Mars/Avril 1999


Les références qui suivent sont publiées dans:

"Proof by Tomatoes ?" A special issue of Mathematics Teacher. November 1998, volume 91, Number 8.

Dodge W., Goto K., Mallinson P. (1998) "I would consider the following to be a proof..." (pp.652-653)

Epp S. (1998) A unified framework for proof and disproof. (pp.708-713)

Izen S. P. (1998) Proof in modern geometry. (pp. 718-720)

Knuth E. J., Elliott R. (1998) Characterizing students's understandings of mathematical proof. (pp.714-717)

Prince A. A. (1998) Prove it! (pp.726-728)

Redmond C., Federici M. P., Platte D. M. (1998) Proof by contradiction and the electoral college. (pp. 655-658)

Reid D. A. (1998) Sharing ideas about teaching proving. (pp. 704-706)

Silver J. A. (1998) Can computers be used to teach proof? (pp. 660-663)

Sowder L., Harel G. (1998) Types of students' justifications. (pp. 670-675)

Szombathelyi A., Szarvas T. (1998) Ideas for developing students' reasoning: a hungarian perspective. (pp. 677-681)

Winicki-Landman G. (1998) On proofs and their perfomances as works of art (pp. 722-725)


Allenby R.B.J.T. (1997) Numbers and proofs. New York: John Wiley & Sons.

Chazan D. (1989) Ways of knowing: High school students' conceptions of mathematical proof. Dissertation Abstracts Order # 9000860. Ann Arbor, MI: UMI.

Gandit M., Masse-Demongeot M.-C. (1996) Le vrai et le faux en mathématiques au collège et au lycée. Grenoble : IREM, Université Joseph Fourier.

Gödel K. et al. (1931) Le théorème de Gödel, (traduction de l'anglais et de l'allemand par J.B. Scherer). Editions du Seuil (Collection Sources du Savoir), Paris, 1989, 185 pages.

Ibañez M., Ortega T. (1997) La Demostración en Matemáticas: Clasificación y Ejemplos en el Marco de la Educación Secundaria, Educación Matemática 9 (2) 65-104

Pickett H. C. (1938) An analysis of proofs and solutions of exercises used in plane geometry tests. New York: Teachers college, Columbia University.

Rossi H. (1995) When is the best proof not the best proof? CBMS Issues in Mathematics Education (American Mathematical Society). 5, 31-53.

Touton F. C. (1919) Solving geometric originals. Contributions to Education No 146, 1924. New York: Teachers college, Columbia University.


 Proof and perception III


Michael Otte

A mathematical object, such as a geometrical point, a number or a function, does not exist independently of the totality of its possible representations, but it is not to be confused with any particular representation, either. It is a general that, as was said, cannot as such be exhausted by any number of its representations. An idea is not to be conceived as a completely isolated and distinct entity in Platonic heaven, but is on the other side not to be confused with any set of intended applications. Primarily for the reasons Gödel had enunciated, namely that the range of possible applications is no definite set at all. Meanings are generals in the sense of referring to an indefinite and undetermined collection of possible applications. Second, two predicates or concepts or functions (or functions of functions) are to be considered as different even if they apply to exactly the same class of objects because they influence mental activity differently and may lead to different developments.


To read more


 Séminaire National de
Didactique des Mathématiques

Didactique, preuve
et environnements informatiques

27 et 28 Mars 1999


Philosophie et mathématiques : sur le quasi-empirisme

Patrick Peccatte

Deux exposés lors du séminaire national de didactique des mathématiques, à Paris, aborderont le thème de la preuve dans le contexte des environnements informatiques d'apprentissage humain...

 Vanda Luengo, Laboratoire Leibniz et
 projet Cabri-géomètre,  IMAG, Grenoble

Analyse des contraintes didactiques pour le développement d'un logiciel educatif,
le cas de la preuve.

 Ferdinando Arzarello, Université  de Turin

De la démonstration dans les Eléments d'Euclide à celle dans l'ordinateur : considérations épistémologiques et didactiques.

Campus de JUSSIEU, 2 place Jussieu, Paris 5eme, amphi 55B
Contact pour le sémininaire :

Jean-Philippe Drouhard ou Michèle Pécal

 A cette URL on trouvera le texte en ligne de l'exposé de  Patrick Pecatte aux Journée d'étude REHSEIS (Recherches Epistémologiques et Historiques sur les Sciences Exactes et les Institutions Scientifiques) le 23 juin 1998.

