Depuis l’entrée en vigueur du Programme de formation de l’école québécoise en 2001, l’astronomie est à nouveau enseignée dans les classes du Québec. Malheureusement, l’école est mal outillée pour enseigner des concepts astronomiques complexes se déroulant pour la plupart en dehors des heures de classe et sur de longues périodes de temps. Sans compter que bien des phénomènes astronomiques mettent en jeu des astres se déplaçant dans un espace tridimensionnel auquel nous n’avons pas accès depuis notre point de vue géocentrique. Les phases de la Lune, concept prescrit au premier cycle du secondaire, sont de ceux-là. Heureusement, l’école peut compter sur l’appui du planétarium, musée de sciences dédié à la présentation, en accéléré et à toute heure du jour, de simulations ultra réalistes de divers phénomènes astronomiques. Mais quel type de planétarium secondera l’école ? Récemment, les planétariums ont eux aussi subi leur propre révolution : ces institutions sont passées de l’analogique au numérique, remplaçant les projecteurs optomécaniques géocentriques par des projecteurs vidéo qui offrent la possibilité de se déplacer virtuellement dans une simulation de l’Univers tridimensionnel complètement immersive. Bien que la recherche en éducation dans les planétariums se soit peu penchée sur ce nouveau paradigme, certaines de ses conclusions basées sur l’étude des planétariums analogiques peuvent nous aider à concevoir une intervention didactique fructueuse dans ces nouveaux simulateurs numériques. Mais d’autres sources d’inspiration seront invoquées, au premier chef la didactique des sciences, qui conçoit l’apprentissage non plus comme la transmission de connaissances, mais plutôt comme la construction de savoirs par les apprenants eux-mêmes, avec et contre leurs conceptions premières. La conception d’environnements d’apprentissages constructivistes, dont le planétarium numérique est un digne représentant, et l’utilisation des simulations en astronomie, complèteront notre cadre théorique et mèneront à la conception d’une intervention didactique à propos des phases de la Lune dans un planétarium numérique s’adressant à des élèves âgés de 12 à 14 ans. Cette intervention didactique a été mise à l’essai une première fois dans le cadre d’une recherche de développement (ingénierie didactique) visant à l’améliorer, à la fois sur son versant théorique et sur son versant pratique, par le biais de multiples itérations dans le milieu « naturel » où elle se déploie, ici un planétarium numérique gonflable de six mètres de diamètre. Nous présentons les résultats de notre première itération, réalisée en compagnie de six jeunes de 12 à 14 ans (quatre garçons et deux filles) dont nous avons recueilli les conceptions à propos des phases de la Lune avant, pendant et après l’intervention par le biais d’entrevues de groupe, questionnaires, mises en situation et enregistrement des interventions tout au long de l’activité. L'évaluation a été essentiellement qualitative, basée sur les traces obtenues tout au long de la séance, en particulier sous la voûte du planétarium. Ce matériel a ensuite été analysé pour valider les concepts théoriques qui ont mené à la conception de l'intervention didactique, d'une part, mais aussi pour faire émerger des améliorations possibles visant à bonifier l'intervention. Nous avons ainsi constaté que l'intervention provoque effectivement l'évolution des conceptions de la majorité des participants à propos des phases de la Lune, mais nous avons également identifié des façons de rendre l’intervention encore plus efficace à l’avenir. / Since the Quebec Education Program came into effect in 2001, Quebec classrooms have again been teaching astronomy. Unfortunately, schools are ill-equipped to teach complex astronomical concepts, most of which occur outside school hours and over long periods of time. Furthermore, many astronomical phenomena involve celestial objects travelling through three-dimensional space, which we cannot access from our geocentric point of view. The lunar phases, a concept prescribed in secondary cycle one, fall into that category. Fortunately, schools can count on support from the planetarium, a science museum dedicated to presenting ultra-realistic simulations of astronomical phenomena in fast time and at any hour of the day. But what type of planetarium will support schools? Recently, planetariums also underwent their own revolution: they switched from analogue to digital, replacing geocentric opto-mechanical projectors with video projectors that offer the possibility of travelling virtually through a completely immersive simulation of the three-dimensional Universe. Although research into planetarium education has focused little on this new paradigm, certain of its conclusions, based on the study of analogue planetariums, can help us develop a rewarding teaching intervention in these new digital simulators. But other sources of inspiration will be cited, primarily the teaching of science, which views learning no longer as the transfer of knowledge, but rather as the construction of knowledge by the learners themselves, with and against their initial conceptions. The conception and use of constructivist learning environments, of which the digital planetarium is a fine example, and the use of simulations in astronomy will complete our theoretical framework and lead to the conception of a teaching intervention focusing on the lunar phases in a digital planetarium and targeting students aged 12 to 14. This teaching intervention was initially tested as part of development research (didactic engineering) aimed at improving it, both theoretically and practically, through multiple iterations in its “natural” environment, in this case an inflatable digital planetarium six metres in diameter. We are presenting the results of our first iteration, completed with help from six children aged 12 to 14 (four boys and two girls) whose conceptions about the lunar phases were noted before, during and after the intervention through group interviews, questionnaires, group exercises and recordings of the interventions throughout the activity. The evaluation was essentially qualitative, based on the traces obtained throughout the session, in particular within the planetarium itself. This material was then analyzed to validate the theoretical concepts that led to the conception of the teaching intervention and also to reveal possible ways to improve the intervention. We noted that the intervention indeed changed most participants’ conceptions about the lunar phases, but also identified ways to boost its effectiveness in the future.

