Uma reavaliação do pensamento lógico de George Boole à luz da história da matemática

The aim of the present study is to reevaluate the logical thought of the English mathematician George Boole (1815 - 1864). Thus, our research centers on the mathematical analysis of logic in the context of the history of mathematics. In order to do so, we present various biographical considerations about Boole in the light of events that happened in the 19th century and their consequences for mathematical production. We briefly describe Boole's innovations in the areas of differential equations and invariant theory and undertake an analysis of Boole's logic, especially as formulated in the book The Mathematical Analysis of Logic, comparing it not only with the traditional Aristotelian logic, but also with modern symbolic logic. We conclude that Boole, as he intended, expanded logic both in terms of its content and also in terms of its methods and formal elaboration. We further conclude that his purpose was the mathematical modeling of deductive reasoning, which led him to present an innovative formalism for logic and, because the different ways it can be interpreted, a new conception of mathematics

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

Fenótipo neuropsicológico de adolescentes com síndrome de Down

This research aimed to contribute to the characterization of a neuropsychological phenotype of adolescents with Down Syndrome (DS). A multicases study of six adolescents (three males and three females, aged 13 to 14 years) diagnosed with DS and treated at two institutions in the city of Natal (Brazil), was conducted. Participants were assessed using the methodological approach developed by Luria, which is composed by four complementary stages. The first one aimed to investigate the qualitative impact of DS in school life and social development of the adolescents; dimensions of behavior and social-affective aspects of the members of the study were investigated. In the second stage participants performed a battery of neuropsychological tests in order to identify strengths and weaknesses in their cognitive functioning. The third stage was incorporated into the second in order to analyze the quality of the activity of the participants along the quantitative evaluation, highlighting strategies used, errors produced among other indicators. Lastly, the fourth stage refers to the intervention with the participants. Although this is not a specific objective of the study, it is argued that the outcome of this research will subsidize the practice of different professionals working with this clinical group. The results of the first stage emphasized the presence of difficulties in social relationships and in school life of observed adolescents. In turn, the second and third stages pointed out to the presence of difficulties in tasks involving logical and abstract thinking, as well as difficulties in expressive language. In relation to visual memory, we observed a better performance in activities of lower complexity, ie, with less interference of executive functioning, particularly in terms of the functions of planning and initiative. Finally, it was found motor and mental retardation, affecting significantly the performance related to different cognitive areas. The results highlighted here can be considered as subsidies for future interventions, suggesting the need for developping projects that take into account different aspects constituents of the human subject, involving not only the individual with developmental changes, as well as their families, teachers, schools and society in general

O estrategista em perspectiva: um estudo sobre o processo de formação de estratégias no ramo varejista de construção civil de Natal e região metropolitana

The strategy research have been widespread for many years and, more recently, the process of formation of the strategies in the individual perspective has also gained attention in academia. Confirming this trend, the goal of this study is to discuss the process of formation of the strategies from an individual perspective based on the three dimensions of the strategic process (change, thinking and formation) proposed by De Wit and Meyer (2004). To this end, this exploratory-descriptive study used the factor analysis techniques, non-parametric correlation and linear regression to analyze data collected from the decision makers of the 93 retail in the industry of construction supplies in the Natal and metropolitan area. As a result, we have that the formation factors of the dimensions investigated were identified in the majority, thus confirming the existence of paradoxes in the strategic process, and that there is a relationship between logical thinking and deliberate formation with the hierarchical level of decision makers.

Um estudo sobre a concepção de paradoxo segundo o pensamento de Augustus de Morgan

This work aims to analyze the concept of "paradox" posed in the work of The Budget Paradox (1872) of mathematical and logical English Augustus De Morgan (1806-1871). Here it is important to note that a large part of this book consists of re-prints of a series of writings by the author in journal Athenaeum, where its performance as auditor of literature. The tests refer to some scientific work produced between the years 1489 and 1866 and the rules of selection for the composition of the work is, basically, the methodological aspects used in the completion or disclosed by such scholars. The concept of paradox is presented in two distinct moments. At first, we found a study of definitions for the term in a philosophical approach, characterizing it as something that requires further investigation; which was complemented with the classic examples of a scientific context. In the second, we present a concept advocated by De Morgan and, under this perspective, that he conceptualized the "paradox" is directly related to the non-usual methods employed in the formulation of new scientific theories. In this study some of these scientific concepts are detailed, where, through the redemption history, engaging in issues of our study Mathematics, Physics, of Logic, among others. Possession of the preliminary analysis and comparison with the design of De Morgan, it became possible to diagnose some limitations in the conceptualization suggested by the author. Further, evidenced, in front of the cases, the nonlinearity of the process of production of knowledge and hence the progress of science

Análise conceitual e pensamento crítico: uma relação complementar na enfermagem

ENDERS, Bertha Cruz ; BRITO RS ; MONTEIRO, Akemi Ywata. Analise conceitual e pensamento critico: uma relacao complementar na enfermagem. Rev Gaucha Enferm, Porto Alegre (RS) 2004 dez;25(3):295-305.

