|
1999 |
Boero P., Garuti R., Lemut E. (1999) About the generation of conditionality of statements and its links with proving. PME XXIII (to appear) Haifa, Israel. |
|
Durand-Guerrier V. (1999) L'élève, le professeur et le labyrinthe. Petit X 50, 57-79. |
|
Epp S. (1999) The language of quantification in mathematics instruction. In Stiff L., Curcio F. (eds.) Developing mathematical reasoning in grades K-12 (pp. 188-197). Reston, VA: NCTM. |
|
Herbst P. G. (1999) The role of the teacher: What do the practices associated with two-column proofs say about the possibilities for argumentation? (Paper presented in the context of the symposium "Fostering argumentation in the mathematics class: The role of the teacher".) AERA 1999 annual meeting. |
|
Rav Y. (1999) Why do we prove theorems. Philosophia Mathematica 3(7) 5-41. |
|
Sekiguchi Y. (1999) Cognitive structures underlying conceptions of mathematical proof. Tsukuba Journal of Educational Studies in Mathematics 18, 45-56. |
|
Steen L. (1999) Twenty questions about mathematical reasoning. In Stiff L., Curcio F. (eds.) Developing mathematical reasoning in grades K-12 (pp. 270-285). Reston, VA: NCTM. |
|
Vadcard L. (1999) La validation en géométrie avec Cabri-géomètre : mesures exploratoires et mesures probatoires. Petit X 50, 5-21 |
|
Wood T. (1999) Creating a context for arguments in the mathematics class. Journal for Research in Mathematics Education 30(2) 171-191. |
1998 |
Carpentier F.-G. (1999) Modélisation des connaissances et de la démonstration pour l'E.I.A.O. de la géométrie. Thèse. Université de Rennes. |
|
Gibson D. (1998) Students' use of diagrams to develop proofs in an introductory analysis course. In: Schonfeld A., Kaput J., and E. Dubinsky E. (eds.) Research in collegiate mathematics education III. (Issues in Mathematics Education Volume 7 pp.284-307). American Mathematical Society. |
|
Harel G., Sowder L (1998) Students' proof schemes: Results from exploratory studies. In: Schonfeld A., Kaput J., and E. Dubinsky E. (eds.) Research in collegiate mathematics education III. (Issues in Mathematics Education, Volume 7, pp. 234-282 ). American Mathematical Society. |
|
Kumagai K. (1998) The justification process in a fifth grade mathematics classroom: From a social interactionist perspective. Reports of Mathematical Education (Journal of Japan Society of Mathematical Education (80) Supplementary Issue 70, 3-38 (in Japanese) <kumagai@juen.ac.jp>. |
Archives |
Hasegawa J., Mii M. (1997) The analysis on the process of geometric proof problems of ninth graders. Journal of JASME: Research in Mathematics Education 3, 137-146. (in Japanese) |
|
Koseki K. (ed.) (1987) Zukei no ronsho shido [Teaching of proof in geometry]. Tokyo: Meiji Tosho. (in Japanese) |
|
Kunimoto K. (1995) A study on a conception of proof of junior high school students. Journal of JASME: Research in Mathematics Education 1, 117-124. (in Japanese) |
|
Kunimune S. (1987) The study on development of understanding about the significance of demonstrations in learning geometrical figures. Reports of Mathematical Education. Journal of Japan Society of Mathematical Education (69) Supplementary Issue 47-48, 3-23 (in Japanese). <ecskuni@ed.shizuoka.ac.jp > |
|
Kunimune S., Kumakura H. (1996) A study on levels of students' understanding of literal expressions. Reports of Mathematical Education. Journal of Japan Society of Mathematical Education (78) Supplementary Issue 65-66, 35-55 (in Japanese). |
|
Miyazaki M. (1992) Students'activity in order to show the generality of a conjecture: How does one student use a generic example to make an explanation? Reports of Mathematical Education. Journal of Japan Society of Mathematical Education (74) Supplementary Issue 57, 3-19 (in Japanese). |
|
Shinzato T. (1995) Student's perception of similarity among geometric proof problems. Journal of JASME: Research in Mathematics Education 1, 125-131. (in Japanese) |
|
Soulé-Beck I. (1994) Quelques aspects linguistiques de la cohérence tectuelle dans un chapitre de manuel scolaire de géométrie. Thèse. Université de Metz. |
|
|
|
Conjecture and proof M. Laczkovich |
J.-P. Drouhard, C. Sackur, M. Maurel, |
This book presents the lecture notes of a one-semester course of the Budapest Semesters in Mathematics (SMP) This course for American and Canadian students was initiated and designed by Paul Erdös, László Lovász, Vera T. Sós and László Babai in 1983-84 with the intention to provide students with an experience of the tradition of Hungarian mathematics. The book is organised in two sections, presenting a large variety of mathematical topics ; the first section focuses on Proofs of impossibility and proofs of existence, the second part focuses on Constructions and Proofs of existence. |
In
mathematics, most statements may be called necessary.
They are not just true or false, in the same way as the
statement "Osnabrück is the birthplace of Erich Maria
Remarque", but they are necessarily true or false, like the
Pythagora's Theorem.
