The dissertation explored didactical situations, in which mathematical concepts in nursery schools are created and specified. It discusses the link between two issues related to institutional pre-school mathematics education. These are: Do children in nursery schools have opportunity to discover mathematical concepts? What is characteristic for didactical situations, in which it happens? Dissertation is organised according to a scheme "theory-methodology-empirical findings". Presented research is realized as qualitative, data material is formed by written narratives, chosen analytical procedures belong to the framework grounded theory method. In the main research I managed not only to compare individual narrations of teachers from nursery schools and identify various teachers´ actions, practises and types of didactical situations, but also to find the form of the mathematical didactical situation in the environment of nursery schools.

5 TITLE: A priori analysis as a part of teacher's lesson planning AUTHOR: Mgr. Hana Nováková DEPARTMENT: Department of Mathematics and Mathematical Education SUPERVISOR: Prof. RNDr. Jarmila Novotná, CSc. This thesis focuses on a priori analysis as a part of teacher's lesson planning. The theoretical background consists of the Theory of didactical situations in Mathematics (TDSM). In TDSM, the a priori analysis is seen as one of the teacher's tools that he/she has when planning a lesson. The goal of the thesis is to analyse differences between a priori analysis as described in TDSM and the reality in teacher's practice, to compare lesson plans of experienced teachers with those of students and demonstrate the significance and application of a priori analysis in teacher's and researcher's practice. The thesis consists of three parts, theoretical, experimental and applicational. In the theoretical part, the main concepts of TDSM linked with a priori analysis are explained and the issue of teacher's lesson planning is presented. The experimental part starts with a pre-experiment. Its results contributed to precise the structure of a priori analysis for further use. During the main experiment, the lesson plans of experienced teachers were compared with those of pre-service teachers. The differences and the...

TITLE: Studentsʼ problem posing as an indicator of mathematical culture of lower secondary students AUTHOR: Mgr. Jiří Bureš DEPARTMENT: Department of Mathematics and Mathematical Education SUPERVISOR: Prof. RNDr. Jarmila Novotná, CSc. ABSTRACT: This thesis is focused on studentsʼ problem posing as an indicator of mathematical culture of lower secondary students. The theoretical background consists of research on problem posing, word problems in mathematics, mathematical culture and the Theory of didactical situations in mathematics. The goal of the thesis is to analyse links between problem posing and studentsʼ mathematical culture through the analysis and description of the posed problems. The thesis consists of two parts, theoretical and research part. In the theoretical part, there are the main findings about studentsʼ problem posing and some approaches to the concepts of word problems and mathematical culture, and the main concepts of the Theory of didactical situations used in the thesis. The research part starts with the analysis of the pre-experiment, which constitutes the basis for creation and characteristics of the conception of mathematical culture of problem posing. These parts are followed by the analysis of the main experiment, which provides the complete description of the posed problems...

This research studies the interaction among the following contexts: natural language, geometrical language and musical language and it can provide new instruments to accord didactical situations and for a deeper understanding of communication processes. It springs from the consideration that the geometrical transformations are usually used in the compositional processes and the “role of the music to learn geometrical transformations” is actually a new study. In the field of the theory of situations by G. Brousseau (1986) we can assume to be in front of a learning teaching-situation including non-teaching situation as the teacher of musical instruments, while transmitting the knowledge of musical language (theoretical-practical) didn’t have the intention to transmit the geometrical transformation.

