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

Dificuldades de aprendizagem em estequiometria: uma proposta de ensino apoiada na modelagem

In order to learn/teach chemistry some themes are relevant, like the stoichiometry, which consists in the study of the weight ratios in the combination of elements and compounds between themselves. This is an underlying subject in the understanding/representation/forethought of chemical reactions. Considering these aspects, our study presents a modeling-based proposal to develop the content of stoichiometry with prospective chemistry teachers. With this aim, we have made a review of literature, which we considered when tried to identify the learning difficulties using both quizzes and pedagogical tests, and then, from those difficulties we could propose a teaching unit for this concept and, consequently the evaluation of our proposal. The participants were chemistry undergraduates at the Universidade Federal do Rio Grande do Norte (UFRN) from assorted levels. As a methodological framework, we rely on the discursive textual analysis to characterize the speech of participants. As main results we observed ideas of appearance or disappearance of matter during chemical transformations, disregard of stoichiometric proportions when using drawings to represent the microscopic level of a reaction and confusion between the magnitude amount of matter and other magnitudes such as mass and volume. The final product is a sequence of instruction, based on the modeling previous research literature , with the goal of improving students ability to articulate the macroscopic and submicroscopic levels of representation of the matter

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)

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

Conectores adversativos na fala do natalense: uma análise funcionalista com implicações para o ensino

This work analyzes the behavior of the adversative connectors in the speech of the user of Natal, with views to suggest implications for the grammar teaching in the high school Portuguese languages classes. It is an investigation that sits on the functionalist paradigm, specifically in the protected ideas for Givón. For so much, data of situations of speech from the corpus Discurso e gramática lingual falada e escrita da cidade do Natal (FURTADO DA CUNHA, 1998). The sample embraces a total of forty interviews, of which the occurrences are cut out whose registrations mark the existence of adversatives constructions in narratives of personal experience and in the opinion reports, modality of oral language, of the mentioned database. The work revisits authors of the grammar, Cunha (1986); Bechara (2006); Perini (2006), among others; authors that contemplate referring approaches to the use of opposition connectors as: Barreto (1999); Tavares (2003); Longhin (2003); Silva (2005); Rocha (2006); Neves (2000, 2006). The results of the panoramic analysis reveal as adversity connectors in use for the habitant of Natal, for recurrence order, the mas, e, aí, agora, só que, no entanto and já. Analyzed the results, the same ones are compared with the treatment presented by the traditional grammar, with application of functional iconicity principle, markdness principle and the prototype of the category is chosen. In the differentiated analysis of the item " agora ", structural profile of the constructions is analyzed that involve the item, semantic profile, times, manners and aspects of the verbs that they wrap up in the constructions in reference, trajectory of grammaticalization and comparison with the prototype of the category. Finally, they are suggested implications of whole the study for the teaching of Portuguese language, in the high school classes

Indícios sincrônicos de gramaticalização: o uso do verbo chegar em orações coordenadas e na perífrase verbal [chegar (e) + v2]: contribuições para o ensino de gramática.

