Formação continuada de professores que ensinam matemática: o papel do ábaco na ressignificação da prática pedagógica

The present dissertation performs a study about abacus part on the continuous education of Elementary School s Mathematic teachers on what concerns the basic operations of addition and subtraction with (re)unification by using the manipulative and/or informatical abacus. Therefore, the research intends to answer the following question: How does a teacher reframe the pedagogical practice while teaching the Decimal Numeral System and the conventional operations of addition and subtraction with (re)unification through manipulative and informatical abacus? In order to do so, we rely ourselves on the Guy Brousseau s Theory of Didactic Situations (TDS) from 1996 that affirms the necessity to trace a way in accordance with the teaching situations that lead the student s learning; and on the work of Pierre Lévy (1993), in which the poles of communication oral, written and virtual create three ways of communication through which the learning process happens. The methodology of this paper was based on the Strategic Research-Action of Franco (2005). The didactic sequence was elaborated in accordance with TDS and used the manipulative and informatical abacus as didactic resource. With the application of the didactic sequence, it was verified that the continued formation of Elementary School s teachers concerning the operations of addition and subtraction on the initial years/levels is pertinent once it has been observed some difficulties of the teachers concerning this mathematical subject. Besides, the analysis of the didactic sequence has allowed one to realize that teachers had some difficulties concerning the numeric representation with order zero, the resolution of operations of addition and subtraction using the manipulative and informatical abacus and the realization of (re)unification on the subtraction with meaning. These observations has been discussed with the teachers and, after that, it has been done some didactic-methodological routings of the operations of addition and subtraction with re(unification) that contributes with the teaching and learning process.

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.

Propriedades dos sistemas de numeração: uma sequência didática em uma abordagem histórica

This paper aims to describe the construction and validation of a notebook of activities whose content is a didactic sequence that makes use of the study of ancient numbering systems as compared to the object of our decimal positional numbering system Arabic. This is on the assumption that the comparison with a system different from our own might provide a better understanding of our own numbering system, but also help in the process of arithmetic operations of addition, subtraction and multiplication, since it will force us to think in ways that are not routinely object of our attention. The systems covered in the study were the Egyptian hieroglyphic system of numbering, the numbering system Greek alphabet and Roman numbering system, always compared to our numbering system. The following teachung is presented structured in the form of our activities, so-called exercise set and common tasks around a former same numbering system. In its final stage of preparation, the sequence with the participation of 26 primary school teachers of basic education

Geometria e arirmética numa visão multicultural: uma experiência pedagógica

This paper aims to build a notebook of activities that can help the teacher of elementary school mathematics. Topics covered are arithmetic and geometry and the activities proposed here were developed aiming print them a multicultural character. We take as a base line developed by Claudia Zaslavsky multiculturalism and reflected in his books "Games and activities worldwide" and "More games and activities worldwide." We structure our work around four themes: the symbol of the Olympic Games, the pyramids of Egypt, the Russian abacus abacus and Chinese. The first two themes allow you to explore basic concepts of geometry while the latter two themes allow us to explore numerical notation and arithmetic operations

A etnomatemática em uma cerâmica da região do Seridó/RN

This work has as objective to describe mathematical knowledge used as tools in the manufacture and marketing of tiles of red ceramic by potters of the Currais Novos village/ RN, located 250 km from the capital of Rio Grande do Norte. For us to reach our objective, we rely on conceptions ambrosianas of Ethnomatematics, besides of the qualitative research in an ethnographic approach. In the empirical part of the research, that went it accomplishes in the period from 2009 to 2012 in the Currais Novos Village, we support the following tools for data collection, semi-structured interviews, field diary, photographs, audio recordings and participant observations. In the analysis of the collected data, we can conclude that there are mathematical knowledge in the management of manufacture and marketing of tiles, often different from the academic mathematics, mainly in the wood cube, on cube of the clays, in the handler with the measures time, the count method , in the arrangement of tiles, in the preparation of the ceramic mass and sale of tiles. Theses knowledge were described and analyzed in the light of the theoretical Ethnomatematics, also supported in official documents, such as Parameters Nacional Curriculares. The analyzes of these knowledge generated subsidies for elaboration of an educational product - a proposal of didactic sequence destined to the Teaching of Mathematics in Elementary and Middle levels for the community schools and region, this proposal is in the Appendix to this work

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

À luz das inquietas sombras: a criatividade da melancolia na linguagem de Dom Casmurro

