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Format: 1 Online-Ressource (xx, 318 Seiten)

ISBN: 9783030615703

Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-030-61569-7

Language: English

Keywords: Mathematik ; Mathematikunterricht

DOI: 10.1007/978-3-030-61570-3

URL: Volltext  (kostenfrei)

URL: Volltext  (kostenfrei)

Author information: Wittmann, Erich Ch. 1939-

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Format: 1 online resource (332 pages)

ISBN: 9783030615703

Note: Intro -- Foreword -- Preface -- Contents -- About the Author -- 1 Unfolding the Educational and Practical Resources Inherent in Mathematics for Teaching Mathematics -- 1 From ``Instruction and Receptivity'' to ``Organization and Activity'' in Teaching -- 2 The Learning Environment ``Calculating with Remainders'' -- 3 Mathematics for Specialists and Mathematics for Teachers -- 4 From ``Instruction and Receptivity'' to ``Organization and Activity'' in Teacher Education -- References -- 2 Teaching Units as the Integrating Core of Mathematics Education -- 1 Discussion of the Status and Role of Mathematics Education -- 2 Problems of Integration -- 3 Some Views on Mathematics Teaching -- 4 Teaching Units as the Integrating Core of Mathematics Education -- 4.1 Some Teaching Units -- 4.2 Teaching Units in Teacher Training -- 4.3 Teaching Units in Didactical Research -- 5 Conclusion -- References -- 3 Clinical Interviews Embedded in the ``Philosophy of Teaching Units''-A Means of Developing Teachers' Attitudes and Skills -- 1 Cooperation Between Theory and Practice Through ``Intermediate Practice'' -- 2 Clinical Interviews as a Special Kind of Intermediate Practice -- 3 Concluding Remarks -- References -- 4 The Mathematical Training of Teachers from the Point of View of Education -- 1 The Problem of Integrating Mathematical and Educational aspects in Mathematics Education and Teacher Training -- 2 The Educational Substance of Subject Matter -- 3 Elementary Mathematics in Teacher Training -- 4 The Elementary Mathematics Research Program of Mathematics Education -- References -- 5 When Is a Proof a Proof? -- 1 Proofs and ``Proofs'' -- 2 Formalism as a Fiction: The Indispensability of Intuition ... -- 3 The Elementary-Mathematics-Research-Program of Mathematics Education -- References -- 6 Mathematics Education as a `Design Science'. , 1 The `Core' and the `Related Areas' of Mathematics Education -- 2 A Basic Problem in the Present Development of Mathematics Education: The Neglect of the Core -- 3 Mathematics Education as a Systemic-Evolutionary `Design Science' -- 4 The Design of Teaching Units and Empirical Research -- 5 And the Future of Mathematics Education? -- References -- 7 Designing Teaching: The Pythagorean Theorem -- 1 Introduction -- 2 Thinking About the Pythagorean Theorem within the School Context -- 3 Understanding the Structure of the Pythagorean Theorem -- 3.1 Different Proofs of the Pythagorean Theorem -- 3.2 Heuristic Approaches to the Pythagorean Theorem -- 3.3 Exploring Students' Understanding of Area and Similarity -- 4 Designing Teaching Units on the Pythagorean Theorem -- 4.1 Approaching the Pythagorean Theorem via the Diagonal of a Rectangle -- 4.2 Japanese Approach to the Pythagorean Theorem -- 5 Reflecting on the Units: Some Key Generalizable Concepts -- 5.1 Informal Proofs -- 5.2 ``Specializing''-A Fundamental Heuristic Strategy -- 5.3 The Operative Principle -- 6 Appendix: Solutions to the Problems in Exploration 3 -- References -- 8 Standard Number Representations in the Teaching of Arithmetic -- 1 Principles of Learning and Teaching -- 2 The Epistemological Nature of Number Representations -- 2.1 Notes on the History