All positive action starts with criticism : hans freudenthal and the didactics of mathematics / Sacha la Bastide-van Gemert.

Springer eBooks

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.

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