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This article describes part of the research done in the IREM of Montpellier, concerning plane Euclidean geometry. Fifty secondary school pupils worked on the following problem: given two circles and a rectangle, what is the largest possible number of points of intersection? The author studies some of the typical trains of thought of the pupils during the course of solving the problem' In this way he introduces and analyses three ideas: elementary thought processes, the bridging of local gaps, the processes of differentiation and integration.  相似文献   

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The purpose of this research was to improve the understanding of 'problems involving combination and complementation';. We presented four different situations to three children with learning difficulties. An analysis of their initial mental representations, procedures, and reflections provided insight as to their thinking process. These mental representations dealt with numbers. They are first seen as physical objects such as representations of quantities, and this influences the choice of procedures to solve the problem. These processes led to the coordination of numbers and relationships within the proposed situation. This shows the impact of the logico-mathematical relation of inclusion. More economical procedures of counting and mental calculation emerge. Hence, we can distinguish solving from understanding.Racute;SUMacute;. Le but de cette étude vise l'amélioration des connaissances eu égard à la construction d'une compréhension de la résolution des situations de réunion et de complément d'ensembles. Nous avons présenté quatre situations diff'rentes à trois enfants en difficulté d'apprentissage. L'étude de leurs représentations mentales initiales, de leurs procédures et de leurs réflexions nous invitent à en apprécier l'évolution. Ainsi, pour ces élèves, les représentations mentales qui émergent de la situation proposée, portent sur les nombres. Ces derniers sont d'abord vus comme objets physiques, puis comme représentants d'une quantité d'objets, ce qui influence le choix des procédures. Les premières réflexions les invitent à coordonner les nombres et les relations entre eux. Nous voyons apparaître l'impact de la relation logico-mathématique d'inclusion. Des procédures plus économiques de comptage et de calcul mental émergent. Nous pouvons alors distinguer la simple résolution d'un problème de la compréhension de ce type de situation.  相似文献   

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In this paper, we try to determine the knowledge which can be drawn from classroom observations, and we consider what are the limitations and the powers of the different ways of using them. The most important limitations come from the observer's paradox (to look for what happens in a natural situation without any observer), and the subjectivity of witnesses. We analyze various pseudo-scientific methods and see that they have more inconveniences than the à l'oeil nu observation.In spite of these limitations, methodical observations (with video-tape, for instance) are a prodigious source of information for teacher-training and for educational research.  相似文献   

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This study deals with the observation of a class composed of children aged 8–9 solving division problems. The analysis aims at differentiating the attitudes of pupils confronted with situations resulting from ‘EMPIRICAL’ learning from those observed in situations involving action resulting from ‘DIALECTIC’ learning. Two learning sequences are described in the course of the study:
  • * The first includes four classical terms which allow the use of empirical methods to find the quotient and the remainder.
  • * The second includes two terms elaborated so that they favour a dialectic of action with the children.
  • The observed differences reveal that:

  • * The repetition of drills of the same nature during the first learning sequence does not result in important variations as far as success and solution procedures are concerned.
  • * On the other hand, during the second learning sequence, all pupils use a more economical solution procedure with high level success rate.
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    Résumé Les histoires de vie comme recherche de construction de sens à partir de faits temporels personnels projettent potentiellement dans l'univers éducatif la totalité de la vie et des vivants. Elles s'inscrivent dans une tradition biographique qui remonte aux bios socratiques comme art d'accoucher de la connaissance. Mais elles semblent aussi portées, ces dernières années, par un mouvement de fond, bio-éthique et biopolitique, qui interroge les modèles professionnels et disciplinaires de formation et d'investissement de la vie. Trois modèles sont dégagés: le modéle biographique ou d'investissement de la vie par un autre; le modèle autobiographique d'auto-investissement de sa vie, et le modèle dialectique ou de co-investissement. Ces modèles obligent l'univers éducatif à repenser les conditions de formation de nouveaux savoirs vitaux: intrusion de nouveaux acteurs sociaux avec des pratiques inédites qui entraînent des transformations de perspectives épistémologiques et méthodologiques selon de nouveaux réseaux de recherche/formation.
    Life histories can be a way of making sense of personal events and can project into the realm of education the whole of life and of living persons. They are part of a biographical tradition which goes back to the Socratic bios, perceived as a means of giving birth to consciousness. But recently they also seem to be part of a fundamental bio-ethical and bio-political movement which questions vocational and discipline-based training and life investment models. Three models are distinguished: the biographical model, in which others invest in the subject's life; the autobiographical model, in which the subject invests in his or her own life; and the dialectical model of co-investment. These models force education to rethink the conditions for the creation of new life knowledge: new social actors are entering the picture, with hitherto unknown practices that are leading to changes in epistemological and methodological perceptions in concert with new research and training networks.

    Zusammenfassung Lebensgeschichten können dabei helfen, persönlichen Ereignissen einen Sinn zu geben, und sie konnen die Gesamtheit des Lebens und lebender Personen in das Königreich Bildung projizieren. Sie sind Teil einer biographischen Tradition, die auf die sokratischen bios zurückgeht. Diese werden als ein Mittel zur Erweckung des Bewußtseins aufgefaßt. Seit kurzem scheinen sie jedoch auch Teil einer fundamentalen bio-ethischen und bio-politischen Bewegung zu sein, die berufliche und auf Disziplin basierende Fortbildungen und Lebensinvestitionsmodelle in Frage stellt. Drei Modelle werden unterschieden: das biographische Modell, in dem andere in das Leben eines Einzelnen investieren; das autobiographische Modell, in dem der Einzelne in sein eigenes Leben investiert und das dialektische Modell einer gemeinsamen Investition. Diese Modelle zwingen das Bildungswesen, die Bedingungen für die Vermittlung neuen Lebenswissens zu überdenken: neue soziale Akteure betreten die Bildungsszene mit neuen bisher unbekannten Praktiken, die zu Veränderungen in epistemologischen und methodologischen Auffassungen im Einverständnis mit neuen Forschungs- und Fortbildungsnetzwerken führen.
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    The 21st century will, we hope, be the century of education or, as Jacques Delors put it in his report for UNESCO, the century of "lifelong learning". But this hope will only be realised if education is the subject and aim of a universal right. This right is enshrined in the 1948 Universal Declaration of Human Rights, which ought to be recognised in all countries of the world as the set of principles that should guide human action. The recognition of these rights should lead to a functioning democracy within educational establishments, where the rules of life should be the same for all: pupils, teachers and administrators. It is no less essential that human rights should constitute guiding principles for educational practice. The United Nations Decade for Human Rights (1995–2004) is an outstanding opportunity for each state to establish a plan of action for a true programme of human rights education.  相似文献   

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    Prior to large experimentations on the teaching of probability theory, it appeared useful to observe some students working for a fairly long time. This observation should make more precise the difficulties of an important aspect when solving probability problems: the modelling aspect. Does systematic use of simulation produce miracles as it is sometimes said? Are the students naturally sensitive to a frequentist approach of probability theory? This paper contains some results on these questions, for example we pointed out for some students an obstacle to the frequentist approach. The results permit to conceive how using simulation for teaching could contribute to an improvement of students' approach to probability.  相似文献   

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    La convention portant création de l'Institut Supérieur Franco-Allemand de Techniques et d'Economie de Sarreguemines (I.S.F.A.T.E.S.), passée entre le Gouvernement de la République Française et le Gouvernement de la République Fédérale d'Allemagne, a été signée le 15 septembre 1978 au sommet franco-allemand d'Aix-la-Chapelle.  相似文献   

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