of Number Representations: From Tools of Teaching to Tools of Learning -- 2.2 Representations in Mathematics -- 3 Selection of Standard Number Representations -- 3.1 Criteria for Selecting and Designing Standard Representations -- 3.2 Fundamental Ideas of Arithmetic -- 3.3 Standard Number Representations -- 4 Some Teaching Units -- 4.1 The Twenty Frame and the Addition Table (Grade 1) -- 4.2 Multiplication Chart (Grade 2) -- 4.3 An Introduction into the Thousand Book (Grade 3) -- 4.4 ``Always 22'' (Grade 3). , 4.5 Place Value Chart (Grade 4) -- 5 Conclusion -- References -- 9 Developing Mathematics Education in a Systemic Process -- 1 Bridging the Gap Between Theory and Practice: … -- 2 (Burst) Dreams -- 2.1 Descartes' Dream -- 2.2 Hilbert's Dream -- 2.3 Comenius' Dream -- 2.4 The `Systemic-Evolutionary'' Versus the ``Mechanistic-Technomorph'' Approach to the Management of Complexity -- 3 Consequences for Mathematics Education -- 4 Substantial Learning Environments for Practising Skills -- 5 Substantial Learning Environments in Teacher Education -- 5.1 Didactics Courses -- 5.2 Mathematics Courses -- 6 Conclusion -- References -- 10 The Alpha and Omega of Teacher Education: Organizing Mathematical Activities -- 1 Introduction -- 2 Mathematics in Contexts -- 3 The Context of Teacher Education -- 4 The O-Script/A-Script Method -- 5 Operative Proofs -- 6 Experiences with the Course -- References -- 11 Operative Proofs in School Mathematics and Elementary Mathematics -- 1 Some Learning Environments with Embedded Operative Proofs -- 1.1 Even and Odd Numbers -- 1.2 Multiplicative Arrow Strings -- 1.3 Egyptian Fractions -- 1.4 Fitting Polygons -- 2 The Concept of Operative Proof -- 3 The Theoretical Background of Operative Proofs -- 3.1 Mathematics as the Science of Patterns -- 3.2 The Quasi-empirical Nature of Mathematics -- 3.3 The Operative Principle -- 3.4 Practicing Skills in a Productive Way -- 4 Concluding Remarks -- References -- 12 Collective Teaching Experiments: Organizing a Systemic Cooperation Between Reflective Researchers and Reflective Teachers in Mathematics Education -- 1 Mathematics Education as a ``Systemic-Evolutionary'' Design Science -- 2 Taking Systemic Complexity Systematically into Account: Lessons … -- 3 Empowering Teachers to Cope with Systemic Complexity as Reflective Practitioners. , 4 Collective Teaching Experiments: A Joint Venture of Reflective Teachers … -- 5 Closing Remarks: The Role of Mathematics in Mathematics Education -- References -- 13 Structure-Genetic Didactical Analyses-Empirical Research ``of the First Kind'' -- 1 Introduction of the Multiplication Table in Grade 2 -- 2 Designing a Substantial Learning Environment for Practicing Long Addition -- 3 Nets of a Cube -- 4 Structure-Genetic Didactical Analyses -- 5 Conclusion -- References -- 14 Understanding and Organizing Mathematics Education as a Design Science-Origins and New Developments -- 1 Origins -- 1.1 The Rise of the Sciences of the Artificial -- 1.2 Developments in Management Theory -- 1.3 Prototypes of Design in Mathematics Education -- 1.4 The Map of Mathematics Education as a Design Science -- 2 Conceptual Developments -- 2.1 The Natural Theory of Teaching: ``Well-Understood Mathematics'' -- 2.2 Structure-Genetic Didactical Analyses -- 2.3 A Differentiated Conception of Practicing Skills -- 2.4 Awareness of Systemic Constraints -- 3 Practical Consequences -- 3.1 Integrating ``Well-Understood Mathematics'' -- 3.2 Designing a Consistent and Coherent Curriculum -- 3.3 Including Operative Proofs -- 3.4 Addressing Teachers as ``Reflective Practitioners'' -- 4 Final Remarks -- References -- Appendix Excerpts from The Book of Numbers (BN).

