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

Obras complementares: um elo entre a leitura e os conteúdos matemáticos

The Federal Government through its Plans and Programs invests in various policies intended to achieve the main goal of the millennium, provide basic education for all. Among them, we highlight in this paper The National Textbook Program, with emphasis on Complementary Works. These works are presented through different genres, such as poems, poetry, short stories, parables, novels, literature, educational materials etc.. providing a range of possible teaching work. However, little is known about the levels of education of teachers as intended. Based on the discussions and studies in this direction, sparked concerns us in the process of teaching and learning in math classes. This made us pay attention to a possibility of study where reading could be included in this process. In this sense, the present study aims at investigating the potential of conceptual and didactic use of Complementary Works on developing the skills of reading and writing mathematics of the first three years of elementary school, and from there, propose a courseware with guidelines for use of these works by teachers of 1st to 3rd year of elementary school. For this, we outline the issues of reading and understanding of mathematical interests as those of our study. In this sense, the proposal was built from the bibliographic works that address the contributions of reading for learning mathematical content, like Machado (2001), Nacarato (2009); Dantas (2011), Smole and Diniz ( 2001). As a result, we created the Guidance for the use of Complementary Works for Teachers to Teach Mathematics with a view to support the practice of teachers and future teachers who teach mathematics. Supported the use of Complementary Works, especially those distributed in public schools by the National Textbook - PNLD and have mathematical content, this guide is intended to present some of the possible use of this feature in math classes. (Education Observatory - Capes / INEP. Ed. 038-2010. TELL Research Group - UFRN - PPGED / PPGEL / PPGECNM - PROPESQ)

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

Conectores sequenciadores em artigos de opinião escritos por vestibulandos: uma questão de marcação linguístia com implicações para o ensino

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

Pré-fabricados lingüísticos: estrutura e funcionamento de sintagmas verbais idiomatizados - por uma abordagem cognitivo-funcional em sala de aula

This work aims at under the cognitive-functional perspective describing, inside the vast domain of the linguistic prefabs, the structure and the functioning of the Idiomatic Verb Phrases (SVIs), produced by speakers of the Portuguese from Brazil, located in Natal (RN). From the functionalist presupposition that the language is used essentially to assist to communicative demands, it is observed that its morphologic-syntactic structure is conditioned to the inherent pragmatic vicissitudes to the verbal interaction of subjects, socially heterogeneous and historically established. It is focalized, in the composition of SVIs, the relationships VT + OD (transitive verb + direct object), characterizing the syntactic-semantic nature of the verb and of the respective verbal complement. Those verb combinations + complement can be interpreted as lexical structures, reflexes of the idiomaticity inherent to conventional constructions already systematized in the users' of the language cultural repertoire. It is sought, still, to glimpse the cognitive and discursive motivations pertinent to that linguistic phenomenon. In the investigative process, are analyzed exclusive data of speech collected in Corpus Discurso & Gramática a lingua falada e escrita na cidade do Natal, organized by Furtado da Cunha (1998). The adopted methodological procedures configure as methods of empiric analysis and use of the intuition, being emphasized the qualitative approach (explanatory) of the data with quantitative support of statistical indicators. It shows, finally, a grating of didactic suggestions on SVIs, for Portuguese's classes, as subsidies to the educational practice in the Medium Teaching and in the course of Letters.

Projetos de letramento na educação de jovens e adultos: o ensino da escrita em uma perspectiva emancipatória

This ethnographical research-action is included in the Applied Linguistics area and its study object is related to literacy projects (KLEIMAN, 2000), since they bring a new sense to the literacy practices in school and emphasizes the agentive writing character and the role of the discursive genres in the formation of literacy agents who aim at the action and the social change. Considering the emancipatory potential that these didactic organizations have in the civic literacy of those who live in social risk and vulnerability situations our aim in this investigation is: to reflect about the role of the redefinition of the literacy school practices and investigate how the action of teachers and students as literacy agents occur. The specific aims are: to promote literacy events which encourage the writing practice for the action and social change; to comprehend how the identity construction of the literacy student-agent occurs by the reflection of its agency process in the literacy projects; to identify teaching strategies and procedures which enable the development of emancipatory language practices; to investigate the axiological values constructed by the learners in and about the writing work in literacy projects. Our discussion is based on the language conception supported by Bakhtin (BAKHTIN/VOLOSHINOV, 2000; BAKHTIN, 1990, 2003); in literacy studies (KLEIMAN, 1995; BAYNHAM, 1995; BARTON; HAMILTON; IVANIC, 2000, LAZERE, 2005); on critical studies which defend the idea that the texts are ideological instruments able to give power to the individuals (MCLAREN, 1988, 1991, 1997, 1999, 2000, 2001; FREIRE, 1971, 1978, 1979, 1982, 1992, 1996, 2001a, 2001b, 2009; GIROUX, 1983, 1986, 1990, 1992, 1997, 1999, 2003; APPLE, 1989); on the social genre approach inspired by the New Rhetoric (BAZERMAN, 2005, 2006, 2007; MILLER, 1984, 2009). The data were generated between 2006 and 2010 in the Youth and Adult Education (YAE), in public schools in Natal-RN. The research permitted us to deduce, firstly, that the redefinition of the work with discursive genres provide the learner to read and write to act discursively in the social world, earning, thus, empowerment, autonomy and emancipation; secondly, that involving the students in literacy projects goes beyond didactic competence related to specificities and content domain. It is necessary that the teacher is certain about to whom, what, why and how to teach and that he/she gets a reflexive posture, becoming a learner as well; thirdly, that through the literacy practices which were developed, the collaborators of the research have constructed a more conscious and a more critical view in relation to the language and to the world where they live through the social-political writing and they have improved as interventive and politicized citizens

