In this paper we consider geometrical construction problems and their role in mathematical education. Owing to the main features of construction problems (accuracy in making conclusions, strict structure, rigorous language and constructivistic nature), they can be fruitfully used in teaching mathematics and computer science. We shall try to shed new light on construction problems, and show how they can be used in exercising mathematical rigor, but also for understanding and illustrating a range of mathematical and computer science theories. For these tasks, we emphasize the motivating role of software tools that can be used for interactive work. One such tool (WinGCLC) will be briefly presented.