Through increasing immigration, the U.S. society is becoming more linguistically and culturally diverse. Yet, as many U.S. language minority groups seek to assimilate, they face many challenges. One challenge is that their home language does not match the dominant language, English, that their children are learning at school. For Korean communities, maintaining Korean language presents a problem for families, especially for the mothers and children. The purpose of this study was to explore the U.S. Korean immigrant mothers' and children's perceptions of and experience with maintaining the Korean language and the effect that has on the development of social capital and cultural identity. I conducted two focus groups--one with mothers, another with their children, using a semi-structured interview protocol. I used narrative inquiry as my qualitative approach and then used thematic analysis to summarize my findings. I identified four major themes: (a) use of Korean language: positive and negative experiences, (b) perspectives on Korean language maintenance: benefits and limitations, (c) effect of parental involvement: provision of social capital, and (d) value of cultural identity formation: acculturation and the reality of learning Korean. This study revealed that parental support for children's heritage language retention seems to have an effect on language maintenance. Thus, because of this seemingly strong relationship, there seem to be significant benefits for children, families, and the overall society when the U.S. educators and other Korean immigrant parents strongly encourage American-born Korean youth to maintain their mother tongue in the U.S.

To make mathematics more significant for the beneficiaries, the problem studied in this thesis is to investigate how to connect mathematical daily practices with educational contexts. The overarching aim is to investigate how to contextualise school mathematics within Rwandan cultural mathematics practices. The content of the thesis reports on the characteristics of mathematical organisations in three workplace settings (taxi driving, house construction and restaurant management) which in turn serve as source for the design of contextualised mathematical activities for student teachers in a teacher education programme. Three levels of mathematical practices are described: (1) mathematical practices that are performed by workers within their respective workplaces, (2) mathematical practices that are performed by student teachers while solving and posing contextualised mathematical tasks for secondary school students, (3) mathematical practices that are carried out by secondary school students. Data gathered from individual and group interviews, transcripts of group discussions and students’ written reports of mathematical work were analysed from the perspective of both activity theory and anthropological theory of didactics. Findings from workplace settings revealed that mathematical organisations performed by workers are characterised by techniques which are functional to the problem at hand, the cultural constraints and the educational background of the workers. As long as they are pragmatic towards the goals of the activity no further justification of the techniques used is needed, resulting in a mathematical organisation with undeveloped know-why (logos). On the contrary, at university and secondary school settings, students justified the used techniques throughout the related taught content of the subject mathematics. Also from each category of mathematical practice, it is shown that while connecting workplaces and educational settings the didactic transposition process was much influenced by the institutional conditions and constraints. / För att göra matematiken betydelsefull för avnämarna är problemområdet som studeras i denna avhandling hur den matematik som finns i samhället kan överbryggas till en undervisningskontext. Syftet med avhandlingen är att undersöka hur man kan kontextualisera skolmatematik i kulturella praktiker i Rwanda. I avhandlingen belyses först matematisk organisation på tre arbetsplatser – i en taxiverksamhet, hos en byggmästare och hos en restaurangägare. Matematik i dessa verksamheter utgör underlag för att konstruera uppgifter för lärarstudenter inom ämnet matematik som först löser uppgifterna och sedan i sin tur konstruerar uppgifter för elever motsvarande årskurs nio i grundskolan. Uppgifterna konstrueras med utgångspunkt i den information studenterna fått om de tre verksamheterna. Datainsamlingen skedde med hjälp av individuella intervjuer, gruppintervjuer och bandinspelade gruppdiskussioner samt studenters och elevers nedtecknade lösningar på respektive uppgifter. Data analyserades med hjälp av aktivitetsteori och antropologisk didaktisk teori. Resultaten från arbetsplatserna visade att matematisk organisation kännetecknades av tekniker som är funktionella för de problem som behövde lösas, de kulturella villkor som förelåg och deltagarnas utbildningsbakgrund. Så länge som teknikerna ledde till önskade mål för verksamheten fanns inga behov att utveckla tekniken som kännetecknades av en matematisk organisation med outvecklad logos. I kontrast till denna strategi sågs studenter och elever i respektive miljöer redovisa de tekniker som användes och motivera dem i enlighet med vad som krävs inom matematikämnet. Den matematiska transpositionsprocessen som utfördes av deltagarna i de olika miljöerna influerades i hög grad av rådande institutionella villkor och begränsningar.

