Author(s): Hans Freudenthal
Edition: 1
Year: 1972
Language: English
Pages: 692
Preface......Page 6
Contents......Page 12
List of Symbols......Page 13
I. The Mathematical Tradition......Page 14
II. Mathematics Today......Page 30
III. Tradition and Education......Page 65
IV. Use and Aim of Mathematics Instruction......Page 77
V. The Socratic Method......Page 112
VI. Re-invention......Page 122
VII. Organization of a Field by Mathematizing......Page 144
VIII. Mathematical Rigour......Page 160
IX. Instruction......Page 168
X. The Mathematics Teacher......Page 175
XI. The Number Concept - Objective Accesses......Page 183
XII. Developing the Number Concept from Intuitive Methods
to Algorithmizing and Rationalizing......Page 255
XIII. Development of the Number Concept - The Algebraic
Method......Page 300
XIV. Development of the Number Concept - From the Algebraic Principle to the Global Organization of Algebra......Page 325
XV. Sets and Functions......Page 345
XVI. The Case of Geometry......Page 414
XVII. Analysis......Page 525
XVIII. Probability and Statistics......Page 594
XIX. Logic......Page 628
Appendix I. Piaget and the Piaget School's Investigations on the
Development of Mathematical Notions......Page 675
Appendix II. Papers of the Author on Mathematical Instruction......Page 691