Marcadores da organização do padrão discursivo narrativo: uma abordagem funcional centrada no uso

This thesis has as its object the Markers Organization Standard Narrative Discourse (MON), from its occurrence in oral and written corpora of different realizations of narrative discourse, considering its locus of occurrence in the narrative and discursive functioning. The research is guided by the Functional Linguistic Usage-Based, approach to which the organization of language is directly linked to the user experience, so that grammar is shaped by discourse. We examined only the narrative portions of Experience Reports, Tales and Legends in the oral and written, as follows: 3 inquiries Corpus Reports Remaining Quilombo (RN); 11 Corpus Legends legends of the Amazon, 14 Tales of Corpus Tales Brazilians and 21 Reports of experiences of Corpus and Discourse Grammar, with about 10,000 words in each corpus. A total of 22 markers were identified, which were: (1) classified according to the locus of occurrence in the narrative structure, as Labov (1972), (2) associated, according to the type of pattern that occur in narrative discourse, (3) described from the discursive function they perform. The research has relevance to the extent it is based speech analysis and offers proposals for productive teaching of mother tongue in which students and teachers can, grounded in language studies, consider living language, as an object of study, based on the National Curriculum Guidelines (OCN) and making use of New Technologies of Information and Communication (NTIC)

Manual do professor, muito prazer em (re)conhecê-lo! Uma análise sociorretorica do gênero

Esta pesquisa de natureza documental e etnográfica se insere no campo da Linguística Aplicada, tendo por objeto de estudo o Manual do Professor, que acompanha o livro didático de Língua Portuguesa, e por objetivo geral (re)conhecer os aspectos sociorretóricos do gênero Manual do Professor. O interesse desta tese está concentrado no uso situado desse gênero, a partir do qual se observam seus aspectos sociorretóricos, a saber: o que está posto no produto, o ambiente de interação onde é encontrado e como é visto por seus usuários em potencial. Em um primeiro momento, produzimos um quadro epistemológico que nos permitiu, dentre outros reparos, (i) compreender gênero textual como ação retórica tipificada baseada numa situação retórica recorrente e (ii) obter um panorama dos programas de governo voltados para a avaliação de coletâneas didáticas, nos quais encontramos aspectos indispensáveis a um Manual do Professor. Os aportes teóricos adotados neste estudo referem-se à concepção sociorretórica dos estudos de gênero textual à luz, sobretudo, de Johns et al. (2006), Bazerman (2011) e Miller (2011). Em um segundo momento, sob o viés da abordagem sociorretórica, procuramos definir o Manual do Professor como gênero textual e apresentamos os aspectos retóricos encontrados nas amostras que analisamos, considerando a organização constitutiva, o contexto de uso desse gênero e as percepções de seus usuários autores e professores. A geração de dados deu-se inicialmente a partir da seleção de três exemplares de Manuais de coletâneas didáticas adotadas no IFRN; em seguida, no sentido de reconhecer as percepções dos usuários desse gênero, realizamos grupo focal com professores e entrevistamos o coautor de uma das coletâneas. Para análise dos dados, elegemos o método etnográfico de análise de gêneros postulado por Reiff (apud JOHNS et al, 2006), que nos permitiu analisar o objeto de estudo em contextos autênticos de uso do gênero. Nossos resultados mostram que o Manual do Professor está inserido num sistema de gêneros e no sistema de atividades profissionais de domínio do professor e não se limita apenas a explicar como está organizado o livro didático do aluno. Outros sete propósitos foram observados, dentre os quais se encontram: possibilitar ao docente uma reflexão sobre a sua prática de ensino e sugerir caminhos para a melhoria do processo de ensino-aprendizagem. Acreditamos que esta pesquisa poderá estimular professores, em relação à importância (e não obrigatoriedade) de consultas periódicas aos Manuais; autores, no que se refere a estabelecer uma interlocução mais pessoalizada com seus leitores em potencial e no sentido de esclarecer ainda mais as facetas do livro didático; e editoras, sobretudo no que tange a recursos de editoração, para que o Manual do Professor se torne mais atrativo

