La lettre de la Preuve

       

ISSN 1292-8763

Janvier/Février 2000
  

2000

Jones K. (2000) The Student Experience of Mathematical Proof at University Level. International Journal of Mathematical Education 31(1) 53-60.

ICME9 TSG-12 "Proof and Proving in Mathematics Education"
On-line contributions by : Bartolini Bussi, Bolite Frant and Rabello de Castro, de Villiers, Douek, Harada with Gallou-Dumiel and Nohda, Healy, Maher and Kiczek, Richard, Roulet, Sekiguchi

 

1999

 

Artmann B. (1999) Euclid - the creation of mathematics. Berlin: Springer Verlag.

Belfort E. (1999) Geometria Dinamîca e demonstrações na fromação continuada de professores. Cabri World 99 (p.34). São Paulo: PUC/SP.

Brown J. R. (1999) Philosophy of mathematics: An introduction to the world of proofs and pictures. New York: Routledge.

Cabrol-Hatimi C. (1999) Un Modèle de Formalisation des Argumentations Naturelles basé sur la notion de Force Persuasive. Application à la Planification des Idées. Thèse. Univesité de Toulouse 1.

Dreyfus T. (1999) Why Johnny can't prove. Educational Studies in Mathematics 38(1/3) 85-109

Ermel (1999) Vrai ? Faux ? ... On en débat ! De l'argumentation à la preuve en mathématiques au cycle 3. Paris: INRP.

Gravina M. A. (1999) A demonstração em geometria: que possibilidades com o Cabri-geometry? Cabri World 99 (p.22). São Paulo: PUC/SP.

Mariotti M. A. (1999) Introducing pupils to proof: the mediation of Cabri. Cabri World 99 (p.20). São Paulo: PUC/SP.

Perry P. (1999) Algunos aspectos de la prueba en la clase de matemáticas. Revista EMA 5(1) 91-96.

Les références qui suivent sont extraites de :
Jean Sallantin, Jean-Jacques Szczeciniarz (eds.) Le concept de preuve à la lumière de l'intelligence artificielle. (Nouvelle Encyclopédie Diderot). Paris : PUF.

Sallantin J., Szczeciniarz J.-J. (1999) Introduction, la preuve à la lumière (?) de l'intelligence artificielle. pp.1-28

Imbert C. (1999) De la connaissance au calcul : implications épistémologiques du cognitivisme. pp.29-58

Szczeciniarz J.-J. (1999) Descartes et Euclide : le cogito comme ultime preuve. pp.59-86

Dosen K. (1999) Le programme de Hilbert. pp. 87-106

de Costaz N., C. A., Béziau J.-Y. (1999) La logique paraconsistante. pp.107-116

Pitrat J. (1999) Vers un métamatématicien artificiel. pp.117-138

Marquis P. (1999) Sur les preuves non déductives en intelligence artificielle. pp. 139-158

Belleannée C., Nicolas J., Vorc'h R. (1999) Vers un démonstrateur adaptatif. pp.159-196

Balacheff N. (1999) Apprendre la preuve. pp.197-236

Curien R. (1999) Preuves de la déduction automatique et analogie. pp.237-254

Sallantin J. (1999) Les cadres probatoires. pp.255-278

Zuber R. (1999) Règles, déduction, grammaire et langage. pp.279-298

Vignaux G. (1999) Des régimes de preuves en langues et discours. pp.299-330

Ferrier D. (1999) La preuve et le contrat. pp.331-350

Gardin J.-C., Renaud M., Lagrange M.-S. (1999) Le raisonnement historique à l'épreuve de l'IA. pp.351-370

      

Archives

Dewey J. (1903) The psychological and the logical in teaching geometry. Educational Review XXV, pp.387-399

Lampert M. (1992). Practices and problems in teaching authentic mathematics. In F. Oser, A. Dick, and J.L. Patry (Eds.) Effective and responsible teaching: the new synthesis. San Francisco: Jossey Bass.

Lanford III O. E. (1986) Computer assisted proofs in analysis. International Congress of Mathematicians. RR IHES/P/87/16 Bures sur Yvettes.

Poincare H. (1903). Review of Hilbert's "Foundations of geometry" (Translated by E Huntington). Bulletin of the American Mathematical Society  10, 1-23.

Weyl H. (1944). David Hilbert and his mathematical work. Bulletin of the American Mathematical Society 50, 612-654.

