All Positive Action Starts with Criticism: Hans Freudenthal and the Didactics of Mathematics
Saved in:
| Main Author: | |
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
Dordrecht
Springer Netherlands
2015
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| Subjects: | |
| Online Access: | UPA01 Volltext Inhaltsverzeichnis Abstract Buchcover |
| Physical Description: | 1 Online-Ressource (XV, 386 p. 39 illus) |
| ISBN: | 9789401793346 |
| DOI: | 10.1007/978-94-017-9334-6 |
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Record in the Search Index
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| adam_text | ALL POSITIVE ACTION STARTS WITH CRITICISM
/ LA BASTIDE-VAN GEMERT, SACHA
: 2015
TABLE OF CONTENTS / INHALTSVERZEICHNIS
ACKNOWLEDGEMENTS
CHAPTER 1: INTRODUCTION - A WAY TO MASTER THIS WORLD’’
CHAPTER 2: MATHEMATICS EDUCATION IN SECONDARY SCHOOLS AND DIDACTICS OF
MATHEMATICS IN THE PERIOD BETWEEN THE TWO WORLD WARS
2.1: SECONDARY EDUCATION IN THE PERIOD BETWEEN THE TWO WORLD WARS
2.1.1: THE ORIGINATION OF THE SCHOOL TYPES IN SECONDARY EDUCATION
2.1.2: SOME SCHOOL TYPES
2.1.3: THE COMPETITION BETWEEN HBS AND GYMNASIUM
2.2: DISCUSSIONS ON THE MATHEMATICS EDUCATION AT THE VHMO
2.2.1: THE INITIAL GEOMETRY EDUCATION AND THE FOUNDATION OF JOURNAL
EUCLIDES
2.2.2: THE BETH COMMITTEE AND THE INTRODUCTION OF DIFFERENTIAL AND
INTEGRAL CALCULUS
2.2.3: THE CONTROVERSY ABOUT MECHANICS
2.2.4: EDUCATING THE MATHEMATICS TEACHER
2.2.5: NEW INSIGHTS AND THE WISKUNDE WERKGROEP (MATHEMATICS WORKING
GROUP)
CHAPTER 3: HANS FREUDENTHAL – A SKETCH
3.1: HANS FREUDENTHAL – AN IMPRESSION
3.2: LUCKENWALDE
3.3: BERLIN
3.4: AMSTERDAM
3.5: UTRECHT
CHAPTER 4: DIDACTICS OF ARITHMETIC
4.1: DATING OF `REKENDIDACTIEK’
4.2: CAUSE AND INTENTION
4.3: TEACHING OF ARITHMETIC IN PRIMARY SCHOOLS
4.4: FREUDENTHAL’S `REKENDIDACTIEK’: THE CONTENT
4.4.1: PREFACE
4.4.2: AUXILIARY SCIENCES
4.4.3: AIM AND USE OF TEACHING OF ARITHMETIC
4.5: `REKENDIDACTIEK’ ‘DIDACTICS OF ARITHMETIC’): EVERY POSITIVE
ACTION STARTS WITH CRITICISM
CHAPTER 5: A NEW START
5.1: EDUCATING
5.1.1: EDUCATING AT HOME
5.1.2: `OUR TASK AS PRESENT-DAY EDUCATORS’
5.1.3: `EDUCATION FOR THINKING’.-5.1.4: `EDUCATING’ IN DE GROENE
AMSTERDAMMER
5.1.5: EDUCATION: A SUMMARY
5.2: HIGHER EDUCATION
5.2.1: STUDIUM GENERALE
5.2.2: THE TEACHERS TRAINING
5.2.3: STUDENT WAGE
5.2.4: HIGHER EDUCATION: A RAMSHACKLE PARTHENON OR A HOUSE IN ORDER?
