Advantages and disadvantages of the use of digital technologies (DT) and especially of computer algebra systems (CAS) in mathematics lessons are worldwide discussed controversially. Many empirical studies show the benefit of the use of DT in classrooms. However, despite of inspiring results, classroom suggestions, lesson plans and research reports, the use of DT – and especially CAS – has not succeeded, as many had expected during the last decades. The thesis of this article is that we have not been able to convince teachers, lecturers at university and parents of the benefit of DT in the classrooms in a sufficient way. In the following, we relate the working with DT to understanding and classroom activities. The basis of the argumentation is a competence model, which classifies – for a special content – the relation between levels of understanding (of the concept), representations of DT and different kinds of classroom activities.