 

  

Argumentation and Mathematical Proof
in Japan

by
Yasuhiro Sekiguchi
Mikio Miyazaki

 

In Western culture, expressing one's own opinion and confronting others are conceived of as deepening the understanding of each other. Here, better understanding of differences between opinions is considered facilitating good human relation. Barnlund pointed out that Japanese traditional culture does not always place the highest value on verbal communication in the communicative activity. The goal of communication in public is a harmony ("wa") among the participants. Difference between opinions among the participants is conceived of as a threat to the harmony. Therefore, people tend to avoid explicit expression of disagreement in public. The harmony is often symbolized by uniformity or homogeneity in appearance, behaviors, expressions, and so on, within a community. Cooperation rather than competition is highly valued within a community. Therefore, a person who disregards the community's obligations sometimes receives rather emotional reactions--e. g., accusation, isolation, or expulsion--than rational ones. It is well-known that even in academic conferences, Japanese do not openly argue with each other very much. Expressing direct opposition is considered impolite: Opposition is usually indirectly or euphemistically expressed.

     

To read more...

 


The Shaping of Deduction
in Greek Mathematics

by
Reviel Netz

 
TSG 12
Proof and Proving in Mathematics Education

Chief organiser
Paolo Boero


Next deadline for paper submissions and reactions

February the 15th

 A review by Christian Marinus Taisbak is  available in The MAA Online Book Review Column.

 A thread of the discussion about this book,  held on the historia-matematica forum is achived in Swarthmore website. Other comments are available on the proof site, just follow the link...

 Following the first ICME9 TSG-12 call, a group of  contributions were received by December the 15th.  These  contributions are avaible on this site.
Reactions and further contributions are expected to be sent by the half of february.
  As far as possible, these reactions and contributions should be reasonably short (about four single-spaced A4 pages, a maximum of 12Ko). They should be submitted in English, as RTF attachments sent to the TSG-12 Chief Organizer.

Un Modèle de Formalisation des Argumentations Naturelles basé sur la notion de Force Persuasive
Application à la Planification des Idées

par
Catherine Cabrol-Hatimi

Thèse préparée au LIHS de l'Université de Toulouse1 et soutenue le 23 décembre 99.
  Les travaux présentés sont dans la thématique "Représentation de connaissances pour la conception du document écrit" développée au laboratoire. La thèse emprunte des idées dans les domaine de la rhétorique, l'I.A., la Planification du discours, et la Communication médiatisée. Un modèle formel d'argumentation naturelle dans un environnement de communication homme-homme via ordinateur est défini. Le but est d'apporter une aide informatique à un auteur d'argumentations.

Philosophy of mathematics: An introduction to the world of proofs and pictures

by
James Robert Brown
  

James Robert Brown's recent book, Philosophy of mathematics: An introduction to the world of proofs and pictures, written in a clear and engaging style, is an excellent introductory text for several topics in the philosophy of mathematics.
  It includes 11 chapters with headings such as: Picture-proofs and Platonism (chapter 3); What is a Definition? (chapter 7); Proofs, Pictures and Procedures in Wittgenstein (chapter 9); and Computation, Proof and Conjecture (chapter 10). The book makes a strong case for a Platonist account of mathematics and for picture-proofs having a legitimate role to play as evidence and justification, a role well beyond heuristic. The author anticipates at least mild resistance to his Platonist stance and sheer hostility to his account of how picture-proofs work. This is why the case for picture-proofs is argued with great care.
  The burden of the book is to demonstrate the effectiveness and power of picture-proofs and to show that they are not only psychologically suggestive and pedagogically important but often can be considered rigorous proofs. Brown‚s arguments are always ingenious and thorough. The reader is given a host of arguments showing how much can be accomplished by means of pictures which is impossible to accomplish using mere algorithms. The reader is also alerted to the fact that pictures can be misleading and that we have to invest efforts in learning how to see pictures and use them correctly.
  I would recommend that mathematics educators read this book and think about it. [Gila Hanna]

Séminaire National de Didactique des Mathématiques

Paris, 14-15 janvier 2000
  

Samedi 15 janvier
- 14h30-16h : Entrer dans la culture des théorèmes par Paolo Boero, Université de Gênes
- 16h15-17h45 : Illustration de la pertinence des mathématiques  discrètes pour la modélisation et la distinction condition nécessaire / condition suffisante par Julien Rolland, Laboratoire Leibniz et IUFM de Grenoble

Dimanche 16 janvier
- 9h-10h15 : Logique et raisonnement mathématique : Variabilité  des exigences de rigueur dans les démonstrations mettant en jeu des énoncés existentiels par Viviane Durand-Guerrier, IUFM de Lyon et LIRDHIST Université Lyon 1
- 10h15-11h30 Réactions et ouverture d'un débat autour de "raisonnements, preuves, démonstrations " par Michèle Artigue

 Les résumés des exposés sont en ligne sur ce site.  Les exposés ont lieu  sur le Campus de Jussieu,  Amphi 55B, 2 place Jussieu, Paris 5ème.
  
