A principal ocupação de nossa pesquisa foi a de elencar e de relacionar elementos teóricos que ajudassem a nós, professores de Física, compreender o potencial didático atrelado às diferentes abordagens frequentemente usadas para atividades experimentais em sala de aula. Com isso, esperávamos obter um caminho teoricamente fundamentado, capaz de subsidiar um planejamento consistente para o uso dessa estratégia em sala de aula, um planejamento que levasse em conta as características epistemológicas e operacionais da atividade escolhida. Nossa aposta inicial era a de que elas (as atividades experimentais) poderiam ser mais bem aproveitadas, em termos didáticos, se fossem usadas no contexto de uma situação-problema. Acreditávamos ser a situação-problema em ensino uma modalidade que viabilizaria a inclusão simultânea dos dois aspectos citados (epistemológico e operacional), o que, a nosso ver, configuraria o uso mais abrangente de atividades experimentais no âmbito escolar. De início realizamos uma revisão de elementos teóricos relacionados tanto às estratégias estudadas - atividade experimental e situação-problema -, como ao tipo de ensino que tais estratégias poderiam, de acordo com a literatura examinada, promover: um ensino conceitual aprofundado com enfoque no desenvolvimento de habilidades e na construção de competências. Paralelamente à revisão, escolhemos as teorias de Chevallard (teoria da transposição didática e teoria antropológica do didático) para entender de que forma o saber expresso por uma prática social poderia ser conciliado com a atividade experimental eleita como modeladora da situação-problema a ser planejada. Em um próximo momento elaboramos, com base na análise feita até esse ponto e na literatura levantada sobre justificativas didáticas para atividades experimentais, categorias de classificação para o uso escolar de atividades experimentais. As categorias foram agrupadas em duas dimensões: de contexto social e de contexto didático. A discussão teórica e a elaboração de categorias abriram caminho para uma reflexão sobre quais seriam os questionamentos básicos que sustentariam o planejamento de uma situação-problema centrada em uma atividade experimental. Finalmente, como último passo, utilizamos a análise e a discussão realizada para avaliar a proposta de atividades experimentais da forma como elas estão apresentadas em dois livros didáticos aprovados no Programa Nacional do Livro Didático (PNLD), e também para examinar dois artigos que discutem o uso de atividades experimentais no ensino. O referencial teórico adotado parece apontar como viável e promissora a união das duas estratégias: atividade experimental e situação-problema. No entanto, os recursos apresentados em livros didáticos e artigos afins não atendem aos requisitos de um planejamento que considera os elementos propostos em nossa pesquisa e exigem do professor, além de muita criatividade, um trabalho intenso de pesquisa, estudo e investigação. / The main occupation of our research was to list and to relate theoretical elements which could help us, physics\' teachers, to comprehend the didactical potential coupled to the different approaches frequently assigned to experimental activities in the classroom. By doing that, we expected to obtain a theoretically reasoned path, which could, in turn, support a solid planning to use this strategy in the classroom; a planning which took into account the epistemological and operational features of the chosen activity. Our first bet was that they (experimental activities) could be better harnessed, in didactical terms, if they were used in the context of a problem-situation. We believed that a problem-situation in school was the kind of modality which would enable the simultaneous inclusion of the two mentioned aspects (epistemological and operational), which, in our point of view, would set the more extensive use to experimental activities in the school scope. Initially, we conducted a review of theoretical elements relating to both the strategies studied - experimental activity and problem-situation - as well as the type of teaching that such strategies could, according to the literature examined, promote: a conceptual depth teaching with a focus on developing skills and building competencies. Alongside the review, we chose Chevallard\'s theories (theory of didactic transposition and anthropological theory of the didactic) to understand how knowledge supported by a social practice could be reconciled with the experimental activity elected as modeler of the problem-situation to be planned. As a next step, we designed, based on the analysis done up to this point and in the selected literature on the didactical reasons for experimental activities, classification categories to the educational use of experimental activities; the categories were grouped into two dimensions: the social context and the learning context. The theoretical discussion and elaboration of categories paved the way for a reflection on what should be the inquiries which would underpin the planning of a problem-situation centered in an experimental activity. Finally, as a last step, we used the analysis and discussion conducted to evaluate the proposal for experimental activities as they are presented in two textbooks approved by Programa Nacional do Livro Didático PNLD, and also to examine two articles that discuss the use of experimental activities in education. The theoretical framework adopted seems to point out as feasible and promising the union of these two strategies: experimental activity and problem-situation. However, contents in textbooks and related articles do not meet the requirements of a planning which considers the elements suggested in our research and thus, would require the teacher, beyond a lot of creativity, an intense work of research, study and quest.

