Ce travail de didactique des mathématiques s'appuie sur le cadre de la Théorie des Situations Didactiques et s'intéresse à l'action conjointe des professeurs et des élèves dans un environnement numérique et à la dynamique que cette action conjointe engage. Il s'appuie aussi sur le cadre théorique de l'approche documentaire, qui complète et prolonge le cadre de l'approche instrumentale : les artefacts numériques présents dans cet environnement sont ainsi considérés comme des éléments du système documentaire des professeurs et des élèves. Considérant l'intégration de ces artefacts dans la classe ordinaire de mathématiques, nous mettons en évidence l'importance de moments particuliers, que nous nommons incidents didactiques, qui engagent des perturbations modifiant la dynamique de la classe. En développant cette notion d'incident didactique, nous construisons un cadre d'analyse permettant de mettre en évidence des phénomènes de genèse documentaire des enseignants et des élèves et d'en suivre les effets, à court ou à long terme, sur l'enseignement et l'apprentissage des mathématiques. Nous montrons que les incidents didactiques peuvent être, sous certaines conditions, des occasions de réorganisation locale et globale des connaissances pour le professeur dans le cadre de son enseignement ou pour l'élève dans son apprentissage des mathématiques / This work of mathematics education based on the framework of the theory of didactic situations, focuses on the joint action of teachers and students in a digital environment. We give an important place to the theoretical framework of documentary genesis, which complements and extends the scope of the instrumental genesis and considers artifacts as well as elements of the digital library system for teachers and students. In the general context of the use of technology in the regular classroom of mathematics, we seek to understand how the incidents are indicative of perturbations that change the dynamic of the class. In developing this notion of didactical incident, we build a framework to highlight the phenomena of documentational genesis of teachers and students and to monitor the short or long term eects on mathematics teaching and learning. We show that the didactical incidents, under certain conditions, oer opportunities for restructuring local and global knowledge for the teacher as part of his teaching or the student's learning of mathematics

La question de l’enseignement du nombre à l’école maternelle est abordée à travers les savoirs et les connaissances mathématiques spécifiques du professeur. Cette thèse s’inscrit dans le cadre de la théorie des situations didactiques. Une modélisation des savoirs mathématiques spécifiques pour l’enseignement du nombre à l’école maternelle est proposée afin d’étudier l’enseignement du nombre de dix enseignants. Le travail est complété par une micro formation relative à des savoirs spécifiques pour la quantité. La thèse étudie l’impact de nouveaux savoirs sur les connaissances mathématiques spécifiques de cinq professeurs. Enfin, les résultats de la recherche sont interprétés par rapport à la formation des enseignants / Teaching numbers in preschool is addressed though the specific mathematical knowledge of the teacher himself. This thesis work comes within theoretical didactical situations. A modeling system for specific mathematical knowledge is suggested in order to study the way ten teachers teach numbers. This work is completed by a short training course related to quantity knowledge. This thesis work analyses the impact of these new specific fields of knowledge for five amongst ten of these teachers. The final result of the research work is highlighted by teachers training.

Made available in DSpace on 2016-04-27T16:58:19Z (GMT). No. of bitstreams: 1 marcia.pdf: 567454 bytes, checksum: 549773993b0ea2b0efbe76289c983b75 (MD5) Previous issue date: 2002-11-19 / Conselho Nacional de Desenvolvimento Científico e Tecnológico / This work is about Mathematics teacher education. It ains to offer a contribution in this area, in terms of understanding the processes by which new mathematical content is adquired and existing knowledge extended. We hope that it helps teachers to develop suitable strategies for working with Geometry in the classroom. This study is founded in BROUSSEAU s theory of situations and in DUVAL s studies about the use of several registers of semiotic representation. We prepared a workshop composed of activities whose focus was quadrilaterals, which was attended by a group of teachers from elementary and secondary school levels. During the workshop, we discussed the theoretical references that had served as a base for selectiing the activities and for the manners in which these were presented. The research question is: how can we work with teachers in ways which result in the acquisition of geometrical knwledge and, at the some time, provide them with inherent didactic knowledge related the geometrical content? Our main hypothesis is that the proposed activities will contribute to the content acquisition and the discussion of the theoretical references to the didactic knowledge improvement. Analyses of the teachers behavior and discussion, during 33 workshop hours, reveals that the activities provoked considerations about definitions, assumpitions, properties of quadrilaterals, theorems and proofs, as well as helping teachers to discover the difficulties they have in using different registers of representation in Geometry. The discussion of the theoretical references made the teachers understand that in their classroom they have usually omitted the action, formulation and validity stages, discussed by BROUSSEAU, presenting Geometry in an institutionalized way / Esse trabalho trata da formação de professores de matemática. Nosso objetivo é oferecer uma contribuição nessa área, tanto no que se refere à aquisição de conteúdos, quanto no aprimoramento de conhecimentos que auxiliem os professores na elaboração de estratégias adequadas para o trabalho com geometria em sala de aula. Fundamentados na Teoria das situações de BROUSSEAU e nos estudos de DUVAL sobre a utilização de diversos registros de representação semiótica, elaboramos uma oficina composta por atividades envolvendo os quadriláteros e a desenvolvemos com um grupo de professores do ensino fundamental e médio. Durante o desenvolvimento da oficina, discutimos com os participantes o referencial teórico que embasou a seleção das atividades e a maneira utilizada para apresentar o conteúdo. A questão investigada é: como trabalhar com formação de professores de forma a contribuir com a aquisição de conteúdos em geometria, proporcionando ao professor conhecimentos didáticos inerentes a esses conteúdos? Nossas principais hipóteses supõem que o desenvolvimento das atividades contribuirá com a aquisição de conteúdos, e a discussão do referencial teórico, com aprimoramento de conhecimentos didáticos inerentes à geometria. A análise das discussões e comportamento dos professores durante as trinta e três horas de oficina, revelaram-nos que as atividades provocaram reflexões sobre definições, conjeturas, propriedades dos quadriláteros, teoremas e demonstrações, bem como ajudou os professores a descobrirem a dificuldade que têm em utilizar diferentes registros de representação em geometria. A discussão do referencial teórico fez com que os professores notassem que, geralmente, têm omitido em suas aulas, as fases de ação, formulação e validação discutidas por BROUSSEAU, apresentando a geometria de forma já institucionalizada