Environnements Informatisés et Mathématiques: quels usages pour quels apprentissages?

Mathematics, seen as a model of pure science, often conveys the image of a science constructing itself in quite poor technological environments; it nevertheless develops by elaborating (and by exploiting) powerful material and symbolic tools. Actually mathematics teaching is closer to this image of mathematics than to mathematical practice: its goal seems to transmit a form of culture rather than efficient computation tools and theoretical means of their control (Kahane, 2002). This situation is viable if the tools can be held at distance, outside the classroom; it is no longer viable when computation tools (essentially calculators) are imported by students themselves inside the classroom and integrated into their mathematical practice. Thus established conflict between the social legitimacy of these tools and their school illegitimacy (Chevallard, 1992) deeply destabilises mathematics teaching itself. We present here a general framework to think about the integration of the tools in the teaching and learning of mathematics. More precisely, we propose:

1. A theoretical approach, which allows us to understand the influence of tools on human activity and in particular on professional and school education processes;
2. An analysis of computerized learning environments, which shows the importance of students' control of their own activity;
3. Some elements that help to think about the temporal and spatial organization of study in such environments and to guide students' activity;
4. A reflection about the conception of pedagogical resources, which is all the more necessary if one wants to facilitate an evolution of teachers' practices.

     

L'histoire de l'éducation au Brésil: traditions historiographiques et processus de rénovation de la discipline

Since the end of the 1980s, Brazilian histoty of education bas been redefined by new historiographical currents. The process of redefinition has taken on particular characteristics because of theoretical and institutional factors involved in the evolution of the discipline as afield of research. The new trends run counter to the historiographical model that dominated the post‐graduate programmes in education of the main Brazilian universities since the 1970s. This model originated in the 1930s and 1940s with the publication of reference works for educational history research. The present essay examines the process of reconfiguration of the discipline with a view to evaluating the restrictions that were imposed upon it.     

Proportionnalité et Pourcentage Chez des Apprentis Vendeurs. Réflexion sur la Relation Mathématiques / Réalité dans une Formation 'en Alternance'

This article presents the results of a research study conducted with apprentices in order to examine the double hypothesis that vocational training incorporating work placement gives the opportunity to construct authentic situations out of the everyday practices of students and that these situations allow students to improve their understanding of mathematical problems. After analysis of workplace situations had shown that the only mathematical concept used by apprentices was that of proportionality applied to percentage calculations, we first analysed the way in which students at several levels handled this idea of percentage. We then devised an experimental framework in order to help the apprentices to transfer their knowledge. RéSUMé: Cet article présente les résultats d'une recherche menée avec des apprentis vendeurs afin de vérifier la double hypothèse qu'un enseignement professionnel en alternance donne l'opportunité de construire des situations authentiques, à partir des pratiques quotidiennes des élèves et que ces situations permettent aux élèves d'améliorer leur compréhension des problèmes mathématiques. L'analyse des situations de travail ayant montré que le seul concept mathématique dont les apprentis ont l'usage est le concept de proportionnalité appliqué aux calculs de pourcentage, nous avons d'abord analysé le comportement d'élèves de plusieurs niveaux face à cette notion de pourcentage. Nous avons ensuite mis en place un dispositif expérimental afin d'aider les apprentis à transférer leurs connaissances. This revised version was published online in July 2006 with corrections to the Cover Date.     

Composantes Privées et Publiques du Travail de l'Élève en Situation de Devoir Surveillé de Mathématiques

In this paper, we propose to give some results about research done from 1989 to 1993 concerning a written assessment situation in math class (les devoirs surveillés) with high school students (16–17 years old) who are following a science oriented curriculum. In particular, we would like to determine if and how the students are sure of the answers they give and if they verify them.Our research methodology consisted of collecting both test papers and scratch pads from all the students in one class, then of interviewing some of them using the explicatory interviewing technique developed by P. Vermersch.In order to study this specific assessment situation, we use a theoretical framework developed by Y. Chevallard concerning an anthropological approach. Then, we introduce the notions of students' private work, meant to remain unseen and during which the verifications (if any) are done, and of a public trace (the test paper) meant to be shown to the teacher and to be evaluated. From a cognitive and didactic point of view, we want to show the importance of taking into account these two components for the analysis of the students' work in problem solving.     

Quelques aspects didactiques du développement de la pensée des enfants dans les mathématiques et la physique

Sans résuméConférence tenue au Congrès sur l'Intégration des enseignements scientifiques, à Varna, 11–19 septembre 1968.     

