Linguagem matemática: uma proposta de ensino e avaliação da compreensão leitora dos objetos da matemática

This paper discusses aspects related to the mathematical language and its understanding, in particular, by students of final years of elementary school. Accordingly, we aimed to develop a proposal for teaching, substantiated by mathematical modeling activities and reading, which takes advantage of the student of elementary school a better understanding of mathematical language for the content of proportion. We also aim to build / propose parameters for the assessment of reading proficiency of the language of the student in analyzing and modeling process, its ability to develop/improve/enhance this proficiency. For this purpose, we develop a qualitative research, with procedures for an action research whose analysis of the data is configured as Content Analysis. We refer to epistemological and didactic, in the studies: Piaget (1975, 1990), Vygotsky (1991, 2001), Bakhtin (2006), Freire (1974, 1994), Bicudo and Garnica (2006), Smole and Diniz (2001), Barbosa (2001), Burak (1992), Biembengut (2004), Bassanezi (2002), Carrasco (2006), Becker (2010), Zuin and Reyes (2010), among others. We understand that to acquire new knowledge one must learn to read and reading to learn it, this process is essential for the development of reading proficiency of a person. Modeling, in turn, is a process which enables contact with different forms of reading providing elements favorable to the development here mentioned. The evaluation parameters we use to analyze the level of reading proficiency of mathematical language proved to be effective and therefore a valuable tool that allows the teacher an efficient evaluation and whose results can guide you better in the planning and execution of their practice

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

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

A criança e a cidade: as transformações da infância numa Natal moderna

The first years of the twentieth century in Natal is characterized by several urban interventions that aim was to change the feature of the city basically rural to another that was in line with cities as models of modernity and civilization. In this case all individuals would have to play important social roles, which included men, women and especially children. It was in this atmosphere of bright future that the children were taken as key parts of an idealized society. Some processes were essential in triggering changes in natal s childhood, among them, operated within the families, that this historic moment in public life sought other possibilities of existence, the school education and the construction of which would be the model for urban education the School Groups, propagators of science as mediators of all knowledge, and finally, the medical interventions that disseminating health and hygiene practices has enabled not only the conservation of child life, but also the possibility of building their individuality in a body healthy. If these processes on the one hand tried to crystallize an ideal image of a child making a child identity directly linked to education and the "body hygiene" on the other, giving specific reflexive autonomy to children, providing them see the world through eyes of subject.

Princípio da Indução Matemática no Ensino Médio

We developed this dissertation aiming its in the process of teaching and learning of the Principle of Mathematical Induction and we set our efforts so that the students of the first year of the high school can assimilate the content having the knowledge seen in the basic education as foreknowledge. With this, we seek to awake in the student the interest on proofs, showing how much it s needed in examples that involve contents that he is already seen

MARISA-MDD: uma abordagem para transformações entre modelos orientados a aspectos: dos requisitos ao projeto detalhado

Aspect Oriented approaches associated to different activities of the software development process are, in general, independent and their models and artifacts are not aligned and inserted in a coherent process. In the model driven development, the various models and the correspondence between them are rigorously specified. With the integration of aspect oriented software development (DSOA) and model driven development (MDD) it is possible to automatically propagate models from one activity to another, avoiding the loss of information and important decisions established in each activity. This work presents MARISA-MDD, a strategy based on models that integrate aspect-oriented requirements, architecture and detailed design, using the languages AOV-graph, AspectualACME and aSideML, respectively. MARISA-MDD defines, for each activity, representative models (and corresponding metamodels) and a number of transformations between the models of each language. These transformations have been specified and implemented in ATL (Atlas Definition Language), in the Eclipse environment. MARISA-MDD allows the automatic propagation between AOV-graph, AspectualACME, and aSideML models. To validate the proposed approach two case studies, the Health Watcher and the Mobile Media have been used in the MARISA-MDD environment for the automatic generation of AspectualACME and aSideML models, from the AOV-graph model

Dos requisitos à arquitetura em linhas de produtos de software: uma estratégia de transformações entre modelos