5.3: THE WISKUNDE WERKGROEP (THE MATHEMATICS STUDY GROUP)
5.3.1: ACTIVITIES OF THE WISKUNDE WERKGROEP
5.3.2: `THE ALGEBRAIC AND ANALYTICAL VIEW ON THE NUMBER CONCEPT IN
ELEMENTARY MATHEMATICS’
5.3.3: `MATHEMATICS FOR NON-MATHEMATICAL STUDIES’
5.3.4: FREUDENTHAL’S MATHEMATICAL WORKING GROUP
CHAPTER 6: FROM CRITICAL OUTSIDER TO TRUE AUTHORITY
6.1: MATHEMATICS EDUCATION AND THE EDUCATION OF THE INTELLECTUAL
CAPACITY
6.2: A BODY UNDER THE FLOOR BOARDS: THE MECHANICS EDUCATION
6.3: PREPARATIONS FOR A NEW CURRICULUM
6.4: PROBABILITY THEORY AND STATISTICS: A TEXT BOOK.-6.5: PAEDAGOGUMS,
PAEDA MAGICIANS AND SCIENTISTS: THE TEACHER TRAINING
6.6: FREUDENTHAL INTERNATIONALLY
CHAPTER 7: FREUDENTHAL AND THE VAN HIELES’ LEVEL THEORY. A LEARNING
PROCESS.-7.1: INTRODUCTION: A SPECIAL PHD PROJECT
7.2: FREUDENTHAL AS SUPERVISOR
7.3: `PROBLEMS OF INSIGHT’: VAN HIELE’S LEVEL THEORY
7.4: FREUDENTHAL AND THE THEORY OF THE VAN HIELES: FROM `LEVEL THEORY’
TO `GUIDED RE-INVENTION’
7.5: ANALYSIS OF A LEARNING PROCESS: REFLECTION ON REFLECTION
7.6: TO CONCLUDE
CHAPTER 8: METHOD VERSUS CONTENT. NEW MATH AND THE MODERNIZATION OF
MATHEMATICS EDUCATION
8.1: INTRODUCTION: TIME FOR MODERNIZATION
8.2: NEW MATH
8.2.1: THE GAP BETWEEN MODERN MATHEMATICS AND MATHEMATICS EDUCATION
8.2.2: MODERNIZATION OF THE MATHEMATICS EDUCATION IN THE UNITES STATES
8.3: ROYAUMONT: A BRIDGE CLUB WITH UNFORESEEN CONSEQUENCES
8.3.1: FREUDENTHAL IN `THE GROUP OF EXPERTS’
8.3.2: ROYAUMONT WITHOUT FREUDENTHAL: THE LAUNCH OF NEW MATH
8.4: FREUDENTHAL ON MODERN MATHEMATICS AND ITS MEANING FOR MATHEMATICS
EDUCATION
8.4.1: THE NATURE OF MODERN MATHEMATICS
8.4.2: MODERN MATHEMATICS FOR THE PUBLIC AT LARGE
8.4.3: THE MATHEMATICIAN IN DER UNTERHOSE AUF DER STRASSE ( IN HIS
UNDERPANTS ON THE STREET )
8.4.4: FAIRY TALES AND DEAD ENDS
8.4.5: MODERN MATHEMATICS AS THE SOLUTION?
8.5: MODERNIZATION OF MATHEMATICS EDUCATION IN THE NETHERLANDS
8.5.1: INITIATIVES INSIDE AND OUTSIDE OF THE NETHERLANDS
8.5.2: FREUDENTHAL: FROM WW TO ‘COOPERATE WITH A VIEW TO ADJUST’
8.5.3: THE COMMISSIE MODERNISERING LEERPLAN WISKUNDE
8.5.4: A PROFESSIONAL DEVELOPMENT PROGRAMME FOR TEACHERS
8.5.5: A NEW CURRICULUM
8.6: GEOMETRY EDUCATION
8.6.1: FREUDENTHAL AND GEOMETRY EDUCATION
8.6.2: FREUDENTHAL ON THE INITIAL GEOMETRY EDUCATION: TRY IT AND SEE
8.6.3: AXIOMATIZING INSTEAD OF AXIOMATICS – BUT NOT IN GEOMETRY
8.6.4: MODERN GEOMETRY IN THE EDUCATION ACCORDING TO FREUDENTHAL
8.7: LOGIC
8.7.1: ``EXACT LOGIC’’
8.7.2: THE APPLICATION OF MODERN LOGIC IN EDUCATION
8.8: FREUDENTHAL AND NEW MATH: CONCLUSION
8.8.1: A LONELY OPPONENT OF NEW MATH?