Submitted by Filipe dos Santos (fsantos@pucsp.br) on 2018-08-08T11:26:23Z No. of bitstreams: 1 José Ronaldo Alves Araújo.pdf: 4382435 bytes, checksum: 618af73b19c06c52b8e0008b9d05ba3c (MD5) / Made available in DSpace on 2018-08-08T11:26:23Z (GMT). No. of bitstreams: 1 José Ronaldo Alves Araújo.pdf: 4382435 bytes, checksum: 618af73b19c06c52b8e0008b9d05ba3c (MD5) Previous issue date: 2018-06-15 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This dissertation presents a qualitative investigation which was carried out within thscope of Statistics teaching and lasted for the potentialities of GeoGebra for an understanding of the Meditation of Central Tendency concepts. Based on the didactic actions, the formulation, validation and institutionalization of the Theory of Didactic Situations, the search was developed through a sequence of activities. The methodological methods for the elaboration, application and analysis of the activities were realized by the Engineering dimensions as preliminary techniques such as a priori analysis, experiment and a posteriori analysis. The participants in the research program was a high school group of the 1st grade in a public school in the state of São Paulo. The application of the class was carried out in a computer lab of the same school and was divided by four sessions of five minutes. The participants, through GeoGebra, treated the data of each activity and were answering the questions of the present study. Ahead of questions and answers, it was possible to identify, from the dialectical practices of the theoretical, the potentialities of GeoGebra for an understanding of the proposed mathematical objectives, such as, in a dialectic of action, the organization of the data and the search for answers to some questions. This organization of the data in tables, lists, ordered lists, graphical representation or even values for the Central Administration classes allows the students, a formulation dialectic, to reflect on the representation of the values in relation to the data set. The various representations of the data in the GeoGebra windows, in a validation dialectic, favor the participation of the participants on the relation of the indicators with the data of their origin. These multiple representations of a set of data allow other questions, allowing the discussion on market conditions, such as the evaluation of trends, which contributed to the teacher, a dialectic of institutionalization with the students, would be able to promote of consolidation of knowledge / Esta dissertação apresenta uma investigação de caráter qualitativo, realizada no âmbito do ensino da Estatística, e teve como objetivo identificar potencialidades do GeoGebra para a compreensão dos conceitos de Medidas de Tendência Central. Com base nas dialéticas de ação, formulação, validação e institucionalização da Teoria das Situações Didáticas, a pesquisa foi desenvolvida por meio de uma sequência de atividades. Os procedimentos metodológicos para elaboração, aplicação e análise das atividades utilizaram aspectos da Engenharia Didática com as análises preliminares, análises a priori, experimento e análises a posteriori. Participaram desta pesquisa alunos da 1ª série do ensino médio de uma escola da rede pública do estado de São Paulo. A aplicação da proposta ocorreu no laboratório de informática da mesma escola, em quatro sessões de cinquenta minutos e os participantes, por meio do GeoGebra, trataram os dados de cada atividade e responderam aos questionamentos do estudo. Diante dos questionamentos e das respostas apresentadas, foi possível identificar, a partir das dialéticas do aporte teórico, potencialidades do GeoGebra para a compreensão dos objetos matemáticos propostos, tais como, em uma dialética de ação, organizar os dados e encontrar respostas para alguns questionamentos. Essa organização dos dados em tabelas, listas, listas ordenadas, representação gráfica ou mesmo valores para as Medidas de Tendência Central permitiu aos alunos, em uma dialética de formulação, refletirem sobre a representação dos valores em relação ao conjunto de dados. As múltiplas representações dos dados nas janelas do GeoGebra, em uma dialética de validação, favoreceram para que os participantes conjecturassem sobre a relação dos valores encontrados com os dados de sua origem. Essas múltiplas representações de um mesmo conjunto de dados permitiram outros questionamentos, possibilitando discussões acerca de possíveis propriedades para as Medidas de Tendência Central, o que contribuiu para que o professor, em uma dialética de institucionalização junto aos alunos, promovesse a consolidação do saber

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.