Additional Edition: Print version: Wittmann, Erich Christian Connecting Mathematics and Mathematics Education Cham : Springer International Publishing AG,c2020 ISBN 9783030615697

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ISBN: 9783030615703 , 3030615707 , 9783030615710 , 3030615715 , 9783030615727 , 3030615723

Content: This Open Access book features a selection of articles written by Erich Ch. Wittmann between 1984 to 2019, which shows how the "design science conception" has been continuously developed over a number of decades. The articles not only describe this conception in general terms, but also demonstrate various substantial learning environments that serve as typical examples. In terms of teacher education, the book provides clear information on how to combine (well-understood) mathematics and methods courses to benefit of teachers. The role of mathematics in mathematics education is often explicitly and implicitly reduced to the delivery of subject matter that then has to be selected and made palpable for students using methods imported from psychology, sociology, educational research and related disciplines. While these fields have made significant contributions to mathematics education in recent decades, it cannot be ignored that mathematics itself, if well understood, provides essential knowledge for teaching mathematics beyond the pure delivery of subject matter. For this purpose, mathematics has to be conceived of as an organism that is deeply rooted in elementary operations of the human mind, which can be seamlessly developed to higher and higher levels so that the full richness of problems of various degrees of difficulty, and different means of representation, problem-solving strategies, and forms of proof can be used in ways that are appropriate for the respective level. This view of mathematics is essential for designing learning environments and curricula, for conducting empirical studies on truly mathematical processes and also for implementing the findings of mathematics education in teacher education, where it is crucial to take systemic constraints into account

Note: Preface -- Introduction -- 1. Teaching Units as the Integrating Core of Mathematics Education. Educational Studies in Mathematics 15 (1984), 25-36 -- 2. Clinical Interviews Embedded in the "Philosophy of Teaching Units" -- A Means of Developing Teachers' Attitudes and Skills. In: Christiansen, B. (ed.), Systematic Cooperation Between Theory and Practice in Mathematics Education, Mini-Conference at ICME 5 Adelaide 1984, Copenhagen: Royal Danish School of Education, Dept. of Mathematics 1985, 18-31 -- 3. The mathematical training of teachers from the point of view of education. Survey Lecture at ICME 6. Journal für Mathematik-Didaktik 10 (1989), 291-308 -- 4. Mathematics Education as a 'Design Science'. Educational Studies in Mathematics 29 (1995), 355-374 -- 5. Standard Number Representations in Teaching Arithmetic. Journal für Mathematik-Didaktik 19 (1998), No. 2/3, 149 -- 178 -- 6. Designing Teaching: The Pythagorean Theorem. In: Cooney, Th. P. (ed.), Mathematics, Pedagogy, and Secondary Teacher Education. Portsmouth, NH: Heineman 1996, 97-165 -- 7. Developing mathematics education in a systemic process. Plenary Lecture at ICME 9. Educational Studies in Mathematics 48 (2002), 1-20 -- 8. The Alpha and Omega of Teacher Education: Stimulating Mathematical Activities. In: Holton, D., Teaching and Learning at University Level. An ICMI Study. Dordrecht: Kluwer Academic Publishers, 2002, 539 -- 552 -- 9. Collective Teaching Experiments: Organizing a Systemic Cooperation Between Reflective Researchers and Reflective Teachers in Mathematics Education. In: Nührenbörger, M. et al. (2016). Design Science and Its Importance in the German Mathematics Educational Discussion. (p. 26-34) Rotterdam: Springer -- 10. Operative Proofs in Schoolmathematics and Elementary Mathematics mathematica didactica 37, H. 2 (2014), 213 -- 232) (transl. from German) -- 11. Structure genetic didactical analyses -- empirical research "of the first kind". In: Błaszczyk, P. & Pieronkiewicz, B. (eds.): Mathematical Transgressions 2015. Kraków: Universitas 2018, 133 -- 150 -- 12. Understanding and Organizing Mathematics Education as a Design Science -- Origins and New Developments. Hiroshima Journal of Mathematics Education vol. 12 (2019), 1- 20.

Additional Edition: Printed edition: 9783030615697

Additional Edition: Printed edition: 9783030615710

Additional Edition: Printed edition: 9783030615727

Language: English

Keywords: Electronic books. ; Electronic books.

DOI: 10.1007/978-3-030-61570-3

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Format: XX, 318 p. 200 illus., 61 illus. in color. , online resource.

Edition: 1st ed. 2021.