Qué se piensa aquí, esencialmente, está a mapear el itinerario de la melancolía creativa en el discurso de Dom Casmurro; es decir, aquél de el cual el valle narrativo de una sensación de la angustia a alçar él él las maneras de la representación en el discurso de Dom Casmurro. El árbol básico en el cual éste estimaba incurre en se basa en el acuerdo de eso que la actual melancolía en el texto del machadiano se puede analizar por las estratagemas de la lengua creativa en la intención de demostrar en él una especie del espacio virtual - el conducir de metáforas, de ironies y del exacerbamento de imágenes - por cuál se prepone el narrador construir su salvación . El propósito es analizar el uso de el proyecto del alegórico y el irónico previstos por el autor en la intención de descubrir pues tales procedimientos contribuyen para crear un texto ese desestabiliza el carácter malsano de la melancolía. Puede propagar lengua creativa de tal manera cuánto otras maneras de la representación de eso las marcas del arte utilizan. Más allá de este traz poético, la contribución de este trabajo también constituye: para componer una escena en la cual el teatralidade de la lengua de Dom Casmurro constituye drama y no tragedia. Después de la pista de los conceptos de los benjaminianas de la melancolía, alegoria, metalenguaje la ironía, vimos que éstos disalign de la voluntad que los estatutos se estabilizaron de las figuras del retórico para consistir mientras que las estrategias de los discursivas. Subyacente a este proceso es posible percibir el flash del rescate de la escritura melancholic, visto bajo luz del saturnine de una mirada que si desea alegórico, en la misma incandescencia de la risa del fáustico

Vinicius de Moraes e Shelley: um exercício de desleitura .

Using Harold Bloom s methodology known as dialectical revisionism we undertake the task of misreading of Vinícius de Moraes (1913- 1980) poems Poética (1950), Operário em construção (1955), Poética II (1960) against Percy Bysshe Shelley (1792-1822) and his poem A Song: Men of England, suggesting that the Brazilian poet trammeled a battle with his poetic triad, in which Operário em Construção is Vinicius s main weapon. It is suggested here that each one of Vinícius´poem represents a step of what Bloom calls anxiety of influence . The misreading proposed confronts the themes and the imagery of the poems, arguing that Shelley and Vinícius are similar when they approach exploitation and working class consciousness according to the Dialectic Marxism pattern, and that Vinícius´s poem was not only inspired by Shelley s, but using one of the strategies suggested by Bloom, he corrects the ideological flaws of Shelley s poem. It is also discussed the possibility that both poems are inspired by Plato´s (428-7 a 348-7 a.C.) allegory of the cave, his concept of justice and the moral construction of the polis defended in A República. Thus, considering the process of misreading, these five poems constitute what Bloom calls a family romance , which is characterizes the phenomenon of melancholy of creativity

Cartas oficiais norte-riograndenses dos séculos XVIII, XIX e XX : constituição e caracterização de um corpus diacrônico

The diachronic studies marked the first decades of the 20th century in Brazilian linguistics, passing by an ostracism period after the 50s. Mainly from the 90s especially with the project, created in 1997, Para a história do português brasileiro (PHPB), which has systemized, in national ambit, the programme related to the area of diachrony the historical studies retake forces and have gradually increased since then. Our work is set in the new scene of Brazilian historical linguistics and it is associated to two research programmes: i) the constitution of a diachronic corpus; ii) the diachrony of text and discourse. As regards the first programme, we made effort to constitute a diachronic corpus of official letters about Rio Grande do Norte, we called cartas oficiais norte-rio-grandenses, written in 18th, 19th and 20th centuries. The chosen for bureaucrat letters occurred for they represent a textual category very productive in historical contexts, mostly 18th and 19th centuries, in which the command of writing was the least and also because they bring, almost always explicitly, the information of where, when, for whom and from whom, as remembers Fonseca (2003). The rules for constituting the corpus were based, although not strictly, on the orientation from PHPB. In respect to the second programme, we set up on the ideas of coserian base came from the studies on discourse traditions (TD) (Koch, 1997; Kabatek, 2006) amongst which that the texts are shaped so as to follow their own tradition (Coseriu, 2007), and we turned to Diplomatics (Belloto, 2002) in order to do the characterization of this corpus by the application of concepts from Diplomatics and TD as well as by the presentation of the structures that form those official letters: their textual genres, a kind of TD, with their macrostructures; and some of their formulaic expressions (microstructures), another sort of TD. This stage of characterizing will pay attention, as far as possible, to the dynamic between tradition and innovation that happen in the actualization of those textual structures along the centuries. This work intends to contribute with the researches connected to Historical Linguistics in Rio Grande do Norte, more specifically the ones related to the constitution of diachronic corpora and to TD; and with the study of official documents, textual category about which there are almost no studies (cf. Silveira, 2007)