Nous avons cherché, dans ce travail doctoral, à caractériser les pratiques de coopération de professeurs, formateurs, encadrants et chercheurs. Ceux-ci ont œuvré à la constitution et la mise en place conjuguées d’une ingénierie didactique sur la construction des nombres au début de l’enseignement primaire. Ils ont fondé pour cela un collectif, considéré comme une institution au sein du projet de recherche Ace-Arithmécole. Nous avons décrit une telle institution au travers d’un dialogue spécifique, le dialogue d’ingénierie.Pour analyser un tel dialogue, nous nous sommes appuyés principalement sur le cadre de la théorie de l’action conjointe en didactique. La notion de contrat / milieu nous a permis d’appréhender les transactions entre les membres du collectif dans une perspective didactique et de montrer qu’elles ont construit des faits d’expérience, c’està-dire des faits appris de l’expérience vécue collectivement. En effet, les transactions ne relèvent pas d’un jeu de questions /réponses entre les protagonistes mais d’un travail d’enquête commune sur la mise en place d’une ingénierie didactique coopérative. Chacun est alors capable de passer du topos de celui qui apprend au topos de celui qui désigne ce qui pourrait être appris, remarqué ou étudié. Au sein de cette nouvelle forme de l’étude, après un certain temps de pratique ingénierique, chacun est à même de réorienter l’action didactique collective et de participer à l’élaboration de praxéologies d’ingénierie. / This doctoral thesis seeks to characterise the cooperative practices of a team of teachers, pedagogical trainers, pedagogical advisors and researchers during the implementation of a didactic engineering on the construction of number concepts for 6-year-old and 8-year-old pupils (first & second grades). The collective group founded by these various actors are viewed as an institution within the research project Acearithmécole with a specific dialogue, that of the engineering dialogue of the project.In order to analyse this dialogue, we use the Joint Action Theory in Didactics. We refer to the notion of the dialectic of contract / milieu in order to identify the transactions between the collective members from a didactic point of view. We show how experience-facts have been developed by these transactions, that is to say facts that have been learnt from the collective, lived experience. Such transactions are not about a game of questions and responses between the various members of the group, but rather the result of a common investigation of the didactic engineering in which each member of the group is able to change learning positions and indicate a factor which they could learn, observe or study. Therefore, after an initial period of engineering practice, this new form of study enables each member to re-orientate the collective engineering action and to take on a share of the construction of the engineering knowledge.