A principal ocupação de nossa pesquisa foi a de elencar e de relacionar elementos teóricos que ajudassem a nós, professores de Física, compreender o potencial didático atrelado às diferentes abordagens frequentemente usadas para atividades experimentais em sala de aula. Com isso, esperávamos obter um caminho teoricamente fundamentado, capaz de subsidiar um planejamento consistente para o uso dessa estratégia em sala de aula, um planejamento que levasse em conta as características epistemológicas e operacionais da atividade escolhida. Nossa aposta inicial era a de que elas (as atividades experimentais) poderiam ser mais bem aproveitadas, em termos didáticos, se fossem usadas no contexto de uma situação-problema. Acreditávamos ser a situação-problema em ensino uma modalidade que viabilizaria a inclusão simultânea dos dois aspectos citados (epistemológico e operacional), o que, a nosso ver, configuraria o uso mais abrangente de atividades experimentais no âmbito escolar. De início realizamos uma revisão de elementos teóricos relacionados tanto às estratégias estudadas - atividade experimental e situação-problema -, como ao tipo de ensino que tais estratégias poderiam, de acordo com a literatura examinada, promover: um ensino conceitual aprofundado com enfoque no desenvolvimento de habilidades e na construção de competências. Paralelamente à revisão, escolhemos as teorias de Chevallard (teoria da transposição didática e teoria antropológica do didático) para entender de que forma o saber expresso por uma prática social poderia ser conciliado com a atividade experimental eleita como modeladora da situação-problema a ser planejada. Em um próximo momento elaboramos, com base na análise feita até esse ponto e na literatura levantada sobre justificativas didáticas para atividades experimentais, categorias de classificação para o uso escolar de atividades experimentais. As categorias foram agrupadas em duas dimensões: de contexto social e de contexto didático. A discussão teórica e a elaboração de categorias abriram caminho para uma reflexão sobre quais seriam os questionamentos básicos que sustentariam o planejamento de uma situação-problema centrada em uma atividade experimental. Finalmente, como último passo, utilizamos a análise e a discussão realizada para avaliar a proposta de atividades experimentais da forma como elas estão apresentadas em dois livros didáticos aprovados no Programa Nacional do Livro Didático (PNLD), e também para examinar dois artigos que discutem o uso de atividades experimentais no ensino. O referencial teórico adotado parece apontar como viável e promissora a união das duas estratégias: atividade experimental e situação-problema. No entanto, os recursos apresentados em livros didáticos e artigos afins não atendem aos requisitos de um planejamento que considera os elementos propostos em nossa pesquisa e exigem do professor, além de muita criatividade, um trabalho intenso de pesquisa, estudo e investigação. / The main occupation of our research was to list and to relate theoretical elements which could help us, physics\' teachers, to comprehend the didactical potential coupled to the different approaches frequently assigned to experimental activities in the classroom. By doing that, we expected to obtain a theoretically reasoned path, which could, in turn, support a solid planning to use this strategy in the classroom; a planning which took into account the epistemological and operational features of the chosen activity. Our first bet was that they (experimental activities) could be better harnessed, in didactical terms, if they were used in the context of a problem-situation. We believed that a problem-situation in school was the kind of modality which would enable the simultaneous inclusion of the two mentioned aspects (epistemological and operational), which, in our point of view, would set the more extensive use to experimental activities in the school scope. Initially, we conducted a review of theoretical elements relating to both the strategies studied - experimental activity and problem-situation - as well as the type of teaching that such strategies could, according to the literature examined, promote: a conceptual depth teaching with a focus on developing skills and building competencies. Alongside the review, we chose Chevallard\'s theories (theory of didactic transposition and anthropological theory of the didactic) to understand how knowledge supported by a social practice could be reconciled with the experimental activity elected as modeler of the problem-situation to be planned. As a next step, we designed, based on the analysis done up to this point and in the selected literature on the didactical reasons for experimental activities, classification categories to the educational use of experimental activities; the categories were grouped into two dimensions: the social context and the learning context. The theoretical discussion and elaboration of categories paved the way for a reflection on what should be the inquiries which would underpin the planning of a problem-situation centered in an experimental activity. Finally, as a last step, we used the analysis and discussion conducted to evaluate the proposal for experimental activities as they are presented in two textbooks approved by Programa Nacional do Livro Didático PNLD, and also to examine two articles that discuss the use of experimental activities in education. The theoretical framework adopted seems to point out as feasible and promising the union of these two strategies: experimental activity and problem-situation. However, contents in textbooks and related articles do not meet the requirements of a planning which considers the elements suggested in our research and thus, would require the teacher, beyond a lot of creativity, an intense work of research, study and quest.