8.8.2: COOPERATE IN ORDER TO ADJUST
8.8.3: KNOWLEDGE AS A WEAPON IN THE STRUGGLE FOR A BETTER MATHEMATICS
EDUCATION
8.8.4: FREUDENTHAL ABOUT THE AIM OF MATHEMATICS EDUCATION
CHAPTER 9: HERE’S HOW FREUDENTHAL SAW IT
9.1: INTRODUCTION: CHANGES IN THE SCENE OF ACTION
9.2: EDUCATIONAL STUDIES IN MATHEMATICS
9.2.1: NOT EXACTLY BURSTING WITH ENTHUSIASM: THE LAUNCH
9.2.2: FREUDENTHAL AS GUARDIAN OF THE LEVEL
9.3: THE INSTITUTE FOR THE DEVELOPMENT OF MATHEMATICS EDUCATION
9.3.1: FROM CMLW TO IOWO
9.3.2: FREUDENTHAL AND THE IOWO
9.4: EXPLORING THE WORLD FROM THE PAVING BRICKS TO THE MOON
9.4.1: OBSERVATIONS AS A FATHER IN `REKENDIDACTIEK’
9.4.2: OBSERVING AS A GRANDFATHER: WALKING WITH THE GRAND-CHILDREN
9.4.3: GRANDDAD HANS: A CRITICAL COMMENT
9.4.4: WALKING ON THE RAILWAY TRACK: THE MATHEMATICS OF A THREE-YEAR OLD
9.4.5: OBSERVING AND THE IOWO
9.5: OBSERVATIONS AS A SOURCE
9.5.1: PROFESSOR OR SENILE GRANDFATHER?
9.5.2: THE PARADIGM: THE ULTIMATE EXAMPLE
9.5.3: HERE IS HOW FREUDENTHAL SAW IT: CONCEPT OF NUMBER AND DIDACTICAL
PHENOMENOLOGY
9.5.4: THE RIGHT TO SOUND MATHEMATICS FOR ALL
9.6: ENFANT TERRIBLE
9.6.1: WEEDING
9.6.2: DRUMMING ON EMPTY BARRELS
9.6.3: FREUDENTHAL ON PIAGET: ADMIRATION AND MERCILESS CRITICISM
9.7: THE TASK FOR THE FUTURE
CHAPTER 10: EPILOGUE - WE HAVE COME FULL CIRCLE
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
ALL POSITIVE ACTION STARTS WITH CRITICISM
/ LA BASTIDE-VAN GEMERT, SACHA
: 2015
ABSTRACT / INHALTSTEXT
THIS STUDY PROVIDES A HISTORICAL ANALYSIS OF FREUDENTHAL’S DIDACTIC
IDEAS AND HIS DIDACTIC CAREER. IT IS PARTLY BIOGRAPHICAL, BUT ALSO
CONTRIBUTES TO THE HISTORIOGRAPHY OF MATHEMATICS EDUCATION AND ADDRESSES
CLOSELY RELATED QUESTIONS SUCH AS: WHAT IS MATHEMATICS AND WHERE DOES IT
START? WHICH ROLE DOES MATHEMATICS PLAY IN SOCIETY AND WHAT INFLUENCE
DOES IT HAVE ON THE PREVAILING VIEWS CONCERNING ITS ACCOMPANYING
DIDACTICS? HANS FREUDENTHAL (1905–1990), PROFESSOR IN MATHEMATICS,
SCIENTIST, LITERATOR, BUT ABOVE ALL MATHEMATICS-EDUCATOR, WAS
INEXTRICABLY LINKED TO THE CHANGES WHICH TOOK PLACE IN MATHEMATICS
EDUCATION AND DIDACTICS DURING THE SECOND HALF OF THE LAST CENTURY. HIS
DIVERSITY AS A SCIENTIST AND HIS INEXHAUSTIBLE EFFORTS TO ESTABLISH THE
DIDACTICS OF MATHEMATICS AS A SERIOUSLY PURSUED SCIENCE, MADE
FREUDENTHAL S INFLUENCE IN THIS AREA CONSIDERABLE. HE FORESAW AN
ESSENTIAL, PRACTICAL ROLE FOR MATHEMATICS IN EVERYONE’S LIFE,
ENCOURAGING STUDENTS TO DISCOVER AND CREATE MATHEMATICS THEMSELVES,
INSTEAD OF IMPOSING A READY-MADE MATHEMATICAL SYSTEM. THE THEORY OF
MATHEMATICS EDUCATION THUS DEVELOPED IN THE NETHERLANDS WOULD GAIN WORLD
FAME IN THE FOLLOWING DECADES. TODAY, IN THE LIGHT OF THE DISCUSSIONS
ABOUT MATHEMATICS EDUCATION, IN WHICH THE CALL FOR `GENUINE’
MATHEMATICS INSTEAD OF THE SO-CALLED KINDERGARTEN -MATHEMATICS CAN BE
HEARD, FREUDENTHAL S APPROACH SEEMS TO BE PASSE. HOWEVER, THE OUTCOME