La caractérisation de la réalité matérielle du paysage impose d’une part de reconnaitre avec précision le cadre physique et d’autre part de saisir les interrelations entre les hommes et l’environnement, conditions indispensables à l’appréciation des origines du modelé du paysage. La compréhension des paysages passés se fonde en partie sur l’analyse de différentes sources documentaires qui permettent ensemble de caractériser bon nombre des évolutions paysagères intervenues notamment depuis l’époque moderne. Toutefois, les aménagements plus anciens ne sont ni localisés ni représentés sur des cartes. Leurs traces sont alors décelées dans le paysage actuel de manière efficace grâce notamment à la mise en oeuvre conjointe de diverses méthodes de détection : la photographie aérienne, enregistrant des variations topographiques ou colorimétriques à la surface du sol et le système LiDAR (Light Detection And Ranging), mesurant les variations microtopographiques à l’aide d’un laser. L’étude d’autres paramètres, imperceptibles à nos sens, permettent également d’appréhender les traces des paysages passés. Les méthodes géophysiques détectent la présence de vestiges ou de structures enfouies qu’aucun indice ne signale en surface grâce à la mesure des propriétés physiques du sol. Il est largement admis que les méthodes de prospection sont susceptibles de fournir des données archéologiques quant à l’occupation du sol et/ou l’exploitation du territoire. A ce titre, elles ont été appliquées depuis plusieurs années sur le site de l’agglomération antique d’Epomanduodurum (Mandeure-Mathay, Doubs) dans le nord Franche-Comté. Cette ville est considérée, par sa taille, son équipement urbain et sa parure monumentale comme la seconde de Séquanie derrière la capitale de cité Vesontio (Besançon, Doubs). Ce travail de recherche se propose donc de comparer, à différentes échelles spatiales, l’apport respectif de plusieurs méthodes de prospection à l’étude de dynamiques naturelles et anthropiques dans un espace géographique de 80 km², centré sur la ville antique, associant un tronçon de plaine alluviale du Doubs aux plateaux calcaires environnants. Durant cette étude, il a été possible, entre autre, de développer des outils aidant à la détection des structures archéologiques et géologiques. Les résultats ont aussi permis de redéfinir en partie la topographie de l’agglomération antique. / The characterization of the material reality of the landscape requires to accurately identify the physical geography and to capture the interrelationships between humans and their environment. These conditions are essential to the estimation of the origins of the landscape shaping. The analysis of documentary sources offers the opportunity to determine the organization of former landscapes and to characterize a large part of their evolutions since the Modern period. However, older land settlements are not localised or symbolised on maps. Their signs are efficiently detected in present landscape through the joint implementation of various detection methods: aerial photography, recording topographic or colorimetric variations on the soil surface, and the LiDAR (Light Detection And Ranging) system, measuring micro-topographic variations using a laser beam. Other methods can be used to identify the elements conserved in present landscape and reflect their past uses. The measure of physical properties of soils by the geophysical methods can detected the presence of archaeological remains or structures buried while nothing is perceptible to the soil surface. It is widely supported that survey methods can provide archaeological data of the land use and / or the exploitation of the territory. Thus, they have been applied since several at the site of the ancient city of Epomanduodurum (Mandeure-Mathay, Doubs) in the north of the Franche-Comte. This city is considered by its size, urban equipment and monuments as the second behind de civitas capital of Sequani, Vesontio (Besancon). This research intends to compare, at different spatial scales, the contribution of several prospecting methods for the study of natural and anthropogenic dynamics in an area of 80 km². The study area is centred on the ancient city and combines a section of the alluvial plain of the Doubs river and the surrounding calcareous plateaus. In this study, it was possible, among other things, to develop tools for the detection of archaeological

Situé en didactique du Français Langue Étrangère (FLE) et notamment en celle de la littérature française au sein de l’université taiwanaise, l’élaboration des dispositifs didactiques tient compte des profils des apprenants locaux qui témoignent d’un trouble identitaire lié au contexte sociohistorique et expriment ainsi un intérêt envers les savoirs socioculturels en vue d’un enrichissement personnel et social. L’enjeu didactique de la lecture-écriture du personnage réside en l’occurrence dans l’exploration de la portée socioculturelle du texte littéraire en vue de la réflexion des apprenants sur des questions identitaires et sur des stratégies narratives liées à la construction du monde fictif et de l’authenticité du personnage favorisant l’identification du lecteur. Pour réaliser ce projet, une enquête sur