Acknowledgements
Chapter 1: Introduction
"A way to master this world{u2019}{u2019}
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 {u2013} a sketch
3.1: Hans Freudenthal {u2013} an impression
3.2: Luckenwalde
3.3: Berlin
3.4: Amsterdam
3.5: Utrecht
Chapter 4: Didactics of arithmetic
4.1: Dating of R̀ekendidactiek{u2019}
4.2: Cause and intention
4.3: Teaching of arithmetic in primary schools
4.4: Freudenthal{u2019}s R̀ekendidactiek{u2019}: the content
4.4.1: Preface
4.4.2: Auxiliary sciences
4.4.3: Aim and use of teaching of arithmetic
4.5: R̀ekendidactiek{u2019} {u2018}Didactics of arithmetic{u2019}): every positive action starts with criticism
Chapter 5: A new start
5.1: Educating
5.1.1: Educating at home
5.1.2: Òur task as present-day educators{u2019}
5.1.3: Èducation for thinking{u2019}.-5.1.4: Èducating{u2019} 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: T̀he algebraic and analytical view on the number concept in elementary mathematics{u2019}
5.3.3: M̀athematics for non-mathematical studies{u2019}
5.3.4: Freudenthal{u2019}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{u2019} level theory. A learning process.-7.1: Introduction: a special PhD project
7.2: Freudenthal as supervisor
7.3: P̀roblems of insight{u2019}: Van Hiele{u2019}s level theory
7.4: Freudenthal and the theory of the Van Hieles: from l̀evel theory{u2019} to g̀uided re-invention{u2019}
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 t̀he group of experts{u2019}
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 {u2018}cooperate with a view to adjust{u2019}
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 {u2013} but not in geometry
8.6.4: Modern geometry in the education according to Freudenthal
8.7: Logic
8.7.1: È̀xact logic{u2019}{u2019}
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{u2019}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 R̀ekendidactiek{u2019}
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.