Depuis l’entrée en vigueur du Programme de formation de l’école québécoise en 2001, l’astronomie est à nouveau enseignée dans les classes du Québec. Malheureusement, l’école est mal outillée pour enseigner des concepts astronomiques complexes se déroulant pour la plupart en dehors des heures de classe et sur de longues périodes de temps. Sans compter que bien des phénomènes astronomiques mettent en jeu des astres se déplaçant dans un espace tridimensionnel auquel nous n’avons pas accès depuis notre point de vue géocentrique. Les phases de la Lune, concept prescrit au premier cycle du secondaire, sont de ceux-là. Heureusement, l’école peut compter sur l’appui du planétarium, musée de sciences dédié à la présentation, en accéléré et à toute heure du jour, de simulations ultra réalistes de divers phénomènes astronomiques. Mais quel type de planétarium secondera l’école ? Récemment, les planétariums ont eux aussi subi leur propre révolution : ces institutions sont passées de l’analogique au numérique, remplaçant les projecteurs optomécaniques géocentriques par des projecteurs vidéo qui offrent la possibilité de se déplacer virtuellement dans une simulation de l’Univers tridimensionnel complètement immersive. Bien que la recherche en éducation dans les planétariums se soit peu penchée sur ce nouveau paradigme, certaines de ses conclusions basées sur l’étude des planétariums analogiques peuvent nous aider à concevoir une intervention didactique fructueuse dans ces nouveaux simulateurs numériques. Mais d’autres sources d’inspiration seront invoquées, au premier chef la didactique des sciences, qui conçoit l’apprentissage non plus comme la transmission de connaissances, mais plutôt comme la construction de savoirs par les apprenants eux-mêmes, avec et contre leurs conceptions premières. La conception d’environnements d’apprentissages constructivistes, dont le planétarium numérique est un digne représentant, et l’utilisation des simulations en astronomie, complèteront notre cadre théorique et mèneront à la conception d’une intervention didactique à propos des phases de la Lune dans un planétarium numérique s’adressant à des élèves âgés de 12 à 14 ans. Cette intervention didactique a été mise à l’essai une première fois dans le cadre d’une recherche de développement (ingénierie didactique) visant à l’améliorer, à la fois sur son versant théorique et sur son versant pratique, par le biais de multiples itérations dans le milieu « naturel » où elle se déploie, ici un planétarium numérique gonflable de six mètres de diamètre. Nous présentons les résultats de notre première itération, réalisée en compagnie de six jeunes de 12 à 14 ans (quatre garçons et deux filles) dont nous avons recueilli les conceptions à propos des phases de la Lune avant, pendant et après l’intervention par le biais d’entrevues de groupe, questionnaires, mises en situation et enregistrement des interventions tout au long de l’activité. L'évaluation a été essentiellement qualitative, basée sur les traces obtenues tout au long de la séance, en particulier sous la voûte du planétarium. Ce matériel a ensuite été analysé pour valider les concepts théoriques qui ont mené à la conception de l'intervention didactique, d'une part, mais aussi pour faire émerger des améliorations possibles visant à bonifier l'intervention. Nous avons ainsi constaté que l'intervention provoque effectivement l'évolution des conceptions de la majorité des participants à propos des phases de la Lune, mais nous avons également identifié des façons de rendre l’intervention encore plus efficace à l’avenir. / Since the Quebec Education Program came into effect in 2001, Quebec classrooms have again been teaching astronomy. Unfortunately, schools are ill-equipped to teach complex astronomical concepts, most of which occur outside school hours and over long periods of time. Furthermore, many astronomical phenomena involve celestial objects travelling through three-dimensional space, which we cannot access from our geocentric point of view. The lunar phases, a concept prescribed in secondary cycle one, fall into that category. Fortunately, schools can count on support from the planetarium, a science museum dedicated to presenting ultra-realistic simulations of astronomical phenomena in fast time and at any hour of the day. But what type of planetarium will support schools? Recently, planetariums also underwent their own revolution: they switched from analogue to digital, replacing geocentric opto-mechanical projectors with video projectors that offer the possibility of travelling virtually through a completely immersive simulation of the three-dimensional Universe. Although research into planetarium education has focused little on this new paradigm, certain of its conclusions, based on the study of analogue planetariums, can help us develop a rewarding teaching intervention in these new digital simulators. But other sources of inspiration will be cited, primarily the teaching of science, which views learning no longer as the transfer of knowledge, but rather as the construction of knowledge by the learners themselves, with and against their initial conceptions. The conception and use of constructivist learning environments, of which the digital planetarium is a fine example, and the use of simulations in astronomy will complete our theoretical framework and lead to the conception of a teaching intervention focusing on the lunar phases in a digital planetarium and targeting students aged 12 to 14. This teaching intervention was initially tested as part of development research (didactic engineering) aimed at improving it, both theoretically and practically, through multiple iterations in its “natural” environment, in this case an inflatable digital planetarium six metres in diameter. We are presenting the results of our first iteration, completed with help from six children aged 12 to 14 (four boys and two girls) whose conceptions about the lunar phases were noted before, during and after the intervention through group interviews, questionnaires, group exercises and recordings of the interventions throughout the activity. The evaluation was essentially qualitative, based on the traces obtained throughout the session, in particular within the planetarium itself. This material was then analyzed to validate the theoretical concepts that led to the conception of the teaching intervention and also to reveal possible ways to improve the intervention. We noted that the intervention indeed changed most participants’ conceptions about the lunar phases, but also identified ways to boost its effectiveness in the future.

