Mathematics
THE NATURE AND UTILITY OF MATHEMATICS
I Interdisciplinarity in School and Teacher Training Programs 1 Introduction 3 Interdisciplinarity 15 II Physics and Mathematics as Interwoven Disciplines 37 Mathematics in History 41 Abstraction of Modern Mathematics 55 Mathematics From the Pupils’ Point of View 77 The Mathematization of Physics 91 The Nature of Science 113 The Relationship between Mathematics and Physics 137 Cardanos Formula and the Van der Waals Gas 157 Linear Differential Operators and the RCL-Circuit 181 III Comparison of Educational Theories 211 Individual Concepts 215 Models and Modeling 257 Development of Knowledge 299 Problem Solving 345 Conclusive Remarks 369