O ensino de funfições trigonometricas através do software geogebra

In this study, we sought to address the weaknesses faced by most students when they were studying trigonometric functions sine and cosine. For this, we proposed the use of software Geogebra in performing a sequence of activities about the content covered. The research was a qualitative approach based on observations of the activities performed by the students of 2nd year of high school IFRN - Campus Caicfio. The activities enabled check some diculties encountered by students, well as the interaction between them during the tasks. The results were satisfactory, since they indicate that the use of software contributed to a better understanding of these mathematical concepts studied

Uma abordagem no ensino de frações baseadas em atividades para o 6º ano do ensino fundamantal

The objective of this work if constitutes in creation a proposal for activities, in the discipline of mathematics, for the 6th year of Elementary School, that stimulates the students the develop the learning of the content of fractions, from the awareness of the insufficiency of the natural numbers for solve several problems. Thus, we prepared a set with twelve activities, starting by the comparison between measures, presenting afterward some of the meanings of fractions and ending with the operations between fractions. For so much, use has been made of materials available for use in the classroom, of forma ludic, for resolution of challenges proposed. Through these activities, it becomes possible students to recognize the necessity of using fractions for solve a amount larger of problems

O estudo das funções quadráticas e sua relação com o cotidiano

Across the centuries, Mathematics - exact science as it is - has become a determining role in the life of man, which forms to use suprir needs of their daily lives. With this trajectory, is characterized the importance of science as an instrument of recovery not only conteudstica, but also a mathematician to know that leads the apprentice to be a dynamic process of learning ecient, able to find solutions to their real problems. However, it is necessary to understand that mathematical knowledge today requires a new view of those who deal directly with the teaching-learning process, as it is for them - Teachers of Mathematics - desmistificarem the version that mathematics, worked in the classroom, causes difficulties for the understanding of students. On this view, we tried to find this work a methodology that helps students better understand the Quadratic functions and its applications in daily life. Making use of knowledge Ethnomathematics, contextualizing the problems relating to the content and at the same time handling the software GeoGebra, aiming a better view of the behavior of graphs of functions cited

Sistema de numeração posicional e a lógica da divisão de inteiros

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

Probabilidade no ensino médio

This thesis aims to show teachers and students in teaching and learning in a study of Probability High School, a subject that sharpens the perception and understanding of the phenomea of the random nature that surrounds us. The same aims do with people who are involved in this process understand basic ideas of probability and, when necessary, apply them in the real world. We seek to draw a matched between intuition and rigor and hope therebyto contribute to the work of the teacher in the classroom and the learning process of students, consolidating, deepening and expaning what they have learned in previous contents

Função Afifim: Teoria e aplicações

In this work we present a proposal to contribute to the teaching and learning of affine function in the first year of high school having as prerequisite mathematical knowledge of basic education. The proposal focuses on some properties, special cases and applications of affine functions in order to show the importance of the demonstrations while awaken student interest by showing how this function is important to solve everyday problems

Um estudo dos sistemas de amortizações SAC e francês no ensino médio apoiado na construção de planilhas Eletrônicas

The aim of this work is to provide a text to support interested in the main systems of amortization of the current market: Constant Amortization System (SAC) and French System, also known as Table Price. We will use spreadsheets to facilitate calculations involving handling exponential and decimal. Based on [12], we show that the parcels of the SAC become smaller than the French system after a certain period. Further then that, we did a comparison to show that the total amount paid by SAC is less than the French System

Área e volume da esfera

In this dissertation, we present a study on the teaching of volume of the sphere and the area of spherical surface. On this topic, a quali-quantitative was taken survey with the objective of identifying how these topics are addressed. For this, we made 14 questions to 30 teachers of Natal and the results of this survey are presented and discussed. After that, we present alternative ways to derive the formulas of the volume of a sphere and the are of a spherical surface

A relação de Euler para poliedros

In this paper we analyze the Euler Relation generally using as a means to visualize the fundamental idea presented manipulation of concrete materials, so that there is greater ease of understanding of the content, expanding learning for secondary students and even fundamental. The study is an introduction to the topic and leads the reader to understand that the notorious Euler Relation if inadequately presented, is not sufficient to establish the existence of a polyhedron. For analyzing some examples, the text inserts the idea of doubt, showing cases where it is not fit enough numbers to validate the Euler Relation. The research also highlights a theorem certainly unfamiliar to many students and teachers to research the polyhedra, presenting some very simple inequalities relating the amounts of edges, vertices and faces of any convex polyhedron, which clearly specifies the conditions and sufficient necessary for us to see, without the need of viewing the existence of the solid screen. And so we can see various polyhedra and facilitate understanding of what we are exposed, we will use Geogebra, dynamic application that combines mathematical concepts of algebra and geometry and can be found through the link http://www.geogebra.org