ISBN: 9783030615703

Content: This Open Access book features a selection of articles written by Erich Ch. Wittmann between 1984 to 2019, which shows how the "design science conception" has been continuously developed over a number of decades. The articles not only describe this conception in general terms, but also demonstrate various substantial learning environments that serve as typical examples. In terms of teacher education, the book provides clear information on how to combine (well-understood) mathematics and methods courses to benefit of teachers. The role of mathematics in mathematics education is often explicitly and implicitly reduced to the delivery of subject matter that then has to be selected and made palpable for students using methods imported from psychology, sociology, educational research and related disciplines. While these fields have made significant contributions to mathematics education in recent decades, it cannot be ignored that mathematics itself, if well understood, provides essential knowledge for teaching mathematics beyond the pure delivery of subject matter. For this purpose, mathematics has to be conceived of as an organism that is deeply rooted in elementary operations of the human mind, which can be seamlessly developed to higher and higher levels so that the full richness of problems of various degrees of difficulty, and different means of representation, problem-solving strategies, and forms of proof can be used in ways that are appropriate for the respective level. This view of mathematics is essential for designing learning environments and curricula, for conducting empirical studies on truly mathematical processes and also for implementing the findings of mathematics education in teacher education, where it is crucial to take systemic constraints into account.

Note: Preface -- Introduction -- 1. Teaching Units as the Integrating Core of Mathematics Education. Educational Studies in Mathematics 15 (1984), 25-36 -- 2. Clinical Interviews Embedded in the "Philosophy of Teaching Units" - A Means of Developing Teachers' Attitudes and Skills. In: Christiansen, B. (ed.), Systematic Cooperation Between Theory and Practice in Mathematics Education, Mini-Conference at ICME 5 Adelaide 1984, Copenhagen: Royal Danish School of Education, Dept. of Mathematics 1985, 18-31 -- 3. The mathematical training of teachers from the point of view of education. Survey Lecture at ICME 6. Journal für Mathematik-Didaktik 10 (1989), 291-308 -- 4. Mathematics Education as a 'Design Science'. Educational Studies in Mathematics 29 (1995), 355-374 -- 5. Standard Number Representations in Teaching Arithmetic. Journal für Mathematik-Didaktik 19 (1998), No. 2/3, 149 - 178 -- 6. Designing Teaching: The Pythagorean Theorem. In: Cooney, Th. P. (ed.), Mathematics, Pedagogy, and Secondary Teacher Education. Portsmouth, NH: Heineman 1996, 97-165 -- 7. Developing mathematics education in a systemic process. Plenary Lecture at ICME 9. Educational Studies in Mathematics 48 (2002), 1-20 -- 8. The Alpha and Omega of Teacher Education: Stimulating Mathematical Activities. In: Holton, D., Teaching and Learning at University Level. An ICMI Study. Dordrecht: Kluwer Academic Publishers, 2002, 539 - 552 -- 9. Collective Teaching Experiments: Organizing a Systemic Cooperation Between Reflective Researchers and Reflective Teachers in Mathematics Education. In: Nührenbörger, M. et al. (2016). Design Science and Its Importance in the German Mathematics Educational Discussion. (p. 26-34) Rotterdam: Springer -- 10. Operative Proofs in Schoolmathematics and Elementary Mathematics mathematica didactica 37, H. 2 (2014), 213 - 232) (transl. from German) -- 11. Structure genetic didactical analyses - empirical research "of the first kind". In: Błaszczyk, P. & Pieronkiewicz, B. (eds.): Mathematical Transgressions 2015. Kraków: Universitas 2018, 133 - 150 -- 12. Understanding and Organizing Mathematics Education as a Design Science - Origins and New Developments. Hiroshima Journal of Mathematics Education vol. 12 (2019), 1- 20. .

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Additional Edition: Printed edition: ISBN 9783030615697

Additional Edition: Printed edition: ISBN 9783030615710

Additional Edition: Printed edition: ISBN 9783030615727

Language: English

DOI: 10.1007/978-3-030-61570-3

URL: https://doi.org/10.1007/978-3-030-61570-3

UID:

Format: 1 Online-Ressource (xx, 318 Seiten).

ISBN: 978-3-030-61570-3

Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-030-61569-7

Language: English

Keywords: Mathematik ; Mathematikunterricht

DOI: 10.1007/978-3-030-61570-3

URL: Volltext  (kostenfrei)

URL: Volltext  (kostenfrei)

Author information: Wittmann, Erich Ch. 1939-

UID:

Format: 1 Online-Ressource (xx, 318 Seiten).

