Une etude sur l'approche du nombre par l'eleve du cours preparatoire

Sans résuméAttachée de recherches en psychologie à I'IREM de Grenoble.Maître-Assistante de mathématiques à l'Université Scientifique et Médicale de Grenoble.First Conference of the International Group for the Psychology of Mathematical Education, Utrecht, August 1977.     

Approche du nombre par des enfants de 6 à 7 ans

Sans résumé     

Les premieres acquistions de la notion de nombre par l'enfant

This paper describes the observation and analysis of clinical interviews with children who had just entered Cours Preparatoire (which is the first year of compulsory education in France: six-year old). The main object of these interviews was to gain information about the first acquisition of the idea of number by children before entering compulsory education, particularly on the following points:

· numerical range in which the child knows the comptine numerique (i.e. chanting or reciting of sequences of numbers such as “one two three four five six seven” for example);

· different uses of this comptine when the child has to solve problems (numbering a given collection, or finding the cardinal number of a given set when an element is added or taken away, or determining the numerical relation which exists between two given collections, or transformating this relation...).

In addition, our study shows how some number properties which apparently are obvious (for teachers), in fact pose very important questions about the acquisition of number concepts by children.     

Analyse des discours non strictement mathematiques accompagnant des cours de mathematiques

Resume Dans cet article, nous travaillons sur le discours non strictement mathématique qu'un enseignant peut tenir en classe de mathématiques; nous nous sommes restreintes à des élèves de plus de 15 ans, et aux moments d'exposition des connaissances. Nous présentons d'abord trois grandes fonctions que l'enseignant peut donner à ce discours (communication, structuration et étiquetage, réflexion), en illustrant notre propos par des exemples empruntés à un même cours de niveau universitaire. Nous cherchons diverses caractéristiques de ces trois fonctions, en dégageant notamment leur lien avec le déroulement même du cours, leur portée éventuelle pour les étudiants, leur lien avec les contenus exposés... Nous en déduisons des pistes de recherches ultérieures, notamment en ce qui concerne la troisiéme fonction, qui nous semble la plus susceptible d'être l'objet d'un travail spécifique de préparation de l'enseignant.

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Analysis of not strictly mathematical discourse in mathematics classes

In this article we examine the discourse which is not strictly mathematical that a teacher might adopt in a mathematics class. We have confined our discussion to students over 15 and to periods of teacher exposition. First we present three major functions of such discourse:communication, structuring and labelling, and reflection. We examine various characteristics of these three functions, primarily to make clear their relevance to the unfolding of the lesson itself, their influence on the students, and their bearing on the material taught, from this we develop lines for future enquiry, notably on the third function, which seems to us to be the most likely focus for specific preparation by the teacher.

     

Ruptures et continuités pédagogiques au terme du cours préparatoire

European Journal of Psychology of Education -     

Formation en cours de service des enseignants et nouvelles pédagogies

As M. Belbenoit's contribution is much lengthier than the articles normally accepted for the ATEE‐journal, the Editorial Secretariat were at first inclined to try to condense it. We found, however, that condensation would not allow a fair representation of the author's views, so decided to publish it in two instalments, of which the first in this issue of the journal.

Puisque I'article de M. Belbenoit est plus long que les articles normalement acceptés par le ATEE Journal, le Bureau de la Rédaction avait pensé en premier lieu à condenser l'article. Cependant nous avons jugé que cette procédure né permettait pas une représentation juste des opinions de l'auteur. Nous avons alors décidée de le publier en deux parties dont voici la premiè're.     

Pour une formation des enseignants à et par l'audiovisuel

Fauquet, M. “Pour une formation des enseignants à et par l'audiovisuel,” Revue ATEE Journal 3 (1980) 7‐23.

Teacher education geared to modern times has to deal with a new and double demand. The development of audiovisual educational technologies demands from an institution that it “educates” a teacher capable of incorporating these innovations into his practice. A training for the educational use of audio visuals presupposes an initiation into the production of audiovisual aids. It implies even more the study of semiology as well as that of psychological and sociological factors in the learning processes and communication aimed at the achievement of educational goals. This training has to be embedded in an education through the considered use of audiovisual aids. In a world where conditioning forces are ever increasing in strength it is essential that the teacher “educates himself” in such a way that he ensures his autonomy and favours that of his pupils. The strategy defined here makes possible a formative evaluation of the teacher training process. It takes as a starting point the awareness brought about by a supervised autoscopy and by discontinued teacher‐training‐periods inspires by micro‐teaching techniques which are themselves improved by sequential training techniques.     

