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

Educação científica no contexto pós-ontológico: por uma concepção plural de conhecimento e educação

The development of this work arises from the research of sociological and philosophical characters contemplating also other approaches which aims to answer the followingquestions: what is the responsibility of science teaching for the image one has about science? ; which scientific education should be designed for nowadays? . After considering the assumptions brought along by rationalism and the criticisms to the illuminist model proposed by sociology and philosophy of science, as well by the biology of the knowing process, going through discussions concerning post-modernity issues, one is given to understand that the image of science has become the central point of discussion in the last hundred years, including what concerns the area of science teaching, and that practically none of those discussions really reached natural science classes indeed. We adopt the term postontological to characterize the recent proposals on philosophy and sociology, because we evaluate that this term allows a better identification of the scientific realism crisis, which supports the existence of an ontological domain which science, and only science, is able to understand. One notices that the general public is not aware of those discussions, mainly if they are science teachers and students. So we believe that discussing the logic in which science is structured, the new understandings concerning the scientific undertaking, especially those of an externalist character, and the relationship between science and society, all of this contributes to build up a science teaching which contemplates a reflective contribution, besides allowing the inclusion of the study of other epistemologies in the educational practice. We argue that a revisionist posture seems to be the most appropriate for the contemporary scientific education, contemplating, besides the teaching of the usual science contents, discussions on the issues involving that knowledge, as well as respecting epistemologies alternative to the modern Western scientific one, in order one can work on the perception of local knowledge generated from other epistemological bases. We describe here practical activities we did involving teachers (short-term courses) and high-school students in an inland school in the Rio Grande do Norte state, in Brazil, as a way to demonstrate the possibility of interventions which can take those conceptions, discussions and changes to the classroom

Atividades experimentais no ensino de biologia em escolas públicas do estado do Rio Grande do Norte, Brasil: caracterização geral e concepção de professores

Recent research has revealed that the majority of Biology teachers believe the practice of experimental activities as a didactical means would be the solution for the improvement of the Biology teaching-learning process. There are, however, studies which signal the lack of efficiency in such practice lessons as far as building scientific knowledge is concerned. It is also said that despite the enthusiasm on the teachers‟ part, such classes are rarely taught in high school. Several studies point pedagogical difficulties as well as nonexistence of a minimal infrastructure needed in laboratories as cause of low frequency in experimental activities. The poor teacher performance in terms of planning and development of classes; the large number of students per class; lack of financial stimulus for teachers are other reasons to be taken into account among others, in which can also be included difficulties of epistemological nature. That means an unfavorable eye of the teacher towards experimental activities. Our study aimed to clarify if such scenario is generalized in high schools throughout the state of Rio Grande do Norte Brazil. During our investigation a sample of twenty teaching institutions were used. They were divided in two groups: in the first group, five IFRN- Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Norte schools. Two of those in Natal, and the other three from the country side. The second group is represented by fifteen state schools belonging to the Natal metropolitan area. The objectives of the research were to label schools concerning laboratory facilities; to identify difficulties pointed by teachers when performing experiment classes, and to become familiar with the conceptions of the teachers in regarding biology experiment classes. To perform such task, a questionnaire was used as instrument of data collecting. It contained multiple choice, essay questions and a semi-structured interview with the assistance of a voice recorder. The data analysis and the in loco observation allowed the conclusion that the federal schools do present better facilities for the practice of experimental activities when compared to state schools. Another aspect pointed is the fact that teachers of federal schools have more time available for planning the experiments; they are also better paid and are given access a career development, which leads to better salaries. All those advantages however, do not show a significantly higher frequency regarding the development of experiments when compared to state school teachers. Both teachers of federal and state schools pointed infra-structure problems such as the availability of reactants, equipments and consumption supplies as main obstacle to the practice of experiments in biology classes. Such fact leads us to conclude that maybe there are other problems not covered by the questionnaire such as poor ability to plan and execute experimental activities. As far as conceptions about experimental activities, it was verified in the majority of the interviewees a inductive-empiric point of view of science possibly inherited during their academic formation and such point of view reflected on the way they plan and execute experiments with students

Vídeo-aula de história da matemática: uma possibilidade didática para o ensino de matemática