Estatística não-extensiva aplicada ao cálculo do calor específico eletrônico em estruturas quasiperiódicas

Systems whose spectra are fractals or multifractals have received a lot of attention in recent years. The complete understanding of the behavior of many physical properties of these systems is still far from being complete because of the complexity of such systems. Thus, new applications and new methods of study of their spectra have been proposed and consequently a light has been thrown on their properties, enabling a better understanding of these systems. We present in this work initially the basic and necessary theoretical framework regarding the calculation of energy spectrum of elementary excitations in some systems, especially in quasiperiodic ones. Later we show, by using the Schr¨odinger equation in tight-binding approximation, the results for the specific heat of electrons within the statistical mechanics of Boltzmann-Gibbs for one-dimensional quasiperiodic systems, growth by following the Fibonacci and Double Period rules. Structures of this type have already been exploited enough, however the use of non-extensive statistical mechanics proposed by Constantino Tsallis is well suited to systems that have a fractal profile, and therefore our main objective was to apply it to the calculation of thermodynamical quantities, by extending a little more the understanding of the properties of these systems. Accordingly, we calculate, analytical and numerically, the generalized specific heat of electrons in one-dimensional quasiperiodic systems (quasicrystals) generated by the Fibonacci and Double Period sequences. The electronic spectra were obtained by solving the Schr¨odinger equation in the tight-binding approach. Numerical results are presented for the two types of systems with different values of the parameter of nonextensivity q

Propriedades magnéticas de multicamadas e filmes finos quasiperiódicos

Conselho Nacional de Desenvolvimento Científico e Tecnológico

Espectro de Polariton de Plasmons e Ondas de Luz em Quasi-Cristais

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

Ondas de spin em nanofilmes nagnéticos acoplados quasiperiodicamente

We studied the spin waves modes that can propagate in magnetic multilayers composed of ferromagnetic metallic films in the nanometer scale. The ferromagnetic films (iron) are separated and coupled through the nonmagnetic spacer films (chromium). The films that make up the multilayer are stacked in a quasiperiodic pattern, following the Fibonacci and double period sequences. We used a phenomenological theory taking into account: the Zeeman energy (between the ferromagnetic films and the external magnetic field), the energy of the magneto-crystalline anisotropy (present in the ferromagnetic films), the energy of the bilinear and biquadratic couplings (between the ferromagnetic films) and the energy of the dipole-dipole interaction (between the ferromagnetic films), to describe the system. The total magnetic energy of the system is numerically minimized and the equilibrium angles of the magnetization of each ferromagnetic film are determined. We solved the equation of motion of the multilayer to find the dispersion relation for the system and, as a consequence, the spin waves modes frequencies. Our theoretical results show that, in the case of trilayers (Fe/Cr/Fe), our model reproduces with excellent agreement experimental results of Brillouin light scattering, known from the literature, by adjusting the physical parameters of the nanofilms. Furthermore, we generalize the model to N ferromagnetic layers which allowed us to determine how complex these systems become when we increase the number of components. It is worth noting that our theoretical calculations generalize all the results known from the literature

Ondas de spin em quasi-cristais magnônicos

In this paper we investigate the spectra of band structures and transmittance in magnonic quasicrystals that exhibit the so-called deterministic disorders, specifically, magnetic multilayer systems, which are built obeying to the generalized Fibonacci (only golden mean (GM), silver mean (SM), bronze mean (BM), copper mean (CM) and nickel mean (NM) cases) and k-component Fibonacci substitutional sequences. The theoretical model is based on the Heisenberg Hamiltonian in the exchange regime, together with the powerful transfer matrix method, and taking into account the RPA approximation. The magnetic materials considered are simple cubic ferromagnets. Our main interest in this study is to investigate the effects of quasiperiodicity on the physical properties of the systems mentioned by analyzing the behavior of spin wave propagation through the dispersion and transmission spectra of these structures. Among of these results we detach: (i) the fragmentation of the bulk bands, which in the limit of high generations, become a Cantor set, and the presence of the mig-gap frequency in the spin waves transmission, for generalized Fibonacci sequence, and (ii) the strong dependence of the magnonic band gap with respect to the parameters k, which determines the amount of different magnetic materials are present in quasicrystal, and n, which is the generation number of the sequence k-component Fibonacci. In this last case, we have verified that the system presents a magnonic band gap, whose width and frequency region can be controlled by varying k and n. In the exchange regime, the spin waves propagate with frequency of the order of a few tens of terahertz (THz). Therefore, from a experimental and technological point of view, the magnonic quasicrystals can be used as carriers or processors of informations, and the magnon (the quantum spin wave) is responsible for this transport and processing