La problématique qui justifie ce travail de recherche s’inscrit dans le paradigme de l’adéquation formation-emploi au Gabon et les conjectures théoriques qui nous ont permis de traiter de cette problématique s’inscrivent dans le paradigme socio-constructiviste en tant que paradigme épistémologique de la connaissance. En se centrant sur le volet formation, cette problématique fait état des dysfonctionnements dont le corollaire se traduit par un faible rendement scolaire des apprenants. Si toutes-fois ce faible rendement scolaire n’était manifestement plus à démontrer, il n’en demeurait pas moins que la diversité et la complexité des causes possibles n’en facilitaient point la visibilité et la lisibilité des solutions possibles. En se penchant un peu plus du domaine de réalité à partir duquel pouvaient prendre naissance les phénomènes observés et récriminés, il était question en effet d’interroger la situation d’enseignement et d’apprentissage en recherchant tous les liens de causalité ou de corrélation possibles entre la qualité des acquis des élèves et la diversité des facteurs susceptibles de favoriser ces insuffisances. Si cette indétermination nous situait entre : - une évidence des faits et - le souci d’élucidation des facteurs explicatifs, les résultats de notre thèse viennent de montrer avec cohérence et très grande significativité, l’existence d’une similarité entre les niveaux de rendement scolaire préexistants et les niveaux des acquis des élèves issus des dispositifs pédagogiques conçus et mis en œuvre par les enseignants dans les classes technologiques. / The problem which prompted this research work, registers in the adequacy between training and employment in Gabon; and the theoretical conjectures that enabled us to treat these problems are related to socio-constructivism as an epistemological paradigm of knowledge. While focusing on training aspects, these problems mention the dysfunctions whose corollary results in poor learning output. However, if these school poor outputs were obviously debatable, the diversity and the complexity of the possible causes did not facilitate the visibility, and the legibility of the possible solutions. Basing on the field from which the phenomena observed and recriminated originated, it comes out that the teaching and training situation, by searching all the possible causal or correlative links between the learners’ background knowledge and the diversity of factors likely to explain the insufficiencies. If this indetermination proves the facts to be obvious and requires clarification of the incriminated factors, the result of our thesis have just shown with coherence and very great clarification, the existence of a similarity/interdependence between the levels of preexistent school output and the levels of learners’ output resulting from the teaching devices designed and implemented by the teachers in technological classes.

Le programme -Une école adaptée à tous ses élèves-, qui s'inscrit dans la réforme actuelle de l'éducation au Québec, nous a amenée à nous intéresser aux représentations dans les grandeurs en mesure en mathématiques des élèves en difficulté d'apprentissage. Nous nous sommes proposés de reconduire plusieurs paramètres de la recherche de Brousseau (1987, 1992) auprès de cette clientèle. La théorie des champs conceptuels (TCC) de Vergnaud (1991), appliquée aux structures additives, a été particulièrement utile pour l'analyse et l'interprétation de leurs représentations. Comme méthode de recherche, nous avons utilisé la théorie des situations didactiques en mathématiques (TSDM), réseau de concepts et de méthode de recherche appuyé sur l'ingénierie didactique qui permet une meilleure compréhension de l'articulation des contenus à enseigner. Grâce à la TSDM, nous avons observé les approches didactiques des enseignants avec leurs élèves. Notre recherche est de type exploratoire et qualitatif et les données recueillies auprès de 26 élèves de deux classes spéciales du deuxième cycle du primaire ont été traitées selon une méthode d'analyse de contenu. Deux conduites ont été adoptées par les élèves. La première, de type procédural a été utilisée par presque tous les élèves. Elle consiste à utiliser des systèmes de comptage plus ou moins sophistiqués, de la planification aux suites d'actions. La deuxième consiste à récupérer directement en mémoire à long terme le résultat associé à un couple donné et au contrôle de son exécution. L'observation des conduites révèle que les erreurs sont dues à une rupture du sens. Ainsi, les difficultés d'ordre conceptuel et de symbolisation nous sont apparues plus importantes lorsque l'activité d'échange demandait la compétence "utilisation" et renvoyait à la compréhension de la tâche, soit les tâches dans lesquelles ils doivent eux-mêmes découvrir les rapports entre les variables à travailler et à simuler les actions décrites dans les