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Mathematics as an Educational Task

  • Authors
  • Hans Freudenthal

Table of contents

  1. Front Matter
    Pages I-XII
  2. Hans Freudenthal
    Pages 1-16
  3. Hans Freudenthal
    Pages 17-51
  4. Hans Freudenthal
    Pages 52-63
  5. Hans Freudenthal
    Pages 64-98
  6. Hans Freudenthal
    Pages 99-108
  7. Hans Freudenthal
    Pages 109-130
  8. Hans Freudenthal
    Pages 131-146
  9. Hans Freudenthal
    Pages 147-154
  10. Hans Freudenthal
    Pages 155-161
  11. Hans Freudenthal
    Pages 162-169
  12. Hans Freudenthal
    Pages 170-241
  13. Hans Freudenthal
    Pages 332-400
  14. Hans Freudenthal
    Pages 401-511
  15. Hans Freudenthal
    Pages 512-580
  16. Hans Freudenthal
    Pages 581-614
  17. Hans Freudenthal
    Pages 615-661
  18. Back Matter
    Pages 662-680

About this book

Introduction

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.

Keywords

algebra calculus education function geometry mathematics

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-010-2903-2
  • Copyright Information Springer Science+Business Media B.V. 1973
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-277-0322-4
  • Online ISBN 978-94-010-2903-2
  • Buy this book on publisher's site