The tracking between models of the requirements and architecture activities is a strategy that aims to prevent loss of information, reducing the gap between these two initial activities of the software life cycle. In the context of Software Product Lines (SPL), it is important to have this support, which allows the correspondence between this two activities, with management of variability. In order to address this issue, this paper presents a process of bidirectional mapping, defining transformation rules between elements of a goaloriented requirements model (described in PL-AOVgraph) and elements of an architectural description (defined in PL-AspectualACME). These mapping rules are evaluated using a case study: the GingaForAll LPS. To automate this transformation, we developed the MaRiPLA tool (Mapping Requirements to Product Line Architecture), through MDD techniques (Modeldriven Development), including Atlas Transformation Language (ATL) with specification of Ecore metamodels jointly with Xtext , a DSL definition framework, and Acceleo, a code generation tool, in Eclipse environment. Finally, the generated models are evaluated based on quality attributes such as variability, derivability, reusability, correctness, traceability, completeness, evolvability and maintainability, extracted from the CAFÉ Quality Model

Políticas públicas e as transformações socioespaciais correlacionadas ao turismo no município de Caicó: uma análise do período 2000 a 2010

The study presents an approach on planning, sociospatial transformations and public touristic policies implemented between 2000 and 2010 in Caicó, encompassing people from the government, private sector and the population of the municipality and informal traders who use the leisure facilities and services arranged in place. As the main goal, the research intends to analyze the performance of public and private sectors correlated to the touristic activity in Caicó city and their reflections in the process changes sociospatial. The dissertation is structured in order to carry out an investigation into the role of public policies to the development of a location with touristic potential, in this case, the municipality of Caicó; to investigate public policies implemented in the touristic industry of Rio Grande do Norte, particularly the actions of PRODETUR-Nordeste focused on the development of the tourism in the countryside, affecting particularly the region of Seridó region and the municipality of Caicó, and, finally, to check the main changes sociospatial verified in Caicó between 2000 and 2010. Cultural issues and certain natural beauties can be seen as attractions that can attract tourist demand, taking into consideration the awakening increasingly more evident quest by the tourist for knowledge of the peculiarities of the region. Several authors have worked in this view, pointing to the cultural aspects of the region as elements that are able to boost the touristic activity. The questions raised in this study was based on a literature, based mainly on authors like Beni, Dias, Cruz, Azevedo and Morais. To obtain the necessary data in the analysis, the methodological procedures used in intensive direct observation, using interviews, applied together with the public representatives who are acting as leaders of the political actions related to tourism in the municipality and members of the private sector related to tourism services such as lodging establishments, food and travel agency and, finally, the local people and informal traders benefited directly or indirectly, with the touristic resources and structure. These research agents were investigated by means of structured forms such as support for analysis. Was detected in the survey that the leisure facilities and services installed in the last decade in the city of Caico has a priority the population of the municipality, is necessary to emphasize that the residents interviewed perceive the importance of these tools for tourist activity. It was also found that the public sector is the main responsible for the observed changes. Therefore, proved to be relevant to study the role public private sector partnerships and population influences, considering that this analysis may contribute to the work of researchers, public administrators and businessmen, may serve as a norteador for planning and development of tourism in the city of Caico

Os jogos com regras na educação matemática inclusiva

This present study aimed to examine the use of games with rules in working with math education in regular classes included in Elementary School, in the municipal education schools of Natal/RN, observing the learning process and development of all students, especially those with disabilities. The theoretical references used are based on Vygotsky's works and other authors from the historical-cultural perspective, as well as researchers in the field of Inclusive Education and Mathematics Education. The investigation was based on the qualitative research guidelines, with the application of semi-structured interviews with educational coordinators and teachers from the schools involved as well as classroom observations, looking for, in the speeches of those involved and in their teaching practices, elements to reflect on the Mathematics Inclusive Education, the use of games with rules -starting from its goals, the participation of disabled students, the pedagogical mediations, up to its accessibility - and from the learning of disabled students. The analysis results showed that the concepts underlying the development of inclusive teaching practices still refer to the clinical-medical paradigm, understanding the student with disabilities from their deficiencies; which teachers use, in their majority, the mathematical games with rules in their classes, but which the teaching mediation, during these activities, still needs to be qualified so that they can, effectively, contribute to the learning and development of all students; students with disabilities do not always participate in games with others colleagues; games with rules are rarely accessible; and that the Universal Design principles are not adopted in the selected classrooms for this study. Thus, it is clear that much remains to be done so that Mathematics Education can contribute to the learning and development of all students, and among those actions the teacher continuing education is recommended