In this work we are disagreeing with the possibility of production and of the use of video-class for the disciplines of history of mathematics by the teachers of elementary e middle school as a way to contribute to the development of their classes. Our goal is to provide to the mathematics teachers the option of connecting social, scientific, cognitive, and didactic aspects of topics in math thoughts to their students. That shall be based in the presence of mathematics in the history of humanity. Thus, we consider possible that teachers and their students can link and relate mathematics to other sciences, education culture, and reflect about the many ways of represent them, as well as the patters of organization of nature and of culture. In this way, they shall be able to observe and interpret situations that involve mathematical questions associated to the various means of historic-epistemological studies already done by other researchers and scholars in the field of history of mathematics who works in creating video-classes. In addition to that, we can use all the available media in order to give edifying dynamics to the mathematical formulations established throughout history. In this sense, we are based and focused on the objectives, which are sustained by educational computer technology, techniques for video making, as well as mathematical teaching proposals and the historical inquiring made by Mendes (2001, 2009a, 2009b). The validating experimentation allowed us to conclude that the techniques we used in the production of the history of mathematics video-classes proved they to be valid ones. They are able to be executed with the minimum of technological resources. In addition, they have the same efficacy as far as classroom use

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

O ser elástico, mola, agulha, trepidação: expressões do homoerotismo em Fernando Pessoa

This Masters thesis investigates and analyzes the homoerotic expressions in Fernando Pessoa s poetry and in his heteronyms : Álvaro de Campos, Alberto Caeiro and Ricardo Reis. Through the elaboration of deceptive strategies as a way to escape from the insults and the constraints, the poet by means of creative runaway lines builds up a homoerotic poetry that differ from the established patterns and representational models of the literature. We can find, bearing in mind a problematic sexuality which overflows in the various I s, of the sinuous identities and the movable boundaries, and intense mask games. They become real in poems, especially by means of sensations, yielding the possibility of a queer discourse and generating a homoerotic poetry. Pessoa s homoerotism is, thus, presented amid friendly relationships, smooth spaces, of heterotrophy of the city, or others space and the closet s aesthetics. Based on this, it is noted the articulations of a performance gender as body scripture and inscription, thus establishing a physical-writing which reveals a transgressive sexuality, with multiple entrances and exits, affirmations and denials that originate paradoxes. In this matter, we develop links between Foucault conceptions (2010a, 2010b, 2011) towards the history of sexuality, friendship and the power-knowledge relations with traces of significance and subjectivity, in processes of faciality and BwO (Body-without-Organs) in Deleuze and Guattari (1996). We still consider the ontological questionings towards the Gay dimension in Eribon (2008) and we raise aspects concerning the construction of the idea of masculinity in Bourdieu (2010). Finally, we base ourselves on Sedgwick s 1993 closet epistemological approach, as well as on Butler s 2012 gender and performance theory, also going through a few Bataille 1987 passages about erotism, that redimension the homoaffective images of the Portuguese poet

Deus, mente e mundo: sobre os conceitos de complicatio, imago e explicatio a partir do diálogo de mente de nicolau de cusa

This work deals with the way how the three themes of traditional metaphysics, namely, God, man, and the world, are rethought through the philosophical speculation of German cardinal Nicholas of Cusa (1401-1464). Due to the comprehensiveness of this subject, our dissertation had as a starting point and constant reference the book that the philosopher wrote in 1450, Idiota. De mente, the second written work that makes up the series of the Idiota (Idiotae libri), whose discussion is developed around the theme of the human mind. From the dialogue of the mind we have built our reflection on some issues and theoretical foundations presented in Idiota. De sapientia and De docta ignorantia, extending it to little more than that. According to Nicholas of Cusa, the human mind, in its creative character in the image of the divine mind, transcends the purely functional considerations commonly assigned to it, that is, those that regard its cognitive nature and epistemological role. In addition to these aspects, Cusanus understands the humana mens as a point of articulation of two other main themes of his metaphysics: God and the world. In this context, through the concepts of complicatioexplicatio and imago, as well as with the intercession between the themes of man as imago Dei and the reason of the microcosm, we present here an introduction to Cusan metaphysics

Exploração sexual comercial de crianças e adolescentes : o estado da arte nas produções acadêmicas em psicologia

