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Mathematics as an Educational Task

  • Book
  • © 1973

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Authors:
  1. Hans Freudenthal
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Table of contents (19 chapters)

  1. Front Matter

    Pages I-XII
    Download chapter PDF

  2. The Mathematical Tradition

    • Hans Freudenthal
    Pages 1-16

  3. Mathematics Today

    • Hans Freudenthal
    Pages 17-51

  4. Tradition And Education

    • Hans Freudenthal
    Pages 52-63

  5. Use and Aim of Mathematics Instruction

    • Hans Freudenthal
    Pages 64-98

  6. The Socratic Method

    • Hans Freudenthal
    Pages 99-108

  7. Re-Invention

    • Hans Freudenthal
    Pages 109-130

  8. Organization of a Field by Mathematizing

    • Hans Freudenthal
    Pages 131-146

  9. Mathematical Rigour

    • Hans Freudenthal
    Pages 147-154

  10. Instruction

    • Hans Freudenthal
    Pages 155-161

  11. The Mathematics Teacher

    • Hans Freudenthal
    Pages 162-169

  12. The Number Concept — Objective Accesses

    • Hans Freudenthal
    Pages 170-241

  13. Developing the Number Concept from Intuitive Methods to Algorithmizing and Rationalizing

    • Hans Freudenthal
    Pages 242-286

  14. Development of the Number Concept — The Algebraic Method

    • Hans Freudenthal
    Pages 287-311

  15. Development of the Number Concept — From the Algebraic Principle to the Global Organization of Algebra

    • Hans Freudenthal
    Pages 312-331

  16. Sets and Functions

    • Hans Freudenthal
    Pages 332-400

  17. The Case of Geometry

    • Hans Freudenthal
    Pages 401-511

  18. Analysis

    • Hans Freudenthal
    Pages 512-580

  19. Probability and Statistics

    • Hans Freudenthal
    Pages 581-614

  20. Logic

    • Hans Freudenthal
    Pages 615-661
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Keywords

About this book

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.

Bibliographic Information

  • Book Title: Mathematics as an Educational Task

  • Authors: Hans Freudenthal

  • DOI: https://doi.org/10.1007/978-94-010-2903-2

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: D. Reidel Publishing Company, Dordrecht-Holland 1973

  • Hardcover ISBN: 978-90-277-0235-7Published: 31 December 1972

  • Softcover ISBN: 978-90-277-0322-4Published: 31 December 1972

  • eBook ISBN: 978-94-010-2903-2Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: XII, 680

  • Topics: Mathematics Education

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