Preuve Proof
Prueba
Web Newsletter
Mars/Avril 1997
Mars/Avril 1997
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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.
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Dreyfus T., Hadas N. (1996) Proof as answer to the question why. Zentralblatt für Didaktik der Mathematik 28 (1) 1-5.Hanna G., Jahnke N. (1996) Proof and Proving. In: Bishop A. et al (eds.) (pp.877-908). International Handbook of Mathematics Education. Dordrecht: Kluwer Academic Publishers.
Paolo Boero "on-line", 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.
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Midlands Mathematics
Education Seminars "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. |
A discussion from the
NCTM-L archive 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 Standards-based curriculum. The NCTM Standards are available on the Web at http://enc.org/online/NCTM/280dtoc1.html |
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 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. |
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The presentation of formal proofs an AI PhD thesis by Martin
Simon
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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?" 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. |
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"L'arithmétique le montre, l'expérience le prouve" un homme politique des années 70, sur France Inter. |
January 1997
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First International Workshop on Proof Transformation and Presentation April 8-10,
1997 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 machine-found 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 machine-found proofs. Techniques have been developed to transform proofs from a machine-oriented formalism into a more readable formalism such as natural deduction (ND) and to abstract and restructure these machine-generated 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, Feb. 28, 1997 Submission and Contact: ptp-97@cs.uni-sb.de Further information: http://jswww.cs.uni-sb.de/~ptp-97 Program Committee Xiaorong Huang Univ. of Toronto/DFKI |
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Dead line 15 june
1997. NCTM 1999 Yearbook on
Mathematical reasoning. |
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