Table of contents

  1. Front Matter
    Pages i-vi
  2. Introduction

    1. Front Matter
      Pages 1-3
    2. Hans-Georg Weigand
      Pages 23-31 Open Access
  3. Functional Thinking

  4. Intuitive Thinking and Visualization

  5. Elementary Mathematics from a Higher Standpoint—Conception, Realization, and Impact on Teacher Education

About this book


This open access book provides an overview of Felix Klein’s ideas, highlighting developments in university teaching and school mathematics related to Klein’s thoughts, stemming from the last century. It discusses the meaning, importance and the legacy of Klein’s ideas today and in the future, within an international, global context. Presenting extended versions of the talks at the Thematic Afternoon at ICME-13, the book shows that many of Klein’s ideas can be reinterpreted in the context of the current situation, and offers tips and advice for dealing with current problems in teacher education and teaching mathematics in secondary schools. It proves that old ideas are timeless, but that it takes competent, committed and assertive individuals to bring these ideas to life. 

Throughout his professional life, Felix Klein emphasised the importance of reflecting upon mathematics teaching and learning from both a mathematical and a psychological or educational point of view. He also strongly promoted the modernisation of mathematics in the classroom, and developed ideas on university lectures for student teachers, which he later consolidated at the beginning of the last century in the three books on elementary mathematics from a higher standpoint.


mathematics education teacher education functional thinking intuitive thinking visualization open access

Editors and affiliations

  • Hans-Georg Weigand
    • 1
  • William McCallum
    • 2
  • Marta Menghini
    • 3
  • Michael Neubrand
    • 4
  • Gert Schubring
    • 5
  1. 1.Universität WürzburgWürzburgGermany
  2. 2.University of ArizonaTucsonUSA
  3. 3.Department of MathematicsSapienza University of RomeRomeItaly
  4. 4.University of OldenburgOldenburgGermany
  5. 5.Universität BielefeldBielefeldGermany

Bibliographic information

  • DOI
  • Copyright Information The Editor(s) (if applicable) and The Author(s) 2019
  • License CC BY
  • Publisher Name Springer, Cham
  • eBook Packages Education Education (R0)
  • Print ISBN 978-3-319-99385-0
  • Online ISBN 978-3-319-99386-7
  • Series Print ISSN 2520-8322
  • Series Online ISSN 2520-8330
  • Buy this book on publisher's site