Mathematics In France Research Articles

프랑스 중학교 수학 교육과정 분석

In this study, I have investigated the middle school mathematics curriculum in France, which was reformed according to the change of ‘Socle commun’ in 2015. I have analyzed the area of ‘algorithms and programming' that was newly introduced into the curriculum. The result shows that the area of ‘algorithms and programming' is effectively connected with all the other mathematical content areas rather than simply being added to the list of existing mathematics content areas. In this process, scratch plays a crucial role. In other words, scratch interweaves traditional mathematical contents with the area of ‘algorithms and programming' and thus creates a new type of mathematics curriculum. The curricular reform in France was made by pursuing algorithmic thinking rather than CT(Computational Thinking). In the age of artificial intelligence, the reform in the curriculum of middle school mathematics in France raises the necessity of introducing this area and scratch into the middle school mathematics curriculum in Korea.

Preface to the French Edition

russell: the Journal of Bertrand Russell Studies n.s. 37 (summer 2017): 252–4 The Bertrand Russell Research Centre, McMaster U. issn 0036–01631; online 1913–8032 c:\users\ken\documents\type3701\red\rj 3701 132 red.docx 2017-08-18 10:38 PREFACE TO THE FRENCH EDITION1 Bertrand Russell Nicholas Griffin, Introduction Russell Research Centre / McMaster U. Hamilton, on, Canada l8s 4l6 ngriffin@mcmaster.ca n 1908 a French translation of Russell’s book on Leibniz was published for which Russell wrote a short preface, published here for the first time in English. Russell's early philosophical work initially attracted more professional attention in France than in England. An Essay on the Foundations of Geometry (1897) was widely reviewed and commented upon in France, and a French translation appeared in 1901. In this Russell had the enthusiastic help of Louis Couturat, who had energetically promoted Russell’s work on geometry and, later, on the principles of mathematics in France. But Couturat, rather surprisingly, does not seem to have played a role in having Russell’s book on Leibniz translated. The person who was instrumental in that was Lucien Lévy-Bruhl (1857–1939). It was he who persuaded French publisher , Félix Alcan, to publish an English translation of Russell’s book and who encouraged Jean Ray (1884–1943), then a student at the Sorbonne, to translate it. He also contributed a preface of his own to the work. Although Lévy-Bruhl is now bestknown for his work on the mentality of “primitive” peoples, he was at the time professor of the history of modern philosophy at the Sorbonne and had written a book on Comte and a history of philosophy in France, as well as L’Allemagne depuis Leibniz (1890). But as a historian of philosophy he fell very much on the historical side of the division between historical and philosophical histories of philosophy that Russell laid out in his preface to the English edition of the Leibniz book. Lévy-Bruhl had consistently argued that philosophical systems should not be studied in isolation from the social, political and intellectual milieu in which they arose, to some degree prefiguring his later socio-anthropological work on “primitive mentality”. All of which makes it the more surprising that he should have taken such an interest in Russell’s book, which places itself firmly on the other side. Russell himself seems to have been unclear about Lévy-Bruhl’s involvement for he asked Ray how he should acknowledge Lévy-Bruhl. In reply Ray provided the wording that Russell used. 1 [La Philosophie de Leibniz, exposé critique par Bertrand Russell, m.a.-f.r.s. Traduit de l’Anglais par Jean Ray and Renée Ray. Avec une Préface de l’Auteur et un AvantPropos par L. Lévy-Bruhl, Professor à la Sorbonne. Paris: Alcan. 1908. Pp. 4, xvi, 233. Reprinted Paris, London and New York: Gordon & Breach, 1970.] f= Preface to the French Edition 253 (Ray also asked Russell to acknowledge his wife as co-translator.) Russell did not take the opportunity the French edition afforded to make changes to the text, as he had done with the French translation of his Foundations of Geometry. His excuse, that he could not take the time away from “another task”, was legitimate enough: he was just beginning to prepare Principia Mathematica for the press. But, as became habitual with him when his book on Leibniz was discussed, he did mention Couturat’s two works on Leibniz which had appeared shortly after his own and which he regarded as confirming his main claim about the centrality of Leibniz’s logic to his philosophy but which, at the same time, led him to accept, what he had denied in his book, that for Leibniz all truths, including contingent ones, are analytic . This is the one substantive matter discussed in the French preface. It is explained in more detail in his review of Couturat’s La Logique de Leibniz (Papers 4: 24) and in the preface to the second English edition (1937) of A Critical Exposition of the Philosophy of Leibniz. No manuscript of the preface is known. he present...