A Longitudinal Study of Mathematical Reasoning: Student Development and School Influences

1999 - 2003

a project runned by
Celia Hoyles
Dietmar Küchemann
  

  
Web Archives

The 1992-1995 issues of the

Bulletin of the
American Mathematical Society

are available online at the Mathematics ArXiv.

 This project follows on from the "Justifying  and  Proving in School Mathematics" project that ran from 1995 to 1999, which investigated high attaining Year 10 students' understanding of proof in the areas of algebra and geometry.
  The aim with the new project is to understand further how students develop their competencies in mathematical reasoning over time and how schools and teachers promote this development.
  To get more information about the project click on the above web icon, to get some information about the first project either follow the links on the new project site, or have a look at the report on-line on the proof site...

  This is a good news announced by Julio Gonzalez   Cabillon, the very efficient manager of the Historia Matematica Forum. In particular this archive includes the controversial article by Jaffe and Quinn on "Theoretical mathematics: Toward a Cultural Synthesis of Mathematics and Theoretical Physics", the famous Thurston reaction and other related papers :

Arthur Jaffe, Frank Quinn. "Theoretical Mathematics: Toward a Cultural Synthesis of Mathematics and Theoretical Physics" Bull. Amer. Math. Soc. (N.S.) 29 (1993) 1-13.

William P. Thurston. "On Proof and Progress in Mathematics". Bull. Amer. Math. Soc. (N.S.) 30 (1994) 161-177.

Michael Atiyah, Armand Borel, G. J. Chaitin, Daniel Friedan, James Glimm, Jeremy J. Gray, Morris W. Hirsch, Saunder MacLane, Benoit B. Mandelbrot, David Ruelle, Albert Schwarz, Karen Uhlenbeck, Rene Thom, Edward Witten, Christopher Zeeman. "Responses to 'Theoretical Mathematics: Toward a Cultural Synthesis of Mathematics and Theoretical Physics'", by A. Jaffe and F. Quinn. Bull. Amer. Math. Soc. (N.S.) 30 (1994) 178-207.

Arthur Jaffe, Frank Quinn. Response to Comments on Theoretical Mathematics". Bull. Amer. Math. Soc. (N.S.) 30 (1994) 208-211.

[NB]

 
Vrai ? Faux ? On en débat !

une publication du groupe ERMEL
de l'INRP

 En mathématiques, au cours moyen,  les élèves ont à débattre pour  déterminer si une proposition est  vraie ou fausse, et pourquoi. Ce  travail de preuve s'appuie sur une  production et une critique d'arguments  mathématiques ; il nécessite le  recours à des connaissances et  l'utilisation de raisonnements.
   Ce livre présente des situations  d'apprentissage comportant des phases de débat argumentatif, il analyse les preuves produites et précise comment le maître peut gérer ces échanges.

from THE MATH FORUM INTERNET NEWS
3 January 2000, Vol. 5, No. 1
    
Mathematical Writing
  
  

 The Math Forum's Internet Mathematics Library offers links to sites that have to do with mathematical   writing. At the college level, here are two good starting points:

 Writing in mathematics - Crannell.
 This guide to writing in mathematics classes, by Dr. Annalisa Crannell of Franklin & Marshall College, offers the checklist she uses and writing assignments from her Pre-Calculus and Calculus I, II, and III classes. Contents include:

- Why Should You Have To Write Papers In A Math Class?
- How is Mathematical Writing Different?
- Following the Checklist
- Good Phrases to Use in Math Papers
- Helpful Hints for the Computer
- Other Sources of Help

  Writing a math phase two paper - Kleiman, Tesler, MIT.
  A discussion of the kind of writing appropriate in a paper submitted to the math department to complete Phase Two of the Massachusetts Institute of Technology's writing requirement, by Steven L. Kleiman with Glenn P. Tesler. Included are: a review of the general purpose of the requirement and the specific way of completing it for the math department; a consideration of the writing itself (organization into sections, use of language, and presentation of mathematics); and a short example of mathematical writing.

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Laboratoire Leibniz
How to publish Cabri figures
on the Web?

Cabri Java Project

Projet Cabri-géomètre

Editeur : Nicolas Balacheff
English Editor :
Virginia Warfield, Editor en Castellano : Patricio Herbst

Advisory Board : Paolo Boero, Daniel Chazan, Raymond Duval, Gila Hanna, Guershon Harel,
Celia Hoyles, Maria-Alessandra Mariotti, Michael Otte,
Yasuhiro Sekiguchi, Michael de Villiers

La lettre de la Preuve

       

ISSN 1292-8763