ISBN: 978-3-030-61570-3

Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-030-61569-7

Language: English

Keywords: Mathematik ; Mathematikunterricht

DOI: 10.1007/978-3-030-61570-3

URL: Volltext  (kostenfrei)

URL: Volltext  (kostenfrei)

Author information: Wittmann, Erich Ch. 1939-

UID:

Format: 1 online resource (XX, 318 p.) : , 200 illus., 61 illus. in color.

Edition: 1st ed. 2021.

ISBN: 3-030-61570-7

Content: This Open Access book features a selection of articles written by Erich Ch. Wittmann between 1984 to 2019, which shows how the “design science conception” has been continuously developed over a number of decades. The articles not only describe this conception in general terms, but also demonstrate various substantial learning environments that serve as typical examples. In terms of teacher education, the book provides clear information on how to combine (well-understood) mathematics and methods courses to benefit of teachers. The role of mathematics in mathematics education is often explicitly and implicitly reduced to the delivery of subject matter that then has to be selected and made palpable for students using methods imported from psychology, sociology, educational research and related disciplines. While these fields have made significant contributions to mathematics education in recent decades, it cannot be ignored that mathematics itself, if well understood, provides essential knowledge for teaching mathematics beyond the pure delivery of subject matter. For this purpose, mathematics has to be conceived of as an organism that is deeply rooted in elementary operations of the human mind, which can be seamlessly developed to higher and higher levels so that the full richness of problems of various degrees of difficulty, and different means of representation, problem-solving strategies, and forms of proof can be used in ways that are appropriate for the respective level. This view of mathematics is essential for designing learning environments and curricula, for conducting empirical studies on truly mathematical processes and also for implementing the findings of mathematics education in teacher education, where it is crucial to take systemic constraints into account.

Note: Preface -- Introduction -- 1. Teaching Units as the Integrating Core of Mathematics Education. Educational Studies in Mathematics 15 (1984), 25–36 -- 2. Clinical Interviews Embedded in the „Philosophy of Teaching Units“ – A Means of Developing Teachers’ Attitudes and Skills. In: Christiansen, B. (ed.), Systematic Cooperation Between Theory and Practice in Mathematics Education, Mini-Conference at ICME 5 Adelaide 1984, Copenhagen: Royal Danish School of Education, Dept. of Mathematics 1985, 18–31 -- 3. The mathematical training of teachers from the point of view of education. Survey Lecture at ICME 6. Journal für Mathematik-Didaktik 10 (1989), 291–308 -- 4. Mathematics Education as a ‘Design Science’. Educational Studies in Mathematics 29 (1995), 355–374 -- 5. Standard Number Representations in Teaching Arithmetic. Journal für Mathematik-Didaktik 19 (1998), No. 2/3, 149 – 178 -- 6. Designing Teaching: The Pythagorean Theorem. In: Cooney, Th. P. (ed.), Mathematics, Pedagogy, and Secondary Teacher Education. Portsmouth, NH: Heineman 1996, 97–165 -- 7. Developing mathematics education in a systemic process. Plenary Lecture at ICME 9. Educational Studies in Mathematics 48 (2002), 1–20 -- 8. The Alpha and Omega of Teacher Education: Stimulating Mathematical Activities. In: Holton, D., Teaching and Learning at University Level. An ICMI Study. Dordrecht: Kluwer Academic Publishers, 2002, 539 – 552 -- 9. Collective Teaching Experiments: Organizing a Systemic Cooperation Between Reflective Researchers and Reflective Teachers in Mathematics Education. In: Nührenbörger, M. et al. (2016). Design Science and Its Importance in the German Mathematics Educational Discussion. (p. 26-34) Rotterdam: Springer -- 10. Operative Proofs in Schoolmathematics and Elementary Mathematics mathematica didactica 37, H. 2 (2014), 213 – 232) (transl. from German) -- 11. Structure genetic didactical analyses - empirical research „of the first kind". In: Błaszczyk, P. & Pieronkiewicz, B. (eds.): Mathematical Transgressions 2015. Kraków: Universitas 2018, 133 – 150 -- 12. Understanding and Organizing Mathematics Education as a Design Science – Origins and New Developments. Hiroshima Journal of Mathematics Education vol. 12 (2019), 1– 20. . , English

Additional Edition: ISBN 3-030-61569-3

Language: English

DOI: 10.1007/978-3-030-61570-3

UID:

Format: 1 online resource (XX, 318 p.) : , 200 illus., 61 illus. in color.

