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

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

Medidas e análise estatística em sinais bioelétricos sobre pontos de acupuntura

In the 20th century, the acupuncture has spread on occident as a complementary practice of heath care. This fact has motivated the international scientific community to invest in research that seek to understand why acupuncture works. In this work we compare statistically volt age fluctuation of bioelectric signals caught on the skin at an acupuncture point (IG 4) another nearby on acupuncture point. The acquisition of these signals was performed utilizing an electronic interface with a computer, which was based on an instrumentation amplifier designed with adequate specifications to this end. On the collected signals from a sample of 30 volunteers we have calculated major statistics and submitted them to pairing t-test with significance leveI a = O, 05. We have estimated to bioelectric signals the following parameters: standard deviation, asymmetry and curtose. Moreover, we have calculated the self-correlation function matched by on exponential curve we have observed that the signal decays more rapidly from a non-acupoint then from an acupoint. This fact is an indicative of the existence of information in the acupoint

Representações espectrais de sistemas complexos: aplicações à síntese de superfícies brownianas fracionárias anisotrópicas, filtragem de sinais e identificação de correlações

In this thesis, we study the application of spectral representations to the solution of problems in seismic exploration, the synthesis of fractal surfaces and the identification of correlations between one-dimensional signals. We apply a new approach, called Wavelet Coherency, to the study of stratigraphic correlation in well log signals, as an attempt to identify layers from the same geological formation, showing that the representation in wavelet space, with introduction of scale domain, can facilitate the process of comparing patterns in geophysical signals. We have introduced a new model for the generation of anisotropic fractional brownian surfaces based on curvelet transform, a new multiscale tool which can be seen as a generalization of the wavelet transform to include the direction component in multidimensional spaces. We have tested our model with a modified version of the Directional Average Method (DAM) to evaluate the anisotropy of fractional brownian surfaces. We also used the directional behavior of the curvelets to attack an important problem in seismic exploration: the atenuation of the ground roll, present in seismograms as a result of surface Rayleigh waves. The techniques employed are effective, leading to sparse representation of the signals, and, consequently, to good resolutions

Efeitos do treinamento aeróbio sobre sinais precoces do remodelamento do ventrículo esquerdo induzido pelo diabetes Mellitus experimental

Our aim was to investigate the effects of an aerobic training program on adverse and early left ventricle (LV) remodeling, using an experimental model of short-term type 1 diabetes (T1D). Wistar rats were divided in 4 groups: sedentary control (SC), trained control (TC), sedentary diabetic (SD) and trained diabetic (TD). T1D was induced by streptozotocin (45 mg/kg). The training program consisted of 4 weeks running on a treadmill (13 m/min, 60 min/day, 5 days/week). At the end of the experiments, hearts were collected for analysis of morphology and transcriptional profile of LV, by focusing on its remodeling. Deaths were recorded during the 4-week period. We verified high mortality among animals of DS group, whereas it was significantly reduced in DT group. DS group also showed an increase in cross-sectional area of cardiomyocytes and fibrosis. TD group exhibited reduction in measures of cardiac trophism, but with respect to collagen content, it was similar to CS group. Analysis of gene expression related to cardiac remodeling revealed decreased expression of collagen I and III, as well as low expression of MMP-2 in DS group. TD group showed decreased levels of mRNA for MMP-9, and unchanged gene expression of MMP-2 when compared with the CS group. The expression of MMP-2 and TGF-1 were increased in CT group. The ratio between gene expression of collagen I and III was increased in the CT group and decreased in diabetic groups. These results establish early changes of the structure and transcriptional profile of LV myocardium. Moreover, they indicate that aerobic exercise training plays specific protection against mechanisms responsible for cardiac damage observed in T1D

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

O gato doméstico (Felis catus) responde à sinais gestuais? possíveis implicações do convívio social

The cats (Felis catus) were domesticated about 9,500 years ago due to the advent of agriculture, being used to control the pests that devastated the food harvested. These animals went through an artificial selection and over generations and millennia had their behavior and morphology changed by humans. This process of domestication by man gave rise to a special ability, the understanding of human pointing gestures, clearly noticed while we feed our pets. Our goal in this study was to assess the comprehension of pointing gestures by cats and also verify the influence that social interactions exerts on the development of this ability. We found that experimental subjects from both groups, solitary animals and social animals, were able to follow human indication in order to find hidden food. However, social interaction had no effect on cats performances. The ability tested here probably evolved during the process of domestication of this species, and social interaction seems to exert little or no influence upon its expression

Papel de sinais cromáticos na identificação de parceiros sexuais em sagüi comum (callithrix jacchus)

