production of the history of mathematics video-classes proved they to be valid ones. They are able to be executed with the minimum of technological resources. In addition, they have the same efficacy as far as classroom use

Ensino de matemática pelo rádio (1950 1970): uma história falada e um documentário didático

This study aimed to describe and analyze aspects of the historical course of teaching Mathematics by Radio Experiences in Rio Grande do Norte, between the decades from 1950 to 1970 in order to organize a documentary (CD-ROM) containing information about Mathematics studied by Radio who have experienced it. In this, we use qualitative research. We seek support in the theoretical framework of cultural history and memory researchers as Certeau (1998), Chartier (1990), Le Goff (2008), Thompson (2002) and Peter Burke (2004). Moreover, we take the elements of oral history. We focus on the teaching of literacy and the primary of the Radio schools in two rural communities - Logradouro and Catolé - who are currently part of the city of Lagoa Salgada (RN) and, with respect to the Junior High School, we stopped in the Course of Madureza at Radio. We used as written sources, especially the documents found in the General Archives of the Archdiocese of Natal (RN) and the employees assigned by the participants of the survey. Our sources come from the oral testimonies of pupils and monitors Lagoa Salgada City, teachers, broadcasters and technicians of Rural Support Service (SAR) Natal (RN). In this study, we identify the geometry Cubação social practices of Lagoa Salgada students. Also identified in the research material, the Global Method with the pedagogy of Paulo Freire, that guided the production of lessons in literacy and primary courses. Content in Mathematics, we find traces of the trend-Empirical activist. In the course of Madureza, there was a tendency formal technique Fiorentini (1995). Finally, as a result of this study, organize and present a documentary (CD-ROM), along with the analysis of this study, containing the history of Mathematics teaching by Radio, from the speech of those who experienced Radio, emphasizing the methodology teaching developed in class, that serves as a reference material for students, professors and researchers.

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

História da ciência como estratégia didática no ensino médio: um breve olhar de conteúdos da óptica

From a critique of aspects of the current teaching of physics, we propose in this paper an investigation into the conceptions of Nature of Science (NOS) submitted by students from the high school level, as well as the inclusion of discussions about some elements of NOS, through the History and Philosophy of Science, understanding them as facilitating strategy for more effective learning of Physics and, more specifically, the contents of optics. Based on the historical period corresponding to Greek antiquity to the mid-nineteenth century, built and applied a teaching unit to a high school class at the Federal Institute of Education, Science and Technology of Rio Grande do Norte (IFRN) Ipanguaçu campus. Our teaching unit involved the reading and interpretation of texts with historical content, observation and assembling five experimental activities, among other activities. Data analysis occurred through questionnaires investigative applied before and after the completion of the teaching unit, as well as questionnaires for content present in the texts. Although not significant, the results indicated that the application of the teaching unit allowed the (re) construction of some conceptions about NOS targets students present in our work, and contribute to a better learning content and greater optical science approach and its nature

Ensinando sobre a natureza da ciência: uma abordagem explícita e contextualizada a partir da história do vácuo

In last decades, the importance of including the contents of the Nature of Science (NOS) in Science Education has been emphasized. Several studies have focused on investigating the conceptions of NOS, supported by students and teachers, as well as design, implement and evaluate proposals that aim to provide a reflection on this theme in the educational context. Considering the complexity of such content, studies indicate the need for explicit and contextualized approaches and the History of Science (HS) is one of the possible paths to this inclusion. We started from the premise that, through a historical study, that aims to discuss the meaning and the basis of our "beliefs", we can know the process of building on what we "believe" and better understand its meaning. This thesis is part of this perspective, proposing to explore the History of the Vacuum, a themed high didactic potential still little used, in order to collaborate with the teaching content of NOS. We present actions on different fronts that originated three products in the context of this research. On the first front, we insert the research and production of instructional materials (three historical texts) to subsidize people interested in the implementation of HPS for educational context through this material. The relevance of this front is justified by the existence of gaps with regard to the production of such material for the context of teacher training. However, we consider that the preparation of instructional material of good quality and accessible does not guarantee that these resources will be used, if they will not be accompanied by discussions in teacher training, on how to use them, contexts and obstacles to be faced. The second part presented refers to the organization and implementation of a workshop for undergraduate students in physics and physics teachers, considering the instrumentalization of these individuals to the preparation and use of teaching strategies to approach aspects of NOS through episodes of History of the Vacuum, as well as the preparation of the text orientation for people interested in implementing the instructional material for secondary education. This guidance text contemplates the difficulties anticipated by the literature of the area and the main challenges faced by the participants about the didactic transposition of HPS for the educational context they were noted during the workshop. The relevance of this second front, in particular, is justified by the existence of gaps with regard to the inclusion of the theme of NOS and the HPS teacher training

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

Uma história de vida e uma vida de histórias: memória e oralidade no Romanceiro de Dona Militana