Dans ce travail de recherche, nous nous intéressons à une étude didactique de l’arithmétique au sens de théorie élémentaire des nombres dans l’objectif d'étudier certains choix de l'enseignement de l’arithmétique en France depuis le début du XX° siècle et d'identifier certaines contraintes institutionnelles après la réintroduction de l’arithmétique dans l’enseignement secondaire au début du XX1° siècle, ainsi que les effets de ces contraintes sur la pratique des enseignants et les acquis des élèves. Nous avons tout d'abord conduit une analyse épistémologique pour décrire les organisations mathématiques et les choix de définitions dans le savoir savant, que nous avons complété par un état des lieux sur les travaux antérieurs dans le monde anglo-saxon d’une part, et dans les travaux français d’autre part. Nous conduisons ensuite une analyse institutionnelle de l’arithmétique dans une perspective écologique pour dégager les différents systèmes de contraintes et de conditions qui pèsent sur les évolutions de ce savoir au cours du processus de transposition didactique interne, en analysant les programmes et les manuels dans deux institutions : au collège et en classe de seconde à partir de la réforme de 1902, jusqu’en 2010. Nous cherchons dans les programmes et les manuels des traces des organisations mathématiques de référence au collège et en classe de seconde pour l’objet d’arithmétique et les différents types de définitions. Nous poursuivons par une étude des rapports personnels des enseignants et des élèves aux objets de savoir en jeu en classe de seconde, pour confronter ensuite les réponses des enseignants avec la réponse de leurs élèves. Nos travaux montrent une très grande instabilité des contenus d’arithmétique dans le curriculum français au collège et à la transition collège/ lycée. / In this research, we are interested in a didactic study of the arithmetical contents, where arithmetic refers to elementary theory of numbers. We aimed to study choices of the teaching of arithmetic in France from the early XXth century and to identify institutional constraints for the reintroduction of arithmetic in the secondary education that occurred in the early XXIth and their effects on teaching practices and students’ experiences. First, we lead an epistemological analysis to describe the different mathematical organizations, and definitions that should be chosen for the teaching of arithmetic that we have completed with a review of previous researches in the Anglo-Saxon world on one hand, and in the French works on the other hand. We lead then an institutional analysis of the arithmetic in an ecological perspective to reveal different systems of constraints and conditions that should have an influence on the evolutions of this knowledge during the process of internal didactic transposition, by analyzing the programs and the textbooks in two institutions: Middle school and the fifth year of High school, from the reform of 1902 till 2010, tracking the mathematical organizations and the definitions. Second, we lead a study of the personal relationships of teachers and students regarding the arithmetical concepts involved in fifth year of high school through two questionnaires, including a comparison between teachers’ answers and the answers of their own pupils. A main result of our research is the great instability of the arithmetical content in the French curriculum at Middle school and at the transition from Middle school into High school.