OF THIS STUDY (WHICH IS MAINLY BASED ON DOCUMENTS FROM FREUDENTHAL’S
VAST PERSONAL ARCHIVE) SHOWS A MORE REFINED PICTURE. THE DIRECT
IDENTIFICATION OF KINDERGARTEN -MATHEMATICS WITH FREUDENTHAL’S VIEW
ON MATHEMATICS EDUCATION IS NOT JUSTIFIED. REALISTIC MATHEMATICS AS
ADVOCATED BY FREUDENTHAL INCLUDES MORE THAN JUST A PRACTICAL
INTRODUCTORY AND SHOULD, AMONG OTHER THINGS, ALWAYS AIM AT TEACHING
GENUINE MATHEMATICS IN THE END
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
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| indexdate | 2024-07-10T01:18:30Z |
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| language | English |
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| spelling | Bastide-van Gemert, Sacha la Verfasser (DE-588)1067087427 aut All Positive Action Starts with Criticism Hans Freudenthal and the Didactics of Mathematics by Sacha la Bastide-van Gemert Dordrecht Springer Netherlands 2015 1 Online-Ressource (XV, 386 p. 39 illus) txt rdacontent c rdamedia cr rdacarrier Education Mathematics Mathematics Education Erziehung Mathematik Erscheint auch als Druckausgabe 978-94-017-9333-9 https://doi.org/10.1007/978-94-017-9334-6 Verlag Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027763220&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027763220&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Abstract SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027763220&sequence=000005&line_number=0003&func_code=DB_RECORDS&service_type=MEDIA Buchcover |
| spellingShingle | Bastide-van Gemert, Sacha la All Positive Action Starts with Criticism Hans Freudenthal and the Didactics of Mathematics Education Mathematics Mathematics Education Erziehung Mathematik |
| title | All Positive Action Starts with Criticism Hans Freudenthal and the Didactics of Mathematics |
| title_auth | All Positive Action Starts with Criticism Hans Freudenthal and the Didactics of Mathematics |
| title_exact_search | All Positive Action Starts with Criticism Hans Freudenthal and the Didactics of Mathematics |
| title_full | All Positive Action Starts with Criticism Hans Freudenthal and the Didactics of Mathematics by Sacha la Bastide-van Gemert |
| title_fullStr | All Positive Action Starts with Criticism Hans Freudenthal and the Didactics of Mathematics by Sacha la Bastide-van Gemert |
| title_full_unstemmed | All Positive Action Starts with Criticism Hans Freudenthal and the Didactics of Mathematics by Sacha la Bastide-van Gemert |
| title_short | All Positive Action Starts with Criticism |
| title_sort | all positive action starts with criticism hans freudenthal and the didactics of mathematics |
| title_sub | Hans Freudenthal and the Didactics of Mathematics |
| topic | Education Mathematics Mathematics Education Erziehung Mathematik |
| topic_facet | Education Mathematics Mathematics Education Erziehung Mathematik |
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