Equações de segundo grau e mudança de variáveis

In this work are presented, as a review and in a historical context, the most used methods to solve quadratic equations. It is also shown the simplest type of change of variables, namely: x = Ay + B where A;B 2 R, and some changes of variables that were used to solve quadratic equations throughout history. Finally, a change of variable, which has been used by the author in the classroom as an alternative method, is presented and the result of this methodoly is illustrated by the responses of a test that was done by the students in classroom

Mecanismos de alojamento de magmas granitóides :exemplo do plúton de Japi(RN)

This dissertation describes the igneous suites of the Japi granitoid pluton, intrusive in the Paleoproterozoic gneiss-migmatite complex of the eastern domain of the Seridó Belt, northeastern Brazil. Field relations show that the pluton is affected by strong deformation associated to the Brasiliano orogeny (known as the D3 phase) , with a NW-trending extensionalleft-hand senestral shear zone (the Japi Shear Zone, JSZ) bordering the intrusive body to the west. Four plutonic suites are found in the main pluton and as satellyte intrusions, besides Iate pegmatite and pink leucogranites. An alkaline granitoid suite, dominated by syenogranites bearing sodic augite (and subordinate hornblende), define a main elliptical intrusion. In its northern part, this intrusion is made up by concentric sheets, contrasting with a smaller rounded stock to the south. These granites display a pervasive solid-state S>L fabric developed under high T conditions, characterized by plastic deformation of quartz and feldspar. It is especially, developed along the border of the pluton, with inward dips. A regular magmatic layering is present sometimes, parallel to the tectonic foliation. The syntectonic emplacement as regards to the Brasiliano (D3) event is indicated by the common occurrence of dykes and sheets along transtensional or extensional sites of the major structure. Field relations attest to the early emplacement of the alkaline granites as regards to the other suites. A basic-to-intermediate suite occurs as a western satellyte body and occupying the southern tail of the main alkaline pluton. It comprises a wide variety of compositional terms, including primitive gabbros and gabbro-norites, differentiated to monzonitic intermediate facies containing amphibole and biotite as their main mafic phases. These rocks display transitional high-K calc-alkaline to shoshonitic affinities. Porphyritic monzogranite suítes commonly occur as dykes and minor intrusives, isolated or associated with the basic-tointermediate rocks. In the latter case, magma mingling and mixing features attest that these are contemporaneous igneous suites. These granites show K-feldspar phenocrysts and a hornblende+biotite+titanite assemblage, displaying subalkaline/monzonitic geochemical affinities. Both suites exhibit SL magmatic fabrics overprinting or transitional to solid-state D3 deformation related to the JSI. Chemical data clearly show that they are related to different parental magmas. Finally, a microgranite suite occurs along a few topographic ridges paralell to the JSI. It comprises dominantly granodiorites with a mineralogy similar to the one of the porphyritic granitoids. However, discriminant diagrams show their distinct calc-alkaline affinity. The granodiorites display an essencially magmatic fabric, even though an incipient D3 solid-state structure may be developed along the JSI. Intrusion relationships with the previous suites, as well as regards to the D3 structures, point to their Iate emplacement. All these suites are intrusive in a Paleoproterozoic, high-grade gneiss-migmatite complex affected by two previous deformation phases (D1, D2). The fabrics associated with these earlier events are folded and overprinted by the younger D3 structures along the JSZ. The younger deformation is characterized by NE-dipping foliations and N/NE-plunging stretching lineations. In the JSZ northern termination the foliation acquires an ENE orientation, containing a stretching lineation plunging to the south. Symmetric kinematic cri teria developed at this site confirms the transpressional termination of the JSZ, as also shown by orthorrombic quartz c-axis patterns. E-W-trending d extra I shear zones developed in the central part of the JSZ are interpreted as antithetic structures associated to the transtensional deformation along the JSZ. This is consistent with its extensional-transcurrent kinematics and a flat-and-ramp geometry at depth, as shown by gravimetric data. The lateral displacement of the negative residual Bouguer anomalies, as regards to the main outcropping alkaline pluton, may be modelized by other deeper-seated granite bodies. Based on numerical modelling it was possible to infer two distinct intrusion styles for the alkaline pluton. The calculated model values are consistent with an emplacement by sheeting for the northern body, as already suggested by satellyte imagery and field mapping. On the other hand, the results point to a transition towards a diapir-related style associated to the smaller. southern stock. This difference in intrusion styles may relate to intensity variations and transtensional sites of the shear deformation along the JSZ. Trace element and Sr and Nd isotopes of the alkaline granites are compatible with their derivation trom a more basic crustal source, as compared to the presently outcropping highgrade gneisses, with participation (or alternatively dominated by) of an enriched lithospheric mantle component. Like other igneous suites in the Seridó Belt, the high LlL contents and fractionated REE patterns of the basic rocks also point to an enriched mantle as the source for this kind of magmatism. Geochemical and isotope data are compatible with a lower crustal origin for the porphyritic granites. On the basis of the strong control of the JSZ on the emplacement of lower crustal (porphyritic and alkaline granites) or lithospheric mantle (basic rocks, alkaline granites or a component of them) magmas, one may infer a deep root for this structure, bearing an important role in magma extraction, transport and emplacement in the Japi region, eastern domain of the Seridó Belt

