The aim of this study is to examine (from a didactic perspective) how two social studies teachers who work in two different elementary schools, grade three, pursue their oral instructions with subject terms. We have selected these four following questions as main evaluation points throughout the study, basing our conclusion upon the information composed from the answers: Which of the five “conceptions of high order thinking” do the teachers value as the purpose for the teaching content? How do the teachers in their use of notions relate to the needs of second language students and how do they reflect on it? How do the teachers use subject-specific notions in their teachings practices? How are students given the opportunity to use, communicate and integrate around notions and how are the teachers reflecting on it? In this study we applied two types of qualitative methods. Six observations combined with interviews in the form of four short unstructured interviews and an in-depth interview with each teacher. Previous research shows that great linguistic skills are a common factor for success in all subjects. Our investigation has been made from a sociocultural theory that promotes learning through interaction with others as well as by receiving support from the teacher, through scaffolding. Our result indicates, in conclusion that the number of second language learners in the class has an impact on how actively the teachers work to concretize abstract notions. The student population determines how they in teaching practices use notions. Social issues also decided how the teachers gave students room to use notions. For teacher no. 2 who worked in an environment where the second language students were a majority, a second language perspective was an obvious matter, whereas teacher no. 1 considered it to be a management issue and a collective responsibility.

Student Number: 0111229X. PhD Thesis. Faculty of Science. School of Education / This study is part of a larger national study, the Learners’ Perspectives Study. The main focus of this particular study is to explore, describe and explain learners’ perspectives regarding the incorporation of the everyday in mathematics. Two Grade 8 mathematics classrooms in two different schools, Umhlanga and Settlers are used as sites for empirical data. Learners’ perspectives are sought through a series of post-lesson interviews with different groups of learners for lessons in which the everyday was summoned for a mathematics lesson. During these interviews, learners whether 1. They welcomed or appreciated the use of the everyday in class or not and 2. The everyday inhibited or enabled easy access to mathematics content. In order to understand the background against which these perspectives are held, mathematics lessons wherein the everyday was incorporated were observed, recorded and transcribed. In addition, teachers’ views about these lessons were explored through interviews and activities which incorporated the everyday were analysed. I used Bernstein’s notions of classification and framing as a theoretical lens through which to account for my observations. It became necessary though, to supplement these through Dowling’s domains of text analysis (esoteric, expressive, public and descriptive). I also introduced the notion of authentic/inauthentic and close/far descriptions. It is a combination of these three broad theoretical frameworks which assisted in the provision of a comprehensive theoretical account. The significance of mathematics-everyday aspect in mathematics education is highlighted by the number of studies, as discussed in the study, and different orientations from which this aspect is engaged. What can be teased out of these studies is that mathematics education debates are seldom informed by the learners’ perspectives. The study suggests that most of the learners who participated in the interviews welcomed and appreciated the use of the everyday in mathematics. However, most learners (particularly from Umhlanga) viewed mathematics as a platform to raise genuine concerns about the everyday used. In contrast, some learners (particularly from Settlers) viewed the everyday as vehicles or see-throughs towards the mathematics content. What this study viii suggests is that, firstly, the everyday is multifaceted and the nature of the context summoned tends to influence views learners hold about the role of the everyday in mathematics. Secondly, the study suggests that learners’ perspectives about the everyday cannot be divorced from the classroom context in which they encounter these everyday contexts.

Este trabalho aborda aspectos básicos do cálculo de probabilidades em espaço finito de probabilidade, aplicados a eventos como lançamentos de moedas, jogos de pôquer, loterias, problemas de nascimento de crianças e problemas com urnas, e tem como objetivo principal exibir, em cada fenômeno aleatório, o espaço finito de probabilidade que é o modelo probabilístico do fenômeno. Em cada exemplo de aplicação, foram definidos os espaços amostrais e a função de probabilidade correspondente, além do evento cuja probabilidade é a resposta do problema apresentado. A visualização concreta do espaço dos eventos associado a um processo aleatório facilita a compreensão do cálculo de probabilidades. / This dissertation approaches basic aspects of the probability calculus in finite probability space, applied to events such as coins tosses, poker matches, lotteries, birth problems and problems with voting machines, and it aims at displaying in each random phenomenon, the finite probability space which is the probability model of the phenomenon. In each working example, the sample spaces and their corresponding probability function have been defined, besides the event whose probability is the response of the problem presented. The concrete visualization of the space of events associated with a random process facilitates the understanding of the probability calculus.

