Adrien-Marie Legendre (1752-1833) e suas obras em Teoria dos Números

The present thesis is an analysis of Adrien-Marie Legendre s works on Number Theory, with a certain emphasis on his 1830 edition of Theory of Numbers. The role played by these works in their historical context and their influence on the development of Number Theory was investigated. A biographic study of Legendre (1752-1833) was undertaken, in which both his personal relations and his scientific productions were related to certain historical elements of the development of both his homeland, France, and the sciences in general, during the 18th and 19th centuries This study revealed notable characteristics of his personality, as well as his attitudes toward his mathematical contemporaries, especially with regard to his seemingly incessant quarrels with Gauss about the priority of various of their scientific discoveries. This is followed by a systematic study of Lagrange s work on Number Theory, including a comparative reading of certain topics, especially that of his renowned law of quadratic reciprocity, with texts of some of his contemporaries. In this way, the dynamics of the evolution of his thought in relation to his semantics, the organization of his demonstrations and his number theoretical discoveries was delimited. Finally, the impact of Legendre s work on Number Theory on the French mathematical community of the time was investigated. This investigation revealed that he not only made substantial contributions to this branch of Mathematics, but also inspired other mathematicians to advance this science even further. This indeed is a fitting legacy for his Theory of Numbers, the first modern text on Higher Arithmetic, on which he labored half his life, producing various editions. Nevertheless, Legendre also received many posthumous honors, including having his name perpetuated on the Trocadéro face of the Eiffel Tower, which contains a list of 72 eminent scientists, and having a street and an alley in Paris named after him

Como vão se formando os professores em física e química: embates entre o ser, o ter e o fazer na formação de licenciandos da UFRN sob a perspectiva da teoria das representações sociais

The purpose of this work is to approach and understand the Social Representations (SR) (MOSCOVICI, 2003) about Physics and Chemistry from people who are major in these courses, as well as their Social Representations about teaching . We took as principle that approaching these representations it would be possible to relate their symbolic contents, in order to show how people who are following the first segments of bachelor degree courses in Physics and Chemistry become teachers, taking into account a psychosocial view. Two source of data was used during this research: Free-association Technique FA (ABRIC, 1994); and Multiple Classification Procedure (MCP) (ROAZZI, 1995). The analytical treatment of the collected data from FA was done according to the proposition of Grize, Vergés and Silem (1987 apud ABRIC, 1994, p. 66). MCP data were analyzed through MSA (Multidimensional Scalogram Analysis) and SSA (Singular Spectrum Analysis) methods associated with the Facet Theory (BILSKY, 2003). The discourses of MCP discussing groups at the moment of explanations were studied by Content Analysis as it was proposed by Bardin (1977) and Franco (2005). Indicative of an approach to the relations with knowledge (CHARLOT, 2000), the connections which aroused from the analyses showed that the group of future majors in Physics thought that this scientific field was based on a rationalist conception, influencing the idealization sense of the phenomena to be explained by Physics. Thus, Physics as school content started to require the student of the fundamental and high school to think abstractly as a cognitive skill of learning. The identifying elements observed in the relations between SR about Physics and Teaching aroused from the antagonism between future majors and their teacher, as well as from the speculation between their fundamental and high school students and themselves, mainly when they had to face the act of teaching due to the obstacles imposed by the own educational system, and by the weakness of the initial preparation. The group of future majors in Chemistry, through its discourses, showed these relations when they conceived empiricist Chemistry and said that teaching was the way of transmission of this knowledge, and didactics of Chemistry teaching was the direction to learning through pedagogic methods in order to lead the students to discoveries. The psychosocial contents which were built and showed from the symbolic relations in the studied SR achieved the relation of identity. This relation revealed identifying elements for these people, resulting from the traffic between their condition as students of Chemistry, and as teachers regarding their work, what placed the current relational contents in the teaching space, named as Knowledge changing and Adaptability . In order to study emerging questions in the discussing environment about formation and teaching professionalization, we focused the psychosocial view on this traffic and managed to observe epistemological practical and pedagogic obstacles that limited a configuration of the teaching work as a professional activity, especially from the particular conditions which led the relations of senses to Physics , Chemistry and Teaching ; and Chemistry and Physics as it was seen in this research. Generally speaking, we noted that these obstacles can denounce such obstacles concerning to the pedagogic doings which mainly impair the learning process of fundamental and high school students