Based on North American Functional Linguistic Theory, our proposal is to describe and analyze the use of verb CHEGAR in verbal periphrasis such as [CHEGAR (E) + V2], where CHEGAR does not demonstrate a significance linked to physical movement. In linguistic literature, such periphrasis has been attributed several functions, related to aspectualization, emphasis of negative segments, and construction of mental spaces, among others. This study considers that the function of verb CHEGAR in the periphrasis in question is to indicate a global aspect, emphasizing a range of semantic-pragmatic nuances such as the sudden, instantaneous, or even abrupt character of the events refered to by the principal verb of the construction (V2), and/or the taking of initiative (sudden) by the agent (in the syntactic role of periphrastic subject), and/or subjective evaluations which go from surprise to frustration. Our objectives are the following: i) to describe and analyze the semanticpragmatic, morphosyntactic and social relationships which characterize the use of CHEGAR in verbal periphrases like [CHEGAR (E) + V2] and in coordinated/juxtaposed speech in which CHEGAR is the principal verb of the first utterance and is an elocution verb and the principal verb of the second; ii) identify, based on this description and analysis, synchrony proof in the grammaticalization of CHEGAR as an auxiliary verb in the periphrasis refered to. There was observed to be a strong similarity between coordinate/juxtaposed and periphrastic constructions. Such similarities strengthen the hypothesis that the use of CHEGAR as a lexical verb in coordinate/juxtaposed structures is the origin of the use of CHEGAR in the periphrastic structure, since the many properties encountered with higher frequency in lexical use are also just as frequently used as auxiliaries. Nevertheless, between the two constructions being studied, sufficient difference can be observed to see that CHEGAR, in the periphrasis [CHEGAR (E) V2], is behaving like an auxiliary verb, and shows typical properties of these types of verbs: i) in 100% of occurrences, it does not have a complement;ii) it has a co-referential subject in 100% of cases; iii) it does not appear with intervening material between it and V2. Besides this, CHEGAR, in periphrases, is predominant in nonneutral evaluation contexts, denoted by V2. Inspired by the results obtained, we propose strategies for the discussion of the [CHEGAR (E) V2] periphrases in both elementary and high schools.

"Tudo" em Natal : definitude, implicaturas e contribuições para o ensino de língua materna

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

Propaganda e discurso ideológico: um estudo dos slogans das campanhas de incentivo à leitura

Considérant que le Brésil est un pays considéré comme «non- lecteurs», nous avons essayé de trouver des solutions pour inverser cette situation d'exclusion sociale à travers des campagnes et des projets. Le slogan était le moyen de la propagande a proposé à cet effet. En étant un peu éclairante, il a été considéré qu'ils étaient peut-être inséré dans un contexte idéologique, en passant, qui faisait alors partie de l'objet d'études en question et, en conséquence, l'objectif était d'étudier comment, dans niveau discursif, les relations sociales de l'idéologie et du pouvoir dans ces dessins slogans verbaux et des campagnes publicitaires pour encourager la lecture. Nous avons utilisé comme instrument de collecte de données en 2007 slogans projets (sept) et l'intensification des campagnes de publicité dans les années 1995 à 2006, peu après la création de la descendance en 1992, où son fonctionnement a été analysé et discours idéologique, en cherchant à identifier les états effets de sens proposé. Nous avons utilisé pour soutenir la perspective de recherche d'analyse du discours de l'école française, affiliée à Pêcheux. Afin de sens les effets sens des tests a été fait une semi-ouverte aux enseignants qui traitent directement avec l'enseignement de la lecture de l'Institut de l'Enseignement Supérieur du Président-Kennedy, situé à Natal / RN. On été appliqués 100 questionnaires, parmi lesquels 60 d‟entre eux utilisés pour l‟analyse. La recherche a démontré par l'analyse, que la façon d'encourager les gens à lire se déplace à travers le modèle principal de la compréhension de la lecture à laquelle les slogans ont été utilisés, en les intégrant dans un discours dominant, qui ne contribue pas de manière significative à l'augmentation le nombre de lecteurs dans le pays. Grâce à l'analyse des slogans et la réception des sujets de recherche, nous nous rendons compte de la diversité et l'idéologie sont présents en elles, révélant tout le temps, la compréhension de la lecture comme une surface pratique, ne mettre en lumière certaines de ses fonctions Importantes au sein d‟um contexte éducatif plus large

Variação, mudança e ensino: o caso dos pronomes possessivos da gente e nosso(a)(s) em uma abordagem sociofuncionalista