Edition: 1st ed. 2021.

ISBN: 3-030-61570-7

Content: This Open Access book features a selection of articles written by Erich Ch. Wittmann between 1984 to 2019, which shows how the “design science conception” has been continuously developed over a number of decades. The articles not only describe this conception in general terms, but also demonstrate various substantial learning environments that serve as typical examples. In terms of teacher education, the book provides clear information on how to combine (well-understood) mathematics and methods courses to benefit of teachers. The role of mathematics in mathematics education is often explicitly and implicitly reduced to the delivery of subject matter that then has to be selected and made palpable for students using methods imported from psychology, sociology, educational research and related disciplines. While these fields have made significant contributions to mathematics education in recent decades, it cannot be ignored that mathematics itself, if well understood, provides essential knowledge for teaching mathematics beyond the pure delivery of subject matter. For this purpose, mathematics has to be conceived of as an organism that is deeply rooted in elementary operations of the human mind, which can be seamlessly developed to higher and higher levels so that the full richness of problems of various degrees of difficulty, and different means of representation, problem-solving strategies, and forms of proof can be used in ways that are appropriate for the respective level. This view of mathematics is essential for designing learning environments and curricula, for conducting empirical studies on truly mathematical processes and also for implementing the findings of mathematics education in teacher education, where it is crucial to take systemic constraints into account.

Note: Preface -- Introduction -- 1. Teaching Units as the Integrating Core of Mathematics Education. Educational Studies in Mathematics 15 (1984), 25–36 -- 2. Clinical Interviews Embedded in the „Philosophy of Teaching Units“ – A Means of Developing Teachers’ Attitudes and Skills. In: Christiansen, B. (ed.), Systematic Cooperation Between Theory and Practice in Mathematics Education, Mini-Conference at ICME 5 Adelaide 1984, Copenhagen: Royal Danish School of Education, Dept. of Mathematics 1985, 18–31 -- 3. The mathematical training of teachers from the point of view of education. Survey Lecture at ICME 6. Journal für Mathematik-Didaktik 10 (1989), 291–308 -- 4. Mathematics Education as a ‘Design Science’. Educational Studies in Mathematics 29 (1995), 355–374 -- 5. Standard Number Representations in Teaching Arithmetic. Journal für Mathematik-Didaktik 19 (1998), No. 2/3, 149 – 178 -- 6. Designing Teaching: The Pythagorean Theorem. In: Cooney, Th. P. (ed.), Mathematics, Pedagogy, and Secondary Teacher Education. Portsmouth, NH: Heineman 1996, 97–165 -- 7. Developing mathematics education in a systemic process. Plenary Lecture at ICME 9. Educational Studies in Mathematics 48 (2002), 1–20 -- 8. The Alpha and Omega of Teacher Education: Stimulating Mathematical Activities. In: Holton, D., Teaching and Learning at University Level. An ICMI Study. Dordrecht: Kluwer Academic Publishers, 2002, 539 – 552 -- 9. Collective Teaching Experiments: Organizing a Systemic Cooperation Between Reflective Researchers and Reflective Teachers in Mathematics Education. In: Nührenbörger, M. et al. (2016). Design Science and Its Importance in the German Mathematics Educational Discussion. (p. 26-34) Rotterdam: Springer -- 10. Operative Proofs in Schoolmathematics and Elementary Mathematics mathematica didactica 37, H. 2 (2014), 213 – 232) (transl. from German) -- 11. Structure genetic didactical analyses - empirical research „of the first kind". In: Błaszczyk, P. & Pieronkiewicz, B. (eds.): Mathematical Transgressions 2015. Kraków: Universitas 2018, 133 – 150 -- 12. Understanding and Organizing Mathematics Education as a Design Science – Origins and New Developments. Hiroshima Journal of Mathematics Education vol. 12 (2019), 1– 20. . , English

Additional Edition: ISBN 3-030-61569-3

Language: English

DOI: 10.1007/978-3-030-61570-3

UID:

Format: 1 online resource (XX, 318 p.) : , 200 illus., 61 illus. in color.