O professor e sua formação linguística: uma interlocução teoria-prática

The work in screen constitutes a study of entitled doutoramento THE teacher and your linguistic formation: a dialogue teoria-prática. In him, the researcher, discoursing on subjects that involve the teaching-learning of the verbal language, it focalizes the importance of the linguistic formation for professionals that act in the years you begin of the Fundamental Education. In that perspective, lens to analyze the interrelações among them you know about the teachers, referring to the language (verbal), mobilized in the process teaching-learning of the production of texts written by the students, enrolled in the years you begin of the fundamental teaching. For so much, it developed a research Colaborativa, of qualitative nature, with four partícipes, being three of them teachers of the empiric field, EETB (pointed school for the " Prova Brasil " (2005) as among the ten Brazilian schools with the worst index of revenue discente in the abilities to read, to write and to interpret) and the other (researcher) educational of UERN. The research made use of several methodological procedures, among which stand out: questionnaire, glimpses, reflexive sessions and cycles of reflexive studies, among others. These specific of the Methodology of the Elaboration Conceptual Ferreiriana, adopted in the process of (re)elaboration, for the partícipes of the language concepts, text, textual gender, spoken language and written language. With relationship to the analytic procedures, those were based in contributions of the theory of the formation of concepts, of the Applied Linguistics and of the archaeology of the elect concepts. The results appear that the process of linguistic formation, established through the research colaborativa and of the methodology of the elaboration conceptual ferreiriana, uniting knowledge of the areas of the Education and of the Language, it was productive and he/she reveals a narrow relationship among the acquired knowledge for the partícipes, the (re)organization of the process teachinglearning of the language and the improvement of the productions written by the students of those educational ones

Pensamento teórico e formação docente: apropriação de saberes da tradição lúdica na perspectiva da teoria da formação das ações mentais por etapas de P. Ya. Galperin

The study investigated the possibility of organizing a didactics unit for formation of hability of identifying and explaining the popular traditional games in the process of licensed formation in physical education. Had basic premised, the thesis formulated by Piorte Yakovleviche Galperin that the fundamental condition that mode determines the student s way of thinking and the theoretical structures thought. Is given by the method of organization activity that form the basis of guiding skills assimilates from this assumption the study defended the thesis that the contents of popular traditional games can be organizeds according the systemic functional-structural focus. As a method to plan a didactics unit that contributes to development of theoretical thought and the professional development of graduates in physical education. In this sense the general goal was studied and develop a training proposal of ability to identify and explain the popular traditional games for physical education teachers oriented to contribute to the development of theoretical thought. In the construction process of the thesis in a first moment was determined the invariant conceptual of popular traditional games from the method of analysis of activity, after was organized the content of popular traditional games according to the structural-functional systems revealing the essential properties elements and levels of relationship.These procedures provided to the construction elements of the concept popular traditional games, and was the basis for planning a didactical unit to the formation of ability to study. These strategies enable to build a set of prepositions to argue, as a result of the increases in the knowledge of the professional formation in physical education. The study was introduced the fallowing contributions; formulated a teaching proposal to develop the ability to identify popular traditional games, as a cultural and historical contribution and the development of an individual, in initial formation of physical education teacher, attuned to the demands of training and use of knowledge that requires this level of education, defined and organized the knowledge of popular traditional games , this enables a teaching able to raise the cognitive abilities and the theoretical concept of personality of graduated in physical education

PENSAMENTO TEÓRICO E FORMAÇÃO DOCENTE: apropriação de saberes da tradição lúdica na perspectiva da teoria da formação das ações mentais por etapas de P. Ya. Galperin

The study investigated the possibility of organizing a didactics unit for formation of hability of identifying and explaining the popular traditional games in the process of licensed formation in physical education. Had basic premised, the thesis formulated by Piorte Yakovleviche Galperin that the fundamental condition that mode determines the student s way of thinking and the theoretical structures thought. Is given by the method of organization activity that form the basis of guiding skills assimilates from this assumption the study defended the thesis that the contents of popular traditional games can be organizeds according the systemic functional-structural focus. As a method to plan a didactics unit that contributes to development of theoretical thought and the professional development of graduates in physical education. In this sense the general goal was studied and develop a training proposal of ability to identify and explain the popular traditional games for physical education teachers oriented to contribute to the development of theoretical thought. In the construction process of the thesis in a first moment was determined the invariant conceptual of popular traditional games from the method of analysis of activity, after was organized the content of popular traditional games according to the structural-functional systems revealing the essential properties elements and levels of relationship.These procedures provided to the construction elements of the concept popular traditional games, and was the basis for planning a didactical unit to the formation of ability to study. These strategies enable to build a set of prepositions to argue, as a result of the increases in the knowledge of the professional formation in physical education. The study was introduced the fallowing contributions; formulated a teaching proposal to develop the ability to identify popular traditional games, as a cultural and historical contribution and the development of an individual, in initial formation of physical education teacher, attuned to the demands of training and use of knowledge that requires this level of education, defined and organized the knowledge of popular traditional games , this enables a teaching able to raise the cognitive abilities and the theoretical concept of personality of graduated in physical education

