Au lecteur ...
La partie principale de cette bibliographie est
constituée d'articles publiés dans des revues,
des livres et des chapitres de livres accessibles par les
réseaux de distribution ordinaires, ainsi qu'aux
thèses. Je compte sur les remarques et suggestions
des utilisateurs pour améliorer cet outil.
Al lector ...
La parte principal de esta bibliografía es
constituida por artículos publicados en revistas,
libros y capítulos de libros accesibles por las redes
de distribución ordinarias, igualmente las tesis. Yo
cuento con las remarcas y sugestiones de los utilizadores
para el mejoramiento de este útil.
To the Reader ...
This bibliography consists to a large part of articles
published in journals, of books, and of chapters of books,
all accessible from normal sources, as well as of theses. I
am counting on remarks and suggestions from users to improve
this tool.
Nicolas
Balacheff
Dreyfus T.,
Hadas N. (1996) Proof as
answer to the question why. Zentralblatt für
Didaktik der Mathematik 28 (1) 15.
Hanna G., Jahnke N.
(1996) Proof and Proving. In: Bishop A. et al
(eds.) (pp.877908). International Handbook of
Mathematics Education. Dordrecht: Kluwer Academic
Publishers.
Paolo Boero "online",
les textes sur la Preuve présentés à
PME par Paolo Boero et de ses collègues :
(1994) Approaching
rational geometry: from physical relationships to
conditional statements.
(1995) Towards
Statements and Proofs in Elementary Arithmetic: An
Exploratory Study about the Role of Teachers and the
Behaviour of Students.
(1996) Some
dynamic mental processes underlying producing and
proving conjectures.
(1996) Challenging
the traditional school approach to theorems: a
hypothesis about the cognitive unity of theorems.
A talk on
proof
Midlands Mathematics
Education Seminars
University of Warwick
Institute of Education
"Students teachers' encounters with formal
proof: convincing themselves and convincing
others"
By: Janet
Ainley, Marcia Pinto and David
Tall
In this seminar we shall contrast the
experiences of students taking a course in
Mathematical Analysis within an education degree
with those of undergraduates following a
traditional mathematics programme. We shall explore
the idea that to train student teachers to be "good
mathematicians" by introducing them to formal
axiomatic methods may be counterproductive because
there is a conflict between their professional
intention as teachers and the formalism of
mathematical proof.

Proofs and
mathematical structure
A discussion from the
NCTML archive
hosted
by the Math Forum
Do the NCTM Standards give short shrift to what
is arguably the most basic and vital mathematical
structure of all: proof? If so, does this
constitute rejecting mathematical structure?
In a previous discussion, "Parent's messages," a
contributor suggested that readers search the
Standards for occurrences of the word 'proof'. This
conversation, "Proofs and Mathematical Structure,"
takes up the effect of the word's omission, the
need for and value of precise mathematical
arguments, the difficulty of translating everyday
language into a form that can be analyzed, and the
call for manuscripts addressing the role and nature
of proof in a Standardsbased curriculum.
The NCTM Standards are available on the Web at
http://enc.org/online/NCTM/280dtoc1.html

Un exposé
sur la preuve
Paris
9 mars 1997
Séminaire National de
Didactique des Mathématiques
"Les mathématiques
discrètes : une alternative à la
géometrie pour L'apprentissage de la
preuve ? Débat à partir de
quelques méthodes spécifiques
(induction, cage à pigeons,
coloration).
Par: Denise
Grenier,
Charles
Payan
Laboratoire Leibniz, CNRS, INPG et UJF
Grenoble
Philippe
Bernat
Enseignant chercheur au CRIN de Nancy, Philippe
Bernat fut l'un des artisans du
développement de nouveaux environnements
pour l'enseignement de la géométrie.
Ses travaux de recherche actuels, à la suite
sa thèse, portaient sur la conception et le
développement de CHYPRE,
un environnement d'aide à la
résolution de problèmes de
géométrie et de construction de
preuve pour des élèves de
collège. Ces travaux ont été
brutalement interrompus par le décés
de Philippe Bernat fin décembre 1996.
Attentif et enthousiaste, il fut le premier
à contribuer à ce site sur la Preuve.
Nous saluons sa mémoire.