Submitted by Jean Medeiros (jeanletras@uepb.edu.br) on 2016-03-23T13:46:36Z No. of bitstreams: 1 PDF - Cícero dos Santos.pdf: 10392440 bytes, checksum: 7d26458c22e6a36db9fd4f916e5b62c8 (MD5) / Approved for entry into archive by Secta BC (secta.csu.bc@uepb.edu.br) on 2016-07-22T15:11:03Z (GMT) No. of bitstreams: 1 PDF - Cícero dos Santos.pdf: 10392440 bytes, checksum: 7d26458c22e6a36db9fd4f916e5b62c8 (MD5) / Made available in DSpace on 2016-07-22T15:11:12Z (GMT). No. of bitstreams: 1 PDF - Cícero dos Santos.pdf: 10392440 bytes, checksum: 7d26458c22e6a36db9fd4f916e5b62c8 (MD5) Previous issue date: 2014-08-29 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / It is notorious the importance of a good geometric vision in the study of certain contents, especially when they are related to Mathematics. In the exact sciences, among the contents that most demanding such vision is the Calculus. This important branch of mathematics is so feared by university students who became the object of study by some researchers. It is not for nothing that the Calculus is a major disciplines responsible for the high levels of disapprovals. Against this reality, this work propose the insertion of notions of Calculus in high school with an approach taken by Winplot software, because we believe that to relate the teaching learning to the use of a appropriate software, we can obtain a better comprehension and, therefore, a reduction in the indices of disapproval of this matter. In the intention to verify the e ectiveness of the proposal, we work with a class of 3rd grade of high school, between April and May 2014. Finally we analyzed this experience and found the e ectiveness of our proposal, with regard to the inclusion of notions Calculus in high school. / É notória a importância de uma boa visão geométrica no estudo de certos conteúdos, sobretudo, quando estes estão relacionados à Matemática. Na área de exatas, dentre os conteúdos que mais exigem tal visão, está o Cálculo. Este importante ramo da Matemática é tão temido por universitários que se tornou objeto de estudo de alguns pesquisadores. Não é a toa que o Cálculo é uma das principais disciplinas responsáveis pelos altos índices de reprovações. Diante dessa realidade, este trabalho propõe a inserção de Noções de Cálculo no Ensino Médio com uma abordagem feita através do software Winplot, pois acreditamos que, ao relacionarmos o ensino-aprendizagem à utilização de um software adequado, podemos obter uma melhor compreensão e, por conseguinte, uma redução nos índices de reprovação. Na intenção de verificar a eficácia da proposta, trabalhamos com uma turma da 3ª série do Ensino Médio, entre abril e maio de 2014. Por fim, fizemos uma análise dessa experiência e constatamos a eficácia de nossa proposta no que diz respeito à inclusão de Noções de Cálculo no Ensino Médio.