les rapports des étudiants locaux avec la littérature française, notamment sur leur conception du personnage, a été effectué sous forme de questionnaire. Le débrouillement des données recueillies contribue à élaborer des séquences didactiques s’appuyant sur un corpus littéraire lié à la féminité des années 1920. Leur mise en pratique dans une classe de FLE en 2015 consiste à étudier des apports des référents culturels tant dans la structuration du système du personnage que dans l’articulation des séquences actionnelles du récit. Cette fonction narrative de l’acte de référence va de pair avec sa fonction pragmatique dans la programmation des tensions narratives, relatives à divers modes d’identification au personnage. Enfin, l’étude de l’acte de référence dans la construction d’un monde fictif permet de dégager la logique interne de la société représentée et les explications des phénomènes sociaux à partir de la situation définie dans le temps et dans l’espace. / The development of a didactic plan for the teaching of French as a Foreign Language (FLE), and especially in French literature at universities in Taiwan, has taken the characteristics of local learners into consideration. It shows that they have experienced an identity confusion related to the socio-historical context, and thus have expressed an interest in socio-cultural knowledge in order to enrich themselves personally and socially. Under the circumstances, the didactic challenge of the characters’ reading and writing is located on examining the socio-cultural significance of the literary texts for the learners’ reflection on identity issues, narrative strategies associated with constructing the fictional world, and characters’ authenticity encouraging the readers’ identification.A survey on the relationship between the local students and French literature particularly on their characters’ conception, has been carried out for this project in the form of a questionnaire. The collation of the data collected providing the development of didactic sequences is underpinned by a literary corpus correlated to femininity of the 1920s. Their implementation in a FLE class in 2015 consists of studying the contributions of the cultural referents in the creation of the characters’ system as well as in the articulation of the sequential actions of narrative. This narrative function of the reference acts is coupled to its pragmatic function on programming narrative tensions corresponding to various modes of the characters’ identification. Finally, the study of reference acts in the making of a fictional world renders it possible to identify the internal logic of the represented society, and the explanations of social phenomena from the situation defined in time and space.

O estudo analisa alguns discursos da Igreja Universal do Reino de Deus (IURD) no sul de Moçambique e problematiza os diálogos desta igreja com aspectos de diferentes contextos religiosos e com o poder político. A inspiração teórica está nos autores que apontaram as implicações políticas de diversas práticas religiosas e dos discursos sobre feitiçaria em contextos africanos (P. Geschiere, H. G. West, e outros) e nos autores que apontaram as dificuldades para designar algo como estritamente político ou estritamente religioso (T. Asad, e outros). Neste sentido, o estudo não partiu de uma definição de religião, mas busca identificar o lugar que a religião ocupou e ocupa em Moçambique. Além da utilização de fontes secundárias, o estudo analisa alguns materiais escritos produzidos pela IURD em Moçambique, alguns programas televisivos, algumas reuniões da IURD em Moçambique, e entrevistas com líderes religiosos moçambicanos. Sem ignorar as continuidades em relação à IURD no Brasil, o estudo aponta que diversas práticas de outros contextos religiosos, principalmente tradicionais e zionistas do sul da África, criaram e criam condições para que os discursos da IURD sejam significativos no sul de Moçambique. / The study analyzes some discourses of the Universal Church of the Kingdom of God (UCKG) in southern Mozambique and problematizes the dialogues of this church with aspects of different religious contexts and with political power. The theoretical inspiration lies in the authors who pointed out the political implications of various religious practices and witchcraft discourses in African contexts (P. Geschiere, H. G. West, and others) and in the authors who pointed out the difficulties to designate something as strictly political or strictly religious (T. Asad, and others). In this sense, the study did not start from a definition of religion, but seeks to identify the place that the religion occupied and occupies in Mozambique. In addition to the use of secondary sources, the study analyzes some of the written materials produced by UCKG in Mozambique, some television programs, some cults of the UCKG in Mozambique, and interviews with Mozambican religious leaders. Without ignoring the continuities in relation to the UCKG in Brazil, the study points out that several practices in other religious contexts, mainly \"traditional\" and Zionist in southern Africa, have created and created conditions for the UCKGs speeches to be significant in southern Mozambique.

