This survey provides an overview of the German discussion on modelling
and applications in schools. It considers the development from the
beginning of the 20th century to the present, and discusses the term
"mathematical model" as well as different representations of the
modelling process as modelling cycles. Different trends in the
historical and current debate on applications and modelling can be
differentiated as perspectives of modelling. Modelling is now one of the
six general mathematical competencies defined in the educational
standards for mathematics introduced in Germany in 2003, and there have
been several initiatives to implement modelling in schools, as well as a
whole range of empirical research projects focusing on teachers or
students in modelling processes. As a special kind for implementing
modelling into school, modelling weeks and days carried out by various
German universities have been established.