The Legacy of Felix Klein.
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Place / Publishing House: | Cham : : Springer International Publishing AG,, 2018. ©2019. |
Year of Publication: | 2018 |
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Weigand, Hans-Georg. The Legacy of Felix Klein. 1st ed. Cham : Springer International Publishing AG, 2018. ©2019. 1 online resource (225 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier ICME-13 Monographs 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. Description based on publisher supplied metadata and other sources. Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. Electronic books. McCallum, William. Menghini, Marta. Neubrand, Michael. Schubring, Gert. Print version: Weigand, Hans-Georg The Legacy of Felix Klein Cham : Springer International Publishing AG,c2018 9783319993850 ProQuest (Firm) https://ebookcentral.proquest.com/lib/oeawat/detail.action?docID=5614174 Click to View |
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Weigand, Hans-Georg. |
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Weigand, Hans-Georg. The Legacy of Felix Klein. ICME-13 Monographs 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. |
author_facet |
Weigand, Hans-Georg. McCallum, William. Menghini, Marta. Neubrand, Michael. Schubring, Gert. |
author_variant |
h g w hgw |
author2 |
McCallum, William. Menghini, Marta. Neubrand, Michael. Schubring, Gert. |
author2_variant |
w m wm m m mm m n mn g s gs |
author2_role |
TeilnehmendeR TeilnehmendeR TeilnehmendeR TeilnehmendeR |
author_sort |
Weigand, Hans-Georg. |
title |
The Legacy of Felix Klein. |
title_full |
The Legacy of Felix Klein. |
title_fullStr |
The Legacy of Felix Klein. |
title_full_unstemmed |
The Legacy of Felix Klein. |
title_auth |
The Legacy of Felix Klein. |
title_new |
The Legacy of Felix Klein. |
title_sort |
the legacy of felix klein. |
series |
ICME-13 Monographs |
series2 |
ICME-13 Monographs |
publisher |
Springer International Publishing AG, |
publishDate |
2018 |
physical |
1 online resource (225 pages) |
edition |
1st ed. |
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. |
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-- 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.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">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.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">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.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">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.</subfield></datafield><datafield tag="588" ind1=" " ind2=" "><subfield code="a">Description based on publisher supplied metadata and other sources.</subfield></datafield><datafield tag="590" ind1=" " ind2=" "><subfield code="a">Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. </subfield></datafield><datafield tag="655" ind1=" " ind2="4"><subfield code="a">Electronic books.</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">McCallum, William.</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Menghini, Marta.</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Neubrand, Michael.</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Schubring, Gert.</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Print version:</subfield><subfield code="a">Weigand, Hans-Georg</subfield><subfield code="t">The Legacy of Felix Klein</subfield><subfield code="d">Cham : Springer International Publishing AG,c2018</subfield><subfield code="z">9783319993850</subfield></datafield><datafield tag="797" ind1="2" ind2=" "><subfield code="a">ProQuest (Firm)</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">ICME-13 Monographs</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://ebookcentral.proquest.com/lib/oeawat/detail.action?docID=5614174</subfield><subfield code="z">Click to View</subfield></datafield></record></collection> |