La thèse étudie l'évolution sous contraintes du milieu que se donnent les élèves dans les cadres des premiers moments d'une activité d'étude et de recherche sur les équations du premier degré à une inconnue en classe de 4°. Le dispositif d'observation - analyses mathématique et didactique a priori soutenant la proposition d'activité, mise en place de groupes au sein des classes, films des interactions au sein du processus de recherche - recourt à une méthodologie de type clinique. Elle autorise une analyse micro-didactique qui, utilisant les récents développements de la théorie Anthropologique du didactique, conclut à la différenciation des milieux, des temporalités et des fonctions au sein des groupes observés et un enrichissement du concept de mémoire didactique. / The thesis studies the evolution under constraints of the milieu that pupils give themselves in the frames of the first moments of an activity of study and research on single-unknown equations of the first degree in class of 4 °.The observation device - a priori mathematical and didactical analyzes supporting the activity proposal, setting up groups within the classes, films of the interactions within the research process - resorts to a methodology of the clinical type. It allows a micro-didactic analysis which, using the most recent developments of the anthropological theory of didactics, concludes with the differentiation of the environments, the temporalities and the functions within the groups observed and an enrichment of the concept of didactic memory.

The article actualizes the system of preparatory pre-school education as a subsystem of education that lacks theoretical management and administration conceptions. It is explained that due to this reason with respect to management processes of educational reform of Lithuania the system of preparatory pre-school education becomes dysfunctional and does not respond to the general trend of changes in education. The thesis discloses theoretical-praxeological bases of management of preparatory pre-school education system, which have self-contextualised in the modern policy of education of Lithuania. With this aim the author of the thesis uses post-modern instruments of social sciences and the humanities and formulates the idea about the necessity of new type managerial knowledge, while making political decisions regarding managerial strategies of preparatory pre-school education and other subsystems of education. Based on the results of qualitative content analysis, which showed up carrying out the analysis of the most important documents on education of modern post-reform period of Lithuania, the following is concluded: to manage preparatory pre-school education system both general and special managerial principles, which are suitable for management of localized subsystems of education in policy change processes, can be applied. The thesis proves that the management of preparatory pre-school education system must be perceived through the paradigms of systemic change of its... [to full text] / Disertacijoje aktualizuojama priešmokyklinio ugdymo sistema, kaip švietimo grandis, stokojanti vadybos ir valdymo teorinių koncepcijų. Aiškinama, jog dėl šios priežasties Lietuvos švietimo reformos valdymo procesuose priešmokyklinio ugdymo sistema tampa disfunkcine ir neatliepia bendrajai švietimo kaitos krypčiai. Disertacijoje atskleidžiami priešmokyklinio ugdymo sistemos valdymo teoriniai-prakseologiniai pagrindai, kurie kontekstualizavosi šiuolaikinėje Lietuvos švietimo politikoje. Tuo tikslu disertacijos autorius naudoja socialinių-humanitarinių mokslų postmodernistinį instrumentarijų ir formuluoja idėją apie naujo pobūdžio vadybinių žinių būtinumą, priimant politinius sprendimus dėl priešmokyklinio ugdymo ir kitų švietimo posistemių valdymo strategijų. Remiantis kokybinio tyrimo rezultatais, kurie išryškėjo atliekant svarbiausių Lietuvos šiuolaikinio poreforminio laikotarpio švietimo dokumentų analizę, formuluojama išvada: priešmokyklinio ugdymo sistemai valdyti galima taikyti tiek bendruosius, tiek specialiuosius vadybinius principus, tinkančius lokalizuotų švietimo sistemos grandžių valdymui politikos kaitos procesuose. Disertacijoje įrodoma, kad priešmokyklinio ugdymo sistemos valdymą būtina suvokti per jos funkcijų sisteminės kaitos paradigmas, orientuojantis į societarinį, sisteminį, institucinį, interpersonalinį bei intrapersonalinį lygmenis, jų tarpusavio sinerginius ryšius, priešmokyklinio ugdymo kaip posistemės bei švietimo sistemos kaitą.

