Geometrizando no segundo ciclo :relato de uma intervenção pedagógica voltada à construção de conceitos geométricos no ensino fundamental

This work has proposed to relate the experience product of a pedagogical intervention, performed in a public institution of teaching situated in this capital. It had as objective to validade the applying of a teaching module of geometry, more specifically about the conceptions of perimeter and área in the second cycle of fundamental teaching. This dissertation has presented the problematic which involves the teaching of geometry in different contexts. It has adopted the broach of the radical constructivism while methodological theoretical referencial through which it has tried to explain the phenomena that involves the teaching and the apprenticeship. It appropriates Jean s Piaget contributions related to the development stages, while referencial that will dialogue in the search by sense and comprehension of the geometric apprenticeship process and it runs over Richard s Skemp (1980) theory in order to explicit the student s apprenticeship according to the levels of instrumental comprehesion and relacional comprehension . The research has presented datum related to initial diagnosis evaluantion, the pedagogical intervention and analysis of the activities and students perfomance displaying still the results of the final evaluation. According to the results got, we could check the students group growth front to the acquisition of the concepts of perimeter and área in comparison with the previous knowledges presented in the initial diagnosis evoluation of the students participants of the research. We have concluded evaluating the objectives of the research, connecting the strategies and reasoning employed by the students in order to resolve the questions and then to reach the objectives proposed by the teaching module. We have presented still the main obstacles to the apprenticeship of such concepts

Reflexões sobre a construção e evolução de conceitos geométricos nas séries intermediárias do ensino fundamental

This thesis represents a didactic research linked to the Post-graduation Programme in Education of the Universidade Federal do Rio Grande do Norte which aimed to approach the construction of the geometrical concepts of Volume of the Rectangular Parallelepiped, Area and Perimeter of the Rectangle adding a study of the Area of the Circle. The research was developed along with students from the 6th level of the Elementary School, in a public school in Natal/RN. The pedagogical intervention was made up of three moments: application of a diagnostic evaluation, instrument that enabled the creation of the teaching module by showing the level of the geometry knowledge of the students; introduction of a Teaching Module by Activities aiming to propose a reflexive didactic routing directed to the conceptual construction because we believed that such an approach would favor the consolidation of the learning process by becoming significant to the apprentice, and the accomplishment of a Final Evaluation through which we established a comparison of the results obtained before and after the teaching intervention. The data gathered were analyzed qualitatively by means of a study of understanding categories of mathematical concepts, in addition to using descriptive statistics under the quantitative aspect. Based on the theory of Richard Skemp, about categorization of mathematical knowledge, in the levels of Relational and Instrumental Understanding were achieved in contextual situations and varied proportions, thus enabling a contribution in the learning of the geometrical concepts studied along with the students who took part in the research. We believe that this work may contribute with reflections about the learning processes, a concern which remained during all the stages of the research, and also that the technical competence along with the knowledge about the constructivist theory will condition the implementation of a new dynamics to the teaching and learning processes. We hope that the present research work may add some contribution to the teaching practice in the context of the teaching of Mathematics for the intermediate levels of the Elementary School

Elaboração de uma sequência didática sobre os conceitos geométricos preliminares ao estudo da trigonometria

This study is qualitative, including literature search and preparation of teaching materials. Your goal is to report the study of geometric problems of character presented in the application of trigonometry and work on the preparation of detailed activities that help in overcoming these difficulties. For this, we read some papers on teaching and learning of trigonometry in order to identify the difficulties encountered during their journey. Then separate the geometric difficulties of character and prepare a list of geometric content and procedures associated with them. Thus, we can organize a notebook with activities that would address most of these concepts. Finally we present the specification of activities called Activity on introductory concepts to the study of trigonometry

Um estudo sobre a aprendizagem de alguns conceitos algébricos e geométricos

The objective of the present work was develop a study about the writing and the algebraic manipulation of symbolical expressions for perimeter and area of some convex polygons, approaching the properties of the operations and equality, extending to the obtaining of the formulas of length and area of the circle, this one starting on the formula of the perimeter and area of the regular hexagon. To do so, a module with teaching activities was elaborated based on constructive teaching. The study consisted of a methodological intervention, done by the researcher, and had as subjects students of the 8th grade of the State School Desembargador Floriano Cavalcanti, located on the city of Natal, Rio Grande do Norte. The methodological intervention was done in three stages: applying of a initial diagnostic evaluation, developing of the teaching module, and applying of the final evaluation based on the Mathematics teaching using Constructivist references. The data collected in the evaluations was presented as descriptive statistics. The results of the final diagnostic evaluation were analyzed in the qualitative point of view, using the criteria established by Richard Skemp s second theory about the comprehension of mathematical concepts. The general results about the data from the evaluations and the applying of the teaching module showed a qualitative difference in the learning of the students who participated of the intervention