Women mathematicians in France in the mid-twentieth century

A short outline of the French system of ‘Écoles normales supérieures’ and ‘agrégations’ serves as the introduction to our account of the careers of the five women who completed a doctorate in mathematics in France before 1960 and became internationally known scientists: Marie-Louise Dubreil-Jacotin (1905–72), Marie-Hélène Schwartz (1913–2013), Jacqueline Ferrand (1918–2014), Paulette Libermann (1919–2007) and Yvonne Choquet-Bruhat (b. 1923). This is followed by a more general description of the place of women on the mathematical scene in France between 1930 and 1960, together with a brief sketch of the accomplishments of some other women and the identification of all those who were active in research before 1960 and became professors in the French university system.

The Institute Henri Poincaré and mathematics in France between the wars

Résumé Cet article présente la création de l’Institut Henri Poincaré (IHP) à Paris comme le résultat d’une stratégie bien précise destinée à moderniser les mathématiques en France par la mise en place d’un processus « concret et institutionnalisé d’internationalisation », comme on l’a dit. Pour sa part, l’entreprise Bourbaki prenait forme au milieu des années trente, après avoir noyauté un séminaire qui se déroulait précisément entre les murs de l’IHP. L’organisation acquit rapidement une certaine reconnaissance qui la reliait à la modernisation des mathématiques. Le principal responsable de la fondation de l’IHP est Émile Borel, que les œuvres philanthropiques de la fondation Rockefeller, et tout particulièrement l’International Education Board, vinrent soutenir dans la planification et le financement initial de l’IHP. Celui-ci favorisa la modernisation des mathématiques de deux manières : non seulement il renforçait les relations entre la physique mathématique et la stochastique — domaine de recherches alors en pleine expansion — mais l’Institut devint aussi un véritable lieu de rencontres, accueillant des mathématiciens français, de Paris ou de province, en même temps que leurs collègues étrangers qui pouvaient désormais effectuer à Paris des séjours de recherches encadrés par cette institution. Les nombreuses invitations à donner des conférences remplissaient cette fonction de même que les rencontres plus « informelles » entre physiciens et mathématiciens qui en résultaient souvent. Dans cet article, nous mettrons en évidence les conditions qui ont permis diverses collaborations auxquelles ont pris part des figures marquantes de l’IHP (comme Borel, Georges Darmois et Maurice Fréchet), Paul Lévy (de l’École polytechnique) ou encore certains de leurs élèves, parmi lesquels on compte des mathématiciens de renom.

A Renaissance Library Rediscovered: The ‘Repertorium librorum Mathematica’ of Jean I du Temps

This article transcribes in full the handwritten list of mathematical books owned by the sixteenth-century French lawyer Jean I du Temps of Blois. Du Temps, a noted expert on chronology and cartography, assembled a substantial collection of works on the mathematical arts, details of which were recorded by one of his pupils towards the end of the century. Du Temps's biography provides a starting point for an analysis of the contents of his library, which is then placed in the context of the renaissance of mathematics in France and of the international book trade.