Cette recherche se situe dans le cadre de la théorie anthropologique du didactique (TAD) et a pour point de départ le constat d’une inégale diffusion des connaissances mathématiques opérationnelles dans les sociétés contemporaines. Au contraire des explications spontanées qui voient l’origine de ce phénomène dans une « propriété » des individus, dont beaucoup seraient rétifs, par nature ou par expérience, au « fait mathématique », cette recherche regarde de telles manifestations comme des symptômes individuels dont il s’agit d’étudier les causes à la lumière de la didactique entendue comme science des conditions et contraintes de tous niveaux déterminant la diffusion (et la non-diffusion) des connaissances. Les résultats obtenus permettent d’envisager une nouvelle définition du contrat gouvernant le rapport des personnes et des institutions à leurs besoins mathématiques. / The framework of this research is the anthropological theory of the didactic (ATD). It takes as its starting point the uneven diffusion of a working knowledge of mathematics in contemporary societies. Unlike most spontaneous causal explanations in terms of “properties” of individuals, many of whom are thought to be averse to mathematics (either by nature or experience), this research construes such manifestations as individual symptoms to be interpreted in the field of didactics, regarded as the science of the conditions and constraints of all levels that determine the diffusion (and nondiffusion) of knowledge. The results arrived at allow us to contemplate the possibility of reconfiguring the relation of persons and institutions to their mathematical needs.

Made available in DSpace on 2016-04-27T17:13:01Z (GMT). No. of bitstreams: 1 Luis Cesar Friolani.pdf: 6668241 bytes, checksum: 46895869e526f407572fc9d5867fbbc0 (MD5) Previous issue date: 2007-05-14 / Made available in DSpace on 2016-08-25T17:25:36Z (GMT). No. of bitstreams: 2 Luis Cesar Friolani.pdf.jpg: 3447 bytes, checksum: 02ba6555a715f9f4f1034dfd61fb2185 (MD5) Luis Cesar Friolani.pdf: 6668241 bytes, checksum: 46895869e526f407572fc9d5867fbbc0 (MD5) Previous issue date: 2007-05-14 / Secretaria da Educação do Estado de São Paulo / Our research had as its aims to verify the organisation of Middle-school mathematics textbooks (Grades 5 to 8) in relation to the topic Data Handling, analyse whether this organisation favours the construction of stochastic thinking and to examine whether the textbooks follow the orientation proposed in the PCN (National Curriculum Parameters). Given that the textbook tends to be the principal pedagogic support used by teachers (Lajolo, 1996 and Dante, 1996), we analyse three textbook collections using as our basis the idea of praxeological organisation (Chevallard, 1995), which involves identifying the tasks, the techniques and the theoretical-technological discourse. We also analyse the levels of statistical literacy, which, according to Shamos (1995), can be classified as cultural, functional e scientific. The results of the research indicate little exploration on the part of the authors in relations to the topic of Data Handling / Nossa pesquisa teve como objetivo verificar qual a organização que os livros didáticos do Ensino Fundamental (5ª a 8ª série) fazem, referente ao tema Tratamento da Informação e se essa organização favorece a construção do pensamento Estocástico e também se eles atendem às orientações propostas pelos PCN. Sendo o livro didático o principal apoio pedagógico dos professores (Lajolo, 1996 e Dante, 1996), analisamos três coleções de livros didáticos segundo a Organização Praxeológica (Chevallard, 1995), em que buscamos identificar as tarefas, as técnicas e o discurso teórico-tecnológico, bem como o nível de letramento estatístico que, segundo Shamos (1995), se classifica em cultural, funcional e científico. Porém os resultados dessa pesquisa indicam a pouca exploração por parte dos autores em relação ao tema Tratamento da Informação

Made available in DSpace on 2016-04-27T17:13:05Z (GMT). No. of bitstreams: 1 Fernando de Simone Neto.pdf: 2174759 bytes, checksum: b215fe75b93caa251c4e99321276d818 (MD5) Previous issue date: 2008-12-27 / Made available in DSpace on 2016-08-25T17:25:35Z (GMT). No. of bitstreams: 2 Fernando de Simone Neto.pdf.jpg: 3620 bytes, checksum: dd457ce0cb0e09276d5bad01b55addf2 (MD5) Fernando de Simone Neto.pdf: 2174759 bytes, checksum: b215fe75b93caa251c4e99321276d818 (MD5) Previous issue date: 2008-12-27 / In this study we have the target of analyzing the Statistics teaching in the High School textbooks approved by PNLEM (2006), and if these ones follow the official recommendations for the High School level. We analyzed six collections according to the Praxeological Organization (Chevallard 1999) considering the mathematical organization suggested by him. Regarding this, we will analyze the tasks, techniques and the theoretical-technological discourse, to verify if it makes the development of statistical literacy possible and the level that the student is able to achieve with the activities inside the textbooks: cultural, functional or scientific. Through the analysis done, we aimed to identify the didactic organization proposed in the textbooks concerning the statistical concepts, to verify if they help the development of statistical literacy, in terms of proportion and distribution of contents. We tried thus, to understand the option of syllabus developed in the didactic collections regarding statistics. We observed that four from the six collections analyzed make possible the achievement of the cultural level of statistical literacy. One collection achieves the cultural level very close to the functional one and another one the functional level that is satisfactory. We can conclude, through this analysis, that the majority of the textbooks indicated for the High School level are not in accordance with the official recommendations and do not develop the skills to interpret, evaluate and discuss data. Consequently, the student will not be able to take decisions concerning daily situations if he depends on the knowledge acquired from these textbooks only / Neste estudo temos o intuito de analisar o ensino da Estatística nos livros didáticos do Ensino Médio aprovados pelo PNLEM (2006), e se estes seguem as recomendações oficiais para o Ensino Médio. Foram analisadas seis coleções segundo a Organização Praxeológica (Chevallard 1999) considerando a organização matemática por ele sugerida. Em relação a esta, analisaremos as tarefas, técnicas e o discurso teóricotecnológico, para verificar se possibilita o desenvolvimento do letramento estatístico e qual nível o aluno tem condições de atingir com as atividades contidas no livro didático: cultural, funcional ou científico. Por meio das análises feitas, procuramos identificar a organização didática das propostas dos livros didáticos em relação aos conceitos estatísticos, para verificar se elas ajudam a desenvolver a construção do letramento estatístico, em termos de proporção e distribuição de conteúdos. Tentamos assim, compreender a opção de currículo desenvolvida nas coleções didáticas em relação à Estatística. Observamos que quatro das seis coleções analisadas possibilitam que se atinja o nível cultural do letramento estatístico. Uma coleção atinge o nível cultural muito próximo do funcional e a outra o nível funcional que é o satisfatório. Podemos concluir, por meio das análises, que a maioria dos livros didáticos indicados para o Ensino Médio não estão de acordo com as recomendações oficiais e não desenvolvem as competências para interpretar, avaliar e discutir dados. Conseqüentemente, o aluno não estará apto a tomar decisões no que diz respeito a situações cotidianas se depender apenas do conhecimento adquirido por meio desses livros

Made available in DSpace on 2016-04-27T16:58:41Z (GMT). No. of bitstreams: 1 Keiji Nakamura.pdf: 1405144 bytes, checksum: 8b57bd3e002695a33fe5b4bdbf0840e3 (MD5) Previous issue date: 2008-05-30 / Sociedade de Cultura e Educação do Litoral Sul / The main objective of this work is to investigate the difficulties that appeared along the history for the development of the mathematical content irrational numbers and which are the approaches present in the text books. The subject irrational numbers is considered important in the basic education of Mathematics and it comes for the students, in the text books, as an obstacle to its full understanding. One of the aspects that can justify such situation is the complexity that the subject shows. However, the irrational number can be worked in a historical-epistemological process, by doing a study of how the transformation of scientific object to an object of teaching in a praxeological organization has been processing. That organization is the final result of a mathematical activity that presents two inseparable aspects: the mathematical practice, that consists of tasks and techniques, and the speech based on that practice that is constituted by technologies and theories. Our analyses point that factors exist which interfere in the process of teaching-learning of irrational numbers related with the praxeological organization of that content in the collections of the text books of the 70s, 90s and 2000. The proof of the irrationality with traditional Euclidian approach served as parameter to evaluate the degree of difficulty and to analyze the type of tasks, techniques and the theoretical-technological speech for the demonstration of the irrational number. The organization points that the most difficulty is in the axiomatic system that should satisfy to two conditions: to be solid, it means, the postulates cannot contradict each other for themselves or for their consequences; to be complete and enough, in the sense of having conditions to prove true or false all propositions formulated in the context of the theory in subject. The proof of the irrationality in a modern Dedekind approach analyzed by the type of tasks, techniques and for the theoretical-technological speech enlarges the numeric domain, joining to the rational numbers a new category of irrational numbers that fill out the gaps of the numeric straight