En 2001, la République Démocratique du Congo s’est vigoureusement engagée avec le soutien de diverses organisations internationales pour réduire la pauvreté à partir de la stratégie de croissance. Dix ans plus tard, ce pays pointait à la dernière place du classement réalisé par le Programme des Nations unies pour le développement (PNUD) en fonction de l’indice du développement humain (IDH) des pays. En marge, ont émergé et se sont développées de multiples initiatives locales fondées sur des stratégies relationnelles et dont certaines sont présentées dans ce travail. Alors que la stratégie officielle contre la pauvreté a échoué, la société a survécu et évolue. En partant de ce constat, cette étude découvre que les approches conceptuelles et les solutions à la base de la lutte contre la pauvreté sont souvent réductrices. Elles se doublent malheureusement souvent d’une certaine tendance à oublier que toute pauvreté n’est pas qu’à combattre : la pauvreté anthropologique – qui est celle de notre condition fragile – est souvent oubliée, la pauvreté volontaire est reléguée au second rang. Finalement, cette étude montre qu’il ne faut pas trop simplifier le problème de la pauvreté afin de redonner du sens aux actions entreprises pour la combattre, et ainsi étendre la portée de ces actions. Cette question du sens est un élément décisif pour bien appréhender la lutte contre la pauvreté : avoir une vision réductrice d’une action revient à en diminuer considérablement la portée. La lutte contre la pauvreté aujourd’hui doit pouvoir redonner du sens à la vie en ayant une vision intégrale de l’existence humaine, intimement liée à l’anthropologie que présente le message chrétien. / In 2001, The Democratic Republic of Congo strongly committed itself, with the support of diverse international organizations, to reduce poverty based on the economic growth strategy. Ten years later the nation found itself at the bottom of the countries produced classification by The United Nations Development Program of the Human Development Index (HDI). Besides that program, several local initiatives have come out and developed, based on relational strategies, some of which are presented in this work. While the official strategy against poverty has failed, the society has survived and progressed. Based on this statement, this study discovers that the conceptual approaches and solutions at the base of the fight against poverty often are constricting. Unfortunately, these restrictive attitudes multiply themselves with some tendencies which tend to forget that all kind of poverty isn’t to be fought : the anthropological poverty – which is that of our fragile condition – is often omitted and voluntary poverty is often relegated to the second place. Finally, this study shows that the poverty problem should not be simplified with the intention of giving sense to the actions adopted to fight it, and in this way extend the scope of these actions. This question of sense is decisive in viewing the fight against poverty : a simplistic vision of an action, means, indeed, a considerable reduction of its scope. Today, the fight against poverty should be capable of giving sense to life incorporating an integral vision of the human existence, intimately related to the anthropology presented by the Christian message.

Made available in DSpace on 2016-04-27T16:57:10Z (GMT). No. of bitstreams: 1 Doutorado Maria Inez Miguel.pdf: 1466295 bytes, checksum: cab4a04224edf6b54669d1e1fa9d3e99 (MD5) Previous issue date: 2005-10-25 / This researche concentrates on the teaching and learning of the Poisson s Model, whose questioning refers to the use of the Mathematical Modeling, to the steps to be considered and to the results both in the didactic interaction and in the acquisition achieved and mistakes made by the participating pupils. We considered the hypotheses that pair-work, computer use and practical experiments might favor the development of the didactical situations in order to validate it or not. For that purpose, a teaching sequence was elaborated based on our interpretation of the Mathematic Modeling Process suggested by Henry (1997) and it was applied to a group of University undergraduates students from the second year of the College of Electric Engineering and Computer Science. We adopted the Didactic Engineering as methodology, which allows for the validation of hypotheses through the confrontation between the two analysis, a priori and a posteriori, and favors the realignment of the activities during the process. The theoretical framework was constructed with some elements of Chevallard s praxeology and Godino s ontological-semiotic approach to cognition and mathematic instruction; the first guided the analysis of the didactic books and the elaboration and presentation of the proposed tasks in the intended sequence; the second was the basis for the determination of meaningful elements in Poisson s Model to be considered in the teaching and guide the result analysis, allowing for the identification of the knowledge acquired that were in accordance with the intended institutional guidelines