Twenty-Five Years with Nicolas Bourbaki, 1949-1973

T he choice of dates is dictated by personal circumstances: they roughly bound the period in which I had inside knowledge of the work of Bourbaki, first through informal contacts with several members, then as a member for twenty years, until the mandatory retirement at fifty. Being based largely on personal recollections, my account is frankly subjective. Of course, I checked my memories against the available documentation, but the latter is limited in some ways: not much of the discussions about orientation and general goals has been recorded.1 Another member might present a different picture. To set the stage, I shall briefly touch upon the first fifteen years of Bourbaki. They are fairly well documented2, and I can be brief. In the early thirties the situation of mathematics in France at the university and research levels, the only ones of concern here, was highly unsatisfactory. World War I had essentially wiped out one generation. The upcoming young mathematicians had to rely for guidance on the previous one, including the main and illustrious protagonists of the so-called 1900 school, with strong emphasis on analysis. Little information was available about current developments abroad, in particular about the flourishing German school (Gottingen, Hamburg, Berlin), as some young French mathematicians (J. Herbrand, C. Chevalley, A. Weil, J. Leray) were discovering during visits to those centers.3 In 1934 A. Weil and H. Cartan were Maitres de Conferences (the equivalent of assistant professors) at the University of Strasbourg. One main duty was, of course, the teaching of differential and integral calculus. The standard text was the Traite d’Analyse of E. Goursat, which they found wanting in many ways. Cartan was frequently bugging Weil with questions on how to present this material, so that at some point, to get it over with once and for all, Weil suggested they write themselves Armand Borel is professor emeritus at the School of Mathematics, Institute for Advanced Study, Princeton, NJ.

Notes: High Standards and Cultural Diversity: Cautionary Tales of Comparative Research—A Comment on “Benchmarking Education Standards” by Lauren B. Resnick, Katherine J. Nolan, and Daniel P. Resnick

A recent article by Resnick, Nolan, and Resnick (1995) analyzed the curriculum and examination system for mathematics in France and the Netherlands. The focus of the article was on how the two countries create and maintain “world class standards” in mathematics. However, the authors overlook the real process by which a country like the Netherlands, which has legal autonomy for individual schools, creates a national consensus around high standards for student learning. This contribution describes the formal, legal status of curriculum and examination standards and also the process by which high standards emerge and are maintained over time. Some attention is also paid to new trends in high-stakes examinations. The Dutch approach toward a balance between local autonomy and national, high standards has considerable relevance to the U.S. setting.

The ignorance of bourbaki

If one looks at the history of mathematics, one sees periods of bursting creativity, when new ideas are being developed in a competitive and therefore very hasty spirit, and periods when people find that the ideas so recently in vogue are inexact, incoherent, and possibly inconsistent. In the latter periods there is an urge to consolidate past achievements. I said "the history of mathematics," but mathematics is a complex sociological organism, and its growth takes place in different branches and in different countries, even different universities, in different ways and at different speeds. Sometimes national groups feel that mathematics in their country is in a bad way: You find an expression of that in the "Introduction" to later editions of Hardy's Pure Mathematics, where he remarks that it was written with an enthusiasm intended to combat the insularity of British mathematics of the turn of the century, which had taken no account of the development of mathematics in France in the 19th century. Indeed, in 1910 France could be proud of her succession of mathematicians such as Legendre, Laplace, Lagrange, Fourier, Cauchy, Galois, Hadamard, Poincar4--a most impressive list of scholars of the highest distinction. But after the first World War, the feeling in France changed, and the young French mathematicians of the day began to consider that the torch of mathematical research had passed to Germany--where there were many great mathematicians building on the past work of Riemann, Frobenius, Dedekind, Kummer, Kronecker, Minkowski, and Cantor , such as Klein, Hilbert, Weyl, Artin, Noether, Landau, and Hausdorff and that French mathematics had gone into a decline.

Rigor and Clarity: Foundations of Mathematics in France and England, 1800–1840

The ArgumentIt has long been apparent that in the nineteenth century, mathematics in France and England developed along different lines. The differences, which might well be labelled stylistic, are most easy to see on the foundational level. At first this may seem surprising because it is such a fundamental area, but, upon reflection, it is to be expected. Ultimately discussions about the foundations of mathematics turn on views about what mathematics is, and this is a question which is answered by a variety of different groups including mathematicians, students, curricular planners, parents, etc. Mathematical practice rests on some kind of mixture of the answers to this fundamental question which come from these diverse groups. Comparing the cultural matrices which supported mathematics in France and Britain in the first decades of the nineteenth century sheds light on the real though often subtle differences in the ways the subject was pursued in the two countries.