Análise conceitual e pensamento crítico: uma relação complementar na enfermagem

O propósito deste trabalho é mostrar a relação entre o processo de análise conceitual e as habilidades de pensamento crítico na enfermagem. Utilizando uma abordagem de ensaio discursivo, argumenta-se que a técnica de análise conceitual promove a criticidade em alunos de enfermagem. Os passos da atividade de análise são examinados quanto às operações cognitivas neles inseridas e que representam habilidades de raciocínio crítico. Reflete-se sobre a análise conceitual como atividade didática na promoção do pensamento crítico em uma experiência com alunos de graduação. Conclui-se que os dois processos se complementam no repensar e no enfrentamento de desafios na enfermagem

Os conflitos de competência normativa do estado regulador brasileiro no setor administrado pela ANP

The dissertation has by objective describe the administrative activity of regulation exercised by independent regulatory agencies, observing that this activity was already done before this structures creation, however, after a really deep administrative reform that had as objective built a Public Administration with more efficiency, it passed to be done with some own peculiarities of these new structures of regulation. The work gave especial attention to what concern the conflicts of normative competency that really often happen between ANP (Agência Nacional do Petróleo, Gás Natural e Biocombustíveis) and the legislatives organs of the Republic Federative of Brazil, because energetic area has unbelievable mater to any country, and the fact of some juridical norm be against the law and be accepted is very dangerous, it affronts the constitutional principle of the legality e may put in risk the democratic Estate of law, them, regulatory dogmatic must be scientifically knows, and developed, thought and especially there are so many doctrinaires divergences about regulation constitutionality. As a theorist point, the investigation got the Logical nocontradiction principle, according Hans Kelsen and Lourival Vilanova thought, doing a philosophical reflection about the system of positive law, in which there are many antinomies, or conflicts of norms, what include the conflicts of the administrative acts expedited by ANP and the legislation of the brazilian regulatory Estate. For a better understanding and exemplify some perplexities treated by the doctrinaire angle, this work did a lucubration about a possibility of a normative conflict between a ANP resolution and the municipal legislation in a specific case, also, brought several jurisprudences for the brazilians courts of justice, that confirm the empiric existence of normative conflicts among ANP s administrative norms and federal legislation. Finally, concludes observing that the regulation is not a legislative competency delegation to regulatory agencies, is just a new exercise of the administrative function, it is a technical specialization of the public administration, that using this know-how can acting with more efficiency, however the normative power of regulatory agencies must respect the empire of law, so in this terms, the dissertation suggests the ponderation of the constitutionals principles of efficiency and legality how form to harmonizing the democratic legitimate inherent to legal norm supremacy, with the perspective of an efficient economic and institutional development

Tramas da (ir)racionalidade contemporânea para a composição do mito-tecno-lógico

The plot myth-techno-logic, contemporary, was developed starting from the dualism myth-reason. In this study, we deepened the alluded dualism taking as reference the historical contexts of the Renaissance and of the Enlightenment, emphasizing the discussion of the economical rationalization as conductive thread of the western development, in which we identified the game of the rational and of the irrational, for assure the superiority of the reason. In the context of that game, we analyzed the implications of the modernization, for the education, in function of the instrumental rationality, responsible for the environment of adaptation of the technological instruments to the scenery of the contemporary modernization. The new context is constituted by points of union and of ruptures among the technique, the science and the myth. Through our analysis, we noticed that the basic needs for the contemporary society were linked to the changes in the production means, for which the machine determine the rhythm of the work and the quality of the product. However, the changes in the productive processes promoted the appearance of the commercial marks that, as we see it, they represented the synthesis of the perfect harmony of the myth, of the technique, of the science and of the technology, in the conduction of the economical rationalization to the contemporary modernization. Thus, the contemporary modernization it arrives us for the economical rationalization, developed with the support of the technician-scientific knowledge and communicated by the articulations of the myth-techno-logical

