Des récréations pour enseigner les mathématiques avec Lucas, Fourrey, Laisant

International audienceSourceURL:file://localhost/Users/evelynebarbin/Desktop/Article-HPM%202016-Actes/HPM2016-+Barbin&Guitart.doc À la fin du xixe siècle, il existe un retour aux récréations mathématiques dans une communauté française de mathématiciens, enseignants et amateurs. La nouveauté de ce retour est la volonté des auteurs d'inscrire les récréations dans l'histoire des mathématiques, de rechercher leur valeur pour l'enseignement et de développer de nouvelles mathématiques pour résoudre les problèmes qui leur sont liés. Nous trouvons ces trois intérêts historiques, pédagogiques et mathématiques chez Édouard Lucas, Émile Fourrey et Charles-Ange Laisant. Les récréations choisies par eux indiquent un continuum entre les trois propos. Avec eux, les récréations ne sont pas seulement un moyen d'amuser et elles deviennent une matière sérieuse à enseigner, selon des conceptions mathématiques et éducatives que nous analysons dans cet article.</p

Apports de l’histoire des mathématiques et de l’histoire des sciences dans l’enseignement

Ce que l’on attend de l’histoire des sciences vis-à-vis de l’enseignement change avec le temps. Aussi nous commençons en resituant les travaux et les formations concernant l’histoire des mathématiques dans les IREM et les IUFM depuis une trentaine d’années. L’histoire des mathématiques convoquée par les enseignants et les formateurs présente trois traits généraux : elle est dépaysante, épistémologique et culturelle. De plus, entre l’histoire d’une science et l’histoire des sciences, il y a des circulations du côté des problèmes, des concepts mais aussi des méthodes. Ainsi, l’histoire des sciences peut servir d’instrument pour une approche pluridisciplinaire des enseignements scientifiques. Nous abordons ensuite les lieux de formation, initiale et continue, des enseignants et les pratiques, la lecture des textes anciens et les problématiques enseignantes. Nous terminons en examinant les enjeux de l’introduction d’une perspective historique dans la classe.Waitings about history of sciences towards teaching change with time. So, we begin with situating works and trainings on history of mathematics in IREM and IUFM since thirty years. History of mathematics developped by teachers and educators offers three general features : it brings change of view about mathematics, it is an epistemological and a cultural history. Furthermore, there are circulations between history of a science and history of sciences, in matter of problems, concepts and also methods. So, history of sciences can serve as a tool for a pluridiscipinary approach of scientific teachings. Then we come to teachers’ education, pre-service and in-service trainings, and to the pratices, the reading of original texts and the problematics of teaching. We finish with examining the stakes of the introduction of an historical perspective in the classroom

Luigi Cremona and Wilhelm Fiedler: the link between descriptive and projective geometry in technical instruction

This paper considers Luigi Cremona’s and Wilhelm Fiedler’s outlook on technical instruction at school and university level, their vision about the educational role of descriptive geometry and its relation to Monge’s original conception. Like Cremona, Fiedler sees a symbiosis between descriptive and projective geometry via the fundamental idea of central projection. The link between projective and descriptive geometry plays a double role: an educational one due to the graphical aspects of the two disciplines and a conceptual one due to the connection of theory to practice. Thus, projective and descriptive geometry contribute to form a class of scientifically educated people, and the link between them epitomizes – in the opinion of Cremona – the link between pure mathematics and its applications. According to Fiedler, the main scope of the teaching of descriptive geometry is the scientific construction and development of “Raumanschauung”, as stated in a paper published in the Italian journal Giornale di Matematiche. The textbooks by Fiedler (1871) and Cremona (1873) were used in Italy to develop the geometry programs for the sezione fisico matematica (physics and mathematics section) within technical secondary instruction. While the relation between projective and descriptive geometry – and, thus, between pure and applied mathematics – had a short life at secondary school level in Italy, at the turn of the century there was a new expansion at university level due to the important role that then mathematicians had in the creation of the Faculty of Architecture