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Notre travail de thèse trouve son origine dans un constat d'échec ressenti durant plusieurs années concernant un enseignement de topologie dans lequel nous prenons une part active, en première année d'université. Nous nous sommes donc donnée comme objectif de développer des pistes d'enrichissement, voire de modifications, de cet enseignement pouvant mener aux acquisitions visées tout en s'inscrivant dans les contraintes institutionnelles qui le délimitent strictement. À partir d'une étude épistémologique de la genèse et du développement de plusieurs notions de topologie, nous avons pu caractériser leurs aspects formalisateur, unificateur et généralisateur. Cette étude, complétée par une analyse comparative de quelques manuels, a contribué à l'élaboration d'un scénario d'enseignement intégrant un certain nombre de leviers didactiques susceptibles de favoriser les apprentissages en topologie des étudiants, en tenant compte toutefois des contraintes déjà signalées. En nous plaçant dans le cadre théorique de la théorie de l'activité spécifiée aux mathématiques, nous avons explicité la description de notre scénario en termes de tâches et d'activités attendues chez les étudiants, avant de l'expérimenter dans notre classe. Les analyses des déroulements en classe associées à celles des productions des étudiants aux différentes évaluations ont permis d'approcher les apprentissages en topologie effectivement réalisés par les étudiants, en relation avec la nature des tâches. Une diminution significative des échecs dans les tâches de manipulation des définitions a été observée. Cependant, il manque aux étudiants une certaine disponibilité des notions de topologie dans les tâches plus complexes que nous avons pu associer à notre scénario. Cette recherche met en évidence l'apport des analyses didactiques menées en amont de l'enseignement dans un travail de type ingénierie pour mieux appréhender ce que leur enseignement doit apporter aux étudiants. Elle pointe également toute l'importance de l'inscription des contraintes institutionnelles dans l'élaboration et l'expérimentation d'un scénario d'enseignement. C'est en mettant en relation ces deux dimensions et les progrès réels mais limités des étudiants que nous avons été en mesure d'apprécier la portée du scénario et d'envisager des alternatives mettant cette fois en cause le curriculum.

En droit communautaire, les notions « souples », « élastiques », les « mots à sens multiples » , dont le contenu est déterminé non pas par leur auteur mais par leur interprète, sont nombreux. Parmi ces notions « floues », certaines, à la fois conceptuelles et fonctionnelles, sont intentionnellement indéterminées parce qu’elles permettent une mesure des comportements et des situations en termes de normalité et nécessitent, pour leur application aux cas d’espèce, des références exogènes au droit. C’est le cas, par exemple, des notions de « bon père de famille », de « bonnes mœurs », de « délai raisonnable », d’« abus de droit », de « confiance légitime », ou encore d’ « ordre public ». Ce type particulier de notion indéterminée constitue un standard. La question se pose de savoir si, et dans quelle mesure, les standards présentent des particularités dans l’ordre juridique de l’Union européenne, du point de vue de leur substance, c’est à dire de leur contenu, et du point de vue de leur fonction. Il apparaît, d’abord, que la spécificité substantielle du standard n’est que partielle. En effet, certains standards sont marqués par une forte coloration communautaire en ce qu’ils touchent au noyau dur de l’intégration communautaire et à la répartition des compétences au sein de cet ordre juridique (les notions de subsidiarité, de coopération loyale notamment). D’autres standards, en revanche, ont une substance proche de celle qui leur est attribuée dans les ordres juridiques nationaux ou internationaux, tout en étant adaptée à la logique de l’ordre communautaire (c’est le cas, par exemple, des notions de confiance légitime, de bonne administration, ou encore de procès équitable). Il apparaît, ensuite, que la spécificité fonctionnelle du standard communautaire est manifeste. Ce type de notion indéterminée joue, en effet, un rôle lié non seulement aux particularités du système juridictionnel de l’Union et à la contribution du juge à l’intégration européenne, mais aussi aux particularités structurelles de l’ordre juridique communautaire.

This study deals with students' notions of the function in society of their future professions. The overall aim is to study what notions are actually represented by the students and to describe the content of these notions. Another aim is to study how the students' notions change during their period of training. Slightly more than 100 students, distributed equally among the higher education programmes of economics, medicine, psychology and engineering, were interviewed when entering these programmes and after a period of approximately three years. The result of the analysis of notions was that five qualitatively different categories of notions could be discerned among students of economics, psychology and engineering, whereas three could be found among students of medicine. The categories run on a dimension from the profession being regarded as manifestations of and subordinate to an economic-political system, to the profession being regarded as manifestations of and subordinate to individual differences. The various categories of notions have been given names intended to, somewhat incisively, summarize their content. The students of economics and engineering changed during their period of training so that a larger number of them conceptualized the profession as a manifestation of individual differences. The students of psychology changed in the opposite direction and the students of medicine remained in the middle position. An analysis of the students' reflections on notions and the conceptualization per se, has also been carried out. This analysis is an attempt at problemizing the relation between notions and actions. It showed that, at the end of their training period, the students of psychology and, to a certain extent, the students of engineering more often than students of economics and medicine, considered the possibilities of acting in accordance to their notions of the ideal function of the professions. Attempts are also made at relating certain changes of the students' notions to specific characteristics of the educational programmes. The importance of students' initial notions for how they change is, however, also analysed and emphasized. The answer to the question of students' change of notions during their period of training can, in other words, be found in the dynamics and in the opposition between students' initial notions and the notions of the professions conveyed by the education. In relation to the goal of higher education to encourage critical thinking in students, the results of this study indicate that the educational programmes, rather than conveying one specific critical notion, should convey an awareness of the fact that there are different notions of the function of the profession. The students would then be stimulated, on the basis of their own initial notions of the profession, to make critical examinations of, to decide on, and to make their own choices of alternative notions. / digitalisering@umu