The Commercial Sexual Exploitation of Children and Adolescents (ESCCA) is a phenomenon that has been given priority in public policy agenda of many democratic governments of Western countries and civil sectors of society, besides the object of studies in different fields of knowledge. Psychology is among these areas and is considered one of the references in the construction of knowledge and actions to confront the phenomenon. However, the epistemological foundations of psychological science are quite different, and so, several are his speeches, knowledge produced and ways of conceiving man and the world. This is evident in the publications of psychology on ESCCA. This work aims to achieve a state of the art of psychology publication in Brazil (in the post-graduation - through theses and dissertations - and journals) on the Commercial Sexual Exploitation of Children and Adolescents. More specifically try to evidence (a) what conceptions of commercial sexual exploitation of children and adolescents the authors lists, (b) what are aimed at research and publications, (c) how the research and issues are justified, and (d) that theoretical approaches the authors are affiliated and methodological possibilities are applied to range the aim proposed in their work. In order to do so, a survey was conducted in the major index sites (eg, BVS-Psi, Capes, theses and dissertations database of university libraries) of the material, covering the period 1990 to 2007. Through research on these sites, we built a database, including information relating to the work sought from specific descriptors for studies in the area of victimization of children and adolescents, with reference to a list provided by Faleiros (2000). After reading the summary of the work, the number of recovered 25 productions was reached - including theses, dissertations and articles. For analysis of the material used in the analysis of thematic content. Two axes themes were established in order to guide the analysis: conceptual elements of commercial sexual exploitation, and theoretical and methodological strategies employed. The axes have as reference for analysis a chapter built on the concept of commercial sexual exploitation, so that all analysis is anchored on it. The analysis points to the existence, still strong, conceptual and terminological confusion about ESCCA. Few studies have not demonstrated this confusion, maintaining a consistent theoretical approach. In relation to the theoretical and methodological strategies, there is a great diversity of approaches in psychology surrounding the phenomenon of ESCCA, enriching levels of understanding and action. This diversity reflects a constitutive heterogeneity of psychological science. We emphasize the perspective of socio-historical psychology, most frequently among the publications. It is hoped that this research will help advance the qualitative approach to ESCCA, especially in the field of psychology, as well as contribute to new research in the area and construction of new means of addressing this human rights violation

Por trás das grades :reflexões sobre a experiência do ser apenado na situação de privação de liberdade

This research has resulted of investigations appeared from our work experience as psychologist in a prison of the state Rio Grande do Norte. It deals with the meeting with prisoner in the search for the rescue of the human being dignity, discovering the being that finds annulled by backwards of the prison. The current debate on the prisoners in Brazil has as focus the creation of efficient strategies in the combat to the criminal acts, not being worried in understanding the historical and social conditions in the context in which such acts develop. Our objective was to reach an understanding of the experience of the prisoner in the situation of freedom deprivation in Natal (RN) city. Its significant social relevance meets in emphasized thematic which intends to be revealing of the not-said one of these citizens. The epistemological space and the vision of adopted human being support in the humanist ideas of the Centered Approach in the Person and construct self, central nucleus of the personality theory proposal by Carl Rogers. We opt to the phenomenological method as way of access to the singularity of the experience of each one of the participants, supporting us in the strategy of the narrative as expression of the lived world. The results had pointed that the investigated experience is through suffering, that is, the way to be in the world of prisoner in the situation of freedom deprivation is felt by him/her as difficult to support. This reality is had by him/her as difficult to control, having a negative emotional repercussion for the self, leading the citizen to the alienation of his/her existential flow in these circumstances. The reflections produced in this work take us to consider that the punishment practices on behalf of a normalization of the behavior, linked to the recovery idea, do not meet to the intention of the arrests, that come demonstrating to the inefficacy of the objectives shown in the law as well as the loss of the human being dignity

O Turismo como um tema de pesquisa: um diálogo epistemológico a partir das produções dos programas de pós-graduação stricto sensu da Universidade Federal do Rio Grande do Norte, no período de 2007 a 2011

The study consists in an analysis of researches with tourism issues, in Master s and Doctoral level, investigating their epistemological trends, regarding the type of study that is being produced and the methods used. It is characterized as exploratory, documental and bibliographical, having undertaken a cross-sectional study which covers the period from 2007 to 2011. It analyzes the context of academically production in tourism, the nature of these researches, the methodological aspects adopted in these theses and dissertations, the philosophical inclinations and the coherence and contribution of the same. This research uses, the Digital Library of Theses and Dissertations (BDTD) and the secretariats of the Academic Centers of the Federal University of Rio Grande do Norte (UFRN) as means to collect data. It employs the technique of sampling by judgment and undertakes the research in various Academic Centers in UFRN, using the method of content analysis. It shows that, from the 643 studies analyzed, 43 of them have themes related to tourism, which characterized this study sample. This study realizes that PPGA is the largest producer of researches on tourism issues, ahead of PPGTur, which ranks the third position, in this aspect. Also realizes that all surveys analyzed are crosssectional and the theme further investigated, with 21% of the sample, is related to the marketing aspects of tourism, with the theme Directors of Hotels and Restaurants (DHR) . This research demonstrates that all sample surveys make use of interviews, and these are, mostly, structured. Also realizes that most of these studies, with 21% of the sample, employ the method of content analysis. The references in Portuguese are surveyed about five times more than the ones in other languages. It estimates that more than half of the sample is characterized as positivist, associated with aspects of functionalism. A minority of 21% of these researches seeks to identify and recommend solutions to the tourism issues, or even represent part of them. This research concludes that the studies in tourism are mostly unifocal, being driven by issues related to the touristic trade. PPGTur produces a number still unrepresentative of studies. The theses and dissertations of the sample are limited and/or unable to analyze the changes of the phenomenon caused by the time. The studies from the sample present criteria and make use of other methods and techniques to associate with the interviews and content analysis to obtain more solid and reliable data and results. They use a low number of references in languages other than Portuguese. Most of these studies, characterized as positivist-functionalist, investigate the functioning, planning, coordination and expectations in organizations, leaving aside other issues, also relevant for tourism. The number of studies aimed at identifying solutions to the problems of tourism, or that even represents part of them, is not expressive