énoncés. En conséquence, les problèmes d'échanges se sont révélés difficiles à modéliser en actes et significativement plus ardus que les autres. L'étude des interactions enseignants et élèves a démontré que la parole a été presque uniquement le fait des enseignants qui ont utilisé l'approche du contrôle des actes ou du sens ou les deux stratégies pour aider des élèves en difficulté. Selon le type de situation à résoudre dans ces activités de mesurage de longueur et de masse, des mobilisations plurielles ont été mises en oeuvre par les élèves, telles que la manipulation d'un ou des étalon(s) par superposition, par reports successifs, par pliage ou par coupure lorsque l'étalon dépassait; par retrait ou ajout d'un peu de sable afin de stabiliser les plateaux. Nous avons également observé que bien que certains élèves aient utilisé leurs doigts pour se donner une perception globale extériorisée des quantités, plusieurs ont employé des procédures très diverses au cours de ces mêmes séances. Les résultats présentés étayent l'hypothèse selon laquelle les concepts de grandeur et de mesure prennent du sens à travers des situations problèmes liées à des situations vécues par les élèves, comme les comparaisons directes. Eles renforcent et relient les grandeurs, leurs propriétés et les connaissances numériques. / -An education system adjusted to all its pupils-, in line with the present reform of the education system of Québec has led us in this project, to examine how students with learning problems deal with numbers and measurements in mathematics. In the present study, our purpose is to double-check many of the parameters defined in the work of Brousseau (1987, 1992). The theory of the conceptual fields of Vergnaud (1991)applied to the additives structures, was particularly useful in our analysis of the facts and the interpretation of their representations. In this work, the methodology we adopted is the Didactic engineering, wich allow a better understanding in articulating the contents to each. Using Theory of didactic situations in mathematics, we examined the didactic approaches the teachers have in their relationship with their students. The data for our study, which is of the exploratory and qualitative type, was collected with twenty six students of the second cycle of the primary school. That data was analysed in conformity with a medthodology of content analysis. The examination of the student's behavior revealed two attitudes. Almost all the students used the first attitude, which is of the procedural type. It consisted in using counting systems more or less sophisticated from the planning to the folowing actions involved. The second attitude implied memorizing for the long term, the result associated with a specific couple of actions and the control of their execution. The observaton of the student's attitudes reveals that the errors they made are related to a semantic disruption in their interpretation of the varied tips and strategies the teachers tried to help them with to solve the different problems. Thus, it appeared to us that the difficulties at the conceptual and symbolization levels were more important when the exchange activity involved their competence to evaluate and activity related to the understanding to the task to achieve. In other terms, they had more difficulty with the tasks where they had to establish by themselves to link between the variables, and simulate the actions involved by those tasks. Consequently, the tasks involving exchange operations happened to be more difficult to translate into actions, and were clearly more problematic than the other tasks. The study of the interaction between teachers and students revealed that only teachers used words in the process, where they used the approach of the control of the actions, or the approach of control of the meaning or both strategies to help students with problems. Depending on the type of problem encountered during these activities of measurements of length and masses, the students had recourse to numerous experiments such as manipulation of the standard measure(s). They proceeded by superimposing, by successive deferments, by folding, by cutting when the standard was exceeding in size; or by reduction or addition of some amount of sand to bring into balance the scale. We noticed also that despite the fact that certain students used their fingers to have a global idea of the external measures of the quantities, many of those same students had recourse to a diversity of other procedures during the same test. The result presented here support the hypothesis that says that the concepts of size and measurement get more meaning in a specific context, where they relate to real situations lived by the students, as well as by direct comparisons. They reinforce and establish links between the so-called sizes, their properties and the numeric knowledge.