L’accès des filles à l’enseignement supérieur au Burkina Faso: choix parentaux,parcours d’étudiantes et défis

Girls’ access to higher education in Burkina Faso: parental choices, student trajectories, challenges – What motivates parents from less well-off backgrounds to invest in extended schooling for their daughters? What drives the girls from these backgrounds to stay in the school system up to university level? Many studies on Burkina Faso’s education system show that there are still disparities between girls and boys at all levels, with the gap widening as the level of studies gets higher. Under these conditions, the prospect of pursuing higher education is less certain for girls from less well-off families. Yet, girls from these backgrounds are relatively present at the University of Ouagadougou. Based on a qualitative survey of students and their parents, this article highlights the social rationale determining the specific educational trajectories of these girls. The level of schooling of the older siblings, the girl’s positon in relation to her siblings, or concern for equity are factors in some parents’ decision to enrol their daughters in school. Parents invoke several reasons to justify sending their daughters to university, one of the most frequent being the argument that their daughters faithfully help them in return. As for the students, they mention various motivations to explain why they have persisted with their schooling and university studies, often in difficult circumstances, notably the desire to help their parents. The article also highlights the importance of family support as a factor in girls attending school and university, as well as in the pursuit and success of their studies.     

Comprendre l'éducation physique à partir de la comparaison: le cas de la France et de l' Espagne

Le but principal de cet article est de comparer à partir des textes législatifs, des enquêtes ministérielles et européennes, et des revues spécialisées en France et en Espagne les propriétés de deux organisations scolaires singulières nommées «éducation prioritaire» ainsi que les mises en ?uvre de l'éducation physique. En nous appuyant sur l'approche de la construction sociale, nous présentons comment ces deux pays européens organisent cet enseignement dans les milieux défavorisés. Une analyse des aspects visibles du système éducatif à l'aide d'indicateurs généralistes (organisation des études, formation des enseignants, dépenses publiques) aurait laissé envisager d'importantes différences. Cependant, la comparaison à l'aide d'indicateurs «plus fins» des mises en ?uvre de l'éducation physique dans les écoles traditionnelles (poids de l'éducation physique, préoccupations gouvernementales et celles des enseignants, programmes d'enseignement) puis dans les milieux difficiles ZEP et CAEP (choix didactiques et pédagogiques) indique de fortes similitudes. Ces différences de résultats soulignent l'intérêt des analyses comparatives secondaires et la nécessité de considérer des analyses détaillées.

The main aim of this study is to compare two particular school organisations labelled ‘priority education’ in France and Spain, in relation to physical education using laws, ministerial and European surveys, and specialised journals. The social constructivist approach has been used to describe how both these European countries organise the teaching of physical education in under‐privileged environments. The analysis of the visible aspects of these educational systems with general indicators (organisation of studies, teacher education, public expenses) seems to imply differences. However, the comparison using more detailed data in the implementation of physical education in traditional schools (weight of the physical education in the system, governmental and teachers concerns, teaching programmes) indicates strong similarities. In addition, didactic and pedagogic choices in physical education in under‐privileged schools appear to be quite similar. These results underline the interest of secondary comparative studies and the necessity of taking into account detailed analyses.     

La Statistique: Fin et Moyen dans la Formation de l'ingénieur

RÉUMÉ

In this paper the recent needs and trends in statistics for engineers are discussed, particularly statistics as a motivating and illustrative tool in engineers' technical and methodological education.

Tendances et besoins recents en matière de statistique pour l'ingénieur. Rôe de motivation et d'illustration de la statistique dans sa formation technique et méthodologique.     

L’héritage de la méthode suédoise d’éducation physique en France: les conflits de méthode au sein de l’Ecole normale de gymnastique et d’escrime de Joinville au début du XXème siècle

The Swedish physical education method has had a singular destiny in France. Originally created by the Swedish Per Henrik Ling (1776–1839), it first spread in France thanks to German doctors. From 1902, the Swedish method became the official method of the Ecole normale de gymnastique et d’escrime de Joinville. It caused serious dissension first within the army, between Georges Hébert, a naval officer attempting to spread his own method called ‘Méthode naturelle’, and Emile Coste, a major at Joinville school who was a resolute supporter of Ling’s method; then within Joinville school, where, from 1905, Georges Demeny, renowned physiologist, tried to impose his French method ‘Eclectique’. The three protagonists would use arguments focused on the rationality of the Swedish method to legitimize or criticize it. But this explicit stake based on the validity of the link between a scientific culture – anatomy and physiology – and a physical education method does not mask the implicit stake of real power.     

Scolarisation,cultures et pratiques scolaires au Brésil: Éléments théoriques et méthodologiques d'un programme de recherche

This article concentrates on some considerations concerning the schooling process in Brazil during the nineteenth and twentieth centuries. Taking as reference the research carried out in the state of Minas Gerais, it particularly focuses on elementary/primary education there. First, it looks at the different schooling models in Brazil during that period of time and argues that educational statistics are one of the most interesting ways to study the representations about this phenomenon. It then looks at the sociocultural consequences of schooling and stresses the importance of educational institutions as a socialisation model for children, young people and society as a whole.     

