1999

	Fiedler A. (1999) Using a Cognitive Architecture to Plan Dialogs for the Adaptive Explanation of Proofs. In: Proceedings of the 16th International Joint Conference on Artificial Intelligence (IJCAI, pp. 358--363). Morgan Kaufmann.
	Flores A. (1999) Mechanical arguments in geometry. Primus 9(3) 241-250.
	Haddas N., Hershkowitz R. (1999) The role of uncertainty in constructing and proving in computerized environment. PME XXIII, Volume 3, pp. 57-64.
	Holland-Minkley A.M., Barzilay R., Constable R.L. (1999) Verbalization of High-Level Formal Proofs. In: National Conference on Artificial Intelligence (AAAI-99).
	Netz R. (1999) The Shaping of deduction in Greek mathematics: A study in cognitive history. Cambridge University Press.

 

Les références qui suivent sont extraites de : Frans H. van Eemeren, Rob Grootendorst, J. Anthony Blair, Charles A. Willard (eds.) Proceedings of the Fourth International Conference of the International Society for the Study of Argumentation. Sic Sat 1999. International Center of the Study of Argumentation.(cederom ref: ISBN 90 74049-04-4)
	Baker M. (1999) The function of argumentation dialogue in cooperative problem-solving. Sic Sat 99, 27-33.
	Hansen, H.V. (1999) Argumental deduction: A programme for informal logic. Sic Sat 99, 311-316
	Johnson R.H. (1999) The problem of truth for theories of argument. Sic Sat 1999, 411-415
	Levi D.S. (1999) Teaching Logic: How to Overcome the Limitations of the Classroom. Sic Sat 99, 514-518
	Oostdam R., de Glopper K. (1999) Students' Skill In Judging Argument Validity. Sic Sat 99, 621-625
	Powers L.H. (1999) Dividing by Zero &endash; and other mathematical fallacies. Sic Sat 99, 655-657
	Simons H.W. (1999) Problematizing Standards Of Argumentation To Students. Sic Sat 99, 742-745
	Wright M.H. (1999) Greek Mythic Conceptions of Persuasion. Sic Sat 99, 889-894

   

1998

	Haddas N., Herschkowitz R. (1998) Proof in geometry as an explanatory and convincing tool. PME XXII, Volume 3, pp. 25-32
	Hoyles C. (1998) Steering Between Skills and Creativity: A Role for the Computer? In: Park H.S, Young M. Choe Shin H., Kim S.H. (eds) Proceedings of the First ICMI-East Asia Regional conference on Mathematics Education (pp. 211-226, pp. 227-242). Korea, Aug. 1998. (Also translated into Korean).
	Hoyles C. (1998) A Culture of Proving in School Mathematics? In: Tinsley J.D. Johnson D. C. (eds) Information and Communications Technologies in School Mathematics (IFIP proceedings, pp.170-181). London: Chapman & Hall,
	Hoyles C., Healey L. (1998) Students Performance in Proving: Competence or Curriculum? Proceedings of First Conference of the European Society for Research in Mathematics Education August 1998, Osnabruck, Germany.
	Mariotti M. A. (1998) Introduzione alla dimostrazione all'inizio della scuola secondaria superiore. L'insegnamento della matematica e delle scienze integrate. 21B(3) 209-252
	Mogetta C. (1998) Il passaggio dall'argomentazione matematica alla dimostrazione in situaione di problem solving: elementi di rottura e di continuità cognitiva. L'insegnamento della matematica e delle scienze integrate. 21B(5) 429-460.
	Netz R. (1998) Greek mathematical diagrams: their use and their meaning. For the Learning of Mathematics 18(3) 33-39

 

Archives

	Guin D., Groupe IREM IA (1989) Réflexions sur les logiciels d'aide à la démonstration en géométrie. Annales de Didactique et de Sciences Cognitives ( IREM de Strasbourg) 2, 89-109.
	Guin D. (1996) A cognitive analysis of geometry proof focused on intelligent tutoring systems. In: Jean-Marie Laborde (ed.) Intelligent Learning Environments : the case of geometry (pp.82-93). Berlin: Springer Verlag.

 

L'argumentation en question par Raymond Duval

Pour initier des élèves de collège aux preuves en mathématiques, l'enseignement a naturellement privilégié la démonstration avec toutes les contraintes de rigueur qu'elle impose. Mais depuis une dizaine d'années on prête davantage d'attention à l'argumentation en tant que moyen de convaincre, soi-même ou les autres. Ce qui est évidemment une condition nécessaire pour qu'une preuve fonctionne comme preuve. Le propos de cette note n'est pas de chercher les raisons de ce déplacement d'intérêt. Certaines sont évidentes : il y a l'accent mis sur le travail de recherche pour lequel la démonstration apparaît comme l'aboutissement, et il y a aussi le caractère incompréhensible, pour beaucoup d'élèves, de l'exigence de démonstration et de ce que cela apporte. Nous allons plutôt considérer ce que l'argumentation recouvre et les questions que son étude soulève. Dans cette perpective, nous aborderons successivement l'émergence d'une problématique de l'argumentation, les deux notions fondamentales pour pouvoir analyser les démarches d'argumentation et nous indiquerons quelques entrées pour étudier la place de l'argumentation dans l'apprentissage des mathématiques.       Pour en savoir plus...