A fábrica de professores e a padronização do conhecimento

This paper concern the general subject of teacher career construction, since the period of the initial formation in the teaching course of pedagogy crossing the first effectives experiences of professional performance, until the reflections about the results of the continuous formation propositions. The specifics subject is the formative quotidian in the teacher s life beyond of the traditional stereotypes about individuals and institutions bring up for discussion a micro sociological approach about the professionals uncertainty and the personal hopes, the teacher displeasures and the pedagogical satisfactions. The epistemological reflection about the different formatives experiences, taking as example the Programa de Formação de Alfabetizadores PROFA (Alphabetizers Formation Program) developed by the Secretaria Municipal de Educação of Natal City, consider the ambiguous tension between the knowledge that the teachers acquire in their formation and the concrete teachers practical since those experiences. The study methodology is based in the qualitative comprehensive research, sustained by observations, impressive reflective accounts, and also in the theoretic analyses with contemporary references to the critical pedagogical through and education sociology. I used the autobiographic reflective account by the writer-researcher in her owner academic and professional way. I propose an image of a teacher s factory in such a way for its conformist aspects to the continuity stands as much the internal contradictions of the system. Gears, pieces and manual instructions are the educational components of this factory as ideological, institutional and technical structures to aim at to limit the critics and the changes. However the teachers thinking and acting with their owner creativity to adapted uncontexted professional knowledge s to their pedagogical lives. Under those analogies I propose the problem of this research the teacher s formation and theirs pedagogical practices- and also examine briefly its theoretic-philosophical and methodological basis. From the analysis and interpretation of my owner experiential life as teacher s educator I put the necessity of re-thinking the teacher s formation in terms to rebound more meaningfully in their pedagogical actuation. I believe an important part of the teacher s formation process is the personal wish to learn more about the office, explicitly connected to human convictions and values such as to a positive professional identity. Thus, the teacher able to reflect about your owner educator life can find the best way to help the students to think critically about their culture and history, valorizing creative exits by themselves to face the conformist social stands connected with school education

A CRONIFICAÇÃO NOS SERVIÇOS SUBSTITUTIVOS NA REDE DE SAÚDE MENTAL DE NATAL/RN

Brazilian Psychiatry Reform, through Psychosocial Care Strategy, has intended to build insane people care practices from community care services which contemplates the subjects complete lives. However, to change the traditional care ways demands the facing of a series of epistemological, political and cultural obstacles. One of the current challenges deals with patients aggravation processes, with management ways, with devices and with professionals, as well as with the assistance network. The purpose of this thesis was to investigate how these aggravation processes has been constituted in Natal mental healthcare network, understanding its effects in the work teams and patients. Theoretical and methodological perspective used was Institutional analysis was, subsidizing the usage of concept-tools as the implication analysis, selfmanagement and self-analysis, and restitution. The research was carried out at the Natal East Sanitary District Mental Healthcare Clinic, with the participation of technicians and patients. The research procedures were: literature and document research on the attendance and the analyzed theme; attendance registers analysis; participating observation of the institutional routine for three months and field log entries; talking groups, one with the team and one with the patients. Two main discussion points are shown: 1. The mental healthcare clinic organization logic and the intersector politics; 2. The work and management processes developed at the mental healthcare clinic. The analysis show diversity in the attended demands in the service, which has favored the patients aggravation, this device and the substitute network processes. The work processes are apart from the political sphere and from the managements processes. In this sense, we show the need to reevaluate the clinic device as well as the management models adopted in the Brazilian Psychiatry Reform context