Objetiva(ação) da medida e contagem do tempo em práticas socioculturais e educativas

This thesis describes and analyzes various processes established and practiced by both groups about the socio-cultural objective (action) the measurement and timing, mobilized some socio-historical practices as the use of the gnômon of the sundial and reading and interpretation of movements celestial constellations in cultural contexts such as indigenous communities and fishermen in the state of Pará, Brazil. The Purpose of the study was to describe and analyze the mobilization of such practices in the socio-historical development of matrices for teaching concepts and skills related to geometric angles, similar triangles, symmetry and proportionality in the training of mathematics teachers. The record of the entire history of investigation into the socio-historical practice, the formative action was based on epistemological assumptions of education ethnomathematics proposed by Vergani (2000, 2007) and Ubiratan D'Ambrosio (1986, 1993, 1996, 2001, 2004) and Alain Bishop conceptions about mathematics enculturation. At the end of the study I present my views on the practices of contributions called socio-cultural and historical for school mathematics, to give meaning to the concept formation and teaching of students, especially the implications of Education Ethnomatematics proposed by Vergani (2000) for training of future teachers of mathematics

Utilizando processos geométricos da história da matemática para o ensino de equações do 2º grau

The present work had as principal objective to analyze the, 9th grade students understanding about the solutions of an equation of the 2° degree, using geometric processes of the History of the Mathematics. To do so, the research had as base the elaboration and application of a group of teaching activities, based on Jean Piaget's construtivism. The research consisted of a methodological intervention, that has as subjects the students of a group of 9th grade of the State School José Martins de Vasconcelos, located in the municipal district of Mossoró, Rio Grande do Norte. The intervention was divided in three stages: application of an initial evaluation; development of activities‟ module with emphasis in constructive teaching; and the application of the final evaluation. The data presented in the initial evaluation revealed a low level of the students' understanding with relationship to the calculation of areas of rectangles, resolution of equations of the 1st and 2nd degrees, and they were to subsidize the elaboration of the teaching module. The data collected in the initial evaluation were commented and presented under descriptive statistics form. The results of the final evaluation were analyzed under the qualitative point of view, based on Richard Skemp's theory on the understanding of mathematical concepts. The general results showed a qualitative increase with relationship to the students' understanding on the mathematical concepts approached in the intervention. Such results indicate that a methodology using the previous student‟s knowledge and the development of teaching activities, learning in the construtivist theory, make possible an understanding on the part of the students concerning the thematic proposal

Práticas etnomatemáticas no Liceu do Paracuri :a propósito dos ornamentos geométricos da cerâmica

The present study analyzes the ethnomatematics practices presents in the creation of the geometric ornaments of the icoaraciense ceramic, originated and still practiced in the neighborhood of Paracuri, District of Icoaraci, belonging to Belém, capital of the State of Pará/Brasil. The object of our study was centered at the workshops supplied by the artisans master of the School of Arts and Occupations, Master Raimundo Cardoso. Referred school provides to its students, formation at fundamental level as well professional formation, through vocational workshops that help to maintain alive the practice of the icoaraciense ceramic. Our interest of researching that cultural and vocational practice appeared when we got in touch with that School, during the development of activities of a discipline of the degree course of mathematics. In order to reach our objective, we accomplished, initially, a research about the icoaraciense ceramic historic, since the first works with the clay until to the main characteristics of that ceramic. Soon afterwards, we discussed on ethnomatematics, culture, knowledge, cognition and mathematical education. At the end, we analyzed the creation of the geometric ornaments of the icoaraciense ceramic, considering the proportion concepts, symmetry and some geometry notions, that are used by the artisans when they are ornamenting the pieces of that ceramic. We verified that, in spite of the artisans, usually, do not demonstrate to possess a bit of domain on the mathematical concepts that they are working with, for instance, the ones of translaction symmetry, rotation and reflection, they demonstrate full safety in the use of those concepts, as well as the capacity to recognize them, even if in a singular specific and very peculiar way, what opens the possibility of a partnership among mathematics teachers and master-artisans of the archeological ceramic and icoaraciense workshops