Sistemas Nanoestruturados: Heteroestruturas Quasi-Periódicas de Nitretos e Cálculos Ab initio em Polimorfos CaCO3

The physical properties and the excitations spectrum in oxides and semiconductors materials are presented in this work, whose the first part presents a study on the confinement of optical phonons in artificial systems based on III-V nitrides, grown in periodic and quasiperiodic forms. The second part of this work describes the Ab initio calculations which were carried out to obtain the optoeletronic properties of Calcium Oxide (CaO) and Calcium Carbonate (CaCO3) crystals. For periodic and quasi-periodic superlattices, we present some dynamical properties related to confined optical phonons (bulk and surface), obtained through simple theories, such as the dielectric continuous model, and using techniques such as the transfer-matrix method. The localization character of confined optical phonon modes, the magnitude of the bands in the spectrum and the power laws of these structures are presented as functions of the generation number of sequence. The ab initio calculations have been carried out using the CASTEP software (Cambridge Total Sequential Energy Package), and they were based on ultrasoft-like pseudopotentials and Density Functional Theory (DFT). Two di®erent geometry optimizations have been e®ectuated for CaO crystals and CaCO3 polymorphs, according to LDA (local density approximation) and GGA (generalized gradient approximation) approaches, determining several properties, e. g. lattice parameters, bond length, electrons density, energy band structures, electrons density of states, e®ective masses and optical properties, such as dielectric constant, absorption, re°ectivity, conductivity and refractive index. Those results were employed to investigate the confinement of excitons in spherical Si@CaCO3 and CaCO3@SiO2 quantum dots and in calcium carbonate nanoparticles, and were also employed in investigations of the photoluminescence spectra of CaCO3 crystal

Estudos ecogenômicos e bioprospectivos de Shewanella ssp

Bacteria trom Shewanella and Geobacter ganera are the most studied iron-reducing microorganisms particularly due to their electron transport systems and contribution to some industrial and environmental problems, including steel corrosion, bioenergy and bioremediation of petroleum-impacted sites. The present study was focused in two ways: the first is an in silico comparative ecogenomic study of Shewanella spp. with sequenced genomes, and the second is an experimental metagenomic work to detect iron-reducing Shewanella through PCR-DGGE of a metabolic gene. The in silico study resulted in positive correIation between copy number of 16S rDNA and genome size in Shewanella spp., with clusters of rrn near lhe origin of replication. This way, the genus is inferred as opportunist. There are no compact genomes and their sequences length varied, ranging from 4306142 nt in S. amazonensis SB2B to 5935403 nt in S. woodyi ATCC 51908, without correIation to temperature range characteristic of each specie. Intragenomic 16S rDNA sequences possess little divergence, but reasonable to resuIt in different phyIogenetic trees, depending on the sequence that is chosen to compare. For moIecuIar detection of iron-reducing Shewanella, it is proposed the mtrB gene as new biomarker. because it codes to a fundamental protein at Fe (III)-reduction. The specific primers were designed and evaluated in silico and resulted in a fragment of 360 pb. In the second study, these primers were tested in a genomic sample from S. oneidensis MR-1, amplifying the expected region. After this successfuI resuIt, the primer set was used as a tool to assess the iron-reducing communities of ShewaneIla genus under an environmental stress, i.e. crude oil contamination in mangrove sediment in Rio Grande do Norte State (Brazil). The primers presented high specificity and the reactions performed resulted in one single band of ampIification in the metagenomic samples. The fingerprinting obtained at DGGE reveaIed temporal variation of Shewanella spp. in analyzed samples. The resuIts presented show the detection of a biotechnological important group of microorganisms, the iron-reducing Shewanella spp. using a metabolic gane as target. It is concluded there are eight or more 16S rDNA sequences in Shewanella genus, with little divergence among them that affects the phylogeny; the pair of primers designed to ampIify mtrB sequences is a viable alternative to detect iron-reducing ShewanelIa in metagenomic approaches; such bacteria are present in the mangrove sediment anaIyzed, with temporal variations in the samples. This is the first experimental study that screened the iron-reducing Shewanella genus in a metagenomic experiment of mangrove sediments subjected to oil contamination through a key metabolic gene