Cette thèse s'intéresse à la relation sujet-objet – l'expérience d'apprentissage vécu par des étudiants universitaires dans le cadre du jeu sérieux Laboratorium of Epidemiology (LOE). Elle porte essentiellement sur la modélisation de phénomènes d'apprentissage – Appropriation et Authenticité – et se veut multidisciplinaire en rassemblant Psychologie de l'Education, Didactique des Mathématiques et Environnements Informatiques pour l'Apprentissage Humain. Le terrain d'expérimentation de cette thèse se place dans le cadre d'un module de Biostatistique dans lequel le jeu sérieux LOE a été implémenté de manière écologique et pérenne. La problématique de recherche porte sur les phénomènes d'appropriation et d'authenticité qui sont formalisés et illustrés, en s'appuyant sur la Théorie des Situations Didactiques (TSD) de Brousseau. Des traces d'activité, des interactions verbales et des entretiens directs ont été analysés au cours de trois années d'utilisation du jeu LOE. Ce travail a permis la construction de concepts tels que « l'appropriation de rôle » par des étudiants dans le contexte d'un jeu sérieux, « l'appropriation de problèmes » par les étudiants que ce soit à travers leurs interactions individuelles avec l'objet (le jeu) ou dans la recherche collaborative de solution aux problèmes, et enfin « la perception de l'authenticité » du jeu. Ainsi, cette thèse montre comment appropriation et authenticité découlent de l'interaction individu-objet. L'appropriation est un élément de l'expérience d'apprentissage à partir duquel l'individu fait sien un objet d'apprentissage dans un processus actif de développement transformationnel dans lequel l'individu reconstruit l'objet qu'il s'approprie à sa manière. Dans le modèle proposé, le processus s'établit par des catégories non nécessairement consécutives : accepter, tester, faire des choix, anticiper et maîtriser. La perception de l'authenticité d'un jeu sérieux par un individu est favorisée par des attributs de l'environnement informatique en raison de l'impact qu'ils produisent chez l'individu. L'authenticité d'un environnement informatique est définie comme un compromis entre trois dimensions élémentaires : réalisme, cohérence interne et pertinence didactique. Une meilleure compréhension de ces phénomènes à la base du processus d'apprentissage contribuera aux études futures sur la qualité de l'enseignement et sur la conception de nouveaux outils, en particulier ceux basés sur le jeu de rôle et l'immersion. / This thesis is interested in the relation subject-object – the learning experience lived by university students in the case of the serious game Laboratorium of Epidemiology. ( LOE). It concerns essentially the modelling of learning phenomena in Didactics of Mathematics – Appropriation and Authenticity – and aims to be multidisciplinary by gathering Psychology of the Education, Didactics of the Mathematics and Technology Enhanced Learning. The thesis field experiment takes place within a discipline of Biostatistics in which the serious game LOE was implemented in an ecological and permanent manner. The search problem concerns the phenomena of appropriation and authenticity which are formalized and illustrated, supported by Brousseau's Theory of the Situations. Tracks of activity, verbal interactions and direct interviews were analysed during the three years of use of the game LOE. This work allowed the construction of concepts such as the "role appropriation" by students in the context of a serious game, the "appropriation of problems" by the students whether individually through interactions with the object (the game) or collaboratively seeking a solution to the problems, and finally "the perception of the authenticity" of the game. In this way, this thesis shows how appropriation and authenticity ensues from the interaction individuals-objects. The appropriation is an element of the learning experience from which individuals makes their own learning objects in an active process of transformational development in which individuals reconstruct the object they appropriate their own away. In the proposed model, the process becomes established by categories not necessarily consecutive: accept, make out a will, choose, anticipate and master. The perception of the authenticity of a serious game by an individual is favoured by attributes of the IT environment due to the impact such attributes produce within individuals. The authenticity of an IT environment is defined as a compromise amongst three elementary dimensions: realism, internal coherence and didactic relevance. A better understanding of these phenomena on the basis of the learning process will contribute to future studies on the quality of teaching and on the design of new tools, in particular those based on role-playing and immersion.