Elaboration des programmes de l'enseignement general du second degre

Sans résumé     

Formation en cours de service des enseignants et nouvelles pédagogies (suite)

As M. Belbenoit's contribution was much lengthier than the articles normally accepted for the “revue ATEE journal”, the Editorial Secretariat were at first inclined to try to condense it. We found, however, that condensation would not allow a fair representation of the author's views, and so decided to publish it in two instalments, of which the first in the preceeding issue (p. 127‐150). This is the second instalment.     

La formation des enseignants du secondaire: la formule belge

The author, drawing upon 37 years’ experience of the training of Secondary teachers in Belgium, offers a critical view of the present situation. His remarks bear upon training for the lower‐Secondary cycle, the system for which—though apparently simple— is in fact complex.

A 1981 reform extended the period of training to three years, but lower‐ and upper‐Secondary training, at University level, are still separate. A greater unity is desirable.

Three principles which should underpin all training are: a planned continuation into in‐service training, the development of practice‐oriented research, and (to allow of flexibility) a unit‐based approach. The length of study is important, since it has implications for maturation.

Finally, the author examines in turn each element in the range of skills, aptitudes and attitudes needed by the student teacher.     

Utilisation conjointe du milieu et des ressources technologiques pour la formation des maîtres

Perusse, P., Décamps, E.A. and Pécot, F. “Utilisation conjointe du milieu et des ressources technologiques pour la formation des maîtres,” Revue ATEE Journal 3(1980)119‐133.

The training of teachers simply must develop. Yet, this development is at times thwarted by the latent conservative attitude of education. The introduction of educational technology, the technical and psychological integration of new teaching practices and more precisely of the latest products of audiovisual research, together with the computerized communications systems could provide the opportunity for that necessary break between the past and the present.

The resulting modification of relationships between those who teach and those who are taught, the new definition of tasks, and more particularly the part given to learners in the training of future teachers will make possible an opening towards the outside world and the coming into existence of a school of responsibility through responsibility. The first experiments show that we still have a long way to go before that aim is achieved.     

Fabrication de problèmes de fraction par des eleves a la fin de l'enseignement elementaire

Résumé Une expérience d'enseignement a été menée avec des élèves de Cours Moyen (Grade 4 et 5). Les élèves ont participé à une activité spécifiquement élaborée, la production de problèmes de fractions, à l'aide d'une terminologie spécifique, grâce à la production et à l'observation d'un ensemble de critères. Ainsi, les interactions au sein de la classe ont été organisées dans le but d'élaborer un système commun de significations, basé sur des outils sémiotiques appropriés, qui ont permis au maître et aux élèves de partager des significations mathématiques. De telles interactions nécessitent une négociation de nouvelles normes sociales qui détermine, pour le maître et les élèves, un nouveau contrat didactique.

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A longitudinal teaching experiment was conducted with fourth and fifth graders. Students participated in a specially designed activity, the production of fraction problems using a specific terminology developed through producing and applying a set of criteria. The interactions within the class were organised with the goal of developing a common system of meanings, based on appropriate semiotic tools, allowing teacher and students to share mathematical significations. Such interactions require a negotiation of new social norms determining, for teacher and students, a new didactic contract.

     

La socialisation des jeunes dans les villes du Tiers-Monde — le cas de l'Afrique

Résumé Les villes du Tiers-Monde sont des laboratoires du changement et de la formation. A partir de la situation de l'Afrique, on étudie ici les processus de socialisation des jeunes dans un environnement où se cotoient tradition et modernité. Les facteurs conduisant à l'exode, les différents circuits de prise en charge des migrants, la nécessité d'affronter la nouvelle vie dans un milieu complexe et souvent impitoyable, créent une situation et un processus d'apprentissage de la vie et du métier féconds d'initiatives et d'innovations. Cet entrainement à la vie est assuré par un réseau informel tissé par des nouvelles interactions sociales et par l'action des masses média.

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Third-World cities constitute quasi-laboratories for the study of change and learning. The present article takes the African situation of merging traditional and modern elements as its starting point and analyzes young people's socialization processes in this context. As a consequence of the activities of migrant organizations, the more general circumstances leading to migration and the fact that people are faced with a new lifestyle in a complex and often merciless environment, an atmosphere is created where learning for life and vocational training abound with initiative and innovation. This learning for life is borne by the informal fabric of new social interactions and the influence of the mass media.