Changes in the teaching of mathematics in France

The movement for reform of mathematical education in France, of which the first signs appeared about 1955, had two main objectives: (a)to reduce the mis-match which had grown up between contemporary mathematics and mathematical education at all levels;(b)to equip all pupils, as far as possible, with a view of mathematics which would enable them to understand and to master the increasing involvement of mathematics across an ever-widening spectrum.

Siegfried et le lycéen

Siegfried le lycéen. This title alludes to a well-known novel by Jean Giraudoux opposing the German to the French caracter. This article underlines the necessity to initiate the pupils of the upper forms into the present aspects of life of the institutions of the German speaking countries. But practical difficulties are also mentioned. In particular certain traditional teaching methods, as well as the extreme importance given to the teaching of mathematics in France. This discipline in its present application is useful to a minority, while it deprives many young people of the time necessary to the efficient learning of foreign languages, and therefore harms a methodical initiation into the way of life and thinking of other countries.

Compliment for Britain

In the issue dated 21 September 1972 of the newspaper Le Dauphine, which circulates in Grenoble and the neighbouring districts of France, Professor Louis Neel, one of the most distinguished physicists of our day and winner of the Nobel Prize in 1970 for his work in magnetism, gave an interview regarding the teaching of 'modern' mathematics in France. To put it mildly, he is against the large scale introduction of such methods in French schools, although he feels that a small proportion of children may benefit from abstract mathematics courses.

International Mathematical Education: The development of the teaching of mathematics in France at the first and second degree levels

Bourbaki and “modern mathematics” originated in France. lt is natural, then, for the rest of the world to ask what effect they have had on the French secondary and preparatory mathematics instruction. Mlle Lucienne Felix is one of the most active leaders seeking reform of a traditional but rigorous mathematical program in the French public schools. In this article Mlle Felix gives a forthright account of the situation in France today.

A Report on the Teaching of Secondary Mathematics in France

Next article FreeA Report on the Teaching of Secondary Mathematics in FranceG. W. MyersG. W. Myers Search for more articles by this author PDFPDF PLUS Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinkedInRedditEmail SectionsMoreDetailsFiguresReferencesCited by Volume 19, Number 7Sep., 1911 Article DOIhttps://doi.org/10.1086/435788 Views: 48 Journal History This article was published in The School Review (1893-1979), which is continued by the American Journal of Education (1979-present). PDF download Crossref reports no articles citing this article.

Scientific Serials

Bulletin of the American Mathematical Society, March.—Prof. Pierpont, in an article on mathematical instruction in France, gives an account of the way in which France is educating students who wish to become mathematicians, and indicates rapidly what positions a talented young man may hope to reach, how he attains them, and what his duties are in the various stages of his progress. He subsequently calls attention to the advantages which Americans can enjoy in studying mathematics in France, particularly in Paris. The article should be useful.—Prof. Ernest W. Brown reviews M. Poincaré's “Cinématique et Mécanismes, Potentiel et Mécanique des Fluides,” the Annuaire of the Bureau des Longitudes for 1900, and the “Elements of Precise Surveying and Geodesy,” by Mansfield Merriman.—Prof. F. Morley gives a sketch of E. Duporcq's “Premiers principes de Géométrie Moderne,” a work to give students, who have some acquaintance with analytic geometry, a liking for the purely geometric point of view.—Prof. F. Cajori briefly notices “Opinions et curiosités touchant la Mathématique d'après les ouvrages Français des xvie, xviie, et xviiie siècles,” by G. Maupin (a work, apparently, which merits a place in a modern “Budget of Paradoxes”), and “La Mathématique: Philosophie, Enseignement,” by C. A. Laisant.—The number closes with the usual items of “Notes” and “Publications.”