Made available in DSpace on 2016-04-27T16:57:09Z (GMT). No. of bitstreams: 1 Roberto Fecchio.pdf: 3774789 bytes, checksum: 41b96ac7dadcae48b7c85961ecc01941 (MD5) Previous issue date: 2011-08-19 / The objective of the survey was to investigate the use of Mathematic Modeling allied to the Interdisciplinarity and to Theory of Didactic Situation, such as facilitator resources on the introduction of the concept of differential equation for students of the Engineering basic cycle. The connection between these resources made possible the elaboration, organization, follow-up and analysis of a didactic sequence, constituted by 15 steps, which involved: Experimentation, Abstraction, Resolution and Validation. In this study, the intention was to answer the following question: Interdisciplinarity activities which use the Mathematic Modeling propitious the learning of differential equations? The research was characterized as qualitative, of action research type, performed with 12 students from the 2nd year of an Engineering course from Great ABC region. It was verified that different compounds of the didactic environment structure can be intermingled with the modeling phases, according to Bassanezi (2002), in an auto-reflexive spiral. Such activity, generated by a real problem has as scenario the position of the professor-researcher before a group of students in an environment constituted by laboratories, classroom, questionings and devolutions, based on the didactic situations proposed by Brousseau (2008). The analysis of the data obtained on the experimentation made possible to assert that the interdisciplinary activities led by steps, according to this work s indications, presented new possibilities of motivation, exploration of contents and results available to the Engineering basic cycle s students. It provided to students gains on the teaching and learning process and possibilities on the application of knowledge in new situations. Problems related to Mechanics, Electricity and other aspects of Physics can serve as starting point for other surveys, using the same theoretical frame of references for the study of 1st and 2nd order differential equations / O objetivo da pesquisa foi investigar a utilização da Modelagem Matemática aliada à Interdisciplinaridade e à Teoria das Situações Didáticas, como recursos facilitadores na introdução do conceito de equação diferencial para os alunos do ciclo básico da Engenharia. A conexão entre esses recursos possibilitou a elaboração, organização, acompanhamento e análise de uma sequência didática, constituída de quinze etapas, que envolveram: Experimentação, Abstração, Resolução e Validação. Neste estudo pretendeu-se responder a seguinte questão: Atividades interdisciplinares que utilizam a Modelagem Matemática propiciam a aprendizagem de equações diferenciais? A pesquisa foi caracterizada como qualitativa, do tipo pesquisa-ação, realizada com doze alunos do 2º ano de um curso de Engenharia da região do grande ABC. Verificou-se que diversos componentes da estrutura do meio didático podem ser intercalados com as fases da modelagem, conforme Bassanezi (2002), em uma espiral autorreflexiva. Tal atividade, gerada por um problema real teve como cenário a posição do professor-pesquisador diante de um grupo de alunos, em um meio constituído por laboratórios, sala de aula, questionamentos e devoluções, embasado nas situações didáticas propostas por Brousseau (2008). A análise dos dados obtidos na experimentação possibilitou afirmar que as atividades interdisciplinares, conduzidas por etapas, conforme indicadas neste trabalho, apresentaram novas possibilidades de motivação, exploração do conteúdo e de resultados ao alcance dos alunos do ciclo básico da Engenharia. Propiciou aos estudantes ganhos no processo de ensino e aprendizagem e possibilidades de aplicação dos conhecimentos em novas situações. Problemas relacionados à Mecânica, Eletricidade e outros aspectos da Física, poderão servir de ponto de partida para outras pesquisas, utilizando os mesmos referenciais teóricos para o estudo de equações diferenciais de 1ª e 2ª ordens