In this work, we analyze the variation and change phenomenon involving the possessive pronouns da gente and nosso(a)(s) in the light of the theoretical referentials of the North-american linguistic functionalism and of the variationist sociolinguistics. At first we present the phenomenon itself, highlighting the fact that few studies have considered it as an object, gap which we will try to fill in with our contribution. In the following chapter, we emphasize concepts and principles of the functionalism and the sociolinguistics that are used as our background for the data analysis. In the third chapter, we present what the normative grammars inform about our object of study, besides synthesizing some works on variation and change involving the personal pronouns nós and a gente. In the following chapter, we analyze the data. We used data from the Discurso & Gramática a língua falada e escrita na cidade do Natal (FURTADO DA CUNHA, 1998) corpus. In this chapter we present the results for the groups of social and linguistic factors which we can control. Grounded on these results, we specify the preferential contexts for employing the pronouns da gente and nosso(a)(s) and we observe that the social motivations, the valorization credited to the forms and the identity marks underly the restrictions exercised in their use by social factor groups, besides obtaining signs of ongoing changes in apparent time (from the age factor groups) and possible use specializations of each form, what helped us verify the course of the grammaticalization process of the referred pronouns in the community of Natal. In the sixth chapter, we make some considerations on the teaching of grammar and propose activities which can be carried on in the classroom involving the possessive pronouns da gente and nosso(a)(s) considering the variation and change issue

A prática de correção textual por professoras de língua portuguesa do ensino médio

Cette recherche analyse les pratiques de correction de textes de l'enseignement du 1, 2 et 3 ème niveau. Nous avons parti de discutions avec les professeurs de Langue Portugaise des troisièmes annèes d‟une école appartenant au enseignement publique, située à la ville d‟Assu RN. L'étude a les postulats théoriques de Cruz (2007), Dellagnelo (1998), Oliveira (2005), Pécora (1999), Ruiz (2001), Serafini (1989), et d‟autres. La méthodologie est de nature qualitative et d‟interpretation, dont le matériel a été constitué à partir des rapports des enseignants professionnels, ainsi que les 92 textes recueillies entre juillet et août 2008. Les dés montrent que la correction se configure comme un travail pratique, qui vise à aider les étudiants à améliorer leur écriture. Les professeurs font la correction d‟une forme mélangée, c'est-à-dire dans le texte apparaissent les corrections orthographiques, lexicales, etc., mais la prédominance de la correction est par rapport aux idées, pour le contenu du texte. Dans ce sens, les professeurs se rendent compte du valeur et de la hiérarchisation des idées discutées par les élèves, les reconnaître comme l'organisation de la sémantique et la séquence du texte. Tous les autres aspects (structurelles, grammaticaux) sont importants, cependant, en général, dans la pratique de correction des études, l‟exposition les idées occupent une place importante. Les marques de correction apparaissent sous la forme de petits billets, qui apprécie également toutes les étapes de l'écriture de texte

O papel da leitura nas aulas de inglês: uma análise segundo a percepção dos professores do ensino médio de escolas públicas estaduais de Natal

This dissertation aims at investigating the teachers beliefs about the role of the reading ability in English at public state high schools in Natal and identifying the social value of the process of learning English for students of a foreign language. From the understanding of studies on reading, both in the field of Cognitive Psychology, as in Gibson & Levin (1975), as in the area of Psycholinguistics, as in Goodman (1970) and Del Re (2006), We researched the teachers perceptions about the skills and competencies that should permeate their educational practices, through their knowledge about theories of language acquisition as Cognitivism (Piaget, 1961) and Social Interactionism (Vygotsky, 1979) and the official documents (PCNEM, 1999; PCN+, 2002 ) that are the parameters for teaching a foreign language. We took into consideration other factors that influence the choice of the goals and the objectives to be worked out, such as: intensity of teachers workload, number of classes and students per class for each teacher, materials and technologies available, among other factors that will play an important role in the choice of the appropriate methodologies. To conduct a case study, two questionnaires were used in the construction of direct interviews with fourteen English teachers in twenty schools. According to data on the teachers beliefs we could find that for them the reading ability does not seem to have an special treatment in the teaching of a foreign language due to factors that undermine this process and therefore make teachers do not realize the real objectives of teaching English at public state high schools in Natal. As a consequence, the current process of education complicates the formation of autonomous learners capable of fighting for a social transformation

