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The Legacy of Felix Klein

  • Book
  • Open Access
  • © 2019

You have full access to this open access Book


  • Is the first collection of Klein’s main ideas on the teaching of mathematics
  • Shows that Felix Klein was a remarkable figure in mathematics and mathematics education
  • Demonstrates that Klein’s ideas are still important in teaching mathematics today
  • Written by authors who have worked with Klein’s ideas on teaching mathematics for many years

Part of the book series: ICME-13 Monographs (ICME13Mo)

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Table of contents (15 chapters)


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 ofview. 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.


“This book is of great interest for those interested in mathematics education and in its history. … It makes clear the depth and subtlety of Klein’s ideas of functional thinking, intuition, and visualisation, and the deep epistemological roots of his idea of elementarisation.” (Michèle Artigue, Educational Studies in Mathematics, Vol. 102, 2019)

Editors and Affiliations

  • Universität Würzburg, Würzburg, Germany

    Hans-Georg Weigand

  • University of Arizona, Tucson, USA

    William McCallum

  • Department of Mathematics, Sapienza University of Rome, Rome, Italy

    Marta Menghini

  • University of Oldenburg, Oldenburg, Germany

    Michael Neubrand

  • Universität Bielefeld, Bielefeld, Germany

    Gert Schubring

Bibliographic Information

  • Book Title: The Legacy of Felix Klein

  • Editors: Hans-Georg Weigand, William McCallum, Marta Menghini, Michael Neubrand, Gert Schubring

  • Series Title: ICME-13 Monographs

  • DOI:

  • Publisher: Springer Cham

  • eBook Packages: Education, Education (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s) 2019

  • Hardcover ISBN: 978-3-319-99385-0Published: 19 December 2018

  • eBook ISBN: 978-3-319-99386-7Published: 11 December 2018

  • Series ISSN: 2520-8322

  • Series E-ISSN: 2520-8330

  • Edition Number: 1

  • Number of Pages: VI, 226

  • Number of Illustrations: 51 b/w illustrations, 53 illustrations in colour

  • Topics: Mathematics Education, History of Mathematical Sciences, Teaching and Teacher Education

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