Edition: 1st ed. 2021.

ISBN: 3-030-61570-7

Content: This Open Access book features a selection of articles written by Erich Ch. Wittmann between 1984 to 2019, which shows how the “design science conception” has been continuously developed over a number of decades. The articles not only describe this conception in general terms, but also demonstrate various substantial learning environments that serve as typical examples. In terms of teacher education, the book provides clear information on how to combine (well-understood) mathematics and methods courses to benefit of teachers. The role of mathematics in mathematics education is often explicitly and implicitly reduced to the delivery of subject matter that then has to be selected and made palpable for students using methods imported from psychology, sociology, educational research and related disciplines. While these fields have made significant contributions to mathematics education in recent decades, it cannot be ignored that mathematics itself, if well understood, provides essential knowledge for teaching mathematics beyond the pure delivery of subject matter. For this purpose, mathematics has to be conceived of as an organism that is deeply rooted in elementary operations of the human mind, which can be seamlessly developed to higher and higher levels so that the full richness of problems of various degrees of difficulty, and different means of representation, problem-solving strategies, and forms of proof can be used in ways that are appropriate for the respective level. This view of mathematics is essential for designing learning environments and curricula, for conducting empirical studies on truly mathematical processes and also for implementing the findings of mathematics education in teacher education, where it is crucial to take systemic constraints into account.

Note: Preface -- Introduction -- 1. Teaching Units as the Integrating Core of Mathematics Education. Educational Studies in Mathematics 15 (1984), 25–36 -- 2. Clinical Interviews Embedded in the „Philosophy of Teaching Units“ – A Means of Developing Teachers’ Attitudes and Skills. In: Christiansen, B. (ed.), Systematic Cooperation Between Theory and Practice in Mathematics Education, Mini-Conference at ICME 5 Adelaide 1984, Copenhagen: Royal Danish School of Education, Dept. of Mathematics 1985, 18–31 -- 3. The mathematical training of teachers from the point of view of education. Survey Lecture at ICME 6. Journal für Mathematik-Didaktik 10 (1989), 291–308 -- 4. Mathematics Education as a ‘Design Science’. Educational Studies in Mathematics 29 (1995), 355–374 -- 5. Standard Number Representations in Teaching Arithmetic. Journal für Mathematik-Didaktik 19 (1998), No. 2/3, 149 – 178 -- 6. Designing Teaching: The Pythagorean Theorem. In: Cooney, Th. P. (ed.), Mathematics, Pedagogy, and Secondary Teacher Education. Portsmouth, NH: Heineman 1996, 97–165 -- 7. Developing mathematics education in a systemic process. Plenary Lecture at ICME 9. Educational Studies in Mathematics 48 (2002), 1–20 -- 8. The Alpha and Omega of Teacher Education: Stimulating Mathematical Activities. In: Holton, D., Teaching and Learning at University Level. An ICMI Study. Dordrecht: Kluwer Academic Publishers, 2002, 539 – 552 -- 9. Collective Teaching Experiments: Organizing a Systemic Cooperation Between Reflective Researchers and Reflective Teachers in Mathematics Education. In: Nührenbörger, M. et al. (2016). Design Science and Its Importance in the German Mathematics Educational Discussion. (p. 26-34) Rotterdam: Springer -- 10. Operative Proofs in Schoolmathematics and Elementary Mathematics mathematica didactica 37, H. 2 (2014), 213 – 232) (transl. from German) -- 11. Structure genetic didactical analyses - empirical research „of the first kind". In: Błaszczyk, P. & Pieronkiewicz, B. (eds.): Mathematical Transgressions 2015. Kraków: Universitas 2018, 133 – 150 -- 12. Understanding and Organizing Mathematics Education as a Design Science – Origins and New Developments. Hiroshima Journal of Mathematics Education vol. 12 (2019), 1– 20. . , English

Additional Edition: ISBN 3-030-61569-3

Language: English

DOI: 10.1007/978-3-030-61570-3