Made available in DSpace on 2016-04-27T16:57:31Z (GMT). No. of bitstreams: 1 Silvio de Brito Marcelino.pdf: 2271607 bytes, checksum: 6b6a10a1167ce96272393b8b040aaa14 (MD5) Previous issue date: 2014-05-13 / This paper describes an investigation into the use of software SuperLogo by a group of teachers of basic education in public schools of the State of São Paulo, specifically in order to understand how these teachers in activity on mathematical problems, acquire fluency in the use of interface, think math questions from the use of digital technology as well as develop / explore mathematical topics from the perspective of computational artifact. The theoretical framework of the study had by reference the Theory of Didactical Situations, the humans-with-media construct and cycle theory (use of technologies for teaching and learning mathematics). The research had qualitative approach, and analyzes were carried out from the point of view of content analysis, employing four sessions, held in a computer lab at a public school, and having by instruments for data collecting informal interviews, a questionnaire, a sequence of activities supported by non-digital technology (pencil and paper) and a didactical sequence built with problems that should be solved with the SuperLogo software. The results indicate that teachers could expand connections between mathematical knowledge available to them and the development of fluency in relation to the interface, and began to express thoughts that indicated the connection of their knowledge with the use of software, which led them to considerate the use of such resources with their student groups in the development of mathematical topics / Este trabalho descreve uma investigação sobre o uso do software SuperLogo por um grupo de professores da Educação Básica de escolas públicas do Estado de São Paulo, especificamente no sentido de compreender de que maneira os mesmos, em atividade sobre problemas matemáticos, adquirem fluência no uso da interface, pensam as questões matemáticas a partir do emprego da tecnologia digital, bem como desenvolvem/exploram temas matemáticos na perspectiva do artefato computacional. O quadro teórico do estudo teve por referência a Teoria das Situações Didáticas, o construto seres-humanos-com-mídias e a teoria do ciclo (uso de tecnologias para ensinar e aprender Matemática). A pesquisa teve caráter qualitativo, e as análises foram realizadas sob o ponto de vista da análise de conteúdo, empregando quatro sessões, realizadas em laboratório de informática de uma escola pública, e tendo por instrumentos de coleta de dados entrevistas informais, um questionário, uma sequência de atividades realizadas com suporte tecnológico não digital (lápis e papel) e uma sequência didática por meio de problemas que deveriam ser resolvidos no âmbito do SuperLogo. Os resultados indicam que os professores puderam ampliar as conexões entre o conhecimento matemático de que dispunham e o desenvolvimento de fluência em relação à interface, bem como passaram a expressar pensamentos que indicavam a conexão de seus conhecimentos com o uso do software, o que os levou a cogitar no emprego de tais recursos com seus grupos de estudantes, no desenvolvimento de temas matemáticos

Made available in DSpace on 2016-04-27T16:57:32Z (GMT). No. of bitstreams: 1 Mariana Dias Goncalves.pdf: 2451301 bytes, checksum: 5cf507f4102f5eb10d5837316c7d19e1 (MD5) Previous issue date: 2014-10-18 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This study aims to analyze a sequence of activities for students of the 8th grade of Elementary School II mediated by the use of SuperLogo software. This teaching sequence has been proposed to develop students‟ learning of the Pythagorean theorem by geometric constructions in the search of a knowledge grounded in reflection, not in the repetition. Preliminary studies, from the literature review, allowed the elaboration of the following research question: How does the development of an educational strategy based on the creation of didactic situations, using the SuperLogo software, can contribute to building meaningful learning related to geometric constructions? The proposed research, a qualitative study, has considered the Theory of Didactical Situations and the conception of didactic contract, both authored by Brousseau (1997), and Theory of Meaningful Learning of Ausubel (2002). With regard to the technological support, have been studied works of Oliveira (2013), Levy (1993), Borba and Villarreal (2005) and Tikhomirov (1981). The analysis of the protocols and discussions of the subjects during the field survey revealed that the proposed activities provoked thoughts about some topics in plane geometry, and permitted the discovery and consolidation of the Pythagorean Theorem. This experiment revealed the advantage of the approach taken towards the construction of a meaningful learning from a new configuration of the didactic contract, rather than