TITLE: Word Problems in the First and Second Year of Primary School AUTHOR: Pavla Weinzettel DEPARTMENT: Departmement of Mathematics and Mathematical Education SUPERVISOR: PhDr. Michaela Kaslová ABSTRACT: This thesis focuses on word problems in maths books for Year One and Two of primary schools, published by Alter and Prodos. The objective is to analyse the word problems set out in these maths books and to classify them according to the following criteria: context, methods of solution, time management, and non- standard types of maths problems. A partial aim of the thesis is a comparison of the textbook word problem analysis and the analysis of those word problems which the students can create themselves. The conclusions of the work point out the importance of the teacher's role in maths teaching and learning. Teachers should use their judgement when using the published maths books and endeavour to expand on them, taking into consideration the above mentioned criteria in order to increase the students' eagerness to not only to solve the maths problems but also to understand as to why they solved them the way they did. The thesis recommends practical tools for teaching material evaluation and for assessing to what extent the students understand what the purpose of word problems is. KEYWORDS: word problem,...

The diploma thesis focuses on didactic and summary analysis of antiquity in elementary school's history textbooks and their comparison. The theoretical part consists of the changes of school system, History education and antique languages from the second part of nineteenth century until the era of the First Czechoslovak Republic. The practical part discusses didactic and summary analysis of selected textbooks. The summary analysis focuses on proportion of political and cultural history, depiction of the historical icons, references and parrarels to the time, when the particular textbook was written and also the way of presentation of each nation (mainly Greeks, Romans, Germans). Keywords: history textbooks, antiquity, Czechoslovakia (1918-1938), education, 20th century

L'institutionnalisation de Zola, comportant à la fois la consécration d'une image officielle et la labellisation d'un corpus textuel, doit être envisagée à travers des manuels scolaires, histoires littéraires, études critiques et générations de lecteurs, en tant que réconciliation des métadiscours et conciliation des horizons d'attente. Linéarités, stratifications, constellations sémantiques et formelles sont des visions différentes d'un même objet de lecture, à savoir le texte naturaliste. Une entité qui parcourt sans cesse, par le biais du paratexte - documents critiques, sons et images - prolongation de la lecture jusque dans la périphérie de l'espace textuel, un chemin à double sens. De l'univocité sémantique longuement promue sur le plan scolaire à travers une critique de l'intentionnalité au trop plein de « déstructuration » menant parfois à un non sens ; puis de l'approche structuraliste comme réaction contre l'historicité atrophiant les sens et claustrant la spontanéité du lecteur à l'approche thématique libérant les fantasmes de la lecture dans un monde de symboles, le texte zolien cherche à joindre son lecteur. Ainsi, tout au long de notre étude, nous sommes allée à sa rencontre. Nous n'avons fait qu'observer, noter et constater. À présent, nous laissons entièrement aux lecteurs le soin de conclure … et de recevoir. / The process institutionalising Zola, implying both a recognition of an official image and the labelling of a textual corpus should be considered, by examining school text books, history of literature books, essays and other critical studies, and readers' generations as reconciliation of metadiscourses and conciliation among several « horizons of expectation ». Semantic and formal linearities, stratifications, constellations are all different sides of the same reading object, i.e. the naturalistic text. This entity travels incessantly along a doubleway road through the paratext, an extension of the reading experience up to the peripherical text area : critical documents, sounds and images. From the semantic univocity, which was longly promoted at school level thanks to an intention-focused criticism, up to an overdestructuration sometimes leading to nonsense ; then, from the structural approach reacting against that historicity which atrophies sense and confines spontaneous reading up to a thematic approach liberating a whole world of symbols, Zola's text tends to reach its reader. Thus, we have tried to join his text all throughout this analysis. Indeed, we have simply observed, noted and attested. From now on, we assume that it belongs to readers to get to a conclusion and… to receive.

