Demonstration,decision and complementation problems and their generation

Relationships between the concept of an exercise, of formulation of the text, of an exercise solution, and of the final result are analysed.

For mathematical exercises, deductive directed reasoning is of special importance. A classification of reasonings gives a basis for the division of the exercises. Among problem exercises, ‘open problems’ and solutions of exercises extended by an approach called in German, ‘Methode der erzeugenden Probleme’, are important from the point of view of didactics.

Empirical studies concerning the influence of the exercise's formulation on the efficiency of its solution, have been carried out for a set of about 16 thousand exercises.