All Positive Action Starts with Criticism

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 fromthe 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.