The Design of a Mathematics Course A Theoretical Reflection

Realistic Mathematics Education has its conceptual framework, that is a theory. This theory evolved from development and research in mathematics education. A course on fractions and many other examples will be analysed in depth with the realistic theory in the background. The leading question will be: "What strategies did the designers of the exemplary educational material use?" Revealing those strategies and making the user conscious of them enables the user to apply them henceforth as tactics for the design in advance. In consequence an important theoretical change of perspective looms ahead. Where the theory was first an after-image, it can now act as a pre-image, i.e. as a model for realistic mathematics education in advance. This is because the tools to farm the theoretical field have been revealed. The question of how to apply the theory has been answered. Freudenthal's ideas provided for a considerable part of the means to make this theoretical step forward.