and those that could be considered learning mistakes. This research lead to the conclusion that not only the use of the Mathematic Modeling is favorable for the study carried out but also that it made it possible for all the modeling steps to be interpreted, adapted and considered essential for the purposes to be achieved, emphasizing that the experiment carried out should be carefully chosen to serve as motivation for the target public and, if possible, contemplate interdisciplinary. Among the several significant elements of Poisson s Model taken as reference, many were acquired by the group of participating pupils. However, some difficulties related to the use of the software, to the interpretation of terms such as: at least, at most, etc and to the symbolic representation persisted throughout the whole process. The construction of Poisson s Model as hypotheses about the experiment carried out proved to be a viable and efficient strategy, guaranteeing relative easiness in the application the model in the most varied situations, including those with proximity with the Binomial Model; that result allows for the suggestion of the introduction of the mentioned model in the way it is presented, replacing the classical way, consisting of definition, example and exercises, or even, through the proximity with the Binomial Model. The use of a software proved to be efficient to expedite the representations and to make it easier for the visualization of properties; however, learning to handle the software cannot be simultaneous to learning the target content under the risk of compromising it. Pair work proved that information exchange, enriched and complemented by the backgrounds of the two individuals involved, allowed for the emergence of new questions and guaranteed greater reliability in the execution of the proposed tasks. / Esta tese é centrada no ensino e na aprendizagem do Modelo de Poisson, seu questinamento refere-se ao uso da Modelagem Matemática, das etapas a serem consideradas e dos resultados, tanto na interação didática como nas aquisições e erros dos alunos participantes. As hipóteses de que o trabalho em dupla, o uso do computador e o experimento realizado na prática pudessem favorecer o desenvolvimento do projeto foram admitidas, a fim de serem validadas, ou não. Para tal, uma seqüência de ensino, elaborada com base nas etapas de Modelagem Matemática de Henry, foi aplicada a um grupo de alunos do segundo ano de graduação em Engenharia Elétrica e Ciência da Computação de uma Instituição de Ensino Superior. No estudo, a metodologia adotada foi a Engenharia Didática que permite a validação das hipóteses pela confrontação entre as análises a priori e a posteriori e favorece o realinhamento das atividades durante o processo. As bases teóricas foram a praxeologia de Chevallard e o enfoque ontológico-semiótico da cognição e instrução matemática de Godino. A primeira norteou a análise dos livros didáticos, a elaboração e a apresentação das tarefas propostas na seqüência pretendida; a segunda fundamentou a determinação de elementos de significado do Modelo de Poisson para serem considerados no ensino e orientar a análise dos resultados, possibilitando a identificação dos conhecimentos adquiridos que estão conforme a pauta institucional e os que podem ser considerados erros de aprendizagem. A pesquisa permitiu concluir que, não só o uso da Modelagem Matemática é favorável ao estudo realizado, como também todas as etapas de modelagem puderam ser interpretadas, adaptadas e consideradas essenciais, para que os objetivos fossem atingidos, salientando-se que o experimento realizado deve ser cuidadosamente selecionado, a fim de servir de motivação aos sujeitos visados e, se possível, contemplar a interdisciplinaridade. Entre os diversos elementos de significado do Modelo de Poisson tomados como referência, muitos foram adquiridos pelo grupo de alunos participantes, embora algumas dificuldades relacionadas à utilização do aplicativo, à interpretação de termos do tipo: ao menos, no máximo, etc., e à representação simbólica persistiram durante todo o processo. A construção do Modelo de Poisson baseada nas hipóteses citadas sobre o experimento realizado mostrou ser uma estratégia viável e eficiente, garantindo relativa facilidade na aplicação do modelo nas mais variadas situações, inclusive, naquelas de aproximação ao Modelo Binomial. O resultado permite que se sugira a introdução do referido modelo nos moldes apresentados, em lugar do modo clássico com definição, exemplo e exercícios, ou ainda, por meio da aproximação ao Modelo Binomial. O uso de um aplicativo mostrou-se eficiente para agilizar as representações e facilitar a visualização de propriedades; no entanto, a aprendizagem da manipulação do aplicativo não pode concorrer simultaneamente com o estudo do conteúdo pretendido sob pena de comprometê-lo. O trabalho em dupla revelou que as trocas de informações, enriquecidas e complementadas pelas duas formações dos sujeitos envolvidos, permitiram o levantamento de novas questões e maior confiabilidade na realização das tarefas propostas.