"Le quasi-empirisme est une orientation de la philosophie des mathématiques datant de la fin des années soixante. Il désigne les mathématiciens, les philosophes et les informaticiens, qui, non seulement placent la pratique de cette discipline au cœur de leur réflexion, mais empruntent également leurs idées essentielles aux sciences empiriques : expérience mathématique, fait mathématique, reconnaissance du rôle fondamental de l'induction, contestation du caractère a priori de la vérité mathématique, faillibilisme, exploration et investigation heuristique systématisées, importance du succès des théories comme critère de leur vérité ou de leur consistance, etc."
Proof is back!

The new version of the NCTM standards which is currently under discussion states clearly in its section 7 devoted to "Reasoning and Proof" that proof should be taught. It was classical in the international research community in mathematics education to emphasise that in the US the teaching of mathematical proof had disapeared (or almost). Things may change, proof is back oversea !

The standards states:

Mathematics instructional programs should focus on learning to reason and construct proofs as part of understanding mathematics so that all students...

  • recognize reasoning and proof as essential and powerful parts of mathematics;
  • make and investigate mathematical conjectures;
  • develop and evaluate mathematical arguments and proofs;
  • select and use various types of reasoning and methods of proof as appropriate.

The interested reader will find all the details at the following URLs :

  Overview of Standard 7: Reasoning and Proof

Elaboration: Grades Pre-K-2

Elaboration: Grades 3-5

Elaboration: Grades 6-8

Elaboration: Grades 9-12


Archives du Web

Qu'est-ce que la vérité mathématique ?

par Hilary Putman

TSG 12
Proof and Proving in Mathematics Education

Chief organiser
Paolo Boero

 Traduction provisoire par Patrick Peccatte du  texte original de :

What is mathematical truth ? in Putnam H. : Mathematics, Matter and Method. Philosophical papers. vol. 1. 1975. Cambridge University Press. pp. 60-78.

Cette traduction est présentée à titre d'illustration, comme une longue citation. Elle est provisoire et volontairement partielle sa reproduction interdite.

Summer Institut

Arithmetic Algebraic Geometry
with Special Emphasis on
Teaching and Learning Proofs

June 20 to July 10 1999
Park City, Utah

Web Archives

Classic Fallacies

a site developed by
Philip Spencer and Joel Chan

 Known as IAS/PCMI, this Institute is  administered by John Polking through the Institute for Advanced Study in Princeton, with major funding from NSF.
   The overall topic for this IAS/PCMI session is Arithmetic Algebraic Geometry -- an active field at the interface of number theory and algebraic geometry that is especially concerned with studying solutions to polynomial equations. With this backdrop, the 1999 Undergraduate Faculty Program will concentrate on the theme of how students learn about proofs in number theory courses and elsewhere.


Guershon Harel or Daniel Goroff

 Our mathematical correspondent has just announced some  startling discoveries, claiming to have found conclusive proof that 1 is equal to 2, that every person in Canada is the same age, that a ladder will fall infinitely fast if you pull on it, and many other results that threaten the very fabric of common sense.
   Of course, you know these things cannot be true. And yet, our correspondent has come up with some quite convincing "proofs" of these facts. Can you discover what is wrong with each of them?
   1=2: A Proof using Beginning Algebra.
   1=2: A Proof using Complex Numbers.
   All People in Canada are the Same Age.
   A Ladder Will Fall Infinitely Fast when Pulled.
   Every Natural Number can be Unambiguously
     Described in Fourteen Words or Less.

8 February 1999, Vol.4, No.6
 What is a proof? How do you write a two-column proof?

a new FAQ from the Math Forum's project Ask Dr. Math

  This new FAQ from the Math Forum's project   Ask Dr. Math provides excerpts from and links to answers from the Dr. Math archives.

 For more discussions pro and con about two- column proofs, search the archives of the newsgroup geometry-pre-college for the words two column proof and browse the threads returned.

See also these three articles from Alexander Bogomolny's interactive monthly column for MAA Online, "Cut the Knot" (you will need a Java-enabled browser):

[N.B.] See also Herbst discussion of two-column proofs in the January/February Proof Newsletter


AERA Symposium, 19 April 1999, Montréal

Fostering argumentation in the mathematics classroom:
The role of the teacher



La bibliographie
Outil de recherche
Cours en ligne
Questions et réponses

A propos du site

The bibliography
Search tool
Online course
Questions and answers

About the site

La bibliografia
Herramienta de busqueda
Curso electronico
Preguntas y repuestas

Con respecto a este servidor

Adresser suggestions et remarques à...
Send remarks and suggestions to...
Enviar comentarios y sugerencias a ...

 The newsletter editor

535 [99 01/02] 2559 [98 11/12] [98 09/10] [98 07/08] [98 05/06] [98 03/04] [98 01/02] 1629 [97 11/12]
97 09/10] [97 07/08] [97 05/06] [97 03/04] [97 01/02]

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, Michael de Villiers