José Paulo Paes, Humanista

La présente recherche examine dans son ensemble l' uvre considérable du "paulista" José Paulo Paes da Silva (1926-1998). La première partie de la recherche fait connaître l'importante activité professionnelle de cet auteur, en situant dans leur contexte particulier les différentes modalités du travail qu'il a régulièrement accompli en tant qu'"éditoraire", traducteur et essayiste. La deuxième partie est consacrée à la lecture critique de sa poésie épigrammatique. La riche bibliographie qui est le résultat de l'effort intellectuel de l'écrivain, est consignée à la fin du volume. Il s'agit donc d'une étude ayant pour but d'esquisser la physionomie littéraire d'une personnalité qui a marqué de sa présence la culture brésilienne dans la seconde moitié du XXe siècle

Pelo escuro: a poesia afro-brasileira de Oliveira Silveira

O presente estudo traz uma reflexão sobre os discursos culturais afro-brasileiros e o lugar ocupado pela poesia em meio a uma sociedade racista. A pesquisa tem como propósito fazer um estudo da poesia de Oliveira Silveira (1968, 1970, 1977, 1981, 1987). Leva-se em consideração a relação da produção poética de Oliveira com as propostas do movimento da Negritude e o diálogo lúcido que o mesmo estabelece com poetas vinculados ao referido movimento e como Silveira sugere dentro da literatura a negritude como uma forma de intersecção na poesia brasileira. A proposta aqui apresentada observa também o hibridismo na poética de Oliveira Silveira ao se enfatizar um olhar sobre uma escrita comovida pelo traço do entre-lugar do discurso. Analisa-se a caracterização de uma literatura gerada pelo tom de denúncia ao desconstruir historicamente o que há muito tempo se estabelece como democracia racial . Em cumplicidade com a poesia regional do Rio Grande do Sul, a poesia de Oliveira vem permeada pela diversidade de ritmos que traduzem o legado da cultura negra mundo afora. Essa pesquisa sustenta-se nos estudos de Eduardo de Assis Duarte (2005, 2011) e Kabengelê Munanga (2008, 2009) sobre Negritude e Identidade na literatura afro-brasileira, que se caracteriza como um movimento de consciência pela reconstrução ou mesmo revisão histórica do que foi apagado no calabouço dos navios negreiros. As leituras de Eduardo de Assis Duarte fomentam novos questionamentos, põem em dúvida a existência de uma identidade essencialista. Aponta-se nessa travessia para uma pluralidade de identidades, construídas por inúmeros grupos culturais na encruzilhada dos diversos momentos históricos. Analisam-se, portanto, a partir da crítica que Stuart Hall (2011) faz ao considerar as ideias de diásporas, as fronteiras das margens no universo da pós-colonização. Por fim, há uma encruzilhada ao se pensar a partir de Kabengelê Munanga, o discurso da negritude e da identidade negra nas relações sociais e culturais afrodescendentes

Os argumentos transcendentais: kant e o problema de hume

This work whose title is "The transcendental arguments: Kant Andy Hume's problem" has as its main objective to interpret Kant's answer to Hume's problem in the light of the conjunction of the causality and induction themes which is equivalent to skeptical- naturalist reading of the latter. In this sense, this initiative complements the previous treatment seen in our dissertation, where the same issue had been discussed from a merely skeptical reading that Kant got from Hume thought and was only examined causality. Among the specific objectives, we list the following: a) critical philosophy fulfills three basic functions, a founding, one negative and one would argue that the practical use of reason, here named as defensive b) the Kantian solution of Hume's problem in the first critisism would fulfill its founding and negative functions of critique of reason; c) the Kantian treatment of the theme of induction in other criticisms would will fulfill the defense function of critique of reason; d) that the evidence of Kant's answer to Hume's problem are more consistent when will be satisfied these three functions or moments of criticism. The basic structure of the work consists of three parts: the first the genesis of Hume's problem - our intention is to reconstruct Hume's problem, analyzing it from the perspective of two definitions of cause, where the dilution of the first definition in the second match the reduction of psychological knowledge to the probability of following the called naturalization of causal relations; whereas in the second - Legality and Causality - it is stated that when considering Hume in the skeptic-naturalist option, Kant is not entitled to respond by transcendental argument A􀁴B; A⊢B from the second Analogy, evidence that is rooted in the position of contemporary thinkers, such as Strawson and Allison; in third part - Purpose and Induction - admits that Kant responds to Hume on the level of regulative reason use, although the development of this test exceeds the limits of the founding function of criticism. And this is articulated in both the Introduction and Concluding Remarks by meeting the defensive [and negative] function of criticism. In this context, based on the use of so-called transcendental arguments that project throughout the critical trilogy, we provide solution to a recurring issue that recurs at several points in our submission and concerning to the "existence and / or the necessity of empirical causal laws. In this light, our thesis is that transcendental arguments are only an apodictic solution to the Hume s skeptical-naturalist problem when is at stake a practical project in which the interest of reason is ensured, as will, in short, proved in our final considerations

