The Legacy of Felix Klein

I Introduction.- Felix Klein - Mathematician, Academic Organizer, Educational Reformer.- What is or what might be the legacy of Felix Klein?.- II . Functional Thinking.- Functional thinking: The history of a didactical principle.- Teachers' meanings for function and function notation in south korea and the United States.- Is the real number line something to be built, or occupied?.- Coherence and fidelity of the function concept in school mathematics.- Strand III: Intuitive thinking and visualization.- Aspects of "Anschauung" in the work of Felix Klein.- The road of the german book praktische analysis into japanese secondary school mathematics textbooks (1943-1944).- An influence of the felix klein movement on the far east.- Felix Klein's mathematical heritage seen through 3D models.- The modernity of the meraner lehrplan for teaching geometry today in grades 10-11: Exploiting the power of dynamic geometry systems.- IV. Elementary mathematics from a higher standpoint-conception, realization, and impact on teacher education.- Klein's conception of ''Elementary Mathematics from a  Higher Standpoint'.- Precision mathematics and approximation mathematics: the conceptual and educational role of their comparison.- Examples of Klein's practice elementary mathematics from a higher standpoint: volume I.- A double discontinuity and a triple approach: felix klein's perspective on mathematics teacher education.

"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)