The Legacy of Felix Klein.
| Main Author: | |
|---|---|
| Other Authors: | , , , |
| Format: | eBook |
| Language: | English |
| Published: |
Cham :
Springer International Publishing AG,
2018.
|
| Edition: | 1st ed. |
| Series: | ICME-13 Monographs
|
| Subjects: | |
| Online Access: | Click to View |
Table of Contents:
- 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.