Beweisen
The presentation of
formal proofs
an AI PhD thesis by Martin
Simon
Technische Universität Berlin, 1996

In this thesis is presented an approach
to the intelligible communication of
formal proofs. Observing a close
correspondence between the activities of
formalproof development and program
development, and using this as a
guideline, the author applies wellknown
principles from program design to proof
design and presentation, resulting in
formal proofs presented in a literate
style, that are hierarchically structured,
and that emphasize calculation.

more : http://cs.tuberlin.de/~simons/

From the Mathedu
Archive:
Proof by induction
Prof.
Williams P. Wardlaw writes: "I like to
introduce induction with a story about painting a
chain. Given my institution, I prefer an anchor
chain. A First Lieutenant (responsible for
painting) orders a Seaman to paint the anchor
chain. Later he asks the Seaman what color he
painted the chain. The Seaman cannot remember, but
is sure that whatever color he painted a given
link, he used the same color for the next link. The
First Lieutenant goes on deck and sees that the
first link, just showing at the top of the hawse
pipe, is chartreuse. What color is (every link of)
the chain?"
The story is followed by a formal
discussion of induction and several examples, such
as a couple of summation formulas and a couple of
inequalities...
Lou Talman adds: Sonneborn's Horse
Lemma states that all horses are the same color.
Its power lies in its immediate applicability to
proofs by contradiction, which assume the form
"Suppose it were not so. Well, that would be a
horse of another color, wouldn't it."
This searchable thread from the MATHEDU
archive cites useful articles and discusses
examples of mathematical proof by induction at both
the high school and the college level.

Ce pourrait
être un proverbe...
"L'arithmétique le montre,
l'expérience le prouve"
un homme politique des années 70, sur
France Inter.

News from the
Budapest Seminar
January 1997

Arzarello
F. (1997) For an ecology of proof in
the classroom.


An AI
Call for Paper and Participation
First
International Workshop on Proof Transformation and
Presentation
April 810,
1997
Castle Dagstuhl, Octavieallee, 66687 Wadern,
Saarland, Germany
Over the past thirty years there has been
significant progress in the field of automated
theorem proving with respect to the reasoning power
of the inference engines: many hard and open
mathematical problems could be proven with a
machine and the use of formal methods in software
engineering and hardware verification is becoming a
reality.
Another important ingredients of a automated
reasoning system, however, is its ability to
communicate with its users. For many applications
such as in a mathematical reasoning assistant, an
effective communication between the system and its
users is critical for the acceptance of a system.
Only if a system also talks his language, a user
will be convinced by machinefound proofs and feel
his understanding of the topic improved.
Many standard representations used by ATP
systems such as resolution proofs or mating proofs,
unfortunately, are difficult to follow even for
professional mathematicians. This holds even more
so, as the machine generated proofs become more
complex (between several hundred and up to several
thousand steps in a single proof). Therefore there
has been a increasing interest in the
transformation and presentation of machinefound
proofs. Techniques have been developed to transform
proofs from a machineoriented formalism into a
more readable formalism such as natural deduction
(ND) and to abstract and restructure these
machinegenerated proofs to produce a textbook
style of proofs in natural language. Another
related line of research concerns the interactive,
graphic or multimedia interface facilities for
theorem provers.
This informal workshop aims to create an
intimate and stimulating setting to bring together
researcher from various fields working with or
interested in this exciting issue to exchange ideas
and results.
Electronic submissions of one page are
solicited. Proceedings containing an extended
version will be published afterwards in a suitable
form. Other people interested in participating are
invited to submit a short description of background
and research interest. To encourage a workshop
atmosphere, priority will be given to those who
submitted a paper.
Topics include (but are not restricted to)
1. Relationship
between logic calculi, including
complexity measures,
2. Mathematical vernacular
3. Transformation of proofs from a
machineoriented formalism to a more
readable formalism like natural
deduction
4. Abstraction and Restructuring of
machinefound proofs
5. Analysis of user requirements for the
interface of ATP systems
6. Cognitive models of human deduction
7. Verbalization of machinefound (formal)
proofs in natural language
Submission
deadline
Feb. 28, 1997
Submission and
Contact: ptp97@cs.unisb.de
Further
information: http://jswww.cs.unisb.de/~ptp97
Program
Committee
Xiaorong
Huang Univ. of
Toronto/DFKI
Jaff
Pelletier Univ. of Alberta
Frank
Pfenning Carnegie Mellon
Univ.
Joerg
Siekmann German Research
Centre for Artificial Intelligence (DFKI)

Other
call for papers
Dead line 15 june
1997.
"The rôle of proof through out the
curriculum" (fall 1998 issue)
Mathematics Teachers, NCTM, 1906 Association Drive
Reston, VA 220911593, USA
NCTM 1999 Yearbook on
Mathematical reasoning.
Information and guidelines: http://www.nctm.org under
"Educational Materials / 1999 Yearbook"
See also Proof
Newsletter January/February 1997

Lettres
précédentes

Past
Newsletters

Noticias
anteriores

97 01/02