Um estudo sobre as origens da Lógica Matemáitca

The present study has as objective to explaining about the origins of the mathematical logic. This has its beginning attributed to the autodidactic English mathematician George Boole (1815-1864), especially because his books The Mathematical Analysis of Logic (1847) and An Investigation of the Laws of Thought (1854) are recognized as the inaugural works of the referred branch. However, surprisingly, in the same time another mathematician called Augutus of Morgan (1806-1871) it also published a book, entitled Formal Logic (1847), in defense of the mathematic logic. Even so, times later on this same century, another work named Elements of Logic (1875) it appeared evidencing the Aristotelian logic with Richard Whately (1787-1863), considered the better Aristotelian logical of that time. This way, our research, permeated by the history of the mathematics, it intends to study the logic produced by these submerged personages in the golden age of the mathematics (19th century) to we compare the valid systems in referred period and we clarify the origins of the mathematical logic. For that we looked for to delineate the panorama historical wrapper of this study. We described, shortly, biographical considerations about these three representatives of the logic of the 19th century formed an alliance with the exhibition of their point of view as for the logic to the light of the works mentioned above. In this sense, we aspirated to present considerations about what effective Aristotelian´s logic existed in the period of Boole and De Morgan comparing it with the new emerging logic (the mathematical logic). Besides of this, before the textual analysis of the works mentioned above, we still looked for to confront the systems of Boole and De Morgan for we arrive to the reason because the Boole´s system was considered better and more efficient. Separate of this preponderance we longed to study the flaws verified in the logical system of Boole front to their contemporaries' production, verifying, for example, if they repeated or not. We concluded that the origins of the mathematical logic is in the works of logic of George Boole, because, in them, has the presentation of a new logic, matematizada for the laws of the thought similar to the one of the arithmetic, while De Morgan, in your work, expand the Aristotelian logic, but it was still arrested to her

As aulas régias da Capitania da Bahia (1759 1827): pensamento, vida e trabalho de nobres professores

Simultanément à l' expulsion des jésuites du contrôles de l' éducaton formeI du royaume portugais, l'Ordre du 28 juin 1759 a décrété une reforme générale aux études, comme une des partie d'un ensemble de mesures modernisatoires qui ont été établisent dans le Royaume et dans ses domaines à la période comprise entre 1750 et 1777, pendant le royaume de D. José I et sous la direction de son principal ministre, Sebastião José Carvalho e MeIo, plus connu par le titre de noblesse de Marquis de Pombal. Notre thèse, locaIisée notament à la Capitanie de Bahia (Capitanie - division politique administrative du Brésil Colonie) entre les années de 1759 à 1827, a comme objet d'études les singularités du magistère bahianais et comme objectif, à partir de Ia référence théorique de l'histoire sociale des idées, comprendre comment les membres de cette nouvelle catégorie professionelle, crée pour préparés des cadres professionels mais bien qualifiés pour exercer leurs fonctions de burocratie de l'État, ont pris contact avec la pensée reforniste ilustré portugais du siècle XVIII, ont été véhiculé autant par des étrangérisés, comme par la législation pombalina (du Marquis de Pombal) et comme cet ensembIe théorique rapporté à la pensée, la vie et le travail d'enseignant de ces premiers représentants du magistère bahianais. L' analyse de la documentation (des lettres, et des ordres royals, des licences officielles pour exercer la fonction, et des serments des professeurs royal pour les plusieurs villages et capitanies; registres de correspondence reçues et envoyées par les chambres des villages; registres et correspondences expédiées par plusieurs autorités; provisions; tous les types de licences et autorisations; désignation; testament et inventaires) montre que les professeurs royals, malgré la quantité pas très nombreuses de membres, ont été extremement actifs sur les décisions les plus importantes de la période de celle qui est connue comme la crise du système colonial, qui, en Bahia, a eu ses particularités dans un mouvement d' émancipation politique seulement au mois de juillet 1823. Finallement, on a le but, dans le contenu de cette thèse de doctorat, d'offrir une connaissance sur l'histoire de l'éducation brésilienne et bahianaise qu' on retrouve encore entouré de doutes, préjugements et imterpretations équivoques qui insistent d'anaIyser le Brésil sous un stigmate du retard du royaume portugais, malgré sa production récente dans l'historiographie

Uma visita ao universo matemático de Lewis Carrol e o (re)encontro com sua lógica do nonsense

Notable mathematics teacher, Lewis Carroll, pseudonym of Charles Lutwidge Dodgson (1832-1898), made the mixture of mathematics with literature a ludic environment for learning that discipline. Author of Alice s Adventures In Wonderland and its sequel Alice Through The Looking Glass, he eventually created a real and complex universe which uses what we call the logic of the nonsense as an element to motivate the development of mathematical thinking of the reader, taking it as well, learn by establishing a link between the concrete (mathematics) and the imaginary (their universe). In order to investigate and discuss the educational potential of their works and state some elements that can contribute to a decentralized math education from the traditional method of following the models and decorate formulas, we visited his works based on the studies of archeology of knowledge (FOUCAULT, 2007), the rational thought and symbolic thinking (VERGANI, 2003) and about the importance of stories and narratives to the development of human cognition (FARIAS, 2006). Through a descriptive, analytical study, we used the literary construction and presented part of our study in form of a mathematical novel, to give the mathematical school a particular charm, without depriving it of its basics properties as discipline and content. Our study showed how the works of Carroll have a strong didactic element that can deploy in various activities of study and teaching for mathematics classes

