The Legacy of Felix Klein by Weigand, McCallum & Menghini
The Legacy of Felix Klein - Table of Contents
PART-I INTRODUCTION
1. Felix Klein—Mathematician, Academic Organizer, Educational Reformer
2. What Is or What Might Be the Legacy of Felix Klein?
PART-II FUNCTIONAL THINKING
3. Functional Thinking: The History of a Didactical Principle
4. Teachers’ Meanings for Function and Function Notation
5. Is the Real Number Line Something to Be Built, or Occupied?
6. Coherence and Fidelity of the Function Concept in School Mathematics
PART-III INTUITIVE THINKING AND VISUALIZATION
7. Aspects of “Anschauung” in the Work of Felix Klein
8. Introducing History of Mathematics Education Through Its Actors
9. The Road of the German Book *Praktische Analysis* into Japanese Secondary School Mathematics Textbooks
10. Felix Klein’s Mathematical Heritage Seen Through 3D Models
11. The Modernity of the Meraner Lehrplan for Teaching Geometry
PART-IV ELEMENTARY MATHEMATICS FROM A HIGHER STANDPOINT
12. Klein’s Conception of Elementary Mathematics from a Higher Standpoint
13. Precision Mathematics and Approximation Mathematics
14. Examples of Klein’s Practice of Elementary Mathematics from a Higher Standpoint
15. A Double Discontinuity and a Triple Approach: Felix Klein’s Perspective on Mathematics Teacher Education
What You Will Learn in The Legacy of Felix Klein
"The Legacy of Felix Klein" by Hans-Georg Weigand, William McCallum, Marta Menghini, Michael Neubrand, Gert Schubring examines the lasting influence of one of the most important figures in modern mathematics. The book places Felix Klein within the broader development of "mathematical history", showing how his ideas reshaped geometry, algebra, and the unity of mathematical thinking.
Weigand highlights Klein’s groundbreaking contributions to "geometry", group theory, and the famous Erlangen Program, which transformed how mathematical structures are understood. Beyond research, the book emphasizes Klein’s role as a reformer of "mathematics education", advocating for stronger connections between pure mathematics, applications, and teaching at all levels.
The book also explores Klein’s impact on scientific culture and international collaboration, presenting him as both a visionary thinker and an influential organizer of academic life. By combining historical analysis with educational insight, Weigand shows how Klein’s ideas continue to shape "modern mathematics" and inspire discussions about "educational reform" today.
Book Details & Specifications
Title:
The Legacy of Felix Klein by Weigand, McCallum & Menghini
Publisher:
Springer
Year:
2019
Pages:
225
Type:
PDF
Language:
English
ISBN-10 #:
3319993879
ISBN-13 #:
978-3319993874
License:
CC BY 4.0
Amazon:
Amazon
About the Author: Hans-Georg Weigand, William McCallum, Marta Menghini, Michael Neubrand, Gert Schubring
The author
Hans-Georg Weigand, William McCallum, Marta Menghini, Michael Neubrand, Gert Schubring
is a German scholar internationally known for his work in "mathematics education" and the "didactics of mathematics". He served for many years as Professor of Mathematics Education at the University of Würzburg, where his research focused on curriculum development, teacher education, and the meaningful use of digital tools in mathematics teaching. As editor of "The Legacy of Felix Klein", Weigand brings a strong historical and educational perspective to Klein’s influence. The volume reflects his commitment to connecting "mathematical thinking" with classroom practice and shows how Klein’s ideas continue to shape modern "education reform" and teacher training.
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