The literature concerning color vision shows a trichromatic advantage in detecting ripe fruits and young leaves, but there are contradictory results. There is also the suggestion of this type of vision being adapted to perceive socio-sexual signals. Indeed, Old World primates utilize the skin color of conspecifics as a factor of attraction. But in New World primates there is no record of a coloration signal in the body that can be utilized by other group members. The present study aims to: 1- test whether there is a relation between coloration of body regions and ovulatory cycle in female Callithrix jacchus; 2- Determine if this species uses visual signals to choose mates that are sexually receptive. We collected feces from six females during one month to quantify progesterone concentration by EIA. Body region coloration was measured using a portable spectrometer and modeled to obtain the quantum catch of each photoreceptor, the opponency channels and chromatic distance between the points in units of JND. We recorded the behavior of six males exposed to three pairs of females with a cycling and a non-cycling female in each pair using a transparent plexiglass apparatus. The color of different body regions presented a correlation between progesterone concentration and the yellow-blue and red-green visual axes, with the genitalia as the region showing the highest correlation. The visual axis more apt to see the color variations was the yellow-blue in dichromats, and in trichromats were the red-green to face, yellow-blue to abdomen and both chromatic axes to genitalia. There was no difference in the signal detectability between trichromats and dichromats, but the perception pattern differed between the phenotypes, with a better signal detection by the dichromat phenotype 562 and the trichromat phenotype 543/562. During the behavioral experiments males presented longer gaze duration in periods of experimental manipulation and gaze duration was always longer towards cycling females compared to non-cycling females. Male locomotion during experimental manipulation was greater than in the control only during the periovulatory period of the female, indicating greater excitement. The behavior of cycling females was more active than the behavior of the non-cycling ones regarding locomotion and touching of the plexiglass division of the apparatus. Male gaze duration to cycling females increased with decreasing progesterone concentration, but none of the coloration parameters was correlated to the mate preference exhibited. This coloration signal can transmit information to animals of the group about fertility of female. Different from the intense red of the genitalia swellings of Old World primates, marmoset female genitalia became more bluish-green in the fertile period. Males chose fertile females and were able to visually identify the periovulatory period of females. Choice is related to progesterone concentration, but our results do not show relation between coloration and mate preference. Maybe some behavioral measure is associated with the choice

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

Códigos de sustentação da linguagem no cotidiano prisional do Rio Grande do Norte: penitenciária estadual de Parnamirim

The quarrel, in this study, tells about the language as social practical in the daily of Parnamirim State Prison that is integrated to the Rio Grande do Norte Penitentiary System - SISPERN, destined for men in fulfilment of penalty privative of freedom, in closed regimen. For the accomplishment of the research, the delimited objectives had been to analyze the language repertoires created in the prisional daily, trying to identify how it´s turned into distinct forms of resistance to the mechanisms of control in penitentiary system; to investigate which are the language repertoires created from the new sociability forms developed among prisoners and identify how the language repertoires are expressed in the daily prisional on relations/exercises of power not-institutionalized. In the methodological aspect, the study is in a qualitative boarding, that has as main instrument the interview. The inquiry was possible by means of using instruments for data collection, like as: the direct comment in the prisional daily duly registered as researcher´s ethnographical procedure, the analysis of interns´ cadastre handbooks and the application of half-structuralized interview, to the subjects of the research. The construction and understanding of the study object had been based on authors who argue on the arrest, as: Foucault, Goffman, Carvalho Filho and, in particular was searched the theorical referencial that approaches the language in a social and cultural perspective: Orlandi, Manfred, Bastos and Candiotto, amongst others. Beyond the normative endorsement of the Brazilian legislation, through the Law of Criminal Execution, of the Criminal Code and the Federal Constitution of the country and the legal apparatus in state scope. Still in the research methodological perspective, after the collection the data had been submitted to an analysis of the speech from Foucalt´s theory and in the Orlandi´s perspective, being also qualitative and quantitative. The results had evidenced that the social and juridical profile of the population in the site inquired is not different of others Brazilian prisons, composed for men, in its majority, with age band between 21 and 30 years old, prisoners for practicing crimes against the patrimony, against life, amongst others, and, in special, criminal recidivists. It evidenced, still, that the daily prisional of PSP is characterized for a sociocultural diversity expressed in the relations of power not institutionalized, that contributes for the formation and division of the groups, each one using a set of language codes/ repertoires sustentation. Therefore, the language, in the daily prisional, is one of the ways to understand the singularity of the sociability relations and as social practicing mediated by relations/exercises of power and antagonistic interests, in which each group aims first of all, their own interests. It represents the complexity of the social relations, in the prisional space, with diverse effects, in function of the situation and the moment. The language in the arrest, beyond the communication function, assumes and represents central element for the sociability human being, contributes for its changings and it´s configured as one of the resistance forms of prisoners against the controling, disciplining and monitoring mechanisms of penitentiary system

Efeitos de tempestades magnéticas em sinais de gps, em Natal, Brasil

Satellites signals present disturbances (scintillations), due to presence of irregularities in the ionospheric plasma. In the present work, we dedicate to the study of the attenuation of these scintillations that is, an improvement in the signal, during the main magnetic storm phase during the period of October 2006 to February 2007. Using amplitude of scintillation 1.5GHz (L1) data of the net of satellites GPS, in the ionospheric station of Natal (5.84o S, 35.20o O, -20o dip) and geomagnetic indices, during the minimum solar cycle (referred to as cycle 23), demonstrating its anti-correlation between magnetic activity (Kp) and index of scintillation () (Bonelli2005 method, that works for solar maximum, Bonelli(2005)). These results show that these storms correspond to category I of Aarons (1991). The magnetic storms can generate irregularities when the electric feld of penetration eastward on the pre-reversal hour intensificating that and can too generate irregularities on midnight and sunlight period. The limitation of the method applied here is that it is not considering some storms that had also occurred during equinox and summer in the Brazilian region. For this reason, we will use additional data of the stations of São João de Cariri (Imager and Photometer) and of the station at Fortaleza (Digissonde data), as aid to analyze these storms. The storms that had been left out by the applied method, fit in the other two categories of Aarons, with one only exception (storm of January, 02). We show that in the day of the main phase of the magnetic storm, and with presence of bubbles (according to data of the Imager and Photometer), the speed of vertical drift ~E ~B (hF=t) is below 20m/s, that is the threshold found for Anderson al., (2004) (>20m/s as condition favorable to the formation of irregularities and increase in the scintillation index). This reduction of the speed is due to solar minimum

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