Made available in DSpace on 2016-04-27T16:57:44Z (GMT). No. of bitstreams: 1 pedro mateus.pdf: 4784866 bytes, checksum: 5324cedfd3255546ef9df1a861bb17cb (MD5) Previous issue date: 2007-02-27 / Fundação Ford / This research aims at analysing and better understanding how currently the concepts of Differential and Integral Calculus are dealt with in some available text-books. The discussion is related with Differential and Integral Calculus because we consider them as a branch of mathematics with enormous contribuition for scientifical and technological progress in our society. The research focuses on text-books analysis because of their outstanding role on teacher s activities in classroom of Differential and Integral Calculus on one hand, and they are source of knowledge for pupil, on another hand. The work is based in the hypotheses that some interfering factors in teaching and learning Differential and Integral Calculus are directly related to the way the text-books of Calculus are organized in didactical and matehmatical terms. Analysing this praxeological organization of text-books may strengthen understanding the causes of difficulties in teaching and learning Differential and Integral Calculus in classroom and may create a sound base to use them correctly and with some initiative. The research question is: what do the available text-books suggest to build the concepts and strategies for teaching and learning Differential and Integral Calculus? The theoritical framework was based on Registers of Semiotic Representation Theory of Duval (2003), the Anthropological Theory of Didactics of Chevallard (1999) and the Theory of Didactical Situations in Mathematics of Brousseau (1970-1990). The first theory served to evaluate the joint degree of registers of semiotic representation used in selected text-books, the second theory was used to analyze the types of tasks, techniques and technological and theoritical discourse whic justifies them. The third theory was used to evaluate the contexts set to expose the mathematical content. The results point out that the joint degree of registers of semiotic representation is weak, because there is preference to use algebric registers and their treatments instead of promoting articulation with conversions of registers; more posed activities are on practical-technical bloc than balancing with technological-theoritical bloc; formal exposition of content is predominant one, instead of taking the contextualization as a thread of ideas to get the formalization / Esta pesquisa tem o objetivo de analisar e compreender melhor como atualmente os conceitos do Cálculo Diferencial e Integral são tratados em alguns livros didáticos disponíveis. A discussão é feita sobre o Cálculo Diferencial e Integral por considerá-lo uma área da Matemática que tem dado grande contributo para o progresso científico e tecnológico. O trabalho focaliza a análise do livro didático pela importância de que ele se reveste na ação do professor em sala de aula do Cálculo Diferencial e Integral e por constituir uma fonte de conhecimento do aluno. A pesquisa assenta-se nas hipóteses de que alguns dos fatores que interferem no processo de ensino e aprendizagem do Cálculo Diferencial e Integral estão diretamente relacionados com a organização didático-matemática dos livros didáticos do Cálculo Diferencial e Integral; analisar esta organização praxeológica dos livros didáticos pode reforçar a compreensão das causas de dificuldades no ensino e aprendizagem do Cálculo Diferencial e Integral e propiciar algumas atitudes tendentes à sua utilização correta e criativa. A questão de pesquisa é: o que é que os livros didáticos disponíveis sugerem quanto à construção de conceitos e estratégias de ensino e aprendizagem do Cálculo Diferencial e Integral? As bases teóricas foram a Teoria de Registros de Representação Semiótica de Duval (2003), a Teoria Antropológica do Didático de Chevallard (1999) e a Teoria das Situações Didáticas de Brousseau (1977). A primeira teoria serviu para avaliar o grau de articulação entre os registros de representação semiótica usados nos livros selecionados, a segunda serviu para analisar o tipo de tarefas, técnicas e o discurso teórico-tecnológico que as justifica; a terceira teoria serviu para avaliar os contextos criados na exposição do conteúdo matemático. Os resultados apontam que a articulação entre os registros de representação semiótica é débil, pois há preferência do uso de registros algébricos e seus tratamentos em vez de promover a articulação com a conversão entre os registros; trabalha-se mais sobre o bloco prático-técnico do que a combinação entre o bloco prático-técnico e o bloco tecnológico-teórico; a exposição formal do conteúdo é a predominante em vez da contextualização como fio condutor das idéias para a formalização