Simulação de fluxo de fluidos em meios porosos desordenados uma análise de efeito de escala na estimativa da permeabilidade e do coeficiente de arrasto

The present study provides a methodology that gives a predictive character the computer simulations based on detailed models of the geometry of a porous medium. We using the software FLUENT to investigate the flow of a viscous Newtonian fluid through a random fractal medium which simplifies a two-dimensional disordered porous medium representing a petroleum reservoir. This fractal model is formed by obstacles of various sizes, whose size distribution function follows a power law where exponent is defined as the fractal dimension of fractionation Dff of the model characterizing the process of fragmentation these obstacles. They are randomly disposed in a rectangular channel. The modeling process incorporates modern concepts, scaling laws, to analyze the influence of heterogeneity found in the fields of the porosity and of the permeability in such a way as to characterize the medium in terms of their fractal properties. This procedure allows numerically analyze the measurements of permeability k and the drag coefficient Cd proposed relationships, like power law, for these properties on various modeling schemes. The purpose of this research is to study the variability provided by these heterogeneities where the velocity field and other details of viscous fluid dynamics are obtained by solving numerically the continuity and Navier-Stokes equations at pore level and observe how the fractal dimension of fractionation of the model can affect their hydrodynamic properties. This study were considered two classes of models, models with constant porosity, MPC, and models with varying porosity, MPV. The results have allowed us to find numerical relationship between the permeability, drag coefficient and the fractal dimension of fractionation of the medium. Based on these numerical results we have proposed scaling relations and algebraic expressions involving the relevant parameters of the phenomenon. In this study analytical equations were determined for Dff depending on the geometrical parameters of the models. We also found a relation between the permeability and the drag coefficient which is inversely proportional to one another. As for the difference in behavior it is most striking in the classes of models MPV. That is, the fact that the porosity vary in these models is an additional factor that plays a significant role in flow analysis. Finally, the results proved satisfactory and consistent, which demonstrates the effectiveness of the referred methodology for all applications analyzed in this study.

Reelaborando conceitos e ressignificando a prática na educação infantil

In this research we described the path of thirty one teachers involved with elementary school, amog which we included ourselves, looking for professional formation that allowed us to understand the function of educating childen. In this sense, this group of teachers begins a process of intentional, systematic and voluntary reflection, in an attempt to give new meanings to daily concepts of life and work, and linking them to their socialpractices. Having as reference the theoretical and methodological principles of socio-historical approach and collaborative research, the Group of Studies: The Dialogue Reflection as Re-meaning of Pedagogical Practice: a continuous education proposal, motivated by the willing and the necessity of re- elaborate knowledge about collaboration, reflection, infant education, playing and development which meets the new and goes the inverse way revisiting concepts and conception already consolidated, confronting and re-meaning them enlightened by one s own effort and the collaboration of pairs, mediated by Cycles of Reflexive Studies and Inter/intrapersonal Sessions. We can affirm that these tools helped the process of reflexivity put into practice by participants, which most important consequence was the theoretical re-meaning and practice in the ambit of infant education. During this investigation, we could see some theoretical and practice presuppositions which permitted to attribute to the exercise of reflexivity in collaboration the means into which the involved people could rescue the actions taken, justified their choices, confronted their theoretical options with their peers and with the systematized knowledge would question their certainties and rebuild in intra-psychological level, the knowledge elaborated socially. To this group which main activity is the docent profession, the personal and professional development constitutes the objective in which actions were articulated and operations which made learning possible as well as professional development

O processo de aprendizagem de professores do ensino fundamental: apropriação da habilidade de planejar situações de ensino de conceitos