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Zusammenfassung Städte der Dritten Welt stellen in gewisser Weise Forschungslaboratorien dar, in denen Veränderungen und Bildungsprozesse beobachtet werden können. Vor dem Hintergrund der gegenwärtigen Situation Afrikas werden im nachfolgenden Artikel Sozialisierungsprozesse von Jugendlichen in einem Umfeld untersucht, in dem Tradition und Moderne miteinander verschmelzen. Aus der Arbeit der diversen Hilfsorganisationen für Migranten, den allgemeinen Faktoren, die zu Migrationsbewegungen führen, und der Notwendigkeit für den Einzelnen, sich einem neuen Leben in einem komplexen und oft schonungslosen Milieu zu stellen, ergeben sich initiativ- und innovationsreiche Lernprozesse für Leben und Beruf des Einzelnen. Diese Bildung für das Leben wird durch die informelle Struktur neuer sozialer Interaktionen und durch die Einwirkung der Massenmedien gewährleistet.

     

L'influence du ‘décor’ et du langage dans des épreuves de type ‘logique’ portant apparemment sur l'implication

Résumé La recherche dont nous donnons ici quelques résultats avait pour but l'étude de différents paramètres dans le comportement de réponse à des problèmes portant apparemment sur l'implication d'une population hétérogène quant aux niveaux scolaires. En comparant les résultats obtenus à des tests suivant a priori les mêmes schémas logiques de raisonnement mais avec des formulations et/ou des décors différents, nous avons mis en évidence l'influence prédominante de ces facteurs dans le processus de résolution, ce qui remet en question, d'une part, l'idée qu'un individu arrivé au sommet de son développement intellectuel soit capable de raisonner, dans certains contextes non mathématiques, suivant des schémas indépendants du problème posé et assimilables à ceux de la logique binaire et, d'autre part, une pédagogie de la logique mathématique à partir d'examples et de situations dits concrets.

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In this article are presented some results of research into different aspects of behavioural response to some implication problems. After comparing the results obtained from tests which followed the same a priori analytical logic formulae, but with different formulations, we took account of the predominant influence of these factors in the solution process, which suggested two ideas; one, that an individual at the peak of his intellectual development is capable of reasoning in certain non-mathematical contexts by following some binary-logic formulae independent of the given problem, and two, the teaching of mathematical logic from so-called concrete examples and situations.

     

La Maîtrise Intuitive des Relations entre Masse,Volume et Masse Volumique Chez des Elèves du Premier Cycle

Three experiments have been devoted to the application of the methodology developped by Anderson, N. H. (1981, 1982) in the framework of the Information Integration Theory to the problem of the mastery by children (14 old) of the relations between the notions of mass, volume and volumic mass. It appears that, having to judge of the mass values of diverses objects from given values of volume and volumic mass, a majority of pupils are able to take account of the positive link between the mass on the one part and the volume and the volumic mass on the other part but apply an additive type integration rule. However, a minority of pupils are able to apply a normatively correct multiplicative rule. Concerning the judgements of volume values from given mass and volumic mass values, and the judgements of volumic mass values from given mass and volume values, a majority of pupils apply a soustractive integration rule. In these two cases however the integration patterns are extremely variegated. The relation between the algebraic level of analysis of the judgement data and an information processing level of analysis of the same data is discussed. The use by teachers of the paradigm presented in the study with the aim of improving upon the current evaluation methods is proposed.     

德彪西钢琴前奏曲《月色满庭台》的音乐分析

《24首钢琴前奏曲》是德彪西最具代表性和创造性的印象主义风格的作品,是印象主义音乐的精华。本文通过对钢琴前奏曲《月色满庭台》的主题动机、曲式、和声以及调式调性等方面的研究,力求探析德彪西创作技法的显著特征,并揭示出这些特征对其形成独特音乐风格的重要意义。     

La Formation par la Recherche: un espoir pour une rénovation des pratiques éducatives

While reforms in education are relatively easy to achieve at a superficial level (structures, statements of objectives) more far‐reaching attempts which seek fundamental changes in teacher attitudes and behaviour are more difficult to achieve because of the teacher's professional autonomy. A strategy found to be effective in Suisse romande has involved teachers closely in the work of educational researchers. The strategy, known as ‘interactive observation’, fulfils three functions: to bring order into the teacher‐learning process, to improve understanding, and to advance in‐service training. The creative and reflective roles demanded by this participation in research makes it easier for teachers to analyse, and where necessary modify, their own professional practices.