Explorando a matemática dentro da calculadora

This dissertation aims to suggest the teacher of high school mathematics a way of teaching logic to students. For this uses up a teaching sequence that explores the mathematical concepts that are involved in the operation of a calculator one of the greatest symbols of mathematics.

Explorando a matemática dentro da calculadora

This dissertation aims to suggest the teacher of high school mathematics a way of teaching logic to students. For this uses up a teaching sequence that explores the mathematical concepts that are involved in the operation of a calculator one of the greatest symbols of mathematics.

História da matemática na formação de professores: sistemas de numeração antigos

This essay aims to present and describe a proposal of insertion of Mathematics History into teachers undergraduation. Such addition proposal is expected to take place as curricular component to be taught on initial undergraduation for mathematics teachers. The selection of contents for the proposal has been based on the national Curriculum Guidelines (DCN, 2001, acronym in portugueses) for bachelor’s degree in Mathematics; the National Curricular Guidelines for Elementary School (PCNEF, 1998, acronym in Portuguese); and the National Curricular Guidelines for High School (PCNEM, 1999, acronym in Portuguese). The curricular component now presented is supposed to take a 60 hour workload, and includes the following topics: History of Ancient Numbering Systems, History of Trigonometriy and History of fuctions. For the sake of exemplification, the topic History of Ancient Numbering Systems is discussed and analysed in detail as practice for the new curricular component.

Repercussões histopatológicas da colostomia no coto colônico distal desfuncionalizado: estudo experimental em ratos

O objetivo deste trabalho foi evidenciar as repercussões histopatológicas da colostomia no segmento desfuncionalizado e, dessa forma, criar um modelo experimental da colite de derivação fecal (CO). Foram utilizados 65 ratos, adultos, da raça Wistar, com peso variando de 220 a 300 g. Os animais foram divididos em 13 grupos, contendo cinco ratos. Do grupo 1 ao grupo 12, os animais foram submetidos a laparotomia mediana, sendo realizada uma colostomia terminal tipo boca única, e observados, por períodos variados de tempo, com o máximo de cem dias. Os animais, após serem mortos, foram necropsiados e retirado o segmento co1ônico desfuncionalizado para a avaliação histopatológica. Essa avaliação consistia de uma análise quantitativa, através da medida da espessura da mucosa colônica, e de uma análise qualitativa, mediante avaliação subjetiva: da presença de infiltrado inflamatório agudo ou crônico na lâmina própria; das alterações na arquitetura das criptas colônicas; da presença de hiperplasia folicular linfóide e de linfócitos na luz dos vasos da submucosa; e da presença de eosinófilos na luz intestinal. No grupo 12, após o 100° dia de pós-operatório (OPO), foi realizada a reconstrução do trânsito intestinal, e, após trinta dias, o cólon descendente foi retirado para a análise histopatológica. O método de Tukey e o teste "t" de Student foram utilizados como parte da análise dos resultados. Verificou-se uma redução estatisticamente significante da espessura da mucosa colônica a partir do 4000PO. Concluiu-se que a colostomia desfuncionalizante realizada em ratos reproduziu alterações histopatológicas compatíveis com a colite de derivação, e que estas mostraram-se reversíveis após a reconstrução do trânsito intestinal