Do dizer teórico às transposições didáticas: por um exercício da contrapalavra no ensino de língua escrita no PROJOVEM

This present work is going to show some results developed in the Master Degree research and the Post Graduation project in Language studies (PPgEL) at UFRN, under the orientation of Professor Maria da Penha Casado Alves. This research has questions showed by the Programa Nacional de Inclusão de Jovens PROJOVEM. Concerned to methodology, the research is based on Applied Linguistics and it is qualitative and documental. The corpus of the research are the Manual de Orientações Gerais and the Guias de Estudo. The documents that were used for the research were Guide for general orientation and the Study Guides.The Manual de Orientações Gerais was chosen because is focused on the teacher and the Guias de Estudo was chosen because are focused on the students. The discussions and analysis were based on Bakhtin (1997; 2003), for his studies about the language in a dialogical point of view, Faraco (2001 and 2008) and Suassuna (2006) for their discussions about the Portuguese Language and Geraldi (1997; 2005 and 2006) and Antunes (2003) for their orientation and discussions about the teaching process of the written language. The analysis made in the Reference Topics point that however the program proposes a kind of rupture with the traditional way of teaching, it could not take this change to the Study Guides (Guias de Estudo). The result is a didactic material that reproduces activities based on a conception of a descriptive and prescriptive teaching. What is concerned about the proposals for the textual production, it is shown that it is given in an artificial way, without any expression and with no link to any communicative context and sometimes, with no relation to the topic it was supposed to be related to

Representações de professores de língua inglesa de Natal-RN: um estudo sistêmico-funcional

Teaching and learning representations have been more and more investigated in the Brazilian applied linguistics field, as it allows the understanding of the teachers representations and how they conceive the learning process. This practice facilitates the planning of actions to improve the educational system. This study aims at identifying, interpreting and discussing some representations related to the identity and professional view of English as a foreign language teachers in different school contexts of Natal-RN. The theoretical and methodological foundation for this research is Halliday s Systemic- Functional Linguistics (1994; HALLIDAY; MATHIESSEN, 2004; EGGINS, 1994, among others). Our goal was to reveal the teachers representations embedded in their language, mainly through the ideational metafunction, as language is the tool we use to express ourselves about the external world (events, qualities, things, etc) and the internal world (thoughts, beliefs, feelings, etc). The research corpus is made of 21 teacher narratives, generated from a questionnaire sent to the teachers, who were divided in two groups: Group 1 (public schools teachers) and Group 2 (private schools and English course teachers). Most of the participants seemed to be satisfied with their professional choice. Many of them see the job as a challenge and an opportunity to transmit knowledge. All of them affirmed that the English teacher is a professional, for different reasons; however, the low professional appreciation was a recurrent aspect among the studied narratives. When asked about where they work, the private school teachers seemed to be more satisfied with the teaching-learning process than the ones from the public schools. We believe that the data analyzed in this study is important to show how some English teachers from Natal-RN see their profession. The results might be used in continuing education courses as food-for-thought in group discussions, as it is extremely important to emphasize and stimulate this practice

Uma proposta de ensino e aprendizagem de Língua Inglesa integrada ao uso das TICS para o desenvolvimento da autonomia dos aprendizes

This study focuses on the teaching and learning of English based on a new theoretical perspective concerning the Zone of Proximal Development (ZPD), which points to the apprehension of metacognitive processes as the way to reach learning autonomy. The theoretical set underline this study is those of a new pedagogy based on the symbiosis of Bruner‟s (2002) and Freire‟s (2009) concepts and in the metacognitive theory. In a social context dominated by the Communication and Information Technologies (CIT), the integration between teacher and learners with the support of the internet has been used as the way to operationalize this new emergent proposal of the theoretical perspectives. The analyses have been conducted through Systemic and Integral Action Research. The results at the end of this study corroborate our hypothesis that the enlargement of spontaneous knowledge of the learners can facilitate the understanding of scientific concepts, stimulating their metacognition and thus promoting their autonomy.