For the International conference on Mathematical Education at Quebec in 1992 the historical development of the German school system and the development and the conditions of mathematics teaching are described. Schulsystem und zur Organisation des Mathematikunterrichts. Schulsystem mit seiner historischen Entwicklung dargestellt sowie die Entwicklungen und Rahmenbedingungen des Mathematikunterrichtes in Deutschland.
Practical arithmetic has a long tradition in mathematics teaching in Germany.
Traditions differed from Hauptschule to Gymnasium. But under the influence of a structural analysis during the sixties a functional approach was developed which was expected to be a successful method in all types of school. But empirical research revealed some deficiencies caused by a mixture of methods used in the classroom. There is a need for a new approach which is based on research about functional thinking. Sachrechnen in der Sekundarstufe 1.