Le programme -Une école adaptée à tous ses élèves-, qui s'inscrit dans la réforme actuelle de l'éducation au Québec, nous a amenée à nous intéresser aux représentations dans les grandeurs en mesure en mathématiques des élèves en difficulté d'apprentissage. Nous nous sommes proposés de reconduire plusieurs paramètres de la recherche de Brousseau (1987, 1992) auprès de cette clientèle. La théorie des champs conceptuels (TCC) de Vergnaud (1991), appliquée aux structures additives, a été particulièrement utile pour l'analyse et l'interprétation de leurs représentations. Comme méthode de recherche, nous avons utilisé la théorie des situations didactiques en mathématiques (TSDM), réseau de concepts et de méthode de recherche appuyé sur l'ingénierie didactique qui permet une meilleure compréhension de l'articulation des contenus à enseigner. Grâce à la TSDM, nous avons observé les approches didactiques des enseignants avec leurs élèves. Notre recherche est de type exploratoire et qualitatif et les données recueillies auprès de 26 élèves de deux classes spéciales du deuxième cycle du primaire ont été traitées selon une méthode d'analyse de contenu. Deux conduites ont été adoptées par les élèves. La première, de type procédural a été utilisée par presque tous les élèves. Elle consiste à utiliser des systèmes de comptage plus ou moins sophistiqués, de la planification aux suites d'actions. La deuxième consiste à récupérer directement en mémoire à long terme le résultat associé à un couple donné et au contrôle de son exécution. L'observation des conduites révèle que les erreurs sont dues à une rupture du sens. Ainsi, les difficultés d'ordre conceptuel et de symbolisation nous sont apparues plus importantes lorsque l'activité d'échange demandait la compétence "utilisation" et renvoyait à la compréhension de la tâche, soit les tâches dans lesquelles ils doivent eux-mêmes découvrir les rapports entre les variables à travailler et à simuler les actions décrites dans les énoncés. En conséquence, les problèmes d'échanges se sont révélés difficiles à modéliser en actes et significativement plus ardus que les autres. L'étude des interactions enseignants et élèves a démontré que la parole a été presque uniquement le fait des enseignants qui ont utilisé l'approche du contrôle des actes ou du sens ou les deux stratégies pour aider des élèves en difficulté. Selon le type de situation à résoudre dans ces activités de mesurage de longueur et de masse, des mobilisations plurielles ont été mises en oeuvre par les élèves, telles que la manipulation d'un ou des étalon(s) par superposition, par reports successifs, par pliage ou par coupure lorsque l'étalon dépassait; par retrait ou ajout d'un peu de sable afin de stabiliser les plateaux. Nous avons également observé que bien que certains élèves aient utilisé leurs doigts pour se donner une perception globale extériorisée des quantités, plusieurs ont employé des procédures très diverses au cours de ces mêmes séances. Les résultats présentés étayent l'hypothèse selon laquelle les concepts de grandeur et de mesure prennent du sens à travers des situations problèmes liées à des situations vécues par les élèves, comme les comparaisons directes. Eles renforcent et relient les grandeurs, leurs propriétés et les connaissances numériques. / -An education system adjusted to all its pupils-, in line with the present reform of the education system of Québec has led us in this project, to examine how students with learning problems deal with numbers and measurements in mathematics. In the present study, our purpose is to double-check many of the parameters defined in the work of Brousseau (1987, 1992). The theory of the conceptual fields of Vergnaud (1991)applied to the additives structures, was particularly useful in our analysis of the facts and the interpretation of their representations. In this work, the methodology we adopted is the Didactic engineering, wich allow a better understanding in articulating the contents to each. Using Theory of didactic situations in mathematics, we examined the didactic approaches the teachers have in their relationship with their students. The data for our study, which is of the exploratory and qualitative type, was collected with twenty six students of the second cycle of the primary school. That data was analysed in conformity with a medthodology of content analysis. The examination of the student's behavior revealed two attitudes. Almost all the students used the first attitude, which is of the procedural type. It consisted in using counting systems more or less sophisticated from the planning to the folowing actions involved. The second attitude implied memorizing for the long term, the result associated with a specific couple of actions and the control of their execution. The observaton of the student's attitudes reveals that the errors they made are related to a semantic disruption in their interpretation of the varied tips and strategies the teachers tried to help them with to solve the different problems. Thus, it appeared to us that the difficulties at the conceptual and symbolization levels were more important when the exchange activity involved their competence to evaluate and activity related to the understanding to the task to achieve. In other terms, they had more difficulty with the tasks where they had to establish by themselves to link between the variables, and simulate the actions involved by those tasks. Consequently, the tasks involving exchange operations happened to be more difficult to translate into actions, and were clearly more problematic than the other tasks. The study of the interaction between teachers and students revealed that only teachers used words in the process, where they used the approach of the control of the actions, or the approach of control of the meaning or both strategies to help students with problems. Depending on the type of problem encountered during these activities of measurements of length and masses, the students had recourse to numerous experiments such as manipulation of the standard measure(s). They proceeded by superimposing, by successive deferments, by folding, by cutting when the standard was exceeding in size; or by reduction or addition of some amount of sand to bring into balance the scale. We noticed also that despite the fact that certain students used their fingers to have a global idea of the external measures of the quantities, many of those same students had recourse to a diversity of other procedures during the same test. The result presented here support the hypothesis that says that the concepts of size and measurement get more meaning in a specific context, where they relate to real situations lived by the students, as well as by direct comparisons. They reinforce and establish links between the so-called sizes, their properties and the numeric knowledge.