Orientador: Roberto Nardi / Banca: Marcos César Danhoni Neves / Banca: Maria Inez Mateus Dota / Resumo: A pesquisa identifica alguns padrões relativos às perspectivas dos professores dos anos iniciais do ensino fundamental em relação ao ensino da astronomia e analisa suas reflexões sobre uma possível inserção deste tema na formação inicial e continuada de docentes. A preocupação com o tema é justificada em função do caráter interdisciplinar da astronomia, uma vez que esta interage facilmente com praticamente todas as disciplinas, possuindo grande potencial educativo, além de se constatar empiricamente uma grande difusão de concepções de senso comum referentes aos fenômenos astronômicos. O estudo, de natureza qualitativa, é norteado por uma revisão crítica da literatura na área e a análise dos discursos de uma amostra de docentes dos anos iniciais do ensino fundamental. As enunciações desses docentes sobre temas astronômicos e suas inquietações em relação ao ensino da astronomia são interpretadas segundo os princípios e procedimentos da análise do discurso em sua linha francesa, conforme divulgado no Brasil por Orlandi (1999). Os resultados apontam para a existência de falhas na formação dos docentes em conteúdos de astronomia e, por outro lado, indicam algumas sugestões metodológicas para a prática de ensino sobre o tema. Assumindo a posição de que os conteúdos são preponderantes no desenvolvimento de competências nos estudantes e embasadas em resultados de pesquisas em educação em ciências e nas sugestões metodológicas decorrentes dos discursos dos sujeitos entrevistados, as conclusões desse estudo fornecem subísios para a elaboração de um programa de educação continuada e/ou inicial, visando uma mudança de postura na prática pedagógica dos docentes / Abstract: The research identifies some relative patterns to the teachers' perspectives of the initial years of the fundamental teaching in relation to the teaching of the astronomy and it analyzes their reflections about a possible insert of this theme in the initial and continuous formation of professors. The concern with the theme is justified in function of the character interdisciplinary of the astronomy, once this interacts easily with practically all the disciplines, possessing great educational potential, besides verifying a great diffusion of conceptions of common sense referring empirically to the astronomical phenomena. The study, of qualitative nature, it is orientated by a critical revision of the literature in the area and the analysis of the discourses of a teacher' sample of the initial years of the fundamental teaching. Those teachers' enunciations about astronomical themes and your inquietudes in relation to the teaching of astronomy are interpreted according to the beginnings and procedures of the discourse's analysis in your french line, as published in Brazil by Orlandi (1999). The results appear for the existence of flaws in the teachers' formation in contents of astronomy and, on the other hand, they indicate some methodological suggestins for the teaching practice on the theme. Assuming the position that the contents are preponderant in the development of competences in the students and based in results of researches in science education and in the current methodoological suggestins of the subjects interviewees' discourses, the conclusions of that study supply subsidies for the elaboration of a program of education continued and/or initial, seeking a posture change in pedagogic practice of the teachers / Mestre

Ao contrário da catenária, o estudo da parábola é encontrado com freqüência nos livros didáticos de matemática. Dois livros didáticos foram analisados para esta pesquisa: o livro de Olavo Freire de 1894, que associa o formato do cabo pênsil ao de uma parábola, e o livro da década de 1970 de Osvaldo Sangiorgi, que relaciona à figura de um balanço a forma de uma parábola. Notamos que esses livros didáticos com oitenta anos de diferença usam a corda suspensa para representar a forma parabólica. Como o formato de um cabo suspenso pelas extremidades sob a ação do seu próprio peso é representado pela catenária, sentimo-nos motivados a pesquisar sobre as curvas e entender por quais delas, afinal, o cabo da ponte pênsil é mais bem representado. Visto que essa dúvida surgiu a partir de livros didáticos, discorremos sobre a função do livro de matemática, na sala de aula, como indicadores do ensino da matemática, de um determinado local, dentro de determinado contexto histórico-político. No decorrer da história da matemática, houve confusão entre essas duas curvas, a qual motivou o estudo da catenária a partir do século XVII. Essa fase da história é conhecida como época das curvas, e em 1600, por Huygens, que se iniciaram seus estudos. Examinamos as curvas catenária e parábola no âmbito da educação e da história da matemática, bem como suas propriedades e aplicações práticas no âmbito da engenharia de pontes