Made available in DSpace on 2016-04-27T16:57:49Z (GMT). No. of bitstreams: 1 Renata Rossini.pdf: 2745582 bytes, checksum: 007ec2ee6081f4135356bd33173b27b8 (MD5) Previous issue date: 2006-11-13 / Conselho de Ensino e Pesquisas / The issues of this research are the conceptions and difficulties of a group of teachers regarding the function concept, and how they overcame them along a continuous formation process. Although there are some studies regarding the students' difficulties and possible obstacles to the teaching and learning of this theme, it is necessary to pay attention on what a formative action means to a group of primary and middle school teachers, since there are not many researches involving teachers. Therefore, this thesis answers to the following questions: Which mathematical organizations are mobilized during the construction of a teaching sequence on functions for an 8th grade of Middle Education? How do the teachers build or rebuild their teacher knowledge on the function concept? The adopted methodology used an action-research as a collaborative investigation, because it propitiates the interaction between the researcher and the teachers and their practice in formation and in action. The theoretical foundation was based on the Anthropological Theory of the Didactic of Chevallard (1999) to model the function concept as Mathematical Organization and Didactic Organization associated with function conceptions such as magnitude interdependence, in and out machine, analytical expression, pattern of regularity of geometric sequences and correspondence between sets. This foundation granted the analysis of some 8th grade mathematics books and teachers' production along a process of continuous formation. As the teachers build the didactic organizations by preparing a didactic sequence for the function teaching and learning for an 8th grade class, they analyse and rebuild their own knowledge on function. At the end, the teachers manage to get relative articulation between the mobilized organizations, and it allow them to innovate and create new exercises. Building a teaching sequence and following its applications in classrooms made the teachers look at their students more positively and also feel more valued at their work / Esta pesquisa trata das concepções e dificuldades de um grupo de professores sobre o conceito de função, da superação das mesmas ao longo de um processo de formação continuada. Embora existam alguns estudos a respeito das dificuldades de alunos e dos possíveis obstáculos ao ensino e aprendizagem deste tema, há necessidade de observar o que uma ação formativa significa para um grupo de professores do ensino fundamental e médio, devido não existir muitos trabalhos de pesquisa envolvendo docentes. Assim, este trabalho responde às seguintes perguntas: Quais organizações matemáticas são mobilizadas durante a construção de uma seqüência de ensino sobre funções para uma 8a série do Ensino Fundamental? Como os professores (re)constroem seus saberes docentes sobre o conceito de função? A metodologia adotada utilizou uma ação-pesquisa no sentido de uma investigação colaborativa, visto que propicia a interação entre pesquisador e professores e sua prática em formação e em ação. O fundamento teórico baseou-se na Teoria Antropológica do Didático de Chevallard (1999) para modelar o conceito de função em termos de Organização Matemática e Organização Didática, associadas às concepções de função: interdependência de grandezas, máquina de entrada e saída, expressão analítica, padrão de regularidade de seqüências geométricas, correspondência entre conjuntos. Este fundamento deu subsídios para a análise de alguns livros de Matemática da oitava série e da produção dos professores ao longo de um processo de formação continuada. À medida que os docentes constroem as organizações didáticas, ao preparar uma seqüência didática para o ensino e aprendizagem de função para uma classe de oitava série, eles (re)constroem os seus saberes sobre função. No final, eles conseguem fazer uma relativa articulação entre as organizações mobilizadas, dando-lhes a possibilidade de criar novos conteúdos. Construir uma seqüência de ensino e acompanhar a sua aplicação em sala de aula fez com que os professores olhassem seus alunos de forma mais positiva e se sentissem mais valorizados no seu trabalho

Made available in DSpace on 2016-04-27T16:57:53Z (GMT). No. of bitstreams: 1 dissertacao_vania_andrade_luz.pdf: 1642035 bytes, checksum: 179a6afec6f9633eb81f44f31826cdea (MD5) Previous issue date: 2007-04-09 / This dissertation consists of a study focused on the teaching of geometrical transformations based on the analysis of exercises suggested in didactical books published since the 1960s in São Paulo State. The realization of this work is supported by an analysis with the following objectives: to examine the completion of the local mathematical organizations according to the Anthropological Theory of Didactics, by Yves Chevallard; to observe how the students main difficulties were approached, based on research by Jaime and Gutiérrez (1996) and Jahn (1998); to compare