Mathematics as an Educational Task

Hans Freudenthal

ISBN 10: 9027702357 / ISBN 13: 9789027702357

Edité par Springer Netherlands Dez 1972, 1972

A propos de cet article

This item is printed on demand - it takes 3-4 days longer - Neuware -Like preludes, prefaces are usually composed last. Putting them in the front of the book is a feeble reflection of what, in the style of mathe matics treatises and textbooks, I usually call thf didactical inversion: to be fit to print, the way to the result should be the inverse of the order in which it was found; in particular the key definitions, which were the finishing touch to the structure, are put at the front. For many years I have contrasted the didactical inversion with the thought-experiment. It is true that you should not communicate your mathematics to other people in the way it occurred to you, but rather as it could have occurred to you if you had known then what you know now, and as it would occur to the student if his learning process is being guided. This in fact is the gist of the lesson Socrates taught Meno's slave. The thought-experi ment tries to find out how a student could re-invent what he is expected to learn. I said about the preface that it is a feeble reflection of the didactical inversion. Indeed, it is not a constituent part of the book. It can even be torn out. Yet it is useful. Firstly, to the reviewer who then need not read the whole work, and secondly to the author himself, who like the composer gets an opportunity to review the Leitmotivs of the book. 696 pp. Englisch.

N° de réf. du vendeur 9789027702357

Détails bibliographiques

• Titre: Mathematics as an Educational Task
• Éditeur: Springer Netherlands Dez 1972
• Date de parution: 1972
• Langue: anglais
• ISBN à 10 chiffres: 9027702357
• ISBN à 13 chiffres: 9789027702357
• Reliure: Buch
• État de l'article: Neu
• Dimensions: 241 L x 160 H x 43 P (en millimètres) 241 millimètres de largeur par 160 millimètres de hauteur par 43 millimètres de profondeur
• Poids: 1197 grammes

A propos de ce titre

Synopsis

Like preludes, prefaces are usually composed last. Putting them in the front of the book is a feeble reflection of what, in the style of mathe- matics treatises and textbooks, I usually call thf didactical inversion: to be fit to print, the way to the result should be the inverse of the order in which it was found; in particular the key definitions, which were the finishing touch to the structure, are put at the front. For many years I have contrasted the didactical inversion with the thought-experiment. It is true that you should not communicate your mathematics to other people in the way it occurred to you, but rather as it could have occurred to you if you had known then what you know now, and as it would occur to the student if his learning process is being guided. This in fact is the gist of the lesson Socrates taught Meno's slave. The thought-experi- ment tries to find out how a student could re-invent what he is expected to learn. I said about the preface that it is a feeble reflection of the didactical inversion. Indeed, it is not a constituent part of the book. It can even be torn out. Yet it is useful. Firstly, to the reviewer who then need not read the whole work, and secondly to the author himself, who like the composer gets an opportunity to review the Leitmotivs of the book.