line. To build techniques to modify and to enlarge the concept of irrationality of other numbers is an approach that explores numbers in the form a+b√2, with rational a and b, and that contributes to overcome the idea that there are few irrational numbers / O objetivo principal deste trabalho é investigar as dificuldades que surgiram ao longo da história para o desenvolvimento do conteúdo matemático números irracionais e quais a abordagens estão presentes nos livros didáticos. O assunto números irracionais é considerado importante na escolaridade básica de Matemática e apresenta-se para os alunos, nos livros didáticos, como um obstáculo a sua plena compreensão. Um dos aspectos que pode justificar tal situação é a complexidade com que esse assunto se manifesta. No entanto, o número irracional pode ser trabalhado em um processo histórico-epistemológico, fazendo-se um estudo de como se tem processado a transformação de objeto científico a objeto de ensino em uma organização praxeológica. Essa organização é o resultado final de uma atividade matemática que apresenta dois aspectos inseparáveis: a prática matemática, que consta de tarefas e técnicas, e o discurso fundamentado sobre essa prática, que é constituída por tecnologias e teorias. Nossas análises apontam que existem fatores os quais interferem no processo de ensino-aprendizagem de números irracionais relacionados com a organização praxeológica desse conteúdo nas coleções dos livros didáticos dos anos 70, 90 e 2000. A prova da irracionalidade com abordagem tradicional euclidiana serviu de parâmetro para avaliar o grau de dificuldade e analisar o tipo de tarefas, técnicas e o discurso teórico-tecnológico para a demonstração do número irracional. A organização aponta que a maior dificuldade está no sistema axiomático que deve satisfazer a duas condições: ser consistente, quer dizer, os postulados não podem contradizer uns aos outros por si mesmos ou por suas conseqüências; ser completo e suficiente, no sentido de se ter condições para provar verdadeiras ou falsas todas proposições formuladas no contexto da teoria em questão. A prova da irracionalidade em uma abordagem moderna dedekindiana analisada pelo tipo de tarefas, técnicas e pelo discurso teórico-tecnológico amplia o domínio numérico, juntando aos números racionais uma nova categoria de números irracionais que vêm preencher as lacunas da reta numérica. Construir técnicas para modificar e ampliar o conceito de irracionalidade de outros números é uma abordagem que explora números na forma a+b2, com a e b racionais, e que contribui para a superação da idéia de que há poucos números irracionais

The general purpose of this thesis is to contribute to further understanding of the academic appointment process explored and defined as participation in a collegial educational process. The appointment process for academic positions has historically been regulated by state authorities ever since the first university was established in Sweden and has continuously been questioned for necessity, procedure etc. The object of study is the appointment process focusing the consideration of teaching skill in appointing academic teachers. A theoretical construction is used as a method in order to grasp what the experts and applicants consider. The thesis draws theoretical inspiration from the French sociologist Pierre Bourdieu especially his work on social practice and his explanations within praxeological knowledge. In this thesis cultural capital, habitus and doxa are used as concepts for constructing a social practice. Inspired by Bourdieu’s concepts, the appointment process is made visible grounded on documentation: judgments of qualifications written by external experts and the applicants’ documentation in their applications. The empirical material on merits is analyzed according to Bourdieu’s indicators on symbolic capacities. The disposition of habitus (as an inner organizing principle) is limited to cultural capital and background demographic data. The indicators on scientific skill are also transmitted into symbolic capacities on teaching skill. Three appointments as assistant professors are analyzed, framed by information on advertisement, description of documentation, time lapse and final decision in appointment committees. The main conclusions are that the experts select whom to appoint using their practical sense unaware of the driving forces, explained as social practice. The experts act in line with the purpose of the assignment and they follow all the rules and instructions. Teaching skill is focused by the applicants and experts as practical mastery in the subject field (pedagogical authority). Selection is explained by the concept of habitus. Another conclusion is the tendency to “nuanced” co-optation similar to when appointments were made by self selection and teaching ability was important in early 19th century. A final conclusion is that in positioning of arguments in shared beliefs (doxa) in questioning the appointment process, researchers in the early years of this century represent heterodox opinions.