the reproduction of routes in teaching geometric constructions / Este trabalho tem como objetivo analisar uma sequência de atividades desenvolvidas para alunos do 8º ano do Ensino Fundamental II, mediada pelo uso do software SuperLogo. Esta sequência didática visava que os sujeitos construíssem uma aprendizagem do Teorema de Pitágoras, a partir de construções geométricas, na busca por um saber menos reprodutor e mais autônomo. Os estudos preliminares realizados a partir da revisão bibliográfica permitiram a elaboração de uma problematização em torno da seguinte questão de pesquisa: De que forma uma estratégia pedagógica baseada na criação de situações didáticas, com uso do software SuperLogo, pode concorrer para a construção de aprendizagens significativas relacionadas às construções geométricas? A investigação proposta, de caráter qualitativo, apoiou-se na Teoria das Situações Didáticas e na concepção de contrato didático, ambas de Brousseau (1997), e na Teoria da Aprendizagem Significativa de Ausubel (2002). No que diz respeito ao aporte tecnológico, foram considerados os trabalhos de Oliveira (2013), Lévy (1993), Borba e Villarreal (2005) e Tikhomirov (1981). A análise dos protocolos e das discussões dos sujeitos durante a pesquisa de campo revelou que as atividades propostas provocaram reflexões a respeito de alguns tópicos da Geometria plana, além de permitirem a descoberta e consolidação do Teorema de Pitágoras. Essa experimentação permitiu constatar a vantagem do enfoque adotado, no sentido da construção de uma aprendizagem significativa a partir de uma nova configuração do contrato didático, ao contrário da reprodução de roteiros no ensino de construções geométricas

Made available in DSpace on 2016-04-27T16:57:37Z (GMT). No. of bitstreams: 1 Eliza Souza da Silva.pdf: 8116412 bytes, checksum: dd5a67c0829fe181eff2da3e6e8e1881 (MD5) Previous issue date: 2015-04-13 / Universidade do Estado do Pará / This research has as object of study the learning of linear transformations by undergraduates in mathematics and was held having as subjects eight students in a class of second year of the Licentiateship Degree in Mathematics from the State University of Pará. The theoretical framework of the investigation rests on the theory of didactic situations, used in order to produce a didactic sequence to investigate how Mathematics Degree students are able to solve conceptual problems related to the topic "linear transformations" in the context of didactic situations using digital technologies. The employed activities are based on a didactic situation architected in order to give to subjects conditions to develop, with autonomy, their own strategies, counting with the computer program GeoGebra 5 as mediating element. The theoretical review pointed to the existence of difficulties on the part of college students in learning linear algebra contents, which were confirmed in this study. The research results showed also that the development of activities based on the conceptual framework presented through a didactic sequence properly planned and with mediation by digital technologies can help students develop autonomy in learning and considerable cognitive gains, despite remaining difficulties related to the conceptual construction / Esta pesquisa tem como objeto de estudo a aprendizagem das transformações lineares por licenciandos em Matemática e foi realizada tendo como sujeitos oito alunos de uma turma do segundo ano do curso de Licenciatura em Matemática da Universidade Estadual do Pará. O referencial teórico da investigação repousa sobre a teoria das situações didáticas, utilizada com o intuito de produzir uma sequência didática com o propósito de investigar de que forma estudantes de Licenciatura em Matemática resolvem problemas conceituais em relação ao tema transformações lineares no âmbito de situações didáticas e com o uso de tecnologias digitais. As atividades empregadas têm por base uma situação didática arquitetada para dar aos sujeitos condições de desenvolverem, com autonomia, suas próprias estratégias, contando, para este fim, com o uso do programa computacional GeoGebra 5 como elemento mediador. A revisão bibliográfica realizada apontou para a existência de dificuldades, por parte dos estudantes universitários, na aprendizagem de conteúdos de álgebra linear, as quais foram confirmadas ao longo deste estudo. Os resultados da pesquisa apontaram, também, que o desenvolvimento de atividades baseadas nos pressupostos teóricos apresentados, por meio de uma sequência didática adequadamente planejada e com mediação por tecnologias digitais pode auxiliar os estudantes a desenvolver autonomia na aprendizagem e ganhos cognitivos consideráveis, ainda que permaneçam dificuldades relacionadas à construção conceitual

