Made available in DSpace on 2016-04-27T16:58:34Z (GMT). No. of bitstreams: 1 Valdenir Francisco Duarte.pdf: 2275326 bytes, checksum: 64718a9487076854ec47a0150adb082d (MD5) Previous issue date: 2007-12-10 / This work, carried out as part of the research project AprovaME developed at the Pontifical Catholic University of São Paulo, has as its aim to verify the advances and the difficulties presented by students in the elaboration of proofs related to the properties of parallelograms. The research procedures adopted during the study drew from the theories of de Parzysz (2001) concerning formal and empirical proofs; the four dimensions involved in the construction of geometrical thinking perception, representations, construction and conception presented by Machado (1995); the representation of information from the point of view of Duval (1995); and the considerations related to logical sequences in Duval e Egret (1989). Using the methodology Didactical Engineering, a sequence of activities was designed and carried out with two groups of students. One group was composed of 8th grade Middle School students and the second of students from the first year of High School. The activity sequence was planned to involve students in, first, the construction of hypotheses and theses on the basis of empirical explorations and, in term, organise, in a deductive form, their propositions in order to elaborate proofs of various properties of parallelograms. The analysis of the students productions illustrates difficulties experienced in the process of argumentation and proof that can be grouped into three categories: difficulties related to the elaboration of proofs, difficulties associated with the acceptance of empirical arguments and difficulties linked to problems in interpreting the problems proposed. The analysis also suggested that as the activity sequence progressed, certain advances in relation to these difficulties occurred. Some students began to carry out calculations without needing to consider particular cases, others presented complete formal proofs and even those who produced incomplete proofs made use of logical reasoning in attempts to express valid arguments. In addition, a positive factor related to the activity sequence was the engagement of students in the analysis of proofs constructed by others / O presente trabalho, vinculado ao projeto AprovaME, desenvolvido na Pontifícia Universidade Católica de São Paulo, tem por objetivo verificar os avanços e as dificuldades apresentadas pelos alunos na elaboração de provas sobre as propriedades dos paralelogramos. Os procedimentos dessa pesquisa foram fundamentados nas teorias de Parzysz (2001) sobre provas formais e empíricas; Machado (1995) sobre as quatro dimensões da construção do pensamento geométrico: percepção, representação, construção e concepção; Duval (1995) sobre formas de representação de informações; Duval e Egret (1989) sobre seqüências lógicas. Usando a metodologia da Engenharia Didática, foram concebidas e aplicadas a alunos da oitava série do Ensino Fundamental e do primeiro ano do Ensino Médio, uma seqüência de atividades que visaram levá-los, de forma empírica, a construir o conceito de hipótese/tese e, de forma dedutiva, a ordenar proposições de modo a elaborar provas das propriedades dos paralelogramos. A análise das produções dos alunos mostra dificuldades no processo de argumentação e prova que podem ser agrupadas em três categorias: dificuldades ligadas à elaboração de uma prova, dificuldades oriundas da aceitação de provas empíricas e dificuldades ligadas à leitura e interpretação de enunciados. A análise também apontou que houve certos avanços nesse processo. Alunos realizaram cálculos sem o apoio empírico, outros apresentaram algumas provas formais completas, e mesmo aqueles que produziram provas incompletas mostraram um raciocínio lógico até o ponto onde elas foram feitas. Além disso, verificou-se que o fato de dois alunos poderem analisar a prova feita pela outra dupla foi um fator muito positivo na seqüência apresentada

Le statut et la fonction de l'entraîneur sportif se sont progressivement développés avec la naissance du sport moderne, à partir de la fin du XVIIIe siècle. Du début du XXe siècle à aujourd'hui, le modèle le plus prégnant est celui du technicien de « terrain » dont les méthodes se construisent avant tout sous l'influence socioculturelle dans laquelle il est « baigné ». À partir des années 1980, le processus de professionnalisation qui s'est développé a eu comme conséquence une subdivision des modèles stabilisés en nombreux profils individuels, qui vont bien au-delà du simple triptyque technicien-meneur d'hommes-stratège, mis en avant dans les différentes représentations de sens commun. L'analyse des discours de vingt entraîneurs sportifs, choisis pour représenter au mieux l'ensemble de cette population, nous permet de confirmer les modèles socioculturels connus, et de faire apparaître des profils individuels variés. Elle permet surtout de mettre en évidence l'ensemble des logiques de professionnalisation de cette population. Qu'elles soient communicationnelles, techniques, organisationnelles ou de formation, ces logiques ont comme intérêt scientifique de montrer comment les entraîneurs sportifs se construisent professionnellement aujourd'hui. / The status and function of the sport coach have steadily developed since the birth of modern-era sport, in the late 18th century. From the early 20th c. to the present day, the most significant model is that of the field technician whose methods have been built under the influence of his or her social and cultural background. The 1980s saw the emergence of a professionalisation process which subdivided the existing patterns into a variety of individual models, going further beyond the mere three-dimensional combination of the technician-leader-strategist that seems to be the most received representation. Material collected from twenty interviews with sport trainers who were chosen as the best possible sample of the population has been analyzed. This analysis both confirms the received social and cultural patterns and highlights various individual models. In particular, it traces all the logical sequences that define the professionalisation of the population.Be they related to communication, techniques, organisation or training, these sequences find their scientific value in the demonstration they make of how sport coaching takes shape nowadays.