Novembre/Décembre 1998



Herbst P. G. (1998) What works as proof in the mathematics class. Ph.D. Dissertation, The University of Georgia, Athens GA. USA


Lopes A. J. (1998) Gestión de interacciones y producción de conocimiento matemático en un dia a dia lakatosiano. Uno, Revista de Didáctica de la matemáticas 16, 25-37

Raccah P.-Y. (1998) L'argumentation sans la preuve : prendre son biais dans la langue. Interaction et cognitions. II(1/2) 237-264.


Les références qui suivent sont publiées dans:
A. Olivier & K. Newstead (1998, Eds.), Proceedings of the 22nd Conference of the International Group for Psychology of Mathematics Education. Stellenbosch, South Africa: University of Stellenbosch.

Arzarello F., Micheletti C., Olivero F., Robutti O. (1998) A model for analysing the transition to formal proofs in geometry. (Volume 2, pp.24-31)

Arzarello F., Micheletti C., Olivero F., Robutti O. (1998) Dragging in Cabri and modalities transition from conjectures to proofs in geometry. (Volume 2, pp. 32-39)

Baldino R. (1998) Dialectical proof: Should we teach it to physics students. (Volume 2, pp. 48-55)

Furinghetti F., Paola D. (1998) Context influence on mathematical reasoning. (Volume 2, pp. 313-320)

Gardiner J., Hudson B. (1998) The evolution of pupils' ideas of construction and proof using hand-held dynamic geometry technology. (Volume 2, pp. 337-344)

Garuti R., Boero P., Lemut E. (1998) Cognitive unity of theorems and difficulty of proof. (Volume 2, pp. 345-352)

Hadas N., Herschkowitz R. (1998) Proof in geometry as an explanatory and convincing tool. (Volume 3, pp. 25-32)

Reid D., Dobbin J. (1998) Why is proof by contradiction difficult? (Volume 4, pp. 41-48)

Rowland T. (1998) Conviction, explanation and generic examples. (Volume 4, pp. 65-72)

Waring S., Orton A., Roper T. (1998) An experiment in developing proof through pattern. (Volume 4, pp. 161-168)

Yackel E. (1998) A study of argumentation in a second-grade mathematics classroom. (Volume 4, pp. 209-216)

Zaslavsky O., Ron G. (1998) Students'understanding of the role of counter-examples. (Volume 4, pp. 225-232)


Barbin E. (1994) The Meanings of Mathematical Proof. In : In Eves' Circles. MAA.

Cardoso V. C. (1997) As teses fabilista a racionalista de Lakatos e a educação matemática. Dissertaçao de Mestrado. Universidad Estadual Paulista. Campus Rio Claro.

Godino J. D., Recio A. M. (1997) Significado de la demostración en educación matemática.

Mueller I. (1981) Philosophy of mathematics and deductive structure in Euclid's Elements. Cambridge, MA: MIT Press.

Nelson R.B. (1993) Proofs Without Words. MAA.

Quast W. G. (1968) Geometry in the high schools of the United States: An historical analysis from 1890 to 1966. Ed. D. Dissertation, Rutgers-The State University of New Jersey. University Microfilms 68-9162. Ann Arbor, MI.

Sekiguchi Y. (1991) An investigation on proofs and refutations in the mathematics classroom. Ed. D. Dissertation, The University of Georgia. University Microfilms 9124336. Ann Arbor, MI.

Senk S. (1989) Van Hiele levels and achievement in writing geometry proofs. Journal for Research in Mathematics Education 20, 209-321.

Zbiek R. M. (1992). Understanding of function, proof and mathematical modelling in the presence of mathematical computing tools: Prospective secondary school mathematics teachers and their strategies and connections. Ph D Dissertation. Penn State University, Graduate School. USA


Intuizione e dimostrazione:
riflessioni su un articolo di Fishbein


Maria Alessandra Mariotti


Alcuni anni fa E. Fischbein (1982) pubblicava un articolo intitolato "Intuition and Proof": le sue riflessioni sul pensiero intuitivo fornivano il quadro di riferimento ai risultati di una ricerca sperimentale sul tema della dimostrazione. Nello spirito di quella discussione intendo sviluppare qualche idea su questo stesso tema.

Credo che l'insegnamento più importante che Efraim Fischbein ci ha lasciato sia il suo approccio originale ai problemi dell'educazione matematica, centrato sulla complessa nozione di "intuizione". Il suo libro "Intuition in science and Mathematics" (1987) presenta una sintesi di questo approccio: in esso è delineata una "teoria dell'intuizione", che viene offerta alla comunità dei ricercatori come strumento utile per l'interpretazione di molteplici fenomeni didattici.

Efraim Fishbein
20/01/1920 - 22/07/1998


Per continuare


Aprendendo e ensinando geometria com a demonstração

Filomena Ap. Teixera Gouvea
Centro das Ciências Exatas e Tecnologia
Pontifíca Unniversidade Católica de São Paulo

A Course on Mathematical Thinking

Byers W., Hillel J. (1998)
Department of Mathematics and Statistics
Concordia University

Nossa pesquisa foi realizada na perspectiva de contribuir para a prática pedagógica do professor de matemática, abrangendo especificamente, conceitos estudados em geometria, no ensino fundamental.
  Propusemos um conjunto de situações de aprendizagem que o professor pode utilizar em sala de aula visando à iniciação progressiva do raciocínio dedutivo, tendo em vista a aprendizagem posterior da demonstração, e permitindo aos alunos, que se apropriem das regras do debate de validação matemática

Contact : Sado Ag-Almouloud
PUC São Paulo, Brasil

Students entering universities have encountered proofs in previous mathematics courses, but more often than not they have a very vague notion of proofs and proof techniques.
 To face this problem, the authors present a course that would put emphasis on the necessary "tools of the trade" for coping with university mathematics rather than cover a lot of new mathematical terrain. They called this course "Introduction to Mathematical Thinking"...

