Analysis of pupils tasks in the use of history in mathematics teaching

International audienceAfter several years of video acquiring and analysis, this paper gives a synthetic view on the different tasks that appear in sessions blending history and mathematics. Based on a typology summarized by the acronym SaMaH (Specific, a-Mathematical and a-Historical tasks), this first reading grid enables the identification of the respective contributions of mathematics and history in a given school activity. This framework also makes visible the particular specific tasks in which the two fields are involved. Then, the analysis of different forms of specific tasks will lead to a new a gradation between H-weak and M-weak sub-domains. This paper mainly gives a quick view on the most important theoretical results at this time only available in author's French publications.</p

La caractéristique géométrique de G. W. Leibniz : présentation et perspectives.

International audience"On ne voit pas encore dans l'Analyse Géométrique une discipline achevée. Même si, en effet, la méthode de Viète et de Descartes permettait d'y faire presque tout par calcul, en faisant la supposition des Éléments, ce sont eux qui, pour la plupart, n'y ont pas encore été réduits." (G.W.Leibniz, La caractéristique géométrique.) C'est par ce constat que débute l'un des textes de Leibniz pour qui, malgré les beaux résultats obtenus par l'approche analytique, il reste à montrer comment les fondements de la géométrie, c'est-à-dire les Éléments d'Euclide, peuvent se ramener à de tels calculs. Leibniz doute que cela soit possible et il propose d'inventer un nouveau langage permettant de rendre compte de la situation des divers objets géométriques d'un problème. Il cherche ainsi une discipline qui se situe en amont des Éléments d'Euclide et dont ils peuvent être déduits. À travers quelques passages, nous nous proposons de présenter cette nouvelle théorie que Leibniz nomme la Caractéristique Géométrique, ou méthode des caractères, qui annonce les développements de l'Analysis Situs et de la topologie

The perfect compass: conics, movement and mathematics around the 10th century.

International audienceGeometry instruments certainly exist since men are interested in mathematics. These theoretical and practical tools are at the crossroads of the sensible world and mathematical abstractions. In the second half of the 10th century, the Arabic scholar al-Sijzı wrote a treatise on a new instrument: the perfect compass. At that time, several other mathematicians have studied this tool presumably invented by al-Quhı. Many works are now available in French and English translations. After an historical presentation of the perfect compass, this article deals with a few passages of al-Sijzı's treatise which show the importance of continuous tracing of curves and provide interesting elements on the role of instruments in the mathematical research process. All these texts can help to understand the importance of motion in geometry which can be easily simulated by geometry softwares and used in a geometry lesson or in teacher training sessions

La nouvelle géométrie de Francesco Patrizi da Cherso

Dans son De spacio physico et mathematico, Francesco Patrizi da Cherso (1529-1597) propose une refonte de la philosophie naturelle dans laquelle l'espace devient le premier concept. Annoncée dans ce premier texte, les conséquences de cette mutation sur ce que doit être la géométrie sont importantes et Patrizi propose dans la Nuova Geometria une réécriture complète des principes de cette discipline. Développées principalement dans les premiers livres autour de réflexions sur le point et la ligne, les thèses proposées par Patrizi sont représentatives des changements épistémologiques ayant permis le passage d'une géométrie vue comme science des figures dans l'espace à une science de l'espace

History in mathematics teaching: current problems and new proposals

International audienceIn the light of recent works on the use of the history of mathematics in education, this article offers an analysis of the theoretical issues that arise in such studies. After the presentation of some intrinsic difficulties of a good definition of the different fields involved (a discipline, its didactic and its history), some new elements for a didactical analysis (double field hypothesis, double field paradox and its handling) are proposed. Applied on a few examples, these concepts are aimed at being part of a new framework for empirical studies on the use of history of mathematics in education

Philosophie des mathematiques et formation des professeurs stagiaires

In this article, through the analysis of teachers training sessions and questionnaires about teachers’ and students’ representations, we present one of the didactic issues of an epistemological training. Teachers’ epistemological views are not only of a platonic type. They are numerous and deeply anchored. Teachers’ representations are generally in agreement with students’ views on mathematics but sometimes, on some specific aspects, they enter in contradiction with them. In these cases, education in philosophy and history of sciences can be helpful in allowing teachers to become conscious that beyond knowledge, they impart a certain vision of mathematics and science

INQUIRY-BASED MATHEMATICS TEACHING, HISTORY OF MATHEMATICS AND NEW COMMUNICATION TOOLS : AN EXCITING CHALLENGE !

International audienceFollowing a European project on the relationships between inquiry based science teaching (IBST), internet and communication tools (ICT) and a third topic, history of science, this article deals with some of the new questions raised by the recent introduction of epistemology, history of science and technology (EHST) in the school curricula. The definition of the inquiry and the role that can be played by epistemological thinking in science education are especially analysed in this text. Based on the analysis of historical examples and many on-line resources, as a first result, a new framework for the elaboration of new resources in IBST, ICT and EHST is given and some opening questions have been pointed out

Former des enseignants à l'histoire des sciences : Analyse et enjeux d'une pratique en mathématiques

National audienceÀ partir de l'étude d'expériences avec des professeurs stagiaires, cet article propose d'explorer de nouveaux outils pour l'analyse de séances de formation à l'épistémologie et à l'histoire des sciences. Les différentes modalités d'entrée dans la tâche que nous mettons en évidence dans la première partie, sont ensuite appliquées à une situation de classe mêlant mathématiques et histoire des sciences. Ce faisant, nous tentons d'expliciter les enjeux de pratiques de formation en histoire des sciences pour la constitution de compétences professionnelles

Inquiry-based mathematics, history of mathematics and new communication tools: an exciting challenge!

International audienceFollowing a European project on the relationships between inquiry based science teaching (IBST), internet and communication tools (ICT) and a third topic, history of science, this article deals with some of the new questions raised by the recent introduction of epistemology, history of science and technology (EHST) in the school curricula. The de nition of the inquiry and the role that can be played by epistemological thinking in science education are especially analysed in this text. Based on the analysis of historical examples and many on-line resources, as a result, a new framework for the elaboration of new resources in IBST, ICT and EHST is given and some opening questions have been pointed out

Inquiry-based mathematics, history of mathematics and new communication tools: an exciting challenge!

International audienceFollowing a European project on the relationships between inquiry based science teaching (IBST), internet and communication tools (ICT) and a third topic, history of science, this article deals with some of the new questions raised by the recent introduction of epistemology, history of science and technology (EHST) in the school curricula. The de nition of the inquiry and the role that can be played by epistemological thinking in science education are especially analysed in this text. Based on the analysis of historical examples and many on-line resources, as a result, a new framework for the elaboration of new resources in IBST, ICT and EHST is given and some opening questions have been pointed out