Made available in DSpace on 2016-06-02T20:29:23Z (GMT). No. of bitstreams: 1 5388.pdf: 1714135 bytes, checksum: 2e73423e7cb34e5a28d3821bd12d4a5b (MD5) Previous issue date: 2013-03-23 / Financiadora de Estudos e Projetos / Working with resolution of situations-problem is of great importance on Mathematics Teaching-Learning process and on Teaching-Learning process of others disciplines, once the human being is all the time challenged to resolve problems in their daily life. The results presented on this assignment contemplate the efforts made for the validation of teaching system of first degree equation with two unknowns to the students from Middle School through situations-problem. The methodology applied was the didactic engineering. The specific goals are diluted on the stages of the methodology which are described on the introduction characterizing the previous analysis. At the stage of the analysis a priori was made the diagnosis of the difficulties presented by the students and theoretical conception. During testing we have developed a didactic sequence that we consider to be appropriate to teaching system of first degree equations bringing to the students ways of resolution, an adapted method of problems resolution, the use of teaching material as graphics board and Geogebra software. The results collected by means of the development of the didactic proposed, as well as the participation of the students on the activities proposed, observed in the analysis a posteriori will be faced with the hypothesis raised on this research assignment for the effect of validation process. We have noticed even though many teachers recognize the importance of the use of situations-problem on Mathematics Teaching, the majority doesn´t do it in satisfactory way, working mainly with the problems proposed in didactics books, without regard stages proposed on the methodology of resolution problems. Through analysis from the results achieved by the students, raising the percentage of hits in solving problems about systems of first degree equation with two unknowns in activities proposed, assessments and simulated test applied by school at the end of academic year, we can conclude that the didactic sequence presented on this assignment could propitiate the learning process. / O trabalho com resolução de situações-problema tem grande importância no processo de ensino-aprendizagem de matemática e de outras disciplinas, já que o ser humano é desafiado a resolver problemas a todo o momento em seu dia a dia. Os resultados apresentados neste trabalho contemplam os esforços realizados para a validação do ensino de sistemas de equação do primeiro grau com duas incógnitas ao aluno de oitavo ano do Ensino Fundamental II através de situações-problema. A metodologia aplicada foi a da engenharia didática. Os objetivos específicos estão diluídos nas etapas da metodologia descritos na introdução caracterizando a análise prévia. Na etapa da análise a priori foi realizado o diagnóstico das dificuldades apresentadas pelos alunos e concepção teórica. Durante experimentação desenvolvemos uma sequência didática, que julgamos ser adequada ao ensino de sistemas de equações do primeiro grau, apresentando aos alunos formas de resolução, um método adaptado de resolução de problemas, a utilização do material pedagógico Prancha de gráficos e do software Geogebra. Os resultados coletados com o desenvolvimento da proposta didática, assim como a participação dos alunos nas atividades propostas observados na análise a posteriori serão confrontados com as hipóteses levantadas neste trabalho de pesquisa para o efeito de validação do processo. Observamos que apesar de muitos professores reconhecerem a importância da utilização de situações-problema no ensino da matemática, a maioria não o faz de forma satisfatória, trabalhando principalmente com os problemas propostos em livros didáticos, sem levar em conta as etapas propostas na metodologia para a resolução de problemas. Através de análises dos resultados obtidos pelos alunos, elevando o percentual de acertos em problemas sobre sistemas de equações do primeiro grau com duas incógnitas em atividades propostas, avaliações e o simulado aplicado pela escola no final do ano letivo, concluímos que a sequência didática apresentada neste trabalho favoreceu o aprendizado.