the teaching proposals of isometries and homoteties current at the time of the movement of reformation of Modern Mathematics to those which followed the publishing of the Parâmetros Curriculares Nationais (Brazilian National Curricular Standards). Initially, we proceeded to a study of the mathematical organization relative to geometrical transformations, a study in which will be examined the symmetries of elements of nature and the arts, the definitions of the main transformations that are part of the program of Ensino Fundamental (equivalent to an eight-year elementary school), besides the identification of historical elements related to the development of Geometry. After that, we will be moving on to the study of the didactical organization, in which researches about the teaching and learning of isometries were verified, as well as official texts as Curricular Guides, Proposals and Standards, besides a few aspects of the movement of reformation of Modern Mathematics in Brazil, and its relationship with the same movement in the United States and France. The analysis of the books was carried out from the grouping of exercises in types of tasks, a qualification used as much for the identification of the resolution techniques, as for the distinction of the technology appropriate to the justification of the former. Following that, we have performed a study of the set of proposed exercises, in which the above-mentioned was complied with, in the second paragraph of this abstract, as objectives of the analysis that was developed. Departing from the adopted theoretical basis, the conclusions of the research indicate that the orientations observed in each of the analyzed periods would not guarantee, per se, that important problems in the teaching of transformations were resolved. As it is known, the period correspondent to the movement of reformation of Modern Mathematics has emphasized the mathematical structure, whereas the period that followed the publishing of the Parâmetros Curriculares highlighted the relationship of isometries and homoteties with superior levels of mathematical determination. In the first case, the visibility of the mathematical work was not highlighted, while in the second one, the absence of technological elements might have compromised the completion of the mathematical organization / Esta dissertação consiste em um estudo focado no ensino de transformações geométricas e organizado com base na análise de exercícios propostos em livros didáticos publicados, a partir dos anos 60, no Estado de São Paulo. A realização deste trabalho apóia-se em uma análise com os seguintes objetivos: examinar a completude das organizações matemáticas locais conforme a Teoria Antropológica do Didático, de Yves Chevallard; observar como foram abordadas as principais dificuldades dos alunos, com base nas pesquisas de Jaime e Gutiérrez (1996) e de Jahn (1998); comparar as propostas de ensino de isometrias e homotetias vigentes à época do movimento de reforma da Matemática Moderna com aquelas que se seguiram à publicação dos Parâmetros Curriculares Nacionais. Inicialmente, procedemos a um estudo da organização matemática relativa a transformações geométricas, estudo no qual são examinadas as simetrias presentes em elementos da natureza e das artes, as definições das principais transformações que fazem parte do programa do Ensino Fundamental, além da identificação de elementos históricos relacionados ao desenvolvimento da geometria. Em seguida, passamos ao estudo da organização didática, no qual se averiguaram pesquisas sobre ensino e aprendizagem de isometrias, textos oficiais como Guias, Proposta e Parâmetros Curriculares, além de alguns aspectos do movimento de reforma da Matemática Moderna no Brasil, e sua relação com o mesmo movimento nos Estados Unidos e na França. A análise dos livros foi feita a partir do agrupamento dos exercícios em tipos de tarefas, qualificação essa utilizada tanto para a identificação da técnica de resolução, como para a distinção da tecnologia apropriada à justificação da primeira. Em seguida, efetuamos um estudo do conjunto dos exercícios propostos, no qual se encaminhou o cumprimento do acima exposto, no segundo parágrafo deste resumo, como objetivos da análise desenvolvida. A partir da base teórica adotada, as conclusões da pesquisa indicam que as orientações observadas em cada um dos períodos analisados não garantiriam, por si, que importantes problemas no ensino de transformações fossem resolvidos. Como sabido, a época correspondente ao movimento de reforma da Matemática Moderna enfatizou a estrutura matemática, ao passo que o período que se seguiu à publicação dos Parâmetros Curriculares destacou a relação de isometrias e homotetias com níveis superiores de determinação matemática. No primeiro caso, a visibilidade da obra matemática não foi destacada, enquanto, no segundo, a ausência de elementos tecnológicos pode ter comprometido a completude da organização matemática