All Positive Action Starts with Criticism Hans Freudenthal and the Didactics of Mathematics /
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 d...
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| Format: | Electronic eBook |
| Language: | English |
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Dordrecht :
Springer Netherlands : Imprint: Springer,
2015.
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| Edition: | 1st ed. 2015. |
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| Online Access: | https://doi.org/10.1007/978-94-017-9334-6 |
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Table of Contents:
- 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.