Investigando o cuidado em equipe de enfermagem em uma UBS da cidade do Natal-RN

On the health area, care is seen as an important concept for professionals. Recently there is a trend, the epistemological point of view, to think carefully as category allowing discuss and re (thinking) practices of humane health care. The objective of this study is to investigate the understanding of care in nursing staff in a Basic Health Unit (BHU) in the city of Natal. The participants were two nurses and two nursing technicians working on the BHU of Guarapes district, located on the west side of Natal - RN. As Theoretical support for data interpretation, was used the concept of care taking, using Heidegger’s theories as reference, through Ayre’s ideas. This is a qualitative research using autobiographical as a methodology. The methodological strategy approach used were focus group and individual interviews. The data were discussed by three angles: knowledge (concepts and theories behind the practical model), technical (the way to do), and ethics (values that bases practices) by hermeneutics Gadamer's dialectic. The results showed the necessity to expand the discussion on care, in practice the understanding of care seems to get narrower concerns with technical success by professionals. The care, as a meeting between beings, the desired humanized care, seems to be understood in parts in theory, but also distances itself from reality in professional practice.

A formação da habilidade de explicar no contexto do ensino médio: o que dizem os livros? o que pensam os professores?

The discussion about explanation in knowledge has been made for decades. Through this course, we present different ways of understanding about what is to explain the history: the primitive ethnographic description, the chronicler, the positivist construction of a historical science and historiography of the second half of twentieth century. Nowadays this discussion needs to be continued both in the general framework of scientific practice as within educational institutions as cognitive - linguistic ability. The focus of our research is by the second approach, which is the explanation as cognitive - linguistic ability. The formation of skills, among them, the explaining one, has been studied by the authors as: (NÚÑEZ 2012; JORBA et al, 2000; SANMARTÍ and IZQUIERDO 2000). This research had as general purpose: to study the processes of formation of the ability to explain social revolution in history classes in high school, by teachers opinion and by content as this theme among history books, in order to support the continuing education of history teachers for high school. Th e qualitative based research used instruments of data collection and analysis protocol for the books prepared for this study, and interviews with teachers. For this, the techniques of content analysis and discourse referenced in Bardin and Orlandi , respec tively were used. At first, the instruments for data collection were developed and validated, while in the second, the data were collected, organized and analyzed. From the answers to the questions of the study results shows that: a) in the analyzed books - do not express the work with the definition of Social Revolution, considering the processes for the formation of this definition, the predominant type of explanation has characteristics of multicausality; proposals for teaching are characterized as eclec tic; b) while teachers speech - it is important the students know the definition of Social Revolution, the ability to explain is more linked to didactic explanation in the classroom than the explanation through epistemological sense. These results indicate that the formation of the ability to explain Social Revolution based in Cultural History approach, are not expressed in the analyzed books, but they can serve as an important resource for this purpose. The discourse of teachers has a potential pointing to the possibility of teaching organization and learning process, based on training or upgrading the explanation skill from the theory of stepwise formation of mental actions and concepts by P.Ya. Galperin. For this purpose, the research constitutes a contri bution to support the continued education of history teachers in high school.

Cenário da produção acadêmica em história da matemática no ensino de matemática: uma análise reflexiva das teses e dissertações (1990-2010)

This research aims to make a reflective analysis about the academic production originated in the stricto sensu post graduation programs in the country, produced in the period of 1990 to 2010, in the field of History of Mathematics, especifically on works about the History of Mathematics in Mathematics education and that present pedagogical proposals that make use of the History of Mathematics in order to teach Mathematics. Defending the thesis that the researches on mathematics education with goals turned to the use of didactic proposals related to the history of mathematic that take in consideration the coherency between epistemological aspects inherent to mathematics history and anthological elements materialized on the conceptions of mathematics and mathematics history and of apprenticeship (implicitly or explicitly exposed) may originate significant contribution to the field of history of mathematics on education. Among these, nine were Master’s Degree dissertations and five PHD’s theses. The reflective analysis was accomplished from two matrixes; one from theoretical nature and the other, ontologic nature, elaborated from the pretexts of Sanches Gamboa, about the epistemological analysis from academic production in the field of Mathematics Education and the following theoretical perspectives in the field of History of Mathematics Education, that are: linear evolutionary theory, structural construtivist operative, evolutionary discontinuous, historical and socialcultural investigation and the use of activities estimulating the usage of verbal and nonverbal expressions. These perspectives were based on the works of Miguel and Miorim, Mendes and Radford. As results, we have detected some established dissonances between the categories related to theoretical and ontologic levels and the pedagogical proposal presented in these researches. On the other hand, we have discovered works that are able to establish consonances between the theoretical and ontological elements and the presented pedagogical proposal. These works carry significative contributions to the field of History of Mathematics applied to Mathematics pedagogical practice, inclusively presenting significative theoretical elements to the production of knowledge recognized as scientific in the Mathematics field