La investigación fue realizada con profesores de los años iniciales de la enseñanza básica, alumnos de la carrera de Pedagogía Licenciatura Plena del PROBÁSICA de Ceará-Mirim (RN). Tuvo como objetivo general el estudio de lo proceso de apropiación de esa habilidad, segundo las siguientes perspectivas teóricas: históricocultural, de L.S. Vygotsky, teoría de la actividad, de A.N. Leontiev, y la teoría de la asimilación por etapas mentales, de P. Ya Galperin. La metodología se desarrolló organizándose en tres etapas: el diagnóstico inicial, con el análisis del nivel de desarrollo de la habilidad de los profesores; el proceso formativo, con la orientación del aprendizaje, el control y la evaluación del desarrollo; y el diagnóstico final, con el análisis del nivel alcanzado en la experiencia. Los instrumentos utilizados fueron: un cuestionario, para la caracterización de los sujetos de la investigación, el planeamiento de enseñanza de los profesores y el diario de clase, donde se registraba lo que ocurrió en cada orientación y realización del proceso formativo. Los resultados referentes a los niveles iniciales del desarrollo de la habilidad han revelado un grado de espontaneidad en el planeamiento de enseñanza de los conceptos. Durante el proceso de enseñanza y aprendizaje, los profesores han expresado sus dificultades, pero también las posibilidades de mudanza para que alcanzaran un nuevo nivel de desarrollo. Para el análisis del nivel inicial y del desarrollo de las habilidades de los profesores para planificar situaciones de enseñanza con la definición y con la identificación, fueron utilizados los siguientes elementos: el dominio del concepto, el dominio de esos procedimientos lógicos y las categorías del planeamiento (objetivos, contenidos, estrategias de enseñanza, control y evaluación). En cada etapa surgieron obstáculos, pero también aspectos que han revelado la posibilidad para aprender una nueva forma de planear, con apropiación de nuevos fundamentos teóricos. La práctica docente se constituyó en un elemento que facilitó la comprensión y la apropiación de las habilidades de planear situaciones de enseñanza de conceptos mediante la definición y la identificación

A obra de triangulis omnimodis libri quinque de Johann Müller Regiomontanus (1436 1476): uma contribuição para o desenvolvimento da trigonometria

Trigonometry, branch of mathematics related to the study of triangles, developed from practical needs, especially relating to astronomy, Surveying and Navigation. Johann Müller, the Regiomontanus (1436-1476) mathematician and astronomer of the fifteenth century played an important role in the development of this science. His work titled De Triangulis Omnimodis Libri Quinque written around 1464, and published posthumously in 1533, presents the first systematic exposure of European plane and spherical trigonometry, a treatment independent of astronomy. In this study we present a description, translation and analysis of some aspects of this important work in the history of trigonometry. Therefore, the translation was performed using a version of the book Regiomontanus on Triangles of Barnabas Hughes, 1967. In it you will find the original work in Latin and an English translation. For this study, we use for most of our translation in Portuguese, the English version, but some doubt utterance, statement and figures were made by the original Latin. In this work, we can see that trigonometry is considered as a branch of mathematics which is subordinated to geometry, that is, toward the study of triangles. Regiomontanus provides a large number of theorems as the original trigonometric formula for the area of a triangle. Use algebra to solve geometric problems and mainly shows the first practical theorem for the law of cosines in spherical trigonometry. Thus, this study shows some of the development of the trigonometry in the fifteenth century, especially with regard to concepts such as sine and cosine (sine reverse), the work discussed above, is of paramount importance for the research in the history of mathematics more specifically in the area of historical analysis and critique of literary sources or studying the work of a particular mathematician

Cinema e educação :interfaces, conceitos e práticas docentes

This project goes beyond the interfacial field of cinema, History and education. We take as our object the epistemological potential of the cinema at the educational scenario, specifically the use of films integrated to the practices of History teachers and educative processes in which we have taken part as a builder. Our objective is to map, initially, the knowledge around this use to search a synthesis and its empirical application. From the methodological point of view, we have made use of different perspectives: (a) interviews with the educator subjects; (b) observation of their practices and formative circumstances; (c) filmic analysis and the relation of the cinema s epistemology with the other areas ones (initially History and further Journalism). Our analysis allowed us to portrait the film such as an epistemological-troubling category, what makes the cinema rather a builder technology and not simply a complementary and illustrative technological resource. Therefore, we have realized that the restriction to the cinema s educational function is linked to the restrictions to the theoretical categories to an only interfacial aspect: historical film as a film which portraits the past (at the historical field) and film on journalism as a film which approaches a single object of Journalism (at the journalistic field). These discussions happen, consequently, at the arena of the nature of cinema s genres (fiction and documentary), which are understood in a naïve way, simpler than its epistemological possibilities, boosted at this research when we analyze the confluence between fiction and reality. The reflections on educative practices and in formation related to the cinema had occurred in three empirical realities: research with professors in performance, practices docent s and accompaniment of students of history. Have to do with our personal career as a teacher and researcher and, when analyzed other practices, have become, unavoidably, the subject and object of this project