La question de l’observance non-médicamenteuse est primordiale dans la prise en chargedes maladies cardiovasculaires chroniques. Des programmes d’éducation thérapeutique dupatient (ETP) sont proposés aux patients afin de les aider à « mieux vivre avec leur maladie »(OMS, 1998). Leurs évaluations sont toutefois décevantes : ils touchent peu de patients etsont peu efficaces.Cette étude porte sur deux populations : des patients (N=19) et des médecins généralistes(N=14). Elle se base sur des entretiens menés auprès des uns et des autres ainsi que desobservations de consultation et de séquences de vie quotidienne. Nous en avons extrait uneanalyse qualitative approfondie ainsi que des éléments quantitatifs afin de mener à bien desanalyses factorielles. Le croisement de ces données permet dans un premier temps demettre en évidence la diversité des Arrière-plans (Searle, 1982, 1985) susceptiblesd’influencer la transformation des conduites des patients et d’en construire une typologie.Elle établit ensuite trois styles thérapeutiques, pratiqués par les médecins généralisteslorsqu’ils sont confrontés à ce type de patients.L’étude de la rencontre de cette diversité anthropologique avec ces différents styles montreque, malgré une configuration plus propice que celles des programmes hospitaliers, larencontre éducative entre médecine de proximité et patients cardiovasculaires ne se faitpas, ou ne se fait que sous certaines conditions bien fragiles. Son analyse sous l’angleanthropodidactique permet toutefois d’ébaucher de nouvelles formes d’ingénieriesdidactiques pour l’ETP et de donner de nouvelles pistes pour la formation des soignants. / Non-medication compliance is essential when taking care of chronic cardiovascular diseases.Therapeutic patient educational (TPE) programs are proposed to patients in order to helpthem to « have a better life with their disease » (WHO, 1998). However, those programs’evaluations are disappointing: they reach very few patients and are not as efficient asplanned.Drawing on semi-structured interviews with general practitioners (GPs, N=14) and patientsdealing with a cardiovascular chronic disease (N=19), and quantitative analysis of datarelated to a potential link between social factors and types of behaviour, this study firstemphasizes the diversity of Backgrounds (Searle, 1982, 1985) which may influence patients’life-style modifications. This work then defines four patient-types and three therapeuticstyles applied by GPs when confronted to those patients. Those styles vary according to GPsrepresentations and attitudes related to therapeutic education and cardiovascular diseases.This study shows that even though GPs are more likely to help with this transformation thanmandatory educational programs, the encounter between them and chronic patients doesnot happen, or only does in very specific and fragile conditions. Nevertheless, this anthropodidacticalapproach allows us to draft new forms of didactic engineering for TPE and to givenew tracks for healthcare professionals training.

Made available in DSpace on 2016-04-27T16:57:34Z (GMT). No. of bitstreams: 1 Edinalva Rodrigues Ferreira.pdf: 3705947 bytes, checksum: ba772663e48a81f8a3029b08d56d4cbd (MD5) Previous issue date: 2014-12-17 / This study investigates obstacles to learning that students of the Youth and Adult Education reveal in the study of fractions. This is a qualitative research with analysis of the activities addressed to a sample of four students of high school 2nd grade students of a public school. The study proposed to discover learning obstacles that students have in relation to such content. The theoretical basis of this research follows the assumption of the Theory of Didactic Situations. The procedures of the study sought to design and implement an instructional sequence in order to answer the research question that is whether and to what extent an instructional sequence, whose preparation takes into account the specificities of students of the Youth and Adult Education, contribute to diagnosis obstacles to the construction of conceptions part-whole and operators, related to fractions. The sequence was organized with three activities that consist of similar problems and applied in three consecutive sessions. The results indicate that the sequence of activities applied in the classroom contributed to that were diagnosed pedagogical and epistemological obstacles concerning to the study of fractions which were revealed in learning situations. The data collected showed that although the subjects are young and adults students who, in their experiences, deal with the fractions and their representations, and the content is treated in all previous series, they recognize a fraction, but not understand the concept, representation and conceptions / Este estudo investiga obstáculos à aprendizagem que os alunos da Educação de Jovens e Adultos revelam no estudo das frações. Trata-se de uma pesquisa qualitativa com análise das atividades resolvidas por uma amostra de quatro alunos do 2ª ano do Ensino Médio de uma escola da rede pública estadual. O estudo se propôs a levantar obstáculos à aprendizagem que alunos da Educação de Jovens e Adultos apresentam em relação ao referido conteúdo. A base teórica desta pesquisa segue o pressuposto da Teoria das Situações Didáticas. Procurou-se elaborar e aplicar uma sequência didática a fim de responder a questão de pesquisa que consiste em saber em que medida uma sequência didática, cuja elaboração leva em conta as especificidades dos alunos da Educação de Jovens e Adultos, contribui para o diagnóstico de obstáculos à construção das concepções parte-todo e operadores, referentes às frações. A sequência foi organizada com três atividades compostas por problemas semelhantes e aplicada em três sessões consecutivas. Os resultados indicam que a sequência de atividades aplicadas em sala de aula colaborou para que fossem diagnosticados obstáculos didáticos e epistemológicos, referentes ao estudo de frações, que se revelam em situações de aprendizagem. Os dados coletados mostraram que apesar de os sujeitos da pesquisa serem alunos jovens e adultos que, em suas vivências, lidam com as frações e suas representações e de o conteúdo ser tratado em todas as séries anteriores, os mesmos reconhecem uma fração, mas não compreendem o conceito, a representação e as concepções