EDUCATION JOURNAL 11 (1999) |
Catia Mogetta and Federica Olivero |
|
This talk will be presented in the framework of the Geometry Working Group chaired by Keith Jones (University of Southampton) during the... St Martin's University College, Lancaster. Saturday 5th June, 1999 |
|
Des conjectures aux preuves Construction des concepts mathématiques Journée d'études mathématiques
organisée en l'honneur de Gilbert Arsac |
|
"Aux périodes d'expansion, lorsque des notions nouvelles sont introduites, [il règne] une période de défrichement plus ou moins étendue, pendant laquelle dominent l'incertitude et la controverse. [...] la génération suivante peut alors codifier [...] élaguer,asseoir les bases, [...] à ce moment règne de nouveau alors sans partage la méthode axiomatique, jusqu'au prochain bouleversement qu'apportera quelque idée nouvelle" Le titre de cette journée rend compte d'une spécificité du travail mathématique : au cours du travail de recherche, avant la phase d'axiomatisation, les concepts se précisent dans l'explicitation progressive des propriétés qui les caractérisent et qui sont nécessaires pour démontrer les conjectures à leur propos. Cette spécificité des mathématiques est aussi un enjeu de leur apprentissage. C'est à l'étude de quelques moments de ce travail mathématique que vous êtes invités. 9h Evolution de l'utilisation de concepts mathématiques par la physique Cette journée est organisée en l'honneur de Gilbert Arsac par quelques collègues qui ont souhaité lui rendre cet hommage pour le travail important qu'il a accompli dans les divers domaines qui lui ont tenu à coeur au cours de sa carrière : les mathématiques avec la théorie des groupes, les problèmes d'apprentissage des mathématiques avec la didactique. Pour ces derniers, les mathématiques savantes sont une référence incontournable comme Gilbert Arsac lui même le montrera. C'est cette efficacité de l'approche mathématique des questions d'apprentissage qui ont guidé son action lorsqu'il était directeur de l'IREM et en tant que chercheur en didactique. Organisation : IREM, IGD (Institut Girard Desargues), LIRDHIST (Laboratoire Interdisciplinaire de Recherche en didactique et histoire des sciences et techniques) avec le soutien du Département de premier cycle, UFR de mathématiques |
Philosophie de la logique Hilary Putnam |
|
|||||||
Traduction
de Patrick Pecatte, texte intégral en ligne
avec l'aimable autorisation des Éditions de
l'Éclat. L'ouvrage correspondant est cependant
toujours disponible, par exemple sur
alibabook (Combas: Éditions de
l'Éclat, 1996. 71 p.) |
||||||||
Philosophie et Mathématiques Thème : Mathématiques et langage Ecole Normale Supérieure |
The TSG-12 activities will encompass the following issues: I. The importance of explanation, justification, and proof in mathematics education; These issues will be considered from the following points of view: (a) Historical and
epistemological, related to the nature of mathematical proof
and its functions in mathematics in a historical
perspective; discussions on the different issues. |
|||||||
Les séances du séminaire ont lieu à 20:30 en salle de conférences, 46 rue d'Ulm |
Disourse on the method René Descartes |
Web Archives Kepler sphere packing problem |
An on-line translation of the famous Descartes' text by James Fieser. The translator allows a free distribution of the corresponding computer file "for personal and classroom use" (see the Copyright indications). This on-line text is a working draft. Possible errors are to be reported to James Fieser "Thus my design is not here to teach the Method which everyone should follow in order to promote the good conduct of his Reason, but only to show in what manner I have endeavored to conduct my own. Those who set about giving precepts must esteem themselves more skillful than those to whom they advance them, and if they fall short in the smallest matter they must of course take the blame for it." (Descartes 1637) Images of Mathematicians on Postage Stamps |
Kepler's problem consists of deciding the most efficient way to pack equal-sized spheres in a large crate. Should each sphere sit right on top of the one beneath? Or should it be arracnged so that the spheres in each higher layer sit in the hollows formed beneath? Kepler believed that for a very large crate, the orange-pile arrangement is more efficient but was unable to prove it. What
exactly is a mathematical proof? The Guardian
raised the old question again last 24 September 1998
when reporting that Thomas Hales of the University of
Michigan claimed that he had proved correct the guess Kepler
made in 1611. The reason to stress again the question on
this occasion is the use by the mathematician in order to
complete his 250 pages proof of about 3 gigabytes of
computer programs and data. Even more: To follow Hales's
argument, you have to download and run his programs, reports
The Guardian. Indeed, this reminds us of the Four
Colour Theorem and its Appel and Aken proof in 1976. |
a virtual forum |
||
Historia-Matematica is a virtual forum for scholarly discussion of the history of mathematics in a broad sense, among professionals and non-professionals with a serious interest in the field, archived at Why Euclid gives geometric constructions in Book II that one might well expect to be postponed until after the general theory of proportion was developed, a thread begun by Roger Cooke: Euclid, Book II (14 Mar 1999) See Heinz Lueneburg's March 23 post, offering a link to dvi files in German from his number theory class, which draws on Euclid's Books VII, VIII, and IX. |
|