Made available in DSpace on 2016-04-27T16:57:40Z (GMT). No. of bitstreams: 1 Cleusiane Vieira Silva.pdf: 6400182 bytes, checksum: 6c0d40d69c8f2b844eb2ae51a0dac0bf (MD5) Previous issue date: 2015-12-14 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This thesis aimed to investigate how an environment of action and reflection that involves the pre-analysis , reflections on the pre-analysis , experimentation with students from Elementary School II , post-analysis and reflections on the post-analysis that is related to a didactic sequence on orthogonal symmetric , interferes in the Mathematics teachers knowledge , in the mentioned level. Nevertheless, this research aimed to answer the following question: how can an environment of action and reflection that is constituted in the times for the Complementary Activities, influence the Mathematics teachers (from Elementary School II) knowledge on orthogonal symmetric? The methodology that was used in this study was based on the presupposition of Didactical Engineering according to Artigue (1995) and on the contributions by Schön (1995; 2000). The theoretical referential had its basis on the Theory of Didactical Situations - Brousseau (1997) - to do a study on the influence of the didactical variables that were chosen in the Math teachers (Elementary School II) procedures and answers, as well as their students , and Margolinas (2002; 2004) to hold an analysis on the teacher s activity, in view of understanding how he/she develops the teaching practice and how it can influence students learning. Yet, the theoretical referential was based in Parzysz Picture of Geometric Paradigms (2001; 2006), in the analysis of the nature of the geometric work that is developed by teachers in the moments of construction and analysis of problem situations, and by students in the moments of interaction with these problems. The studies by Grenier (1988) were used as a reference in order to observe the students conceptions of Elementary School II according to orthogonal symmetric. The analysis of the registers that had been provided by the students made it possible the identification of conceptions that are related to the orthogonal symmetric some of them corroborate with the results from studies done by Grenier (1988); other ones seem to be specific in the group of investigated students. The analysis of registers of Math teachers also showed some concepts about orthogonal symmetric, and these conceptions seem to be related to the way this concept is presented in the course books. During the investigation, teachers had the opportunity to evaluate their own practice and reflected on the teaching methods they were using, to really know if they were working or not with their students. It was noted that an environment of action and reflection that is constituted at school, have influence on Math teachers knowledge, but this influence is limited / Esta tese teve por objetivo investigar como um ambiente de ação e reflexão, que envolve a pré-análise, reflexões sobre a pré-análise, experimentação com alunos do Ensino Fundamental II, pós-análise e reflexões sobre a pós-análise relacionadas a uma sequência didática sobre a simetria ortogonal, interfere nos saberes docentes de professores de Matemática desse mesmo nível de ensino. Portanto, foi pretensão desta pesquisa responder à seguinte questão: como um ambiente de ação e reflexão constituído nos horários destinados às Atividades Complementares (A.C.) pode influenciar os saberes docentes de professores de Matemática do Ensino Fundamental II, sobre a simetria ortogonal? A metodologia utilizada para este estudo apoiou-se nos pressupostos da Engenharia Didática, segundo Artigue (1995) e nas contribuições de Schön (1995; 2000). O referencial teórico baseou-se na Teoria das Situações Didáticas de Brousseau (1997), para fazer um estudo sobre a influência das variáveis didáticas escolhidas nos procedimentos e respostas de professores de Matemática do Ensino Fundamental II e de seus alunos, e Margolinas (2002; 2004), para realizar a análise da atividade do professor no sentido de compreender como esse profissional desenvolve sua prática docente e como esta influência na aprendizagem dos alunos. O referencial teórico baseou-se ainda no quadro dos Paradigmas Geométricos de Parzysz (2001; 2006) na análise da natureza do trabalho geométrico desenvolvido por professores nos momentos de resolução e análise das situações-problema e por alunos nos momentos de interação com essas mesmas situações-problema. Foram utilizados, como trabalho de referência, os estudos de Grenier (1988) para observar as concepções de alunos do Ensino Fundamental II quanto à simetria ortogonal. A análise nos registros fornecidos pelos alunos propiciou a identificação de concepções relativas à simetria ortogonal, algumas corroboram os resultados obtidos nos estudos realizados por Grenier (1988), outras parecem específicas do grupo de alunos investigado. A análise nos registros de professores de Matemática também expôs algumas concepções acerca da simetria ortogonal, cujas concepções parecem estar relacionadas à forma como esse conceito é apresentado nos livros didáticos. Durante a investigação, os professores avaliaram a própria prática e ponderaram sobre os métodos de ensino adotados por eles, no sentido de observar se tais métodos estão ou não surtindo efeito na aprendizagem de seus alunos. Constatou-se que um ambiente de ação e reflexão, constituído na escola, influencia nos saberes docentes de professores de Matemática, embora sua influência seja limitada

Submitted by Filipe dos Santos (fsantos@pucsp.br) on 2017-08-10T12:01:28Z No. of bitstreams: 1 Marcelo dos Santos Gomes.pdf: 1203156 bytes, checksum: f31d8b3dc2b1afe5a4fe1fa8f33f7022 (MD5) / Made available in DSpace on 2017-08-10T12:01:29Z (GMT). No. of bitstreams: 1 Marcelo dos Santos Gomes.pdf: 1203156 bytes, checksum: f31d8b3dc2b1afe5a4fe1fa8f33f7022 (MD5) Previous issue date: 2017-06-28 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This research had the objective of reflecting upon the possible relations between Gamification and the Theory of Didactical Situations. To achieve aforementioned objective, it was developed a bibliographical research that allowed to comprehend and define what gamification is and consequently, the need of studying the links between gaming and math learning and teaching. Even though the gamification theme is becoming bigger in the academic means e in the educational practice, the number of published researches is still little. Hence, a study about gamification and its approaches has been made, and thus, the definition of Karl Kapp has been adopted as it’s believed that his definition better allowed the analysis of gamification as a teaching strategy through the optics of the Theory of Didactical Situations in Mathematics from Guy Brousseau. To help connecting the teaching strategy and theory, researches with focus on teaching and learning of mathematics have been used, which have conducted us to the following observations: the importance and the need to further study gamification, before employing its potentialities, associate gamification and other theories and don’t be limited only to the usage of theories enjoyed by game designers, the importance of more dialogues between teachers and game designers occurring to enrich the use of gamification. Finally, the importance that gamification considers the fundamental role of institutionalization in the learning of a new knowledge, the restructuring of a previously learnt knowledge, or even the improvement of some mathematical skills / A presente pesquisa teve como objetivo fazer reflexões a respeito das possíveis relações entre a Gamificação e a Teoria das Situações Didáticas. Para cumprir tal objetivo, foi desenvolvida uma pesquisa bibliográfica que possibilitou compreender e definir o que é gamificação e, consequentemente, a necessidade de estudar as associações de jogos com o ensino e aprendizagem de matemática. Embora o tema gamificação venha crescendo no meio acadêmico e na prática educacional, o número de pesquisas publicadas ainda é pequeno. Mediante essa constatação, realizou-se um estudo sobre a gamificação e suas abordagens e, assim, adotou-se a definição de Karl Kapp, por acreditar que seja a definição que melhor propiciou analisar a gamificação como uma estratégia de ensino pela óptica da Teoria das Situações Didáticas de Guy Brousseau. Para auxiliar na relação entre estratégia didática e teoria, foram utilizadas pesquisas com enfoque no ensino e aprendizagem de matemática, que conduziu às seguintes observações: a importância e a necessidade de aprofundar-se mais a respeito da gamificação, antes de munir-se de suas potencialidades, associar a gamificação a outras teorias e não se limitar somente ao uso de teorias usufruídas por designers de jogos, a importância de ocorrerem mais diálogos entre professores e designers de jogos para enriquecer o uso da gamificação. Por fim, a importância de a gamificação considerar o papel fundamental da institucionalização na aprendizagem de um novo saber, da restruturação de um saber já assimilado ou, até mesmo, do aprimoramento de algumas habilidades matemáticas