La Mesure des Effets Pédagogiques des TIC : Pièges et Illusions du Découpage du Réel et de L'administration de la Preuve

La forte incitation actuelle de la part des autorités scolaires À recourir aux médias numériques en classe pose une nouvelle fois la question des arguments mis en avant. Et comme À l'occasion d'incitations antérieures (télévision scolaire, audiovisuel, informatique éducative), partisans et détracteurs s'appuient sur différents travaux qui attestent ou non de telle ou telle amélioration ou dégradation. Cette contribution se propose de montrer que les concepts et les modèles convoqués dans certains travaux, y compris les nÔtres et notamment le programme IN-TELE (Internet-Based Teaching and Learning), établissent entre les situations d'enseignement-apprentissage considérés comme classiques et celles qui sont supposées innovantes des distinctions parfois non pertinentes, qui se traduisent par des résultats outrageusement significatifs ou non significatifs. C'est donc le schéma modèle-observation-interprétation que nous interrogeons en suggérant que les outils de pensée disponibles et les procédés d'observation mis en m uvre aujourd'hui dans les différentes disciplines académiques qui s'intéressent aux usages pédagogiques des TIC contraignent, voire altèrent, notre compréhension des phénomènes éducatifs induits par les 'nouveaux' médias. Measuring the pedagogic effects of CIT: traps and illusions of cutting out actuality, and the

administration of proof. The strong current encouragement of school authorities to have recourse to digital media in the classroom poses once again the question of the arguments that have been advanced. And, as at the tine of earlier encouragement, (for school television, audiovisual, educational informatics), partisans and detractors rely on different works which support, or not, such-and-such a praise or detraction. This contribution attempts to show that the concepts and the models brought together in certain works, including our own and notably the IN-TEL (Internet-Based Teaching and Learning) programme, which establish between the teaching-training situations considered as classic and those which are supposed to be innovative, distinctions which sometimes are not pertinent, which are translated into results which are outrageously significant – or non-significant. It is, then, the schema of model-observation-interpretation that we question in suggesting that the mental tools available and the observational procedures used today in the different academic disciplines which are interested in the pedagogic use of CIT constrain us to see, may even, alter our understanding of the educational phenomenon introduced by the 'new' media. Analyse der pädagogischen Auswirkungen von ICT (Information and Communcation Technologies) : Fallen und Illusionen aus der Wirklichkeit, sowie die Beweisführung. Die gegenwärtig stark geförderte Umstellung des Unterrichtsmaterials auf digitale Medien durch die Schulbehörden, stellt erneut die bereits vorgebrachten Argumente in Frage. Und wie schon bei vorangegangenen Einführungen (von Schulfernsehen, Audiovision, pädagogische Informatik) beziehen sich Befürworter und Gegner auf verschiedene Studien, die den Nutzen oder Unnutzen attestieren. Dieser Beitrag versucht aufzuzeigen, dass herangezogene Konzepte und Modelle in verschiedenen Arbeiten - einschliesslich der unseren und insbesondere des Programms IN-TELE (Internet-Based Teaching and Learning) - sich zwischen klassischen Bildungssituationen und denen als innovativ angenommenen wiederfinden - auch wenn diese Unterscheidung nicht immer treffend ist. Wir stellen also das Schema Modell-Observation-Interpretation in Frage, indem wir suggerieren, dass die heute applizierten Denkmodelle und Observationsverfahren - der verschiedenen akademischen Disziplinen, die sich für den pädagogischen Gebrauch von ICT interessieren - für unser Verständnis des pädagogischen Einflusses durch Multimedia hinderlich sind, ja wenn nicht sogar deren Gebrauch nachteilig beeinflussen.     

Usages Éducatifs des Technologies de L'information et de la Communication: Quelles Compétences pour les Enseignants?

Abstract

The purpose of this article is to present, some results of recent research into the competence of teachers in the field of educational use of information and communication technology in France.     

Esclaves,Militaires et Libéraux: les Chemins de l’Enseignement Mutuel au Brésil (1808–1854)

Mutual/monitorial teaching was officially introduced in Brazil under the “Decree of the First Letters” on 15 October 1827. Such a decree was the first law on National Public Instruction of the Brazilian Empire and proposed the establishment and the adoption of the Lancasterian approach in elementary schools. This study analyses the beginning of the mutual/ monitorial teaching in Brazil between 1815 and 1827 and the political‐administrative obstacles to its implementation from 1827. Such an approach was influenced by the Société pour l’instruction élémentaire, founded in France in 1815 to promote the diffusion of mutual teaching. It also analyses the teachers’ formation based on the theoretical and practical principles of the mutual/monitorial teaching as explained in Baron de Gérando’s book, widely diffused in Latin America, Cours Normal des instituteurs primaires, ou Directions relatives à l’Education Physique, Morale et Intellectuelle dans les Ecoles Primaires (1832).     