The purpose of this study is to examine stabilization and change in students' notions of division of labour, wage differentiation and reproduction of labour force. A description is given of the development and application of a qualitative method for the analysis of interviews within the framework of a theory-generating evaluation of long-term effects of higher education. A central concept is notion, the theoretical and methodological development of which up to a strict description of the content is presented in different categories. A model is presented of the structural features of notions. A theoretical revaluation of ideological reproduction is outlined and reconnected with the initial theoretical frame of reference. The empirical data consist of transcribed interviews with students of economics, medicine, psychology and engineering. The interviews were made on two occasions: when the students entered their educational programmes and after a period of about three years. The initial number of students involved were 25-27 from each educational programme. The results of the empirical analyses show initial différencies in students' ideological shaping, both within and between educational programmes. For a majority of students notions remain stable over time. Occurring changes lack general characteristics. For students of medicine and engineering changes in notions of differentiation of wages are unidirectional and fairly common while students of psychology change their notions in another direction but not to the same extent. Changes in notions of division of labour are more common among students of economics and psychology than in other groups but the direction of change is not the same in the two groups. Changes in students' notions can be said to depend on initial notions, educational programme, and societal aspect subject to the analysis. The study ends with some reflections on qualitative methods and theory generating evaluation. / digitalisering@umu

The purpose of this dissertation is to study the vocational and career education in upper secondary school and to answer the question if and how this education contributes to the socialization of the younger generation to the various sectors and positions of working life. The ambition was also to acquire more general knowledge of the mechanisms generating different classroom discourses. The main problem thus deals with how and why an objective reality, in this case the working world, is transformed into various teaching situations and how and why it grows into different classroom discourses. In accordance with the theoretical frame of reference, career education is regarded as a transmission of ideologies and as part of the social reproduction process. By analogy with this approach the training effects have been studied in terms of transmitted opinions and notions in various aspects of education and working life. For a period of one year we observed the instruction in social studies and vocational teaching in four different course programmes of upper secondary school. The empirical studies also include interviews with teachers and students in nursing and metalwork course programmes, in economics, in social sciences and in natural sciences as well as employees in the metalwork and health-care sector. The main aim was to study the notions of education and working life of various interested parties in relation to the notions transmitted in the course programmes. The results show that there are great differences in vocational teaching in the different course programmes, in spite of the fact that the content of this teaching is supposed to be almost identical according to the curriculum. In an attempt to explain the formation of education we have formulated a "content-related steering group theory". In simplified terms this means that the content of education is characterized by certain predominant structures of thought characteristic of both the social field (sector) and the social stratum (level) towards which the education is primarily directed. The predominant structures of thought are brought into the classrooms through the students' individual and historical relations with the world of work. These structures then function as a generating and controlling mechanism for the classroom discourse. The teacher will, more or less unconsciously, adjust the content of his or her teaching to the predominant structures of thought of the selection of students forming his or her class. Our analysis ends in the assumption that the differences in structures of thought between students in various course programmes are reinforced during the time spent in upper secondary school - not so much as a result of the education itself, but more as a result of the different social environments of different student categories to which the education is adapted. / digitalisering@umu