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

This work is a reflection on the results of an experimentation carried out on secondary school students of between 16 and 18 from various classes. The experimentation aims at identifying the implicit ideas they use when asked to solve a certain mathematical problem. In particular, in giving them these problems an heuristic approach was suggested, and the differences between this and a purely deductive approach were measured. Analyzing the different approaches used by the students and the difficulties they had in distinguishing between argumentative and demonstrative operations has given rise to a reflection on the use of software such as Geogebra and Excel.

This work is a reflection on the results of an experimentation carried out on secondary school students of between 16 and 18 from various classes. The experimentation aims at identifying the implicit ideas they use when asked to solve a certain mathematical problem. In particular, in giving them these problems an heuristic approach was suggested, and the differences between this and a purely deductive approach were measured. Analyzing the different approaches used by the students and the difficulties they had in distinguishing between argumentative and demonstrative operations has given rise to a reflection on the use of software such as Geogebra and Excel.

Cette thèse questionne l'enseignement de la proportionnalité à des élèves de 11 à 16 ans relevant de l'adaptation scolaire et de la scolarisation des élèves handicapés. Les travaux de didactique des mathématiques ont montré l'inaboutissement fréquent du projet d'appropriation de la proportionnalité auprès des élèves jusqu'au collège, et tout particulièrement en ASH.Afin de savoir si une adaptation peut se faire sans dénaturer le savoir, nous proposons donc une progression sur l'enseignement de la proportionnalité en classe de Quatrième SEGPA.Nous insistons sur l'importance de l'organisation des savoirs au sein de cette progression et sur la pertinence des contextes et des valeurs des variables didactiques numériques. Les analyses de nos observations se font dans le cadre de l'analyse statistique implicative, de la Théorie des Situations Didactiques ainsi que de la double approche utilisée dans l'analyse des pratiques des enseignants.La mise en œuvre de la progression construite nécessite pour les enseignants des connaissances mathématiques. Afin de réactiver ces connaissances, nous proposons des représentations symboliques qui illustrent les techniques de résolution de problèmes relevant de la proportionnalité simple. / The purpose of this thesis is to investigate the teaching of proportionality to 11 to 16-year old pupils registered in special-needs schools including pupils with more severe learning disabilities.Studies related to the teaching of mathematics have shown that the understanding of proportionality by pupils up to middle school age and more particularly by children with significant learning difficulties is often inappropriate. In order to find out if an adjustment can be made without any impact on the knowledge requirements, we experimented a teaching plan concerning the learning of proportionality by children with special-needs in the context of our study. We insist on the importance of the organization of the different types of knowledge within this teaching plan and also on the relevance of backgrounds and values of numerical didactical parameters. Analysis of our observations is carried out with statistical implicative analysis, Theory of Didactical Situations and with the frame of the double approach used to analyse the practices of teachers.The implementation of such a teaching plan requires, for teachers, mathematical knowledge. In order to reactivate this knowledge, we propose a symbolic scheme for each resolving technique applied to problems involving direct proportionality.