Correspondance entre élèves : conditions d’une activité mathématique « créative » et problématisée à la fin du lycée

In this article, we characterized the forms of reasoning of French high school students (from Terminal Scientifique) in the course of an exchange of messages around the solution of a mathematical problem. Our goal was to determine whether or not the students make use of creative and investigative forms of reasoning. The results show that in the experimental conditions of the ‘mathematical correspondence,’ the students displayed an unusual mathematical problem-solving activity, one that is indeed more creative and investigative than those typically found in a classroom activity. The results are accompanied by an effort to explain the conditions that allowed for this unusual activity to develop and to suggest some paths to use this setting in the classroom, so as to facilitate better learning in problem-solving contexts and the transition from high school to university.     

Culture Politique,Scolarisation et Pratiques d’Appropriation: la Méthode Mutuelle dans le Minas Gerais (Brésil) au XIXe Siècle

This contribution deals with the adoption of the Lancasterian Monitorial System of Education in the State of Minas Gerais (Brazil) during the nineteenth century. The authors analyse the adoption of this device in the normalization of educational practices in schools and in the consolidation of the school system in the region. The structure and culture of a society, which still heavily relied on the work of slaves, framed the appropriation of this pedagogical innovation. The ambivalence between the rhetoric of freedom and independence and the search for new disciplinary devices pervaded all educational efforts and it also did so in the process of appropriation of the method. Along these lines, the authors present the discussion of the liberal elites of the region favouring the method, some new devices introduced in the culture of punishment, and the attitudes of the teachers faced with this innovation.     

De Genève à Belo Horizonte,une histoire croisée: circulation,réception et réinterprétation d’un modèle européen des classes spéciales au Brésil des années 1930

L’organisation des classes homogènes selon le niveau de développement mental des élèves et celle des classes spéciales pour les enfants en retard scolaire eut lieu dans les écoles élémentaires de Belo Horizonte, au Brésil, pendant les années de 1930, dans le cadre d’une réforme du système d’éducation, à laquelle participèrent des spécialistes étrangers, et en spécial la psychologue russe Helena Antipoff (1892–1974). Le projet des classes spéciales alors établies et leurs transformations dans le contexte brésilien sont étudiés à partir de données documentaires publiées entre 1930 et 1940. Née en Russie, Antipoff a fait des études supérieures en France (1910–1911), comme stagiaire dans le laboratoire Binet-Simon, et à Genève (1912–1914), à l’Institut Jean-Jacques Rousseau, où elle exerça ultérieurement les fonctions d’assistante d’Édouard Claparède (1926–1929). Notre hypothèse est que les classes spéciales créées à Belo Horizonte le furent sur le modèle genevois, et constituèrent un important exemple de circulation et diffusion de connaissances au niveau international, ainsi que de construction de repères dans le domaine de l’éducation spéciale au Brésil. Ainsi, la division des classes par niveau intellectuel mesuré par des tests d’intelligence, l’idée de “l’école sur mesure” proposée par Claparède, le dialogue avec les méthodes suggérées par Alice Descouedres démontrent les relations avec le modèle genevois. En même temps, l’interprétation des résultats des tests comme manifestation d’une forme d’ “intelligence civilisée” et les adaptations des exercices d’orthopédie mentale pour développer cette intelligence demandée par l’école montrent les transformations du modèle dans le contexte brésilien.     

Une personnalité du monde de l’Éducation nouvelle: Charles Ange Laisant (1841–1920) et son combat politique pour une éducation rationnelle fondée sur la science

In the world of nineteenth‐century educators Charles Ange Laisant occupies a special place. Laisant’s training, which was that of the French elite, opened up an administrative career but at the same time he continued to work and publish in the subject area of mathematics. His research demonstrates that he was clearly an accepted member of the scientific world, and he met the most eminent mathematicians of his day. Laisant played a major role in structuring the mathematical community, both nationally and internationally. He participated prominently in the battle that led to a change in the status and teaching of science in many countries in the early twentieth century. He is also one of those individuals who dedicated themselves to the renewal of pedagogy and to the goals of the new education. Yet, Laisant is still largely unknown; perhaps because of the profusion of his activities and interests he remains beyond the limits of traditional analysis. The author has chosen here, after retracing Laisant’s life in all its diversity, to focus on the profound unity of thought that characterised his mind. Laisant’s life as an educator allows us to understand how politics, science and teaching were inextricably linked, and to witness how personalities so diverse, even opposing, could come together to pursue common goals of educational reform.