The Legacy of Felix Klein.

Intro -- Contents -- Introduction -- 1 Felix Klein-Mathematician, Academic Organizer, Educational Reformer -- 1.1 Felix Klein's Upbringing, Education, and Academic Career -- 1.2 The Characteristics of Klein's Methods -- 1.3 Educational Reform and Its Institutional and International Scope -- Bibliography -- 2 What Is or What Might Be the Legacy of Felix Klein? -- 2.1 Felix Klein as a Sensitised Mathematician -- 2.2 Felix Klein Recognized Problems and Described Them in Detail -- 2.3 Felix Klein Thought About Solutions for Problems -- 2.4 Felix Klein Suggested Changes not Only in General, but also in a Specific Way -- 2.5 Felix Klein Asked for Change Not Only on the Organizational Level, but He also Suggested Changes in the Way Mathematics Should Be Taught at University -- 2.6 Felix Klein Was-Like Many of Us-(also) Driven by External Requests, but When He Was Involved in an Activity, He Was Extensively Committed -- 2.7 Felix Klein Permanently Critically Considered and Reconsidered His Own Ideas -- 2.8 Final Remark -- References -- Functional Thinking -- 3 Functional Thinking: The History of a Didactical Principle -- 3.1 The Demand for Functional Thinking in the Meraner Lehrplan, 1905 -- 3.2 Education in the Habit of Functional Thinking in Arithmetic, Algebra, and Geometry -- 3.2.1 Functional Dependencies in Arithmetic and Algebra Teaching -- 3.2.2 The Principle of Movement and Functional Thinking in Geometry -- 3.3 Functional Thinking and Mental Representations in Differential Calculus -- 3.4 Conclusion -- Appendix -- References -- 4 Teachers' Meanings for Function and Function Notation in South Korea and the United States -- 4.1 Introduction -- 4.2 A Focus on Meanings Instead of on Knowledge -- 4.3 Our Perspective on Productive Meanings for Function -- 4.4 Method -- 4.5 Results -- 4.6 Discussion -- References.

5 Is the Real Number Line Something to Be Built, or Occupied? -- 5.1 Introduction -- 5.2 The Construction Narrative of the Real Number Line -- 5.3 Difficulties with the Construction Narrative -- 5.3.1 The Whole Number/Fraction Divide -- 5.3.2 The Continuum Gap -- 5.4 The Occupation Narrative of the Real Number Line -- 5.5 Quantity, Unit, Measure, Number -- 5.6 Who Was Vasily Davydov? -- 5.7 Conclusion: What Is Achieved by the Occupation Narrative of the Number Line? -- References -- 6 Coherence and Fidelity of the Function Concept in School Mathematics -- 6.1 Introduction -- 6.2 The Definition of Function in School Mathematics -- 6.3 Probing the Image of Function in the Internet Brain -- 6.3.1 Mathematical Coherence -- 6.3.2 Mathematical Fidelity -- 6.4 Concluding Thoughts -- References -- Intuitive Thinking and Visualization -- 7 Aspects of "Anschauung" in the Work of Felix Klein -- 7.1 Core Demands for Modernizing the Teaching of Mathematics at Secondary Schools -- 7.2 Intuition in Mathematics Teaching in Higher Education -- 7.3 Intuition in Felix Klein's Lectures -- 7.3.1 Sensate, Idealizing and Abstract Intuition -- 7.3.2 Intuition and the Function Concept -- 7.3.3 Proof Through Intuition -- 7.4 Intuition and the Genetic Method -- 7.5 Conclusion -- References -- 8 Introducing History of Mathematics Education Through Its Actors: Peter Treutlein's Intuitive Geometry -- 8.1 Introduction -- 8.2 History of Mathematics in Mathematics Education -- 8.3 Treutlein's Models and Textbooks in the University Education of Mathematics Teachers -- References -- 9 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 -- 9.1 Background and Objective of This Paper -- 9.2 The Influence of Klein on the Far East: The Case of Japan.

9.3 Integration of Algebra and Geometry with Mechanical Instruments -- 9.4 Embedded German Praktische Analysis in the Japanese Textbook for Cluster I (1943) -- 9.5 The Influence of Klein: Germany or Origins from UK and US? -- 9.6 Conclusion -- References -- 10 Felix Klein's Mathematical Heritage Seen Through 3D Models -- 10.1 Introduction -- 10.1.1 Klein's Vision for Visualisations -- 10.1.2 Four Threads of Klein's Vision for Teaching and Learning Mathematics -- 10.2 Building on Klein's Key Ideas in Today's Classrooms and Seminars -- 10.2.1 Interplay Between Abstraction and Visualisation -- 10.2.2 Discovering the Nature of Objects with the Help of Small Changes -- 10.2.3 Linking Functional Thinking with Geometry -- 10.2.4 The Characterization of Geometries -- 10.3 Klein's Ideas on Visualisation and Today's Resources for the Mathematics Classroom as an Introduction to Research Activities -- References -- 11 The Modernity of the Meraner Lehrplan for Teaching Geometry Today in Grades 10-11: Exploiting the Power of Dynamic Geometry Systems -- 11.1 Introduction -- 11.2 Teaching Space Geometry in School -- 11.3 The Content of the Activity -- 11.4 Activities -- 11.5 Conclusions -- References -- Elementary Mathematics from a Higher Standpoint-Conception, Realization, and Impact on Teacher Education -- 12 Klein's Conception of 'Elementary Mathematics from a Higher Standpoint' -- 12.1 Introduction -- 12.2 A Differing View of Elementary Mathematics -- 12.3 Differing Views of the Relation Between Academic Mathematics and School Mathematics -- 12.4 Implications of the Term "Advanced" -- 12.5 The Concept of Elements -- 12.6 Klein's Practice -- 12.7 Modernism and the Challenge by Set Theory -- 12.8 Concluding Remarks -- Bibliography -- 13 Precision Mathematics and Approximation Mathematics: The Conceptual and Educational Role of Their Comparison.

13.1 The Lecture Course of Felix Klein -- 13.2 First Example: Empirical and Idealised Curve -- 13.3 Second Example: Iterated Inversion with Respect to Three Touching Circles -- 13.4 Third Example: Gestalt Relations of Curves -- 13.5 Conclusion -- References -- 14 Examples of Klein's Practice Elementary Mathematics from a Higher Standpoint: Volume I -- 14.1 Introduction -- 14.2 Klein's Didactic Perspective -- 14.3 Klein's Historical Perspective -- 14.4 Klein's Mathematical Perspective -- 14.5 Higher Mathematics from an Elementary Standpoint? -- 14.6 A Higher Standpoint: First Conclusions -- References -- 15 A Double Discontinuity and a Triple Approach: Felix Klein's Perspective on Mathematics Teacher Education -- 15.1 A Double Discontinuity -- 15.2 A Triple Approach -- 15.2.1 Arithmetic, Algebra, Analysis -- 15.2.2 Geometry -- 15.2.3 Precision Mathematics and Approximation Mathematics -- 15.3 Klein and Mathematics Teacher Education -- References.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2023. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.