Mathematics as an Educational Task 作为教育任务的数学 英文原版 Hans Freudenthal

基本信息

Format Hardback | 680 pages

Dimensions 155 x 235 x 46.48mm | 2,530g

Publication date 01 Jun 1973

Publisher Springer

Imprint Kluwer Academic Publishers

Language English

Edition Statement 1973 ed.

Illustrations note XII, 680 p.

ISBN10 9027702357

ISBN13 9789027702357

页面参数仅供参考，具体以实物为准

书籍简介

像序曲一样，序曲通常是最后谱写的。 把它们放在书的前面是一个虚弱的反射,装置建立电气自动方式风格的专著和教科书,我通常叫四氢呋喃教训的反演:为了适合打印,到结果应该发现的逆顺序; 特别是作为结构画龙点睛的关键定义被放在了前面。 多年来，我一直将教学的倒置与思想实验进行对比。 确实，你不应该以你想到的方式将你的数学传达给其他人，而是如果你当时知道你现在所知道的，你可能会想到，如果他的学生 学习过程得到指导。 这实际上是苏格拉底教给美诺的奴隶的教训的要点。 思想实验试图找出学生如何重新发明他期望学习的内容。 我在序言中说它是教学倒置的微弱反映。 事实上，它不是本书的组成部分。 它甚至可以被撕掉。 不过还是很有用的。 首先，对评论家来说，他们不需要阅读整部作品，其次，对作者自己来说，他们像作曲家一样，有机会回顾这本书的主题动机。  

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.

目录

I. The Mathematical Tradition.- II. Mathematics Today.- III. Tradition and Education.- IV. Use and Aim of Mathematics Instruction.- V. The Socratic Method.- VI. Re-invention.- VII. Organization of a Field by Mathematizing.- VIII. Mathematical Rigour.- IX. Instruction.- X. The Mathematics Teacher.- XI. The Number Concept - Objective Accesses.- XII. Developing the Number Concept from Intuitive Methods to Algorithmizing and Rationalizing.- XIII. Development of the Number Concept - The Algebraic Method.- XIV. Development of the Number Concept - From the Algebraic Principle to the Global Organization of Algebra.- XV. Sets and Functions.- XVI. The Case of Geometry.- XVII. Analysis.- XVIII. Probability and Statistics.- XIX. Logic.- Appendix I. Piaget and the Piaget School's Investigations on the Development of Mathematical Notions.- Appendix II. Papers of the Author on Mathematical Instruction.

作者简介

汉斯·弗洛伊登塔尔（Hans Freudenthal，1905 年 9 月 17 日 - 1990 年 10 月 13 日）是一位犹太裔德国出生的荷兰数学家。 他对代数拓扑学做出了重大贡献，并且对文学、哲学、历史和数学教育也很感兴趣。

Hans Freudenthal (17 September 1905 – 13 October 1990) was a Jewish-German-born Dutch mathematician. He made substantial contributions to algebraic topology and also took an interest in literature, philosophy, history and mathematics education.