Dynamic simulation of the THAI heavy oil recovery process

Toe-to-Heel Air Injection (THAI) is a variant of conventional In-Situ Combustion (ISC) that uses a horizontal production well to recover mobilised partially upgraded heavy oil. It has a number of advantages over other heavy oil recovery techniques such as high recovery potential. However, existing models are unable to predict the effect of the most important operational parameters, such as fuel availability and produced oxygen concentration, which will give rise to unsafe designs. Therefore, we have developed a new model that accurately predicts dynamic conditions in the reservoir and also is easily scalable to investigate different field scenarios. The model used a three component direct conversion cracking kinetics scheme, which does not depend on the stoichiometry of the products and, thus, reduces the extent of uncertainty in the simulation results as the number of unknowns is reduced. The oil production rate and cumulative oil produced were well predicted, with the latter deviating from the experimental value by only 4%. The improved ability of the model to emulate real process dynamics meant it also accurately predicted when the oxygen was first produced, thereby enabling a more accurate assessment to be made of when it would be safe to shut-in the process, prior to oxygen breakthrough occurring. The increasing trend in produced oxygen concentration following a step change in the injected oxygen rate by 33 % was closely replicated by the model. The new simulations have now elucidated the mechanism of oxygen production during the later stages of the experiment. The model has allowed limits to be placed on the air injection rates that ensure stability of operation. Unlike previous models, the new simulations have provided better quantitative prediction of fuel laydown, which is a key phenomenon that determines whether, or not, successful operation of the THAI process can be achieved. The new model has also shown that, for completely stable operation, the combustion zone must be restricted to the upper portion of the sand pack, which can be achieved by using higher producer back pressure

Chorégraphie et Cinétographie : une mutation de l’écriture de la danse

La première écriture de la danse (chorégraphie) est présentée dans un ouvrage de 1700, Chorégraphie ou l’art de décrire la Danse de Raoul Auger Feuillet. Cette écriture a connu un succès durable et elle est toujours en usage pour les danses baroques. En 1928, Rudolf Laban propose une cinétographie, destinée à écrire les mouvements, y compris ceux de la danse. Cette nouvelle écriture ne ressemble pas du tout à celle de Feuillet. Nous proposons d’analyser et de qualifier une profonde mutation d..

Lois de la nature et lois des instruments au XVII e Siecle

Le discours logique de la physique aristotélicienne correspondait bien aux besoins d�une physique causale, mais il ne convient pas à la « nouvelle physique » du XVIIe siècle, à la recherche des règles exprimées par des relations mathématiques qui régissent les effets de la nature. La question est alors d�examiner quel discours pourra légitimer les résultats obtenus, quelle nécessité sera mise en avant, quel lien sera entretenu, quel sera l�ordre du nouveau discours scientifique. Nous proposons dans cet article d�analyser le rôle des instruments dans la réponse qui est donnée par les scientifiques, comme Galilée, Mersenne, Descartes, Pascal et Newton. En particulier, nous relevons que les instruments n�apparaissent pas comme des individus isolés, mais qu�ils constituent un monde bien réglé par des relations d�équivalence, de substitution et de composition. L�équivalence entre les instruments désigne leurs rapprochements par leurs effets, elle autorise la substitution dans les raisonnements, mais aussi dans les expériences. Les scientifiques composent les instruments entre eux, pour démontrer des propositions qui du coup s�organisent entre elles : l�ordre de composition des instruments peut ordonner l�ordre du discours scientifique. L�enchaînement des instruments construit une nécessité intelligible dans un processus de compréhension qui englobe, intègre et relie des phénomènes. C�est quand cette nécessité « éprouvée » est devenue une croyance sur la nature, que les lois des instruments deviennent des lois de la nature

L'histoire des mathématiques et Repères-IREM

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The dialectic relation between physics and mathematics in the XIXth century

The aim of this book is to analyse historical problems related to the use of mathematics in physics as well as to the use of physics in mathematics and to investigate Mathematical Physics as precisely the new discipline which is concerned with this dialectical link itself. So the main question is: When and why did the tension between mathematics and physics, explicitly practised at least since Galileo, evolve into such a new scientific theory?   The authors explain the various ways in which this science allowed an advanced mathematical modelling in physics on the one hand, and the invention of new mathematical ideas on the other hand. Of course this problem is related to the links between institutions, universities, schools for engineers, and industries, and so it has social implications as well.   The link by which physical ideas had influenced the world of mathematics was not new in the 19th century, but it came to a kind of maturity at that time. Recently, much historical research has been done into mathematics and physics and their relation in this period. The purpose of the Symposium and this book is to gather and re-evaluate the current thinking on this subject. It brings together contributions from leading experts in the field, and gives much-needed insight in the subject of mathematical physics from a historical point of view