Archives du Web Le rôle constitutif de l'organisation discursive et interactionnelle dans la construction du savoir scientifique par Lorenza Mondada	The Shaping of deduction in Greek mathematics by Reviel Netz
	I may claim that if there is a book to read before  the end of the century, it is this one. Reviel Netz analysis of the "shaping of deduction in Greek mathematics" may play in the mathematics education community a role as stimulating as the one of Lakatos did a decade ago. A way is open to go beyond the classical reference to the Greck "miracle" or the Greeck "revolution". The way Netz relates the structure of deductive arguments to the practice of Greeck mathematics shades a new light on the relations between visual and textual dimensions of mathematical writings, as well as on the idea of formalism.   At the level of the method as well, this study has a lot to teach us. Especially because the search for facts led Netz to what could be described as a copernician revolution, trying to unfold "the unreflective practice of deductive texts".   In this last issue of the Lettre de la Preuve for the year 1999, I am very pleased to be able to offer to the reader a presentation Reviel Netz made of his book on the occasion of a talk given at Harvard in April 1999, et une analyse par  Gilbert Arsac qui donna un cours essentiellement  centré sur cet ouvrage lors de l'Ecole d'Eté de  Didactique des mathématiques en Août 1999. [NB]
"Lorsqu'on réfléchit aux rapports complexes entre dire   et savoir, il est utile d'expliciter d'une part quels sont les présupposés qui fondent les conceptions en jeu du dire et du savoir et d'autre part quels sont les matériaux empiriques à partir desquels ces présupposés sont matérialisés dans des analyses. Ce travail d'explicitation est important dans la double mesure où ces termes ont été utilisés dans le cadre de traditions disciplinaires et philosophiques très diverses et où la condition d'une approche rigoureuse nous semble reposer sur l'exigence d'articuler une position théorique claire à une réflexion analytico-empirique cohérente avec elle."   "Notre champ de réflexion [concerne] les activités professionnelles de chercheurs scientifiques: c'est en effet un domaine heuristique où les conceptions du discours et de la connaissance ont fait l'objet de nombreux débats et controverses et où les pratiques observables des acteurs permettent d'analyser des processus complexes où s'imbriquent savoirs constitués et savoirs en voie d'élaboration, évidences discursives et remises en question, constructions discursives d'objets de savoir au cours d'actions et d'interactions, actions à la fois

The Future of Secondary School Geometry. by Michael de Villiers

Web Archives Proofs in mathematics by Alexander Bogomolny

The future of secondary school geometry  cannot be separated from our better  understanding of cognitive and didactical issues related to its teaching and learning, but also to a large extent it cannot be separated from the progress in the design and implementation of computer-based learning environements - namely dynamic geometry software.Michael de Villiers addresses here all these issues in a text he prepared for a Plenary lecture at the "Geometry Imperfect" conference which was held in October 1996 at the University of South Africa.   The reader will find here an on-line version of his conference, with a lot of examples, even lively ones illustrating new theorems which de Villiers has coined using modern technology to support his intuition and explorations. [NB]

"I am not sure it's possible to evict drills altogether  from  the  math classroom. But I hope, in time, more emphasis will be put on the abstract side of mathematics. Drills contain no knowledge. At best, after sweating on multiple variations of the same basic exercise, we may come up with some general notion of what the exercise is about. (At worst, the sweat and effort will be just lost while the fear of math will gain a stronger foothold in our conscience.) Moreover, if it's possible at all for a layman to acquire an appreciation of math, it's only possible through a consistent exposure to the beauty of math which, if anywhere, lies in the abstractedness and universality of mathematical concepts.   Non-professionals may enjoy and appreciate both music and other arts without being apt to write music or paint a picture. There is no reason why more people couldn't be taught to enjoy and appreciate math beauty."

CALL FOR CONTRIBUTIONS   TSG 12 Proof and Proving in Mathematics Education Chief organiser Paolo Boero

The TSG-12 activities will encompass the following issues: I. The importance of explanation, justification, and proof in mathematics education; II. Conditions for building proofs in classrooms; and III. Long-term building of mathematical ideas related to proof making. These issues will be considered from the following points of view: (a) Historical and epistemological, related to the nature of mathematical proof and its functions in mathematics in an historical perspective; (b) Cognitive, concerning the processes of production of conjectures and construction of proofs; (c) Social-cultural aspects for student construction of proofs; (d) Educational, based on the analysis of students' thinking in approaching proof and proving, and implications for the design of curricula Selected contributions will introduce discussions on the different issues. Keeping into account this general orientation, all people interested in contributing to the debate which will prepare the activity of TSG 12 at ICME9 are invited to write a 4-pages text (maximum of 12Ko) in English, and to send it as a RTF attachment to Paolo Boero... The Proof Newsletter website will host these contributions which will then be made accessible through that chanel. For the sake of the debate, it would be important to make available a first set of contributions as soon as possible. For this reason, people interested in taking part in the first round of debate are invited to send their contributions before december the 15th.

from THE MATH FORUM web site     Ask Dr. Math about proofs

False Proofs, Classic Fallacies   There are lots of "proofs" that claim to prove something that is obviously not true, like 1 + 1 = 1 or 2 = 1. All of these "proofs" contain some error that most people aren't likely to notice. The most common trick is to divide an equation by zero, which is not allowed (in fact, you cannot ever divide by zero.) If a "proof" divides by zero, it can "prove" anything it wants to, including false statements.   What is a proof? How do you write a two-column proof?   Students often ask about proofs: what they are, how to understand them, and, often, how to write two-column proofs. Some answers can be found on Ask Dr. Archives.

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