  To read more

Cut The Knot!
An interactive column using Java applets

Proofs Without Words

Alex Bogomolny

Mathématiques d'ailleurs
Nombres, formes et jeux dans les sociétés traditionnelles

Marcia Ascher
Traduction de l'anglais : Karine Chemla et Serge Pahaut

 In the beginning, when there was no language to
 express general mathematical ideas, proofs without words were the proofs. Martin Gardner wrote, "There is no more effective aid in understanding certain algebraic identities than a good diagram.
  One should, of course, know how to manipulate algebraic symbols to obtain proofs, but in many cases a dull proof can be supplemented by a geometric analogue so simple and beautiful that the truth of a theorem is almost seen at a glance." A classical example concerns triangular numbers...

Gleaned from


Les ouvrages d'ethnomathématique en langue française ne sont pas nombreux. Celui-ci est une traduction d'un ouvrage de la mathématicienne américaine Marcia Ascher par une mathématicienne, Karine Chemla, et un anthropologue, Serge Pahaut.
  Les traducteurs reconnaissent, en posant le regard sur des cultures qui nous sont éloignées, que "pour dire qu'il y a des mathématiques là-dedans, il faut savoir ce que sont les maths", mais que probablement cela ne suffit pas et ils conviennent de ce que "reconnaître une activité mathématique ne va pas de soi."
  La question soulevée par de tels travaux est celle de savoir ce "que sont les mathématiques", ou encore ce qui distingue l'activité mathématique d'autres activités. Comme le discute Mariotti a propos des travaux de Fishbein, l'examen des critères de validation acceptés est probablement une voie pour avancer sur ce terrain difficile. Cela fait sourire par avance les traducteurs, mais il est pourtant vrai que le risque est grand de tomber dans un effet Jourdain par générosité. (N. B.) 

Math by Proof
What is it, and why should we?

R. B. Jones

On recherche pour publication dans la "Lettre de la Preuve" un compte-rendu de lecture de cet ouvrage du point de vue de la preuve.

Glané dans


The answer proposed by Jones (click on the icon on the left) seems influenced by a view of proof by computer-science which goes even beyond the classical mathematical opinion. Jones shows a confidence in formalisation which under-estimates the resistance of concepts to the attemps of rigour to capture them.
  Nevertheless a site interesting to browse to get an insight of one of the possible views on mathematical proof (N. B.)

Gleaned from

TSG 12: Proof and Proving in Mathematics Education

be ready... pre-register !

Web Archives

What is "Proof"?! - in mathematics...

Michael Hugh Knowles

O fortalecimento das demonstrações em geometria elementar na virada do século XX

Michel Guillerault
Laboratoire Leibniz

 In 1996, the Palo Alto Institute for Advanced
 Studies posted on the web texts on Proof in mathematics. They are still on-line and I recently bumped into them.
  These texts seem to go along two lines at the same time, adressing fundamental problems in mathematics and mathematical practices.
  This piece is less about what is "proof" in mathematics than "what does mean the theorem of Gödel" for the mathematical practice. (N. B.)

Some readers may want to engage the discussion, the Proof Newsletter is open to such initiative.

No fim do século XIX e início do século XX, há uma preocupação de se estabelecer a geometria elementar sobre bases sólidas. Apresentamos aqui a contribuição a este debate de Louis gérard, professor em Lyon e depois em Paris, especialista em geometria não euclideana (tese, 1892) e bastante preocupado em apresentar os teoremas da geometria elementar de uma maneira a mais rigorosa possível.

L'Affaire Sokal,
ou la querelle des impostures

Yves Jeanneret

Impostures scientifiques,
les malentendus de l'affaire Sokal

Baudoin Jurdant (ed.)
Web Archives

What is a proof?

Rob Corless

 "In my opinion, proofs are for mathematicians;  something we keep for ourselves, because the barbarians do not appreciate them."
  This is a statement which contrasts strongly with the thesis developed by Mariotti in this issue of the Proof Newsletter. Even more if one thinks of the consequences Corless draws from his claim:
  "So I use statements of theorems only in this course (with a few exceptions). I prove almost nothing. Instead of giving a quasi-proof, I spend time explaining the hypotheses, and give examples of what happens if the hypotheses are not met. This teaches precision, and is a preliminary to proof."
(N. B.)

L'affaire Sokal concerne-t-elle les  mathématiques? Probablement pas directement. En revanche elle peut donner quelques thèmes de réflexion aux chercheurs en didactique des mathématiques. A nous de voir...
(N. B.)

Glané dans

12 October 1998, Vol.3, No.41
  Famous Problems in the History of Mathematics
Isaac Reed

 An investigation of some of the great problems that have inspired mathematicians throughout the ages.  Included are problems suitable for middle and high school math students, with links to solutions, biographies, references, and other math history sites. Problems include:

- The Bridges of Konigsberg : a problem that inspired the great Swiss mathematician Leonard Euler to create graph theory, which led to the development of topology
- The Value of Pi : discovering the value of and different expressions for the ratio of the circumference of a circle to its diameter
- Puzzling Primes understanding the properties of the prime numbers and the difficulty of finding primes
- Famous Paradoxes : Zeno's Paradox and Cantor's Infinities
- The Problem of Points : an age-old gambling problem that led to the development of probability by French mathematicians Pascal and Fermat
- A Proof of the Pythagorean Theorem : a proof that relies on Euclidean algebraic geometry, and is thus beautifully simple
- A Proof that e is irrational a proof by contradiction that relies on the expression of e as a power series

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Cabri Java Project

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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