pênseis e na arquitetura. Amparamo-nos em leituras específicas de construção e história de algumas pontes pênseis e chegamos a visitar a Ponte Estaiada em São Paulo ainda em edificação, para entendermos como os engenheiros utilizam as propriedades das curvas catenária e parábola em sua construção. Os resultados revelaram que, surpreendentemente, o exemplo adotado no livro de Olavo Freire para representar uma parábola não levou em consideração o que acontece na prática da engenharia das pontes pênseis, e o ressurgimento do exemplo do balanço no livro de Osvaldo Sangiorgi, pareceu reforçar a tese de que havia, sim, certa confusão entre as duas curvas. Utilizando o software gráfico Winplot, construímos as curvas catenária e parábola e pudemos visualizar as diferenças ou similaridades entre elas. Finalizando, comprovamos algebricamente a aproximação entre as curvas catenária e parábola e a definição de parábola no ponto de vista da engenharia. / Unlike the catenary, the study of the parabola is often found in textbooks of Mathematics. Two textbooks were analyzed for this research: the book of Olavo Freire, 1894, which combines the format of the cable suspended to a parabola, and the book of the decade of 1970 of Osvaldo Sangiorgi, which relates to the figure of a stock as a parabola. Note that these textbooks with eighty years of difference used the rope suspended to represent the parabolic shape. As the format of a cable suspended by the extremities under the action of its own weight is the catenary, we felt motivated to search on the curves and understand how, after all, the cable of the suspension bridge is best represented. Since this question came from textbooks, we studied the basis of the book of Mathematics in the classroom, as indicators of teaching Mathematics in a given location, within a certain historical and political context. Throughout the history of Mathematics, there was confusion between these two curves, which led the study of catenary from the seventeenth century. This phase of history is known as the curves season, and in 1600, by Huygens, who started their studies. We have audited the catenary curves and parabola in education and the history of Mathematics, and its properties and practical applications in the Engineering of suspension bridges and architecture. Supported us in specific readings of history and construction of some suspension bridges and even payed a visit to the bridge Estaiada in Sao Paulo which is still under construction, to understand how the engineers use the properties of the catenary curves and parabola in its construction. The results showed that, surprisingly, the example used in the book of Olavo Freire to represent a parabola did not bring into account what happens in the practice of Engineering of the suspension bridges, and the resurgence of the example of the balance sheet in the book of Osvaldo Sangiorgi seemed to strengthen the argument that there was some confusion between the two curves. Using the software chart Winplot, the catenary and parabola curves were built and we could visualize the differences or similarities between them. At last, using algebra we proved the rapprochement between the catenary curves and definition of parabola in terms of Engineering.

Este trabalho aponta os caminhos distintos que foram utilizados historicamente para a obtenção da expressão hoje denominada força de Lorentz e analisa os conceitos de força propostos por Newton e Mach e os vários significados já propostos para campo. Além disso, realiza uma comparação entre as teorias de Lorentz e Einstein sobre o Eletromagnetismo, descreve um modelo de éter do início do século XX que parece não ter sido ainda refutado, e faz um esboço das concepções de alguns renomados físicos sobre o éter. Como conclusões gerais, constatamos que por vezes os fundamentos da Dinâmica e do Eletromagnetismo não são exatamente apresentados de uma perspectiva histórica nos livros didáticos, que ocorrem alguns equívocos históricos nestes livros, e que a hipótese de existência de um éter merece maiores estudos. / In this work the Lorentz\'s force historical backgrounds was investigated. Moreover, the concepts of force as proposed by Newton and Mach were analyzed, and the several already proposed meanings for field were also compared. A comparison between the theories of Lorentz and Einstein on the foundations of Electromagnetism was also carried out. A model of ether proposed in the beginning of the century XX was discussed and it seems it has not been refuted so far. Outlines of the conceptions of famous physicists on ether had been supplied. As general conclusions we observe that sometimes the bases of the Dynamic and the Electromagnetism in nowadays text books do not seem to be exactly presented from a historical perspective, that some historical mistakes are found within these books, and that the hypothesis about the existence of some kind of ether deserves more studies.