O ensino da história e o pensamento reflexivo-crítico da professora no 3º ano do Ensino Fundamental

This collaborative research is a qualitative approach, from historical and cultural perspective, made about a teacher of third grade of basic education in the area of history, in the municipality of Caicó / RN. It has as objective to investigate, in a collaborative action, if the design process of teaching and learning the discipline of history based on the relationship before / after allows the development of critical reflective thinking of the teacher in school practices. The theoretical and methodological approaches are supported in the postulates of Vygotsky (1998), Rubinstein (1973) and Linblinskaia (1979), among others, whose understanding has led us to reflect if the teacher develops the reflective critical-thinking in history discipline classes. The complexity of the study led us to an analysis exercise, using different methodological procedures, such as: bibliographic review of the literature, considering also the literature of the history area, interviews, observation in the classroom, video recordings and reflective sessions, enabling clarify the construction and reconstruction of thought that the teacher had been developing during the process of teaching and learning. The test results point to a dichotomy between theory and practice, and also to a certain fragility in the position of professor in teaching and learning the discipline of history, at the third grade of basic education. The teacher recognizes that she requires a theoretical deepening with more intensity, as a process of continuous training to improve the practice of teaching in history school, though, stating in her speech that her teaching practice is based on critical reflection. However, she presents serious limitations in classroom practices. We conclude that, although she has shown willing to work on a critical perspective of reality, showed also poor change at school practices, starting to reflect about her own actions, pointing her limits and the changes needed that didn t become reality yet. It s necessary a formative process for her. The study therefore showed that even with the sessions and reflective of deepening theoretical studies, the teacher does not change its profile, while maintaining its traditional vision in any pedagogical action. This research recommends the formation of school groups for further studies and discussion on the practices of education in history area from a reflective-critical thought perspective as a mean of personal and professional development

Estudos da relação entre fromaçãodocente e desenvolvimento do pensamento: redimensionando o olhares

Este trabajo trata de un estudio sobre la relación entre la formación continuada de los profesores y el desarrollo del pensamiento teórico. Es nuestro objetivo comprender la relación entre la formación profesional de los profesores de los años iniciales de la Enseñanza Primaria y el desarrollo de su pensamiento. En términos específicos pretendemos reconstruir los procesos formativos de las profesoras, identificando sus necesidades y los elementos que interfieren en su práctica pedagógica; diagnosticar la fase del desenvolvimiento del pensamiento y dar inicio al proceso formativo de desenvolvimiento del pensamiento; además de analizar la conexión entre ese proceso y la elaboración conceptual, tomando como referencia el concepto de pensamiento. La referencia empírica se constituye de profesoras de la Escuela Municipal Professor Arnaldo Monteiro Natal/RN, que actúan en los grados iniciales de la Enseñanza Primaria y da Educación Infantil. Para desencadenar el proceso investigativo utilizamos como referencial teórico el materialismo histórico-dialéctico como método para análisis de los fenómenos, por entender que a través de esa lógica es que podremos buscar los elementos que nos darán sustentación a una mediación pedagógica que puede posibilitar mayor eficacia en la comprensión de los fenómenos. Recorreremos a pesquisa colaborativa, una vez que es nuestra intención desenvolver una acción investigativa compartida, teniendo en vista buscar medios para resolver los problemas que la práctica pedagógica nos impone. La investigación colaborativa posibilita al sujeto partícipe reflexionar, ser investigador y co-constructor da su práctica. Así, algunos procedimientos metodológicos fueron considerados adecuados para que pudiésemos alcanzar los resultados deseados, como Reuniones, Sondeado Diagnóstica, Ciclos de Estudios Reflexivos, Sesiones Reflexivas y la Autobiografía de Formación. Ni todas las profesoras están en el nivel de elaboración conceptual, en función del proceso vivido a lo largo de nuestras vidas, aún así, toda a trayectoria de la pesquisa posibilitó la descubierta de aspectos significativa sobre nuestro objeto de investigación. Para hacer el análisis de ese proceso nos utilizamos de las teorías de Vigotski, Guetmanova, Kopnin, Rubinstein. Podemos decir que, en la perspectiva de la colaboración, la reflexión sobre la práctica puede desencadenar una nueva mirada del profesor sobre su proceso de formación, el desenvolvimiento de su pensamiento y la acción desarrollada con su alumno. No fue posible verificar, en la práctica, los resultados de nuestro trabajo, ya que, ese no era nuestro objetivo, mas nuestras fallas presentan mudanzas teóricas significativas. Entretanto, resaltamos que las conclusiones a que llegamos están lejos que se acaben , una vez que es un tema complejo, que puede posibilitar el surgimiento de nuevos estudios, de nuevas pesquisas, de nuevos conocimientos

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