A teoria de Dienes no ensino de transformação de medidas de comprimento, área e volume no curso de pedagogia

The study was aimed to test a teaching module on the Zoltan Paul Dienes theory, focusing on the content: The transformation of measurements: length, areas and volumes. The study based on constructivist theory consisted in a methodological intervention with students of the 7th period of the Course of Pedagogy, in Central Campus, Federal University of Rio Grande do Norte (UFRN). A preliminary study with 40 students called diagnostic evaluation found that students did not understand the concept of measurements transformation and its processing steps. The latter was performed only with the help of the table of measurements transformation with no understanding of the content. He applied a pretest, a set of activities and a post-test. The latter was used as a tool for evaluation of the student learning process. The answers of these ones were evaluated according to the concept of reflective abstraction of Jean Piaget, one of the authors who influenced the Dienes theory

A história escolar e a teoria da atividade: relações e possibilidades formativas no ensinar e aprender

This study investigates the manner in which the Activity Theory by Alexei Nikolaevich Leontiev contributed to the performance of a teacher who teaches History at the 8th year of elementary school, Escola Estadual Coronel Fernandes, in Luís Gomes - RN city. Her goal is to analyze the contributions of this theory in her teaching practice. It was opted by collaborative approach as formative strategy and was used as procedures for training of knowing the courses of study and thoughtful reflection sessions. It was used as techniques in the development of these cycles, the semistructured interview and the reflection sessions, the autoscopy and observation in real life. Regarding the theoretical foundation, held in these cycles, the teacher demonstrated to have appropriated some contributions from Activity Theory, besides relating them to her practice and understanding her importance to the improvement of teaching and learning of History. Concerning to the reflection sessions, the analysis showed that the participant has used of constructions of this theory and improved their practice, developing lessons of History so as to encourage student participation in oral and promote his integral development. The educational process, carried out on the practice of teacher, has shown an increase in her conscious learning that contributed to the improvement in their professional development. Before these findings, as needs for new thinking, this research recommends, especially the organization of teaching activities, based on this theory, which allows the teacher to improve the teaching and learning process contributing to student's full education

Formação da habilidade de interpretar gráficos cartesianos em licenciandos em química segundo a teoria de P. Ya. Galperin

It has been remarkable among the Science Teaching debates the necessity that students do not learn only theories, laws and concepts, but also develop skills which allows them to act towards a critical citizenship. Therefore, some of the skills for the natural sciences learning must be taught consciously, intentionally and in a planned way, as component of a basic competence. Studies of the last twenty years have shown that students and teachers have plenty of difficulties about skills development and, among several, the skill of interpreting Cartesian graphics, essential for the comprehension of Natural Science. In that sense, the development of that type of professional knowledge during the initial education of future Chemistry teachers has become strategic, not only because they need to know how to use it, but also because they need to know how to teach it. This research has as its general objective the organization, development and study of a process of formation of the skill of interpreting Cartesian graphics as part of the teachers professional knowledge. It has been accomplished through a formative experience with six undergraduate students of the Teaching Degree Course of Chemistry of Universidade Federal do Rio Grande do Norte (UFRN Federal University of Rio Grande do Norte), in Brazil. In order to develop that skill, we have used as reference P. Ya. Galperin s Theory of the Stepwise Formation of Mental Actions and Concepts and its following qualitative indicators: action form, degree of generalization, degree of consciousness, degree of independence and degree of solidness. The research, in a qualitative approach, has prioritized as instruments of data collecting the registering of the activities of the undergraduate students, the observation, the questionnaire and the diagnosis tests. At the first moment, a teaching framework has been planned for the development of the skill of interpreting Cartesian graphics based on the presupposed conceptions and steps of Galperin s Theory. At the second moment, the referred framework has been applied and the process of the skill formation has been studied. The results have shown the possibility of develop the skill conscious about the invariant operation system, with a high degree of generalization and internalized the operational invariant in the mental plane. The students have attested the contributions at that type of formative experience. The research reveals the importance of going deeper about the teaching comprehension of the individualities tied to the process of internalization, according to Galperin s Theory, when the update of abilities as part of the teaching professional knowledge is the issue