Ziel der vorliegenden Dissertation ist es, Formen kultureller Produktion und ihre Anbindungen an sprachliche und politische Realitäten am Beispiel der kanadischen Provinz Québec darzustellen. Die Existenz des französischsprachigen Québec und seiner Differenz ist nicht gegen das englischsprachige Kanada zu erklären, sondern mit diesem. Identitätsreferenzen und Geschichtsbilder sind Teil öffentlicher Bekundungen, ob nun journalistischer, künstlerischer, schulpolitischer oder anderer Art. Gefragt wird nach der Bedeutung historischer Tatsachen für die Gegenwart und dem spezifischen Gebrauch der Geschichte, ihren Helden und Machern in diversen narrativen Formungen an den Schnittpunkten von Öffentlichkeit und Erinnerung. Die verwendeten Quellen decken die Bereiche Film, Literatur, Presse und Politik ab; besonderes Augenmerk wurde auf Schulbuchtexte aus dem Geschichtsunterricht der Sekundarstufe gelegt. Es konnte gezeigt werden, dass sich in zahlreichen Instanzen der Auseinandersetzung nicht etwa anglokanadische und frankokanadische (oder „englische“ und „französische“) Kontrahenten gegenüberstehen, sondern dass die Konfliktparteien oft nicht diesseits und jenseits der Sprachbarriere liegen. Dies konnte am Beispiel der verwobenen Beziehungen von liberaler politischer Macht in Ottawa und dem ultrakonservativen katholischen Klerus Québecs im 19. und 20. Jahrhundert illustriert werden. Gleichzeitig zeigt sich, dass heterogene Strukturen in konkreten Situationen durch wirksame Grenzziehungen gewissermaßen ausgeblendet werden können. Die entstehenden Trennungslinien hatten und haben in Kanada und in Québec sprachliche, religiöse, politische und ethnische Formen, die in Momenten der Krise zu Matrizen bekannter Solidaritäten werden. Im Ergebnis der Untersuchungen steht das Fazit, dass Kanada als Föderation die Sezession Québecs nicht als Ganzes überleben würde. Die Alternative zur gegenwärtigen politischen Gestalt wäre somit nicht Québec auf der einen und ein verbleibendes „English Canada“ auf der anderen Seite, sondern ein weiteres Aufbrechen der bisherigen Kohäsion. Darüber hinaus konnte ein Zusammenhang zwischen der auffälligen Besonderheit einer mehrheitlich katholischen und französischsprachigen Bevölkerung und der großen englischen Monarchie in Amerika aufgezeigt werden. / This Ph.D. thesis aims at an analysis of various forms of cultural production and links with linguistic and politic realities in the Canadian Province Québec. The existence of a French-speaking Québec and its difference cannot be explained without considering “the rest of Canada” as a major factor. Identity references and images of history are seen as public expressions in journalistic, artistic, educational or other forms. The present relevance of historical facts, the specific usage of history, its heroes and its makers are of special interest in narratives operating at the intersection of public sphere and memory politics. Various sources were used in the process of research: film, literature, the press and politics. Special attention was given to history text books in English and French used for secondary level courses in Québec schools. In a number of conflicts the opponents were not on both sides of the language barrier representing „english“ and „french“ interests. One example studied is the case of the intricate relations between liberal political power in Ottawa and the conservative Catholic Church in Québec. At the same time, heterogeneous structures seem to be faded out in specific situations when powerful lines of separation are drawn. In critical situations solidarities are formed in Canada and Québec along the lines of language, religion, politics and ethnic background. As a result of the study it became clear that the separation of Québec from Canada would result not in two parts, Québec and “English Canada” but that the cohesion of the present federation would eventually dissolve into much smaller parts. It also became clear that there is an integral relation between the distinctness of a population with a catholic and French-speaking majority and the English monarchy present in America.