Este estudio trata de establecer relaciones sobre la importancia del fenómeno sociocultural que emerge de Doña Militana para la cultura potiguar. Para tanto tomamos sus recuerdos de los romances como parte de un contexto social, relacionados con el tiempo y el espacio, que afecten a la vida material y moral de su grupo social. Resaltamos, por lo tanto, el fenómeno de la memoria individual en su relación con la memoria colectiva. Proponemos, en este sentido, suponer que el mantenimiento y permanencia de estos romances en la memoria de la romancera revelan una dinámica de su grupo social para la formación de su identidad. En este sentido, nos servimos como referencial teórico de los estudios de Maurice Halbwachs, en lo que respecta a los debates sobre la memoria colectiva, en paralelo a los estudios de Paul Zunthor cuando se trata de las funciones de la oralidad para la formación de la identidad. Para llevar a cabo los trabajos es de fundamental importancia, por supuesto, el relato de vida de la propia Doña Militana en confronto con los simbolismo culturales contenidos en los romances, con el objetivo que flagremos las (co)incidencias que demarquen la identidad de sus vínculos de identidad con el universo cultural en que está insertado. Como resultado, se tomó como objeto de análisis desde la deposición presentadas en las entrevistas, hasta los romances en sus aspectos poéticos, lingüísticos y mitológicos, incluyendo los significados que el desempeño de la romancera muestra. Objetivamos, por lo tanto, una comprensión dialógica de la relación entre la memoria individual (el caso de Doña Militana) con la memoria colectiva, sobre la base de un hipotético concepto que subyace a la aparente singularidad de este fenómeno - un hecho aislado en cierta medida - una razón intrínseca y compleja que se revela como la punta de un iceberg, al que convergen motivos históricos inconscientes de un patrimonio cultural

O trágico em lavoura arcaica

El escritor de São Paulo Raduan Nassar, lanza en 1975, su primera novela intitulado Lavoura arcaica. En su narrativa de estreno, el escritor nos trae la historia de un adolescente, André, que intenta destruir la plantación de su padre, Iohána. A través de sus sermones, el patriarca predicaba la moderación, la disciplina y la obediencia a las leyes impuestas por él, construyendo así, un mundo de ilusiones, donde el amor era una máscara para la hipocresía. En esta tensa relación, padre e hijo, representaciones místicas de Apolo y Dionisio, emprenden una contienda discursiva sobre la negación y la afirmación de la existencia. De ese modo, considerando la relación de lucha e integridad entre el impulso apolíneo y dionisiaco existentes en el romanticismo nassariano, la propuesta de este trabajo es presentar una lectura de lo trágico en Lavoura arcaica a partir de la perspectiva nietzscheana sobre el género trágico. Para eso, recorrimos al concepto desarrollado por Nietzsche en su obra, desde su primer libro O nascimento da tragédia (2007a), A visão dionisíaca do mundo (2005 a) y Ecce homo (2008 b).

A letra escarlate como romance histórico: uma história de fragilidade humana e tristeza

The objective of this paper is to analyze the work of the American writer Nathaniel Hawthorne (1804 - 1864), The Scarlet Letter (1850), in the light of the contributions of Literature and History of the American people in the context of New England. Accordingly, we highlight aspects that justify the inclusion of the work as a historical novel, especially based on the reading of The Historical Novel (1936-37) written by Georg Lukács. The diversity of voices and social interrelationships that come out of the main characters of the plot of the novel, as well as their contextual buildings, constituted as important traces to understanding the novel as being of historical value. During our study, we found out that it is in the plots of the novels that the characters reflect, at the same time, the specific conditions of their singularities, the general trends of the historical process and the social conditions from which they arise. We also could see that it is in their singularities that lie special tendencies of human beings. Our references to this study came from scholars as Howard (1964), Bakhtin (1998), Eagleton (2006), Todorov (2009), Zabel (1947), Sellers (1985), Cunlife (1986), Candido (1993) and Schwarz (1981)

Razão: origem, crise e respostas contemporâneas

The philosophical discussion has been present throughout the whole history of reason, for philosophy and reason have been always closely linked. In the following work, Reason, origin, crises and contemporary answers I go into the history of the rational and demonstrative thought, focusing on how rationality can be thought about in contemporary philosophy. To answer this question I discuss the principle of philosophy, the mythical period and the thoughts of Heraclito , Parmenides , Plato and Aristotle in relation to reason and rationality. Also discussed is the medieval period and the philosophical use of logic and the criticism of Aristotle s thoughts, especially focusing on the criticism of Hegel and Luckasiewicz of the non contradiction principle. Lastly I discuss the development of reason in present day philosophy, mainly how modern logics could be putting at stake Aristotle s model of reason

Lógica condicional

The main goal of this work is to clarify the central concepts involved in the study of formalization of conditional sentences. More specifically, it has been done a comparative analysis of the two greater and more traditional proposals of conditional formalization (Lewis 1973c e Adams 1975). These proposals were responsible for the creation of a way of analysis that still present in the current debate about this subject. This work pursues to explain the principal assumptions held within these proposals. According to certain disambiguation techniques from Bennett (2003) and Lycan (2005), this work tries to explicit how these assumptions connect to the aims sought by the initial approaches. The following results show that there is a not declared presumption, the definition of the object of study of these theories, i.e., the definition of conditional sentence. This work argues that despite of not explicitly declared the definition of the study object has a central role in the intelligibility of the debate itself

Sistemas de lógica modal em dedução natural

Formalization of logical systems in natural deduction brings many metatheoretical advantages, which Normalization proof is always highlighted. Modal logic systems, until very recently, were not routinely formalized in natural deduction, though some formulations and Normalization proofs are known. This work is a presentation of some important known systems of modal logic in natural deduction, and some Normalization procedures for them, but it is also and mainly a presentation of a hierarchy of modal logic systems in natural deduction, from K until S5, together with an outline of a Normalization proof for the system K, which is a model for Normalization in other systems