Fases e criticalidade no modelo ashkin - teller de três cores

The usual Ashkin-Teller (AT) model is obtained as a superposition of two Ising models coupled through a four-spin interaction term. In two dimension the AT model displays a line of fixed points along which the exponents vary continuously. On this line the model becomes soluble via a mapping onto the Baxter model. Such richness of multicritical behavior led Grest and Widom to introduce the N-color Ashkin-Teller model (N-AT). Those authors made an extensive analysis of the model thus introduced both in the isotropic as well as in the anisotropic cases by several analytical and computational methods. In the present work we define a more general version of the 3-color Ashkin-Teller model by introducing a 6-spin interaction term. We investigate the corresponding symmetry structure presented by our model in conjunction with an analysis of possible phase diagrams obtained by real space renormalization group techniques. The phase diagram are obtained at finite temperature in the region where the ferromagnetic behavior is predominant. Through the use of the transmissivities concepts we obtain the recursion relations in some periodical as well as aperiodic hierarchical lattices. In a first analysis we initially consider the two-color Ashkin-Teller model in order to obtain some results with could be used as a guide to our main purpose. In the anisotropic case the model was previously studied on the Wheatstone bridge by Claudionor Bezerra in his Master Degree dissertation. By using more appropriated computational resources we obtained isomorphic critical surfaces described in Bezerra's work but not properly identified. Besides, we also analyzed the isotropic version in an aperiodic hierarchical lattice, and we showed how the geometric fluctuations are affected by such aperiodicity and its consequences in the corresponding critical behavior. Those analysis were carried out by the use of appropriated definitions of transmissivities. Finally, we considered the modified 3-AT model with a 6-spin couplings. With the inclusion of such term the model becomes more attractive from the symmetry point of view. For some hierarchical lattices we derived general recursion relations in the anisotropic version of the model (3-AAT), from which case we can obtain the corresponding equations for the isotropic version (3-IAT). The 3-IAT was studied extensively in the whole region where the ferromagnetic couplings are dominant. The fixed points and the respective critical exponents were determined. By analyzing the attraction basins of such fixed points we were able to find the three-parameter phase diagram (temperature £ 4-spin coupling £ 6-spin coupling). We could identify fixed points corresponding to the universality class of Ising and 4- and 8-state Potts model. We also obtained a fixed point which seems to be a sort of reminiscence of a 6-state Potts fixed point as well as a possible indication of the existence of a Baxter line. Some unstable fixed points which do not belong to any aforementioned q-state Potts universality class was also found

Setor escuro do universo: uma análise termodinâmica

Significant observational effort has been directed to unveiling the nature of the so-called dark energy. However, given the large number of theoretical possibilities, it is possible that this a task cannot be based only on observational data. In this thesis we investigate the dark energy via a thermodynamics approach, i.e., we discuss some thermodynamic properties of this energy component assuming a general time-dependent equation-of-state (EoS) parameter w(a) = w0 + waf(a), where w0 and wa are constants and f(a) may assume different forms. We show that very restrictive bounds can be placed on the w0 - wa space when current observational data are combined with the thermodynamic constraints derived. Moreover, we include a non-zero chemical potential μ and a varying EoS parameter of the type ω(a) = ω0 + F(a), therefore more general, in this thermodynamical description. We derive generalized expressions for the entropy density and chemical potential, noting that the dark energy temperature T and μ evolve in the same way in the course of the cosmic expansion. The positiveness of entropy S is used to impose thermodynamic bounds on the EoS parameter ω(a). In particular, we find that a phantom-like behavior ω(a) < −1 is allowed only when the chemical potential is a negative quantity (μ < 0). Thermodynamically speaking, a complete treatment has been proposed, when we address the interaction between matter and energy dark

Aplicações da q-Álgebra em física da matéria condensada

We address the generalization of thermodynamic quantity q-deformed by q-algebra that describes a general algebra for bosons and fermions . The motivation for our study stems from an interest to strengthen our initial ideas, and a possible experimental application. On our journey, we met a generalization of the recently proposed formalism of the q-calculus, which is the application of a generalized sequence described by two parameters deformation positive real independent and q1 and q2, known for Fibonacci oscillators . We apply the wellknown problem of Landau diamagnetism immersed in a space D-dimensional, which still generates good discussions by its nature, and dependence with the number of dimensions D, enables us future extend its application to systems extra-dimensional, such as Modern Cosmology, Particle Physics and String Theory. We compare our results with some experimentally obtained performing major equity. We also use the formalism of the oscillators to Einstein and Debye solid, strengthening the interpretation of the q-deformation acting as a factor of disturbance or impurity in a given system, modifying the properties of the same. Our results show that the insertion of two parameters of disorder, allowed a wider range of adjustment , i.e., enabling change only the desired property, e.g., the thermal conductivity of a same element without the waste essence