Localização de faltas em linhas de transmissão usando morfologia matemática

This work an algorithm for fault location is proposed. It contains the following functions: fault detection, fault classification and fault location. Mathematical Morphology is used to process currents obtained in the monitored terminals. Unlike Fourier and Wavelet transforms that are usually applied to fault location, the Mathematical Morphology is a non-linear operation that uses only basic operation (sum, subtraction, maximum and minimum). Thus, Mathematical Morphology is computationally very efficient. For detection and classification functions, the Morphological Wavelet was used. On fault location module the Multiresolution Morphological Gradient was used to detect the traveling waves and their polarities. Hence, recorded the arrival in the two first traveling waves incident at the measured terminal and knowing the velocity of propagation, pinpoint the fault location can be estimated. The algorithm was applied in a 440 kV power transmission system, simulated on ATP. Several fault conditions where studied and the following parameters were evaluated: fault location, fault type, fault resistance, fault inception angle, noise level and sampling rate. The results show that the application of Mathematical Morphology in faults location is very promising

Modelagem Matemática e Computacional de fenômenos eletrocinéticos em meios porosos carregados eletricamente

In this work we present a mathematical and computational modeling of electrokinetic phenomena in electrically charged porous medium. We consider the porous medium composed of three different scales (nanoscopic, microscopic and macroscopic). On the microscopic scale the domain is composed by a porous matrix and a solid phase. The pores are filled with an aqueous phase consisting of ionic solutes fully diluted, and the solid matrix consists of electrically charged particles. Initially we present the mathematical model that governs the electrical double layer in order to quantify the electric potential, electric charge density, ion adsorption and chemical adsorption in nanoscopic scale. Then, we derive the microscopic model, where the adsorption of ions due to the electric double layer and the reactions of protonation/ deprotanaç~ao and zeta potential obtained in modeling nanoscopic arise in microscopic scale through interface conditions in the problem of Stokes and Nerst-Planck equations respectively governing the movement of the aqueous solution and transport of ions. We developed the process of upscaling the problem nano/microscopic using the homogenization technique of periodic structures by deducing the macroscopic model with their respectives cell problems for effective parameters of the macroscopic equations. Considering a clayey porous medium consisting of kaolinite clay plates distributed parallel, we rewrite the macroscopic model in a one-dimensional version. Finally, using a sequential algorithm, we discretize the macroscopic model via the finite element method, along with the interactive method of Picard for the nonlinear terms. Numerical simulations on transient regime with variable pH in one-dimensional case are obtained, aiming computational modeling of the electroremediation process of clay soils contaminated

Os condomínios horizontais fechados e as transformações socioespaciais na cidade de Natal/RN/

The process of urbanization of Natal city has been going in the last years by importants changes, mainly, because we can observe the development of a new kind of housing: the horizontal closed condominiums, from 1995 began to expand quickly on the city. In this way, the present study has as objective analyse the expansion of the horizontal closed condominiums on the urban area of Natal. Emphasizing the sociogeographic changes that these ventures engender. For this, we have done a research that was based on quantitative procedures, however, preferring a qualitative approach. So, data were gathered from sources and procedures: the first, we performed a literature search and document on issues related to the relevant issues in libraries, public and privates institutions; The second, in accordance with the procedures, or the production of informations, performed enterview and implemetation of questionnaires with key stakeholders involved with the expansion of horizontal condominiums in Natal. Within this perspective, our research showed that the expansion of demand in the city, the existence of volume of land in areas suitable for the production building, the formation of capital property, the appearance of new points of modern consumption, the actions of the state and the low cost of production of these enterprises, are factors that have been decisive in the expansion of the horizontal condominiums in Natal. Also, we can observe that the process of production of the urban space from the horizontal condominiums comes in providing the redefinition of land use in areas that appear, because they expand into outlying areas of Natal, changes in its structure and its pattern of socio segregation, observing that the condominiums put the diferents social groups living side by side, but not mantaining relationships among them, the emergence of spaces to homogenization, the fragmentation of the urbanization, the privatization of the city and several environmental problems. In short, we believe that the horizontal expansion of condominiums is enabling a number of social changes to Natal city