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

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

Análise de Agrupamentos Com Base na Teoria da Informação: Uma Abordagem Representativa

Currently, one of the biggest challenges for the field of data mining is to perform cluster analysis on complex data. Several techniques have been proposed but, in general, they can only achieve good results within specific areas providing no consensus of what would be the best way to group this kind of data. In general, these techniques fail due to non-realistic assumptions about the true probability distribution of the data. Based on this, this thesis proposes a new measure based on Cross Information Potential that uses representative points of the dataset and statistics extracted directly from data to measure the interaction between groups. The proposed approach allows us to use all advantages of this information-theoretic descriptor and solves the limitations imposed on it by its own nature. From this, two cost functions and three algorithms have been proposed to perform cluster analysis. As the use of Information Theory captures the relationship between different patterns, regardless of assumptions about the nature of this relationship, the proposed approach was able to achieve a better performance than the main algorithms in literature. These results apply to the context of synthetic data designed to test the algorithms in specific situations and to real data extracted from problems of different fields

Reestruturação da disciplina "Física I" do Curso de Tecnólogo em Gerência de Obras de Edificações do CEFET/PB

The aim of the present paper is to reorganize a discipline on technological physics so that the construction site of civil engineering becomes a natural environment of learning, providing the learner with the association between theory and practice as well as allowing the subject to process, in real time, information generated from his cognitive constructions and his contextualizations. Thus, a sequence of actions was taken into account: firstly, the programme was developed in the classroom, sharing with its contextualized information through experiments done under supervision by the learners in laboratories; secondly, the data which associate physics with construction were collected and, to do so, technical visits to construction sites were realized, providing the learner the association between the theory and the practice in a suitable site to the constructivist approach. As a result, the first discipline on physics of the Curso de Tecnólogos em Gerência de Obras de Edificações do CEFET/PB was re-structured in terms of syllabus, methodology, application and evaluation. In fact, this work deals with a dynamic process that gathers and gives emphasis to teaching, learning, technology, information, creativity, competence and abilities in a constructivist learning process and, as a consequence, having allowed institutional engagement

O Ensino de medidas e grandezas através de uma abordagem investigatória

This work relates our experience in an investigative practice in the classroom, carried out in State School Jorge Fernandes , located in Natal - RN, having as objective to validate the applying of a education module about Measures and Largenesses in Primary Teaching. We used the constructivist approach; using to Richard s Skemp (1980) theory in order to explicit the students learning according to their comprehension levels. Initially, we carry out an exploratory research to check the participant s previous knowledge. Then, we developed an intervention to validate an education module, structured from needs pointed out from results of the initial research, analyzing the students advances through the final evaluation, displaying growth stages of group front to the knowledge about the matter approached. Finally, we presented our reflections about our experience; putting forward suggestions of the teachers activities, aiming at contributing to the improvement of their practices in classroom during the approach of subject for us investigated

A difícil aceitação dos números negativos: um estudo da teoria dos números de Peter Barlow (1776-1862)

The present study seeks to present a historico-epistemological analysis of the development of the mathematical concept of negative number. In order to do so, we analyzed the different forms and conditions of the construction of mathematical knowledge in different mathematical communities and, thus, identified the characteristics in the establishment of this concept. By understanding the historically constructed barriers, especially, the ones having ontologicas significant, that made the concept of negative number incompatible with that of natural number, thereby hindering the development of the concept of negative, we were able to sketch the reasons for the rejection of negative numbers by the English author Peter Barlow (1776 -1862) in his An Elementary Investigation of the Theory of Numbers, published in 1811. We also show the continuity of his difficulties with the treatment of negative numbers in the middle of the nineteenth century

Teoria histórico-cultural e suas implicações na atuação do professor de educação física escolar

This article presents a theoretical search and aims to introduce the main categories of historical-cultural theory and discuss its implications for the physical education teacher's work inside the school and also emphasizes this theory and its methodological proposal as an important way to build the scholar physical education in a critical perspective aiming to change the school and the students conscious and personality. The Vigotskian school of human development it is taken as an important reference to understand the scholars in their vital process of development and helps the teachers in general, and physical education teachers in specific, to consider the activity ( vital activity) as important instrument to get the humanization and liberty of human being, inside the school and inside the contemporary society.