Conceitos e práticas educativas nos regimentos escolares no Rio Grande do Norte (1910 1930)

This research aims to analyze the concept of childhood in the dimension of educational practice, which is present in the regimental school and historically constructed power relations during the period 1910 to 1930, in Rio Grande do Norte. To contextualize this study, it is necessary to address the Bylaws of the School Groups (1915), the Internal Isolated Schools (1925) and Education Reform (1916). The expansion of education in the State, aiming at preparing the individual for the new capitalist social order was the concern of all governments of the first republic. During this period, the school is conceived as a privileged scenario of a set of practices aimed at disciplining the children, to explore, in some respects, the concept of childhood. Over time, this cocepção was constructed historically. In addition, the school receives children, which in the late nineteenth and early twentieth century, are inserted into an educational process in line with the state, embodied in laws, regulations and school discursive practices

A formação de conceitos no ensino de graduação em enfermagem à luz da teoria da aprendizagem significativa

The Theory of Meaningful Learning (TML) described by David Paul Ausubel offers a proposal for the teaching strategies to provide a more active and effective student learning. The projection of the TML practice is demonstrated through the development of concept maps (CM) technique, created by Joseph Donald Novak, which presents as a strategy, method or schematic feature, which is an indicator to identify the cognitive organization of the knowledge acquired by students. The survey was conducted in the light of TML in relation to learning concepts involving students of undergraduate nursing in a public university in the state of Rio Grande do Norte. Thus, the study aimed to compare the concept learning of students of undergraduate nursing, when subjected to different forms of education, to point approaches that promote more effective and meaningful results. It was a quasi - experimental study with a qualitative analysis, conducted with students of the Undergraduate Nursing of the Universidade Federal do Rio Grande do Norte (UFRN), approved by the Research Ethics Committee/UFRN Certification of Presention for Ethics Appreciation (CPEA) in 11706412.3.0000.5537. The study took place at two different times and involved content on complications mediate postoperative surgical wound in the same discipline with students who attended the 5th semester of the degree course in Nursing. For the viability of data collection, in the second half of 2013, we used the technique of CM, to represent the concept of complications mediate postoperative surgical wound covered in the classroom. CM were built at a different time from that of the discipline, with the support of tutors and preceded by a brief description and explanation about the form of preparation and application. In this study were subjected, 31 students of undergraduate nursing, registered in the discipline of Integral Attention to health I. In the first stage, 18 students participated in the survey, they had the teaching intervention based on TML, and in the second stage, all students participated in the lesson provided curriculum with the responsible teacher of the subject, on the same issue occurred. At the end of each meeting, the students 11 developed concept maps with the aid of software Cmap Tools®. Data analysis happened upon the technique of content analysis, supported by a conceptual map "glass", previously developed by researchers and aid in the preparation of the categories in which the concepts found were classified. The study found that the teaching intervention based on TML with the help of CM, managed to develop in students a more expressive teaching learning process than just classroom curriculum with the traditional teaching method, and also that the association between the intervention motion teaching with the traditional method and the use of the technique of CM encourages the student the ability to articulate the various acquired knowledge as well as apply them in real situations

Desenvolvimento de um sistema para aplicação dos conceitos da tecnologia cad3d-bim na indústria moveleira

In this work was developed an information system to apply the concepts of CAD3D-BIM technology for the design activities of the furniture industry. The development of this system was based in an architecture comprised of two modules: a web interface to management the metadata of models from furniture's library and the combination of three-dimensional CAD software with a specific plugin to access the information from this model. To develop this system was also used a Data Base Management System (DBMS) designed to storage the information from models in a hierarchical way, based on concepts of Group Technology (GT). The centralization of information in a single database allows the automatic availability of any changes to all participants involved in a particular project when it‟s happens. Each module from system has its own connection to this database. Finally was developed a prototype from a 3D virtual environment to help create Virtual Reality projects in the web. A study from available technologies to create 3D web applications for execution in websites was done to support this development. The interconnection between modules and the database developed allowed the assembly of a system architecture to support the construction and exhibition of projects of the furniture industry in accordance with the concepts proposed by BIM (Building Information Modeling), using as object of study the furniture industry of state of Rio Grande do Norte