Research on the mathematical behavior of children over the past forty decades has considerably renewed and augmented the body of evaluative tests of the results of learning (Lester, 2007). Research however, has provided very little knowledge about the means of improving students’ performance on these tests. Nevertheless teachers, students, and others are being pressured to improve students’ performance, but in order to concentrate on basic skills, the learning itself is made more difficult and slower. The combination of requirements has led to a variety of uncontrolled phenomena such as meta-didactical slippage (Brousseau, 2008). The purpose of this study was to: (a) understand the nature of meta-didactical slippage that occurred in a ninth grade predominantly African American mathematics classroom; and (b) describe how these meta-didactical slippages affect students conceptual understanding on a unit of study of ninth grade mathematics. The study was a descriptive, qualitative, case study that employed ethnographic techniques of data collection and analysis. The theory of didactical situations in mathematics (Brousseau, 1997) served as the theoretical lens that grounded the interpretation of the data, because it enabled the researcher to isolate moments of instruction, action, formulation, validation, and institutionalization in the mathematics teaching and learning process. The study was conducted over a period of 15 weeks in one, ninth grade class of 23 predominantly African American students at a high school in a southeastern state. Data was crystalized using multiple data collection techniques: (a) collection of document artifacts, which included student work samples and teacher lesson plans; (b) interviews conducted with the teacher; (c) researcher introspection; and (d) direct observation. Data was analyzed using ethnographic and discourse analysis techniques, including domain analysis, coding, situated meaning, and the big “D” discourse tool. The study found four themes, which illustrated the nature meta-didactical slippages: (a) over-teaching, (b) situational bypass, (c) language and symbolic representation, and (d) the design of didactical situations.

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.

Le sujet de ce travail est d'étudier les moyens de permettre aux étudiants de fin de secondaire d'accéder aux raisons de savoir étroitement liées à la construction des concepts de l'Analyse, et à leur formalisation. La thèse explore cette question et développe un cadre théorique pour l’élaboration d’ingénieries qui visent ce sens et cette nécessité. Ce cadre théorique, conçu au sein de celui de la TSD, repose sur l’élaboration d’un modèle de rationalités et d’adaptations de la TSD notamment aux niveaux heuristiques. Le débat scientifique en classe apparait comme un choix adapté pour la mise en oeuvre d’ingénieries dans ce cadre. Une ingénierie relative à la notion de limite et sa définition formelle est développée puis expérimentée. Les résultats laissent entrevoir chez les étudiants une certaine appropriation du formalisme de la définition de limite, ainsi qu’un lien plus construit entre les objets mathématiques (suites, fonctions) manipulés dans différents cadres lors des situations adidactiques et la définition formelle. / The aim of this work is to study the means necessary to allow students to accede to the raison d'être of the knowledge involved in the building of notions of Calculus and Analysis. The thesis deals with this question and develops a theoretical frame for the conception of engineering which aims this sense and this necessity. This theoretical frame, designed in TDS theory, stands on a model of rationalities and some adaptations of TDS mainly on heuristic levels. We deploy the scientific debate construct to design lessons based on this frame. A didactic engineering aiming at the notion of limit and its formal definition is developed and experimented. Productions resulting from this work suggest a best appropriation of the definition of a limit, as well as a better link between the mathematical objects handled in situations (sequences, functions…) and the formal definition.