Esta dissertação pretende, mediante a análise de livros didáticos aprovados pelo PNLD 2005 - Plano Nacional do Livro Didático, trazer à luz discussões a respeito dos gêneros narrativos ficcionais nas escolas hoje. O trabalho se inicia com o levantamento e discussão das principais correntes teóricas acerca da narrativa e teorias da narratividade. A partir daí, buscando conceituar gêneros do discurso e tipos de texto, eixo norteador desta pesquisa, apresentamos elementos da discussão recente sobre o assunto entre os pesquisadores na área de ensino de língua portuguesa. Em seguida, procuramos analisar a forma como esses conceitos aparecem nos documentos oficiais - PCN e PNLD. Por fim, apresentamos a análise de duas coleções didáticas (Português: Linguagens de William Roberto Cereja e Thereza Cochar Magalhães e Português: Uma proposta para o letramento de Magda Soares) dirigidas a alunos do Ensino Fundamental II à luz das discussões anteriores. Com a discussão teórica sobre a presença dos gêneros do discurso e tipos de texto nos documentos oficiais e livros didáticos e a análise do livro didático de Português para o Ensino Fundamental II, pretendemos levantar questões sobre a importância da produção do texto narrativo ficcional na escola hoje. / This dissertation aims at discussing the narrative genres in schools today. The first part presents the main theoretical studies about narrative and narratology. By the study on discourse genres and types of text, main trait of this research, it is intended to show elements of a recent discussion among researchers in the field of teaching Portuguese. Next, it is investigated the concepts of genre and text in the official documents - PCN and PNLD. Finally, it is presented an analysis of two collections of books (Português: Linguagens de William Roberto Cereja e Thereza Cochar Magalhães e Português: Uma proposta para o letramento de Magda Soares) intended for Ensino Fundamental II students. By presenting a discussion on discourse genres and types of texts in the official documents and text books and an analysis of Portuguese text books, it is intended to raise questions on the importance of fiction writing in schools today.

Este trabalho aponta os caminhos distintos que foram utilizados historicamente para a obtenção da expressão hoje denominada força de Lorentz e analisa os conceitos de força propostos por Newton e Mach e os vários significados já propostos para campo. Além disso, realiza uma comparação entre as teorias de Lorentz e Einstein sobre o Eletromagnetismo, descreve um modelo de éter do início do século XX que parece não ter sido ainda refutado, e faz um esboço das concepções de alguns renomados físicos sobre o éter. Como conclusões gerais, constatamos que por vezes os fundamentos da Dinâmica e do Eletromagnetismo não são exatamente apresentados de uma perspectiva histórica nos livros didáticos, que ocorrem alguns equívocos históricos nestes livros, e que a hipótese de existência de um éter merece maiores estudos. / In this work the Lorentz\'s force historical backgrounds was investigated. Moreover, the concepts of force as proposed by Newton and Mach were analyzed, and the several already proposed meanings for field were also compared. A comparison between the theories of Lorentz and Einstein on the foundations of Electromagnetism was also carried out. A model of ether proposed in the beginning of the century XX was discussed and it seems it has not been refuted so far. Outlines of the conceptions of famous physicists on ether had been supplied. As general conclusions we observe that sometimes the bases of the Dynamic and the Electromagnetism in nowadays text books do not seem to be exactly presented from a historical perspective, that some historical mistakes are found within these books, and that the hypothesis about the existence of some kind of ether deserves more studies.

Ao contrário da catenária, o estudo da parábola é encontrado com freqüência nos livros didáticos de matemática. Dois livros didáticos foram analisados para esta pesquisa: o livro de Olavo Freire de 1894, que associa o formato do cabo pênsil ao de uma parábola, e o livro da década de 1970 de Osvaldo Sangiorgi, que relaciona à figura de um balanço a forma de uma parábola. Notamos que esses livros didáticos com oitenta anos de diferença usam a corda suspensa para representar a forma parabólica. Como o formato de um cabo suspenso pelas extremidades sob a ação do seu próprio peso é representado pela catenária, sentimo-nos motivados a pesquisar sobre as curvas e entender por quais delas, afinal, o cabo da ponte pênsil é mais bem representado. Visto que essa dúvida surgiu a partir de livros didáticos, discorremos sobre a função do livro de matemática, na sala de aula, como indicadores do ensino da matemática, de um determinado local, dentro de determinado contexto histórico-político. No decorrer da história da matemática, houve confusão entre essas duas curvas, a qual motivou o estudo da catenária a partir do século XVII. Essa fase da história é conhecida como época das curvas, e em 1600, por Huygens, que se iniciaram seus estudos. Examinamos as curvas catenária e parábola no âmbito da educação e da história da matemática, bem como suas propriedades e aplicações práticas no âmbito da engenharia de pontes pênseis e na arquitetura. Amparamo-nos em leituras específicas de construção e história de algumas pontes pênseis e chegamos a visitar a Ponte Estaiada em São Paulo ainda em edificação, para entendermos como os engenheiros utilizam as propriedades das curvas catenária e parábola em sua construção. Os resultados revelaram que, surpreendentemente, o exemplo adotado no livro de Olavo Freire para representar uma parábola não levou em consideração o que acontece na prática da engenharia das pontes pênseis, e o ressurgimento do exemplo do balanço no livro de Osvaldo Sangiorgi, pareceu reforçar a tese de que havia, sim, certa confusão entre as duas curvas. Utilizando o software gráfico Winplot, construímos as curvas catenária e parábola e pudemos visualizar as diferenças ou similaridades entre elas. Finalizando, comprovamos algebricamente a aproximação entre as curvas catenária e parábola e a definição de parábola no ponto de vista da engenharia. / Unlike the catenary, the study of the parabola is often found in textbooks of Mathematics. Two textbooks were analyzed for this research: the book of Olavo Freire, 1894, which combines the format of the cable suspended to a parabola, and the book of the decade of 1970 of Osvaldo Sangiorgi, which relates to the figure of a stock as a parabola. Note that these textbooks with eighty years of difference used the rope suspended to represent the parabolic shape. As the format of a cable suspended by the extremities under the action of its own weight is the catenary, we felt motivated to search on the curves and understand how, after all, the cable of the suspension bridge is best represented. Since this question came from textbooks, we studied the basis of the book of Mathematics in the classroom, as indicators of teaching Mathematics in a given location, within a certain historical and political context. Throughout the history of Mathematics, there was confusion between these two curves, which led the study of catenary from the seventeenth century. This phase of history is known as the curves season, and in 1600, by Huygens, who started their studies. We have audited the catenary curves and parabola in education and the history of Mathematics, and its properties and practical applications in the Engineering of suspension bridges and architecture. Supported us in specific readings of history and construction of some suspension bridges and even payed a visit to the bridge Estaiada in Sao Paulo which is still under construction, to understand how the engineers use the properties of the catenary curves and parabola in its construction. The results showed that, surprisingly, the example used in the book of Olavo Freire to represent a parabola did not bring into account what happens in the practice of Engineering of the suspension bridges, and the resurgence of the example of the balance sheet in the book of Osvaldo Sangiorgi seemed to strengthen the argument that there was some confusion between the two curves. Using the software chart Winplot, the catenary and parabola curves were built and we could visualize the differences or similarities between